allzermalmer

Truth suffers from too much analysis

Posts Tagged ‘Induction’

Fallacy of Evidentialism

Posted by allzermalmer on August 18, 2013

There are two philosophers, who are taken to be generally representative of Evidentialism. These two philosophers are David Hume and C.K. Clifford. These two philosophers have two quotes that are examplars of their Evidentialism thesis. They are, respectively, as follows.

“A wise man, therefore, proportions his belief to the evidence…when at last [a wise man] fixes his judgement, the evidence exceeds not what we properly call probability.” – David Hume in “Of Miracles” (Italics are Hume’s)

“We may believe what goes beyond our experience, only when it is inferred from that experience by the assumption that what we do not know is like what we know…It is wrong in all cases to believe on insufficient evidence” – W.K. Clifford in “The Ethics of Belief

Thomas Huxley,

Huxluy Evidence

Those quotes from these three writers are taken as representative of Evidentialism, and thus the Evidentialist Principle. The statements they make might appear to carry some validity & they might even seem to be sound.

However, Karl Popper holds that they are not valid. He also doesn’t hold that they are sound. They even contradict all empirical systems or all empirical propositions. They forbid us from ever believing or holding to any empirical system or empirical proposition, they forbid us from ever believing or holding to any scientific hypothesis or scientific proposition. But the problem of Induction applies to both the truth of this matter of fact assertion and the probability of the truth of this matter of fact assertion.

Both of the propositions contain signs of being based on Induction. Hume points out that a wise man will fix their judgements on a proposition when the evidence indicates that it is probable. Clifford points out that we may infer from experience what goes beyond our experience, but this is based on hypothesis that unknown is similar to the known.

Both of the propositions show that Evidentialism is founded on Induction, or inductive inferences.

Hume, supposedly, showed that it is logically impossible to infer the unknown from the known. It is logically impossible to derive the unknown from the known. Thus, Evidentialism is founded on a logical impossibility.

“The problem of the source of our knowledge has recently been restated as follows. If we make an assertion, we must justify it; but this means that we must be able to answer the following questions.

How do you know? What are the sources of your assertion?’ This, the empiricist holds, amounts in its turn to the question,

‘What observations (or memories of observations) underlie your assertion?’ I find this string of questions quite unsatisfactory.” – Karl Popper in “The Sources of Knowledge and Ignorance

Popper presents the Evidentialist Principle, in that quote, as saying that “If we make an assertion, we must justify it“. If you make an assertion, then you must justify it, or making an assertion implies must justify the assertion. You would have to answer one question, ‘How do you know? What are the sources of your assertion?’, and have to answer another question, ‘What observations (or memories of observations) underlie your assertion?’. 

As Popper points out, the Evidentialist Principle is an answer to The Problem of Source of Knowledge. So we may suppose that Evidentialism and Induction are to be based on the Source of a proposition or an empirical proposition. It seeks that the source of a proposition to be justified.

Criticizing or discrediting a proposition because of the source has some similarity to the Genetic Fallacy: “if the critic attempts to discredit or support a claim or an argument because of its origin (genesis) when such an appeal to origins is irrelevant.”

With the Genetic Fallacy, a proposition is being discredited, or supported, because it is “paying too much attention to the genesis of the idea rather than to the reasons offered for it”. The origin, or source, of the proposition is used to discredit, or support, the proposition.

Evidentialism would discredit a proposition because the source of the proposition is without justification.

We also find that David Hume presents an example of the questions that Popper finds to be unsatisfactory.

“All reasonings concerning matter of fact seem to be founded on the relation of cause and effect. By means of that relation alone we can go beyond the evidence of our memory and senses. If you were to ask a man, why he believes any matter of fact, which is absent; for instance, that his friend is in the country, or in France; he would give you a reason; and this reason would be some other fact; as a letter received from him, or the knowledge of his former resolutions and promises…All our reasonings concerning fact are of the same nature. And here it is constantly supposed that there is a connexion between the present fact and that which is inferred from it. Were there nothing to bind them together, the inference would be entirely precarious.

When it is asked, What is the nature of all our reasonings concerning matter of fact? the proper answer seems to be, that they are founded on the relation of cause and effect. When again it is asked, What is the foundation of all our reasonings and conclusions concerning that relation? it may be replied in one word, Experience. But if we still carry on our sifting humour, and ask, What is the foundation of all conclusions from experience? this implies a new question, which may be of more difficult solution and explication.” – David Hume in “Sceptical doubts concerning the operations of the understanding” (Italics are Hume’s)

David Hume himself goes down the line of questioning that Popper brings up. For example, suppose that some assertion is made like “all ravens are black”. This assertion is what Hume calls a Matter of Fact, i.e. Synthetic proposition or Contingent proposition. It is Possible that it is true that “all ravens are black” and it is possible that it isn’t true that “all ravens are black”. This starts a line of questioning once this assertion is presented.

Question: What is the nature of reasoning concerning that matter of fact?
Evidence: The assertion is founded on the relation of cause and effect.
Question: What is the foundation of reasoning and conclusion concerning that relation of cause and effect?
Evidence: The relation of cause and effect of that assertion is founded on Experience.

These two questions follow a basic form that Popper is bringing up, and the type of basic form that Popper finds unsuitable, or the type of basic form of Evidentialism that is unsuitable. The basic reason for this is because another question follows from the answer to the previous two questions.

Question: What is the foundation of that conclusion drawn from experience?

This new question is where the Problem of Induction arises, or what Popper calls The Logical Problem of Induction.

If all Ravens are Black then justified in the relation of cause and effect. If justified in the relation of cause and effect then justified by experience. If justified by experience then experience is justified by Induction. So if all ravens are black then justified by Induction. But, Induction isn’t justified. So assertion all ravens are black isn’t justified. Therefore, Evidentialism would make it so that the assertion all Ravens are Black isn’t justified. This applies to all matters of fact, and thus all empirical and scientific assertions.

“It is usual to call an inference ‘inductive’ if it passes from singular statements (sometimes called ‘particular’ statements), such as accounts of the results of observations or experiments, to universal statements, such as hypotheses or theories. Now it is far from obvious, from a logical point of view, that we are justified in inferring universal statements from singular ones, no matter how numerous; for any conclusions drawn in this way may always turn out to be false: no matter how many instances of white swans we may have observed, this does not justify the conclusion that all swans are white. The question whether inductive inferences are justified, or under what conditions, is known as the problem of induction.” – Karl Popper in “The Logic of Scientific Discovery” (Italics are Popper’s)

The Problem of Induction comes about because Induction relies on statement that is a matter of fact assertion, but this matter of fact assertion cannot, in principle, be inductively justified. So either all reasonings concerning matter of fact seem to be founded on experience or not all reasonings concerning matter of fact seem to be founded on experience.

This is a logical problem because either Induction relies on a statement that is either a contingent proposition or necessary proposition. We can call this the “Principle of Induction”. But the Principle of Induction can’t be a necessary proposition because the negation of the Principle of Induction is possible to be false. A necessary proposition can’t be possible to be false. So it is possible that Principle of Induction is true and it is possible that isn’t true that Principle of Induction is true. Therefore, the Principle of Induction is a contingent proposition.

Hume points out that matter of facts about dispositions and universal propositions are matters of facts. Thus dispositional propositions and universal propositions are contingent propositions. Dispositional propositions describe law-like behavior and universal propositions describe lawful behavior or law-like behavior. These would both be contingent propositions, and so we wouldn’t be justified, based on Induction, in asserting those dispositional propositions or universal propositions.

We wouldn’t be justified, based on Evidentialism, when it came to assertions about dispositional propositions or universal propositions. Science wouldn’t be justified, based on Evidentialism, when it came to assertions about dispositional propositions or universal propositions. But science is full of assertions about dispositional propositions and universal propositions. Therefore, science wouldn’t be justified in asserting dispositional propositions and universal propositions.

“[Hume] tried to show that any inductive inference- any reasoning from singular and observable cases (and their repeated occurrence) to anything like regularities or laws- must be invalid. Any such inference, he tried to show, could not even be approximately or partially valid. It could not even be a probable inference: it must, rather, be completely baseless, and must always remain so, however great the number of the observed instances might be. Thus he tried to show that we cannot validly reason from the known to the unknown, or from what has been experienced to what has not been experienced (and thus, for example, from the past to the future): no matter how often the sun has been observed regularly to rise and set, even the greatest number of observed instances does not constitute what I have called a positive reason for the regularity, or the law, of the sun’s rising and setting. Thus it can neither establish this law nor make it probable.” Karl Popper in “Realism and the Aim of Science” (Italics are Popper’s)

The assertion “all ravens are black” isn’t justified as true under Evidentialism and “all ravens are black” isn’t jusified as probably true under Evidentialism. Hume himself points out that the wise man doesn’t fixate his judgement on an assertion in which the evidence exceeds what we properly call probability. In other words, the Evidentialist doesn’t hold to assertions in which the evidence exceeds what we properly call probability. So Evidentialist only hold to assertion in which evidence shows it is true or probably true. So “all ravens are black” is only held by an Evidentialist if evidence shows it is true or at least probably true.

Popper presents a solution to the Problem of Induction, and thus treats assertions differently from Evidentialism. Popper rejects Induction, and thus rejects Evidentialism. The source of an assertion has nothing to do with either discrediting the truth of a proposition or supporting the truth of a proposition.

Matter of fact propositions, or scientific propositions, don’t discredit or support the source of an assertion. Science doesn’t support the truth of a proposition or support the probability of a proposition. It, basically, seeks to discredit the truth of a proposition. Science seeks to show that the proposition is false, not that the proposition is true or probably true. Science always seeks to discredit it’s proposition and not to support it’s propositions. So scientific propositions are, in principle, possible to show they are false and never show they are true or probably true. This includes both dispositional propositions and universal propositions.

In other words, Evidentialism seeks both positive justifications for assertion and negative justifications for assertion. Evidentialism would be based on “full decidability”. Falsifiability, or Falsification, seeks only negative justifications for assertions. Falsifiability would be based on “partial decidability” . These negative justifications, for Falsifiability, basically state that scientific assertion hasn’t been demonstrated false as of yet. This never indicates a positive justification for the assertion being true or probably true.

“The problem of induction arises from an apparent contradiction between the basic empiricist requirement (only experience can decide the truth or falsity of a scientific statement) and Hume’s insight into the logical impermissibility of inductive decision (there is no empirical justification of universal statements). This contradiction exists only if we assume that empirical statements must be empirically “fully decidable”, that is, that experience must be able to decide not only their falsity, but also their truth. The contradiction is resolved once “partially decidable” empirical statements are admitted: Universal empirical statements are empirically falsifiable, they can be defeated by experience.” – Karl Popper in “The Two Problems of The Theory of Knowledge” (Italics are Popper’s)

For Falsifiability, the source of an assertion is irrelevant when judging whether the assertion is either true or false, and the source of an assertion is irrelevant when judging whether justified in believing that assertion is true or probably true. The source of an assertion is irrelevant for the justification of the assertion. Would have to rely on Induction, and Induction isn’t justified itself. The only justification of an assertion, specifically an empirical assertion, is that it is possible to show that assertion is false. An empirical assertion has the possibility to be shown false, but it doesn’t have the possibility to be shown true (or probably true).

Science, thus, doesn’t care of the source of an assertion. Science is justified in believing, or holding to, an empirical proposition because that empirical proposition allows for the possibility that can be shown that it is false, but hasn’t been shown that it is false yet. For example, science would be justified in believing the empirical proposition that “all ravens are orange” if wasn’t for “some ravens are black”. It would be a negative justification, since don’t have another empirical proposition that contradicts it, or shows that it is false.

One of the basic mechanisms of Falsifiability is that works by deductive inference. Modus Tollens forms an example of deductive inference that Falsifiability uses. Given the conditional claim that the consequent is true if the antecedent is true, and given that the consequent is false, we can infer that the antecedent is also false.

If an empirical assertion is true implies another empirical assertion is true & the other empirical assertion is false, then original empirical assertion is false.

Principle of Modus Tollens:If all ravens are orange implies no ravens are not orange & some ravens are black, then not all ravens are orange. This is how the negative justification of empirical assertions works, which is deductive inference of modus tollens. It wouldn’t be possible for “not all ravens are orange” to be false. So it must be true.

The Principle of Modus Tollens is a necessary truth, which is different from the Principle of Induction. The Principle of Induction isn’t a necessary truth. It is possible that the Principle of Induction is false. So it might be true.

An assertion that is the conclusion of the Principle of Induction, or the assertion of a wise man that reviewed the Evidence, might be true. An assertion that is the conclusion of the Principle of Modus Tollens, or the assertion of a foolish man that never reviewed the Evidence, must be true.

The truth that the Principle of Modus Tollens always produces truth. It is similar to negative theology. It isn’t true that “all ravens are orange” & it isn’t true that “no ravens are not orange”. Each time saying what is true because true isn’t those false statements, since it is true that “not all ravens are black”.

The contradiction between “all ravens are orange” and “not all ravens are orange” are exclusive, they both can’t be true and no intermediary empirical propositions between them. If know that “all ravens are orange” is false then know that “not all ravens are orange” is true. All ravens are orange implied no ravens are not orange & some ravens are black. Therefore, it is necessarily true that not all ravens are orange. If Know that “not all ravens are orange” is true then “not all ravens are orange” is true. “Not all ravens are orange” is true.

Both the Principle of Modus Tollens are dealing with scientific propositions. The scientific propositions are possibly true or possibly false. If combine scientific propositions with the Principle of Induction, then scientific proposition infered might be true. If combine scientific propositions with Principle of Modus Tollens, then scientific proposition infered must be true. The negative justification allows for things that aren’t possibly not true & hold to statements that are only true, while positive justification allows for things that are only possibly true & hold to some statements that aren’t only true.

So Evidentialist like David Hume, or C.K. Clifford, would be justified in holding some scientific propositions that aren’t only true. Evidentialist would hold to both true statements and false statements. While the Non-Evidentialist, which follows Falsifiability or negative justification, would hold only to true statements. The Non-evidentialist wouldn’t be justified in asserting a scientific statement, even though conclusions drawn from it must be true.

Thus, Evidentialism is fallacious because the assertions that it concludes to be justified in holding, based on the evidence, aren’t truth-preserving. It’s conclusions of justified scientific propositions aren’t based on the evidence or derived by positive support it receives from the evidence. However, it is completely opposite with Non-Evidentialism of Falsification, or it isn’t fallacious.

The Evidentialist would be acting irrationally by seeking their justification, while the Falsifiabilist, which is necessarily a Non-Evidentialist, would be acting rationally by not seeking the Evidentialist justification.

Huxley’s assertion, in his examplar of Evidentialism, mentions that “merciless to fallacy in logic.” But we later find out that Evidentialism isn’t “merciless to fallacy in logic”, but is founded on a fallacy in logic itself. David Hume recognized this, even though exemplar of Evidentialism. Instead, he went about acting irrationally by seeking a (positive) justification of proposition by evidence & the rest of Evidentialism followed, like C.K. Clifford and Thomas Huxley. They would all go about by searching for evidence that proposition is true and end right back in the same place.

Finding Evidence

So we finally come full circle with the fallacy of Evidentialism, and find the source of the Evidentialist fallacy.

Advertisements

Posted in Philosophy, Science | Tagged: , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | Leave a Comment »

Hume and The Impossibility of Falsification

Posted by allzermalmer on May 5, 2013

Hume’s logical problem of induction as Hume presents it and Popper presents it, deals with contingent statements. The affirmation or the negation of the same contingent statement is possible. Take the contingent statement that “All Swans are White”: It is both possible that “All Swans are White” and it is also possible that  not “All Swans are White”. Logic alone cannot decide if “All Swans are White” is either true or false. So it would be decided by some other way as to wither its affirmation or negation to be true. Hume, and Popper, say that experience cannot show the truth of the contingent statement “All Swans are White”.

“Hume’s argument does not establish that we may not draw any inference from observation to theory: it merely establishes that we may not draw verifying inferences from observations to theories, leaving open the possibility that we may draw falsifying inferences: an inference from the truth of an observation statement (‘This is a black swan’) to the falsity of a theory (‘All swans are white’) can be deductively perfectly valid.” Realism and The Aim of Science

(H) Hypothesis: All Swans are White
(E) Evidence: This is a Black Swan

Hume, as Popper takes him in his problem of induction, showed that we cannot show that (H) is true, no matter how many individual swans that are white we have observed. To show that (H) is true, we must verify every case of (H). (H) is a Universal statement, its scope is that of all times and all places. The universal statement is both omnipresent and omnitemporal in its scope. It makes no restriction on temporal location and spatial location. (E) makes a Singular statement, its scope is of a particular time and a particular place. It makes a restriction on temporal location and spatial location. Popper held that we can know (E) is true, ‘This is a Black Swan’. Thus, we cannot know (H) All Swans are White but we can know (E) This is a Black Swan.

Hume’s logical problem of induction, as Popper takes it, goes something like this:

(i) Science proposes and uses laws everywhere and all the time; (ii) Only observation and experiment may decide upon the truth or falsity of scientific statements; (iii) It is impossible to justify the truth of a law by observation or experiment.

Or

(i*) Science proposes and uses the universal statement “all swans are white”; (ii*) Only singular observational statements may decide upon the truth or falsity of ‘all swans are white’; (iii*) It is impossible to justify the truth of the universal statement ‘all swans are white’ by singular observational statements.

It is taken as a fact that (i) or (i*) is true. So there is no question about either (i) or (i*). So the conflict of Hume’s logical contradiction arises between (ii) and (iii) or (ii*) and (iii*). Popper accepts (iii) or (iii*). So the only way out of Hume’s logical problem of induction is to modify or reject (ii) or (ii*) to solve the contradiction.

Popper thus solves Hume’s logical problem of induction by rejecting (ii) or (ii*) and replacing it with a new premise. This new premise is (~ii).

(~ii) Only observation and experiment may decide upon the falsity of scientific statements
Or
(~ii*) Only singular observation statements may decide upon the falsity of ‘all swans are white’.

Popper rejects (ii) or (ii*), which basically said that only singular observation statements can show that either universal statements are true or false. Popper rejects this because of (iii), and says that Singular observation statements can only show that universal statements are false. Popper believes, as the quote at the beginning of the blog says, that Hume’s logical problem of induction doesn’t show that we can’t show that a universal statement is false by a singular observational statements. But is this what Hume showed to be true?

It does not appear that Hume’s logical problem of induction even allows Popper to escape with the modification of (ii) to (~ii). It appears that Hume’s logical problem of induction does not allow Popper to escape from “fully decidable” to “partially decidable”, i.e.  decide both truth or falsity to cannot decide truth but only falsity.

Take the singular observational statement that Popper gives in the quote, i.e. ‘This is a black swan’. It is a singular statement, but the statement contains a universal within it, it contains “swan”. “Swan” are defined by their law-like behavior, which are their dispositional characteristics, and is a universal concept. These dispositions are law-like, and thus universal in scope as well. And by (iii) we cannot determine if something is a “swan” because of that. The concept “swan” is in the same position as “all swans are white”. They are both universal, and because of (iii) cannot be shown to be true.

“Alcohol” has the law-like behavior, or disposition, or being flammable. So if we were to say that ‘This is alcohol’. We would have to check all the alcohol that existed in the past, present, future, and all places in the universe in which it was located. We would have to light them to see if they catch fire, and thus flammable. Only than could we say that “This is alcohol”, and know that it is alcohol. But to do so would be to verify a universal through singulars, which is impossible by (iii).

In fact, Hume even talks about dispositions and law-like behavior in his talks about the problem of induction. For example, Hume says that “we always presume, when we see like sensible qualities, that they have like secret powers, and expect that effects, similar to those which we have experienced, will follow from them.” Hume is specifically attacking dispositions as well, which means he is attacking universal concepts and universal statements.

“Our senses inform us of the colour, weight, and consistence of bread; but neither sense nor reason can ever inform us of those qualities which fit it for the nourishment and support of a human body…The bread, which I formerly eat, nourished me; that is, a body of such sensible qualities was, at that time, endued with such secret powers: but does it follow, that other bread must also nourish me at another time, and that like sensible qualities must always be attended with like secret powers?” Enquiry’s Concerning Human Knowledge

From Popper’s point of view, science can only show the falsity of a universal statement through the truth of a singular statement. The singular statement would have to contradict the universal statement and the singular statement would have to be true.

(h) If it rained then wet ground.
(e) Not a wet ground
(c)Thus, it didn’t rain.

If we assume that both (h) and (e) are true, then we accept a contradiction. Contradictions can’t possibly be true. So we know that at least one of these two must be false. But which one is false and which one is true, (h) or (e).

But how can we show the truth of a singular observational statement when it relies on a universal concept, and universal concepts fall for (iii) just as much as universal statements? Hume’s position of the logical invalidity of of induction, i.e. (iii), also holds not only with universal statements but also universal concepts, i.e. law-like behavior/ dispositional characteristics. How does Popper respond to this?

Popper accepts the invalidity of reaching universal statements through experience, but takes it that we accept singular observational statements based on conventions. We conventionally accept the singular observation statement as true.

Hume’s logical problem of induction shows this:

(H) All Swans are White
(E) This swan is black

Now we may either accept (H) as a convention or accept (E) as a convention, or both as conventions. Popper rejects accept (H) as a convention, because you cannot show that a convention is false. Showing something false is what (~ii) was used to solve the original problem of induction. He wants to show that (H) is false, which is consistent with (~ii), but the only way to do that is if (E) can be shown true. But (E) contains a universal concept and (iii) prevents us from experiencing dispositions or law-like behaviors, i.e. Swan or Alcohol. (iii) applies just as much to universal statements as it does to universal concepts. (E) is based on universal concepts and so has to be accepted as a convention, to escape (iii), in order to show that (H) is false and be consistent with (i) and (~ii). (H) has to have the ability to be shown false to be falsifiable, and not being a convention means it has the ability to be shown false.

Contrary to what Popper thinks, Hume’s logical problem of induction doesn’t even allow you to show a falsifying instance. Thus, following full implications of Hume’s logical problem of induction, we can neither show the truth of a universal statement or show the falsify of a universal statement.

Posted in Philosophy | Tagged: , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , | Leave a Comment »

Avicenna’s Response to Meno’s Paradox

Posted by allzermalmer on December 18, 2012

Avicenna (Ibn-Sina) was an Arabic philosopher who wrote a book called The Healing. In Book 1, the sixth  chapter is called “On the Manner of Apprehending (iābah) Unknown [Things] (al-majhūlāt) from Known [Things] (al-malūmāt).” This is a response to Meno’s Paradox presented to Socrates about learning or coming to obtain new knew knowledge. The response of Avicenna is translated into English by Michael E. Marmura

“Every seeking (malab) of these [unknown things] is only achieved by means of existing, realized things. Here, however, there is a place for doubt, namely, that [with respect] to the thing whose entity (al-dhāt) is nonexistent [and] whose existence is impossible, how is one to conceive it so as to answer the question “What is it?” when asked about it, so that thereafter one could ask “Does it exist?” For if no meaning (manan) for it is realized in the soul, how can one judge it to be either realized or not realized, when the impossible has no form in existence? How, then, would a form of it be taken into the mind so that that conceived thing would constitute its meaning?

[To this] we say: this impossible [thing] is either (a) singular, having  neither composition nor separability [of parts] (wa lā tafīl), [or (b) composite]. If [(a), singular], it would not be at all conceivable except by some kind of analogy (muqāyasa) with the existent and in relation to it. This would be similar to our saying “vacuum” and “the contrary of God.” For vacuum is conceived as belonging to bodies as though a recipient, and the contrary of God would be conceived as belonging to God in the way the hot relates to the cold. Thus the impossible would be conceived in terms of a possible thing to which it relates, being conceived in relation to it and likened to it. In itself, however, it is neither conceivable nor intellectually apprehendable (lā maqūlan), nor would it have any being (wa lā dhāta lahu).

As for [(b)], which has some sort of composition and separable parts, such as the goatstag, the phoenix, or a human that flies, what is first conceived is their separable parts whose existence is not impossible. Thereafter there is conceived for the parts some kind of connections, analogous to the connections that obtain for the separable parts of existing composite entities. There would thus be three things, two of them consisting of parts, where each by itself [can] exist, and the third a composition of them. This in some respect is a conceived composition, because composition inasmuch as it is a composition is one of the things that exist. In this way it yields the meaning signifying the nonexistent’s name. Thus the nonexistent is only conceived because of the prior conception of existing things.

We now say: if a judgment about a universal is realized for us, its first  realization being self-evident, as, for example, “every human is an animal” and “the whole is greater than the part,” or evident by induction or experiment (tajriba) in the ways things are believed to be true (p.73) without the help of a [demonstrative] syllogism (qiyās), we would know potentially the judgment over every particular beneath it, but we would be ignorant of it in [its] actuality. Thus, for example, we would not know that Zayd, who is in India, is an animal. In actuality we would be ignorant of this because thus far we would have known [it] only potentially, since we have known that every human is an animal. In actuality we would be ignorant of it because one needs to add to this knowledge another knowledge, or two other [instances] of knowledge, for the potential to become actual. This is because we must know that Zayd exists and know that he exists as a human. If then through the senses we attain immediate cognition (marifa) that he exists and that he is a human, without this being sought after (malūban) through a [demonstrative] syllogism or [this being]taught, and if this is connected with [universal] knowledge (ilm), which is realized for us, also without a [demonstrative] syllogism, in [the] manner by which the connection that in itself brings about a third knowledge [takes place], we would then know that Zayd is an animal. It would thus be the case that from the combining of immediate cognition (marifa) and [universal] knowledge (ilm), knowledge [of the specific particular] comes about for us. Of the two, immediate cognition comes about through sensation, [universal] knowledge through the intellect. Immediate cognition would have come to us at a temporal moment, whereas [universal] knowledge is prior to it.

That which comes about from both of them may well have been sought by us, and we [may have] sought its principles, which bring us to it, or it could have been something to which we have been led by reason of the sufficiency of its causes without our seeking it. With all this, the conception of the thing sought after and its principles must precede every instance of it.

It may also happen that it is not like this, but that the judgment of the universal would have come about for us by a [demonstrative] syllogism, and the judgment of the particular would have come about by another [demonstrative] syllogism, such that if the two are combined, a third instance of knowledge is realized. But even if this is the case, the first syllogisms would have been through self-evident premises or else acquired by induction, experiment, or sensory perception without a syllogism, as we will make clear later.

Then, if a questioner should ask someone and say, “Do you know that every dyad is even?” it is known that the answer would be, “I know this.” [The questioner] would then come back and say, “Is what is in my hand even or odd, and is the number of people in such and such a city even or odd?” If it is answered, “We do not know this,” [the questioner] will come back and say, “You then do not know that every numerical dyad is even; for what is in my hand is a dyad, but you did not know that it is even.”

It is said in The Teaching [of Aristotle] that some people have answered this incorrectly, saying, “We only know that every dyad known to us is even.” But this answer is false; (p. 74) for we know that every existing dyad, whether known or not known, is even.

Rather, [our own] response to this would be, “We did not say that we know every dyad that is even, so that if we did not know that [the] two things [in the hands of the questioner] constitute a dyad our statement is contradicted”; we also did not say, “We know of everything that is a pair, that it is a pair, so that [consequently] we know that it is even.”

Rather, we said one of two things: either that every dyad that we know, we know it to be even; or every dyad in itself, whether we know it or not, is in itself even. As for the first disjunct, it is not contradicted by the doubt mentioned. As for the second [disjunct], it consists of general knowledge, not contradicted by our ignorance [of some aspect belonging to it]. This is because even though we do not know whether what is in the hand of so and so is even or not even, the meaning of our knowledge that every dyad is even stands established and is not false. But what we would be ignorant of is included in our potential, not actual, knowledge. Ignorance of it would not be an ignorance in actuality of [all of] what we have. If we come to know that what is in [the questioner’s] hand is a
dyad, and we remember the thing which was known to us, [namely, that every dyad is even,] we would immediately know that what is in his hand is even. What we are ignorant of is other than that which we know. It is not the case that if we do not know whether or not something is even because we do not know whether or not it is a dyad that this falsifies our knowledge that whatever is a dyad is even. We would then have also known that in one respect that thing is even. With this the doubt raised ceases.

It was mentioned that Meno, who addressed Socrates regarding the  nullification of teaching and learning, said to him, “The seeker of some kind of knowledge will either be seeking knowledge of what he [already] knows, in which case his quest would be inconsequential, or else he would be seeking knowledge of what he does not know—[In this case,] how would he know it, once he attains it? This is akin to one who seeks a runaway slave he does not know. If he finds him, he would not recognize him.”

Socrates then undertook in refuting him (p. 75) to present [Meno] with a geometrical figure, establishing for him how the unknown, after being unknown, is captured through the known. This, however, is not logical discourse. For he showed that this is possible, bringing about a syllogism that yielded as a conclusion the possibility of what Meno brought about by a syllogism that yielded other than its possibility. [As such,] he did not resolve the doubt.

Plato, on the other hand, undertook to resolve the doubt, saying that  learning is recollection. In this he attempted to convey that the thing being sought had been known prior to the quest and prior to [its] attainment, but it was only being sought because it had been forgotten. Once the investigation led to the thing sought, it was remembered and learned. Thus the seeker would have known something he had [previously] known. It is as though Plato had acquiesced to the doubt and sought toescape from it and fell into an impossibility. This is something we have treated in exhaustive detail in our solution to it in our summary of the book on the Syllogism.

Still with all this we say: if what is being sought after is known for us in every respect, we would not seek it; and if unknown for us in every respect we would not seek it. It is, [however,] known to us in two respects, and unknown in one respect. For it is known to us conceptually in actuality, and known to us potentially in terms of assent. It is unknown to us in being specified with actuality, even though it is also known to us [as] being not specified with actuality. If, then, we have had previous knowledge that every thing which is of a certain character is of that character,  without [that knowledge] having been sought after, but by an inborn rational act, or through sensation, or some other [similar] ways of knowing, we would attain in potentiality knowledge of numerous things. If through sensation we apprehend some of these particulars without our seeking them, they would immediately fall within [the category] of being actual, within the [category] of first knowledge. This, in some respect, would parallel step by step what Meno had brought about in the example of the runaway slave.

For we would know at first the thing sought after conceptually, as we would know the runaway slave at first conceptually. And we know prior to this what would bring us to knowing it by assent, just as we would know the road [taken by the slave] prior to our knowing the place of the runaway slave. For if we follow the path to what is being sought after, and we have had a previous conception of it and of the road leading to it, and [if] we reach it, we would have apprehended the thing sought after. [This is] similar to our travelling path to the runaway slave when we have a previous conception of his self, and of the road leading to him  Once we reach him, we would recognize him, even if we had never seen the runaway slave at all [before]; but we would have conceived for him a distinguishing mark (alāma), [which indicates] that everyone having this mark is a runaway.

If there were added to this some knowledge occurring not by acquisition but coincidentally by observation, or [some knowledge] occurring by acquisition, demonstration, testing, and cognizing, and we found that mark on a slave, we would know that he is a runway.

The distinguishing mark would thus be like the middle term in the  syllogism. Our grasping that distinguishing mark in a slave would be like the minor term. Our knowledge that whoever has this mark is a runaway is akin to the prior occurrence for us of the major premise; and our finding the runaway would be akin to the conclusion. This runaway, moreover, would not have been known to us in every respect; otherwise we would not have sought him. Rather, he was known to us by way of conception, unknown to us as regards [the physical] place [where he is]. Hence, we would be seeking him with respect to his being unknown, not with respect to his being known. Once we recognized him and caught him, there would have occurred through [our] demonstrative quest knowledge of him which [previously] did not exist. This only happened on account of the combination of two causes of knowledge, one being [knowledge of] the way and its leading to him, the second, his being the object of sense apprehension.

The unknown things sought after are similar to this: they are known by the combination of two things. The first is something which is prior for us, namely, that B is A, which parallels the first cause in the example of the runaway slave; the second is a thing which occurs immediately, namely, our sensory cognition that C is B, which equals the second cause in the example of the runaway slave. Just as the two causes there necessitate the apprehension of the runaway slave, similarly the two causes here necessitate the apprehension of what one is seeking. It is not the case that what he, [that is, Meno,] demanded as a condition, [namely,] that whatever is not known in every respect would not be known when attained, is admitted. Rather it is every thing unknown in every respect that is not recognized when attained. If, however, knowledge of a thing which had been known [before] had been pursued, [the prior knowledge of it] would constitute potential knowledge of a part of what is being sought after, it being like a distinguishing mark for it. Itwouldthen only require something to connect with it to change it into actuality. As soon as that which actualizes it is connected with it, the thing sought after is attained.

[Now] that it has been established how mental (dhihnī) instruction and  learning takes place and that this takes place only through previous knowledge, we must have first principles for conception and first principles for assent. If every instruction and learning was through previous knowledge, and every existing knowledge is through instruction and learning, the state of affairs would regress ad infinitum, and there would be neither instruction nor learning. It is hence necessary that we have matters believed to be true without mediation, and matters that are conceptualized without mediation, and that these would be the first principles for both assent and conceptualization.”

Posted in Philosophy | Tagged: , , , , , , , , , , , , , , , , , | Leave a Comment »

Why Science Doesn’t Invoke Metaphysics

Posted by allzermalmer on November 1, 2012

All those things in italics come from Popper, and those that are in bold & italics  are my own personal emphasis and not Popper’s.

But before I get to that, I want to start out by making one big distinction. There is the distinction between statements that are logically necessary and those that are logically contingent.

Logically Necessary: For each x, if x is logically necessary, then x’s affirmation is logically possible and x’s negation is not logically possible.
Logically Contingent: For each x, if x is logically contingent, then x’s affirmation is logically possible and x’s negation is logically possible.

Popper thinks that things that are Logically Necessary are not in the domain of empirical science. Logically Necessary statements make no claim about reality or what exists, while those things that are Logically Contingent do make claims about reality or what exists. Logically Contingent statements are what empirical science deals with. But from within this domain of Logically Contingent statements, Popper is going to make a distinction.

His distinction is basically this: Not for every statement, if statement is logically contingent, then logically possible for humans to verify that statement is actually true instead of possibly true.

This is because it relies logical distinction between singular statements and universal statements.  “The raven is black in color” or “There exists at least one x, such that x is raven and x is black in color”, are examples of “Singular statements”. They are a proposition that asserts that a particular individual has (or has not) some specified attribute. “All ravens are black in color” or “For every x, if x is raven, then x is black in color”, are examples of “Universal statements”. They are a proposition that refers to all the members of a class. The members of class could have all sorts of particular individual things contained in them, like all ravens that have existed, are existing, or will exist. This can be logically infinite domain in time and space. Singular statements are at specific times and specific places, not all times and all places. So these are logically distinct from one another.

One of the basic points is that sense experience, or observation, is of particular things or individuals. We do not have sense experience, or observation, of all times and places, or all things that have existed, are existing, or will exist. In other words, observation only gives singular statements but science, or empirical science, seeks universal statements that apply to all particular things, for all times and all places. Empirical science is seeking universal statements that apply to singular statements, like universal statements that apply to all particular ravens.

“The fact that theories are not verifiable has often been overlooked. People often say of a theory that it is verified when some of the predictions derived from it have been verified. They may perhaps admit that the verification is not completely impeccable from a logical point of view, or that a statement can never be finally established by establishing some of its consequences. But they are apt to look upon such objections as due to somewhat unnecessary scruples. It is quite true, they say, and even trivial, that we cannot know for certain whether the sun will rise tomorrow; but this uncertainty may be neglected: the fact that theories may not only be improved but that they can also be falsified by new experiments presents to the scientist a serious possibility which may at any moment become actual; but never yet has a theory had to be regarded as falsified owing to the sudden breakdown of a well confirmed law. It never happens that old experiments one day yield new results. What happens is only that new experiments decide against an old theory. The old theory, even when it is superseded, often retains its validity as a kind of limiting case of the new theory; it still applies, at least with a high degree of approximation, in those cases in which it was successful before. In short, regularities which are directly testable by experiment do not change. Admittedly it is conceivable, or logically possible, that they might change; but this possibility is disregarded by empirical science and does not affect its methods. On the contrary, scientific method presupposes the immutability of natural processes, or the ‘principle of the uniformity of nature’.

There is something to be said for the above argument, but it does not affect my thesis. It expresses the metaphysical faith in the existence of regularities in our world (a faith which I share, and without which practical action is hardly conceivable).*1 Yet the question before us— the question which makes the non-verifiability of theories significant in the present context—is on an altogether different plane. Consistently with my attitude towards other metaphysical questions, I abstain from arguing for or against faith in the existence of regularities in our world. But I shall try to show that the non-verifiability of theories is methodologically important. It is on this plane that I oppose the argument just advanced.

I shall therefore take up as relevant only one of the points of this argument—the reference to the so-called ‘principle of the uniformity of nature’. This principle, it seems to me, expresses in a very superficial way an important methodological rule, and one which might be derived, with advantage, precisely from a consideration of the non-verifiability of theories.*2 (I mean the rule that any new system of hypotheses should yield, or explain, the old, corroborated, regularities. See also section *3 (third paragraph) of my Postscript.

Let us suppose that the sun will not rise tomorrow (and that we shall nevertheless continue to live, and also to pursue our scientific interests). Should such a thing occur, science would have to try to explain it, i.e. to derive it from laws. Existing theories would presumably require to be drastically revised. But the revised theories would not merely have to account for the new state of affairs: our older experiences would also have to be derivable from them. From the methodological point of view one sees that the principle of the uniformity of nature is here replaced by the postulate of the invariance of natural laws, with respect to both space and time.  I think, therefore, that it would be a mistake to assert that natural regularities do not change. (This would be a kind of statement that can neither be argued against nor argued for.) What we should say is, rather, that it is part of our definition of natural laws if we postulate that they are to be invariant with respect to space and time; and also if we postulate that they are to have no exceptions. Thus from a methodological point of view, the possibility of falsifying a corroborated law is by no means without significance. It helps us to find out what we demand and expect from natural laws. And the ‘principle of the uniformity of nature’ can again be regarded as a metaphysical interpretation of a methodological rule—like its near relative, the ‘law of causality’.

One attempt to replace metaphysical statements of this kind by principles of method leads to the ‘principle of induction’, supposed to govern the method of induction, and hence that of the verification of theories. But this attempt fails, for the principle of induction is itself metaphysical in character. As I have pointed out in section 1, the assumption that the principle of induction is empirical leads to an infinite regress. It could therefore only be introduced as a primitive proposition (or a postulate, or an axiom). This would perhaps not matter so much, were it not that the principle of induction would have in any case to be treated as a non-falsifiable statement. For if this principle— which is supposed to validate the inference of theories—were itself falsifiable, then it would be falsified with the first falsified theory, because this theory would then be a conclusion, derived with the help of the principle of induction; and this principle, as a premise, will of course be falsified by the modus tollens whenever a theory is falsified which was derived from it. *3 (The premises of the derivation of the theory would (according to the inductivist view here discussed) consist of the principle of induction and of observation statements. But the latter are here tacitly assumed to be unshaken and reproducible, so that they cannot be made responsible for the failure of the theory.) But this means that a falsifiable principle of induction would be falsified anew with every advance made by science. It would be necessary, therefore, to introduce a principle of induction assumed not to be falsifiable. But this would amount to the misconceived notion of a synthetic statement which is a priori valid, i.e. an irrefutable statement about reality. Thus if we try to turn our metaphysical faith in the uniformity of nature and in the verifiability of theories into a theory of knowledge based on inductive logic, we are left only with the choice between an infinite regress and apriorism.” The Logic of Scientific Discovery pg. 249-252

Popper is trying to make the distinction between a metaphysical principle and a methodological principle. He is trying to point out that science is a methodology without metaphysical principles. The line of demarcation between science and metaphysics is falsifiability or refutability.  He holds that “we must choose a criterion which allows us to admit to the domain of empirical science even statements which cannot be verified.” (pg. 18) Popper’s line of demarcation for statements that are allowed into science, or more specifically universal statements allowed into empirical science. “But I shall certainly admit a system as empirical or scientific only if it is capable of being tested by experience. These considerations suggest that not the verifiability but the falsifiability of a system is to be taken as a criterion of demarcation.*3 In other words: I shall not require of a scientific system that it shall be capable of being singled out, once and for all, in a positive sense; but I shall require that its logical form shall be such that it can be singled out, by means of empirical tests, in a negative sense: it must be possible for an empirical scientific system to be refuted by experience.” (pg. 18)

We can verify singular statements, it is logically possible for us to find out if that statement is true. If we have not verified that it is actually true, we cannot infer that it is actually false. It is still logically possible that it is true. So we find out that we can, at least in principle, verify the truth of a singular statement. However, it is not logically possible for us to affirm a universal statement, like empirical claims of science. However, we can show that they are false. We cannot verify them but we can falsify them. We falsify these universal statements with one singular statement, or one observation, which the universal statement does not logically allow for, i.e. says is not logically possible to be true if the universal statement is true. This can be shown by simple modus tollens.

Universal Statement: All ravens are black.
Singular Statement: This raven is white.
Conclusion: Some ravens are not white.

or

Universal Statement: No ravens are not black.
Singular Statement: This raven is not black.
Conclusion: Some ravens are not black.

or

Universal Statement: For each x, if x is a raven, then x is black.
Singular Statement: There exists at least one x, such that x is a raven and x is not black.
Conclusion: Not each x, if x is raven, then x is black.

What needs to be kept in mind that the Universal statement has a logical equivalent as “No ravens are not black.” So it logically excludes a raven that is white, since white is the logical opposite of black, so it is not black.

Popper shows that if we do accept a metaphysical principle (i.e. a universal statement) which is logically contingent, then it means it is possibly true or possibly false. And if we choose to invoke a metaphysical principle in our science, and we derive another universal statement from it, then when that derived universal statement is refuted by observation, then the universal statement and the one it was derived from are shown to be false. For example, assume that “All ravens on Earthare black” is a metaphysical principle. We may derive that “All ravens on Earth in  in the United States are black”. When we observe that one particular raven on Earth in the United States is not black, which means that “All ravens on Earth in the United States are black” and “All ravens on Earth are black” are false.

Metaphysical Statement: All ravens on Earth are black.
Scientific Statement: All ravens on Earth in the United States are black.
Observation: This raven on Earth in the United States is not black.
Conclusion: Not all ravens on Earth in the United States are black & Not all ravens on Earth are black.

This means that if someone believes that science holds to the metaphysical principle of induction, then it was shown to be false by scientific theories that are false. Now as a methodology there is nothing wrong with holding to it, because methodology makes no truth claim itself. Also, the example of causality is an example, if we take it as a metaphysical principle that science is based on. So this would mean that science would hold to this metaphysical principle and derive other statements from this principle and test them with experience or observation. From this we find that one of our theories made a false prediction, which means that the metaphysical principle of causality has been shown to be false by experience as well, and all other theories that were derived from the metaphysical principle, but have not been shown false yet, would also by logical implication be false. The same thing would hold with naturalism, physicalism, materialism, dualism, or the world is parsimonious or simple, or determinism, or indeterminism, or presentism and eternalism, and etc.

Now science, or experience, would have never been able to verify these metaphysical principles in the first place. There would be no support for them to be derived from experience. It would still be logically possible for them to be true, but we cannot find out if they are actually true. Experience cannot help us to figure out if they are actually true or possibly true, no matter the amount of observations we make that are consistent with them. But science may use methodological principles in its activities, but holding to those methodological principles does not mean that one is logically obliged to hold to the metaphysical principles.

What is even more interesting is that if we do try to make some sort of inductive argument, we could argue that since science has used metaphysical principle x, and science continually comes up with false theories, or refuted theories, it will continue to derive false theories from that metaphysical principle. But of course, once something was refuted we have shown that it is logically impossible to be true. However, we can still use it and we may derive “true” theories, or theories that have not been shown to be false by observation, yet. This is because anything follows from a logical contradiction. This means you can derive both true statements and false statements. So it would not be surprising if the metaphysical principle also helped you to derive theories that have not been shown false by observation as of yet (even though still logically possible to be shown false with next observation).

Here is an example from basic logic which will rely on two basic rules of logical inference. These two rules are Disjunctive Addition and Disjunctive Syllogism.

Rule 1 – Disjunctive Addition: Given that a statement is true, we can infer that a disjunction comprising it and any other statement is true, because only one disjunct needs to be true for the disjunctive compound to be true.

Example:
Premise: It is snowing
Conclusion: Either it is snowing or it is raining

Rule 2 – Disjunctive Syllogism: Because at least one disjunct must be true, by knowing one is false we can infer that the other is true.

Example:
Premise: Either the New York Yankees will win the pennant or the Baltimore Orioles will.
Premise: The Yankees will not win the pennant.
Conclusion: Therefore, the Orioles will win the pennant.

For it can easily be shown that these rules permit us to deduce from a pair of contradictory sentences, for instance, from the two sentences,  ”  The sun is shining ” and “The sun is not shining “, any sentence whatsoever.  Let us take these two premisses (a) “The sun is shining”  (b) “The sun is not shining “.  We can deduce with the help of rule (1) from the first of these premisses, the following sentence:”The sun is shining or Caesar was a traitor “. But from this sentence, together with the second premiss (b), we can deduce, following rule (2), that,Caesar was a traitor. And by the same method we can deduce any other sentence. This is extremely important, for if we can deduce any sentence whatsoever, then, clearly, we can always deduce any negation of any sentence whatsoever: It is clear that instead of the sentence “Caesar was a traitor ” we can, if we wish, deduce “Caesar was not a traitor “. In other words, from two contradictory premisses, we can logically deduce anything, and its negation as well. We therefore convey with such a contradictory theory-nothing. A theory which involves a contradiction is entirely useless, because it does not convey any sort of information.”

Logically possible Affirmation: The sun is shining.
Logically possible Negation: The sun is not shining.

The sun is shining. Therefore, by rule 1, The sun is shining or Ceasar was a traitor. But now the sun is not shining. Therefore, by rule 2, Ceasar was a traitor; The sun is not shinning. Therefore, by rule 1, The sun is not shinning or Ceasar was not a traitor. But now the sun is shinning. Therefore, by rule 2, Ceasar was not a traitor. Rule 1 allows you to pull up any premise you want, and be able to affirms this premise and also negate this premise by using Rule 2. So if you affirm a logical impossibility, anything and everything you want follows. They contain no “content” or “information” for empirical science. This is because empirical science wants to eliminate theories because they said something cannot happen and it was found that it did happen. Since there is a contradiction, we know it is logically impossible for the theory to be true.

This process of elimination, though, does not tell you which theories are true. It just says what is not true. There are still many other logically possible universal statements that have not been eliminated by singular statements, or observations, as of yet.

(This will be updated at least 24 hours after posting or publication). Edits need to be done.

Posted in Philosophy | Tagged: , , , , , , , , , , , , , , , , , , , , | Leave a Comment »

Did Popper Solve The Problem of Induction?

Posted by allzermalmer on October 3, 2012

Karl Popper said that he believed he had solved the “Problem of Induction”, or what he called “Hume’s Problem”. But did Karl Popper really solve the Problem of Induction or Hume’s Problem? Maybe we should (1) take a look at what Popper considered to be Hume’s problem, and (2) see what Popper says his solution to the problem is. (Whether or not Popper did correctly identify Hume’s problem, is of no concern here).

Before we do this, I think we should start out with something basic, or part of basic, logic.

(A) Universal Quantifier Affirmative (All S are P): For each x, if x is S, then x is P
(E) Universal Quantifier Negation (No S are P) : For each x, if x is S, then x is not P
(I) Existential Quantifier Affirmative (Some S are P): There exists at least one x, such that x is S and x is P
(O) Existential Quantifier Negation (Some S are not P): There exists at least one x, such that x is S and x is not P

“All of the categorical propositions illustrated above can be expressed by using either the universal quantifier alone or the existential quantifier alone. Actually, what this amounts to is the definition of the universal quantification of propositions in terms of existential quantification and the definition of existential propositions in terms of universal quantification.” p. 349 Formal Logic: An Introductory Textbook by John Arthur Mourant

Now this means that the Universal Quantifier (UQ) can be expressed in a logically equivalent form to an Existential Quantifier (EQ), and the Existential Quantifier can be expressed in a logically equivalent form to Universal Quantifier. For something to be logically equivalent means they mean the same thing in a logical sense. Logically equivalent statements have the exact same truth. One can’t be true and the other false, for this would mean they are both necessarily false.

Universal Quantifiers to Existential Quantifiers

A: For each x, if x is S, then x is P    There does not exist at least one x, such that x is S and x is not P
E: For each x, if x is S, then x is not P    There does not exist at least one x, such that x is S and x is P
I: Not for each x, if x is S, then x is not P    There exists at least one x, such that x is S and x is P
O: Not for each x, if x is S, then x is P   There exists at least one x, such that x is S and x is not P

A: For each x, if x is Crow, then x is Black  ↔  There does not exist at least one x, such that x is Crow and x is not Black
E: For each x, if x is Crow, then x is not Black  ↔  There does not exist at least one x, such that x is Crow and x is Black
I: Not for each x, if x is Crow, then x is not Black  ↔  There exists at least on x, such that x is Crow and x is Black
O: Not for each x, if x is Crow, then x is Black  ↔  There exists at least on x, such that x is Crow and x is not Black

Existential Quantifiers to Universal Quantifiers

A: There does not exist at least one x, such that x is S and x is not P    For each x, if x is S, then x is P
E: There does not exist at least one x, such that x is S and x is P     For each x, if x is S, then x is not P
I: There exists at least one x, such that x is S and x is P   Not for each x, if x is S, then x is not P
O: There exists at least one x, such that x is S and x is not P    Not for each x, if x is S, then x is P

A: There does not exist at least one x, such that x is Crow and x is not Black  ↔  For each x, if x is Crow, then x is Black
E:
There does not exist at least one x, such that x is S and x is P  ↔  For each x, if x is Crow, then x is not Black 
I:
There exists at least one x, such that x is Crow and x is Black  ↔  Not for each x, if x is Crow, then x is not Black
O:
There exists at least one x, such that x is Crow and x is not Black  ↔  Not for each x, if x is Crow, then x is Black

It needs to be pointed out first that there are two types of statements.
(1)Necessary Truth: Statement whose denial is self-contradictory.
(2) Contingent Truth: One that logically (that is, without self-contradiction) could have been either true or false.

(1a) “All bachelors are unmarried males”
(2a) “Justin Bieber is an unmarried male”

A necessary truth is said to have no empirical content. A contingent truth is said to have empirical content.

Hume’s problem was that he found that he cannot justify induction by demonstrative argument, since he can always imagine a different conclusion.

What Popper takes to be “Hume’s Problem”

“It is usual to call an inference ‘inductive’ if it passes from singular statements (sometimes called ‘particular’ statements), such as accounts of the results of observations or experiments, to universal statements, such as hypotheses or theories. Now it is far from obvious, from a logical point of view, that we are justified in inferring universal statements from singular ones, no matter how numerous; for any conclusions drawn in this way may always turn out to be false: no matter how many instances of white swans we may have observed, this does not justify the conclusion that all swans are white. The question whether inductive inferences are justified, or under what conditions, is known as the problem of induction.” pg. 3-4 Logic of Scientific Discovery

“The root of this problem [of induction] is the apparent contradiction between what may be called ‘the fundamental thesis of empiricism’- the thesis that experience alone can decide upon the truth or falsity of scientific statements- and Hume’s realization of the inadmissibility of inductive arguments.” pg. 20 Logic of Scientific Discovery

Here’s an Inductive argument

Singular: (P1) There exists at least one x, such that x is Crow and x is Black
Singular: (P2) There exists at least one x, such that x is Crow and x is Black

Universal: (C) For each x, if x is Crow, then x is Black

Popper’s Solution to “Hume’s Problem”

“Consequently it is possible by means of purely deductive inferences (with the help of the modus tollens of classical logic) to argue from the truth of singular statements to the falsity of universal statements. Such an argument to the falsity of universal statements is the only strictly deductive kind of inference that proceeds, as it were, in the ‘inductive direction’ that is, from singular to universal statements.”pg. 21 Logic of Scientific Discovery

Here’s Popper’s solution

Universal: (P1) For each x, if x is Crow, then x is not Black
Singular: (P2) There exists at least one x, such that x is Crow and x is Black
Universal: (C) Not for each x, if x is Crow, then x is not Black

Singular statement leads to a universal statement. From there exists at least one x, such that x is Crow and x is Black, the conclusion is reached that not for each x, if x is Crow, then x is not Black.

Here’s Poppers understanding of Induction: “It…passes from singular statements…to universal statements…”

Here’s Poppers solution to the ‘Problem of Induction: “Such an argument to the falsity of universal statements is… from singular to universal statements.”

So going from singular statement to universal statement can be justified by  going from singular statements to universal statements. This falls for the problem of induction again, because this is a circular argument that is used to defend induction.

Posted in Philosophy | Tagged: , , , , , , , , , , , , , , , , , , , , | Leave a Comment »

Popper, Hume, Induction, Falsifiability, and Science

Posted by allzermalmer on September 30, 2012

Here are some interesting things from Karl Popper on Falsification and Induction, or Hume on Induction.

“we merely have to realize that our ‘adoption’ of scientific theories can only be tentative; that they always are and will remain guesses or conjectures or hypotheses. They are put forward, of course, in the hope of hitting upon the truth, even though they miss it more often than not. They may be true or false. They may be tested by observation (it is the main task of science to make these tests more and more severe), and rejected if they do not pass…Indeed, we can do no more with a proposed law than test it: it is no use pretending that we have established universal theories, or justified them, or made them probably, by observation. We just have not done so, and cannot do so. We cannot give any positive reasons for them. They remain guesses or conjectures- though well tested ones.” Realism and the Aim of Science

Now someone might wonder how we cannot give any positive reasons for establishing the universal theories, or justified them, or made them probable, by all the observations that confirm its predictions on tests. This comes from what Popper takes to be Hume’s problem of induction.

“[Hume] tried to show that any inductive inference- any reasoning from singular and observable cases (and their repeated occurrence) to anything like regularities or laws- must be invalid. Any such inference, he tried to show, could not een be approximately or partially valid. It could not even be a probable inference: it must, rather, be completely baseless, and must always remain so, however great the number of the observed instances might be. Thus he tried to show that we cannot validly reason from the known to the unknown, or from what has been experienced to what has not been experienced (and thus, for example, from the past to the future): no matter how often the sun has been observed regularly to rise and set, even the greatest number of observed instances does not constitute what I have called a positive reason for the regularity, or the law, of the sun’s rising and setting. Thus it can neither establish this law nor make it probable.” Realism and the Aim of Science

I think it should be pointed out, Hume did bring up that the basic idea of induction was that “we suppose, but are never able to prove, that there must be a resemblance betwixt those objects, of which we have had experience, and those which lie beyond the reach of our discovery.” Induction is also done in other ways besides going from particular statements to universal statements.

[I.] Move form particular statement to particular statement.
In 1997 the Chicago Bulls beat the Utah Jazz in the NBA Finals. In 1998 the Chicago Bulls beat the Utah Jazz in the NBA Finals. Thus, the Chicago Bulls will win against the Utah Jazz the next time they play in the NBA Finals.

[II.] Move from general statement to general statement.
All NFL teams made tons of money this year. Thus, all NFL teams will make tons of money next year.

[III.] Move from general statement to particular statement.
All NFL teams made tons of money this year. Thus, the Ravens will make tons of money next year.

[IV.] Move from particular statement to general statement.
This crow is black. Thus, all crows are black.

Each of these, though, follow what Hume points out for Induction. They are going from the known to the unknown, which does not have to include the future or past.Hume also says that the only thing that can take us from the known to the unknown is causality, or a necessary connection between two events to form a necessary causal relation. But Hume already pointed out that this relation is not found by experience. So Hume comes to the conclusion that since the necessary relation between cause and effect or continuation of that relationship, is not shown by experience nor demonstrative,  or that the principle of induction is not known by experience or demonstrative, but that they are creations of the human imagination that cannot be shown to be true based on experience or reason, and any justification of them will either rely on an infinite regress or circular reasoning. So they cannot be proven to be true.

This would mean that when science proposes either a causal connection, or what will happen in the future, or what happens beneath sensible qualities, cannot be proved by experience to be true , or by reason to be true, or even held to be probably true. IOW, we are not justified in proposing things beyond what is known, since they cannot be shown to be true or probably true. So scientific hypotheses are unjustified and cannot be shown to be true or probably true, or natural laws cannot be shown to be true or probably true or justified.

Popper comes along and tries to save science, in some way. But you notice where his position eventually leads as well. He admits with Hume that we cannot demonstrate the truth of a scientific hypothesis or explanation; we cannot show by experiment the truth of a scientific hypothesis or explanation; we cannot show that a scientific hypothesis or explanation is probably true. All we can do is show if they are false. We can give negative reasons to a scientific hypothesis or explanation by it failing its severe experimental/observational tests. This is because it follows the demonstrative inference of modus tollens and disjunctive syllogism, so we can demonstrate that a scientific hypothesis or explanation is false.

So falsifiability, or refutabilty, can show you only that a scientific hypothesis or explanation is false. Refutability cannot demonstrate that the hypothesis or explanation is true, or has been shown by experience to be true, or is probably true.  It can only tell you that it may be true, and it has not failed any of its tests so far. It doesn’t even appears to care if something is true, only that it can be shown to be false.

And here are Hume on what Induction is, or relies on.

“that which we have had no experience, must resemble those which we have had experience, and nature continues uniformly the same.” Treatise of Human Nature:  Book I (Of the Understanding), Part III (Of Knowledge & Probability), Sect.VI.Of the Inference from the Impression to the Idea

“probability is founded on the presumpition of a resemblances betweixt those objects, of which we have had experience, and those, of which we have had none…” Treatise of Human Nature:  Book I (Of the Understanding), Part III (Of Knowledge & Probability), Sect.VI.Of the Inference from the Impression to the Idea

“Thus not only our reason fails us in the discovery of the ultimate connexion of causes and effects, but even after experience has informed us of their constant conjunction, it is impossible for us to satisfy ourselves by our reason, why we should extend that experience beyond those particular instances, which have fallen under our observation. We suppose, but are never able to prove, that there must be a resemblance betwixt those objects, of which we have had experience, and those which lie beyond the reach of our discovery.” Treatise of Human Nature:  Book I (Of the Understanding), Part III (Of Knowledge & Probability), Sect.VI.Of the Inference from the Impression to the Idea

“we always presume, when we see like sensible qualities, that they have like secret powers, and expect that effects, similar to those which we have experienced, will follow from them.” An Enquiry Concerning Human Understanding: Section IV. Sceptical Doubts Concerning the Operations of the Understanding, Part II

“all arguments from experience are founded on the similarity which we discover among natural objects, and by which we are induced to expect effects similar to those which we have found to follow from such objects.” An Enquiry Concerning Human Understanding: Section IV. Sceptical Doubts Concerning the Operations of the Understanding, Part II

“From causes which appear similar we expect similar effects. This is the sum of all our experimental conclusions.” An Enquiry Concerning Human Understanding: Section IV. Sceptical Doubts Concerning the Operations of the Understanding, Part II

 

 

 

Posted in Philosophy | Tagged: , , , , , , , , , , , , , , | Leave a Comment »

Sherlock-Holmesian Reasoning

Posted by allzermalmer on September 22, 2012

Sherlock Holmes is the “[t]he only unofficial consulting detective”, and he had a certain method of reasoning in his “detecting”. This is laid out in the “The Sign of Four” by Sir Arthur Conan Doyle. One chapter is called “The Science of Deduction“, which goes over Holmes basic outline of reasoning. I have altered the format of The Science of Deduction reproduced here by trying to put it more into a Dialectical format.

Those portions that are italicized are not done so in the story itself. I have italicized them myself in order to show important features of Sherlock Holmes method of detection, or method of reasoning. These help to form the basic outlines, or characteristics, of his method propounded here. These are what I shall call Holmesian Reasoning, or Holmesian Thinking.

“Sherlock Holmes took his bottle from the corner of the mantel piece, and his hypodermic syringe from its neat morocco case. With his long, white, nervous fingers he adjusted the delicate needle and rolled back his left shirtcuff. For some little time his eyes rested thoughtfully upon the sinewy forearm and wrist, all dotted and scarred with innumerable puncture marks. Finally, he thrust the sharp point home, pressed down the tiny piston, and sank back into the velvet lined armchair with a long sigh of satisfaction.

Three times a day for many months Watson had witnessed this performance, but custom had not reconciled his mind to it. On the contrary, from day to day he had become more irritable at the sight, and his conscience swelled nightly within him at the thought that he had lacked the courage to protest. Again and again he had registered a vow that he should deliver his soul upon the subject; but there was that in the cool, nonchalant air of his companion which made him the last man with whom one would care to take anything approaching to a liberty. Sherlock Holmes great powers, his masterly manner, and the experience which Watson had had of his many extraordinary qualities, all made Watson diffident and backward in crossing him.

Yet upon that afternoon, whether it was the Beaune which Watson had taken with his lunch or the additional exasperation produced by the extreme deliberation of his manner, he suddenly felt that he could hold out no longer.

Watson: “Which is it today? Morphine or cocaine?”

Holes raised his eyes languidly from the old black letter volume which he had opened.

Holmes: “It is cocaine, a seven-per-cent solution. Would you care to try it?”

Watson : “No, indeed. My constitution has not got over the Afghan campaign yet. I cannot afford to throw any extra strain upon it.”

Holes smiled at Watson’s vehemence.

Holmes: “Perhaps you are right, Watson, I suppose that its influence is physically a bad one. I find it, however, so transcendently stimulating and clarifying to the mind that its secondary action is a matter of small moment.”

Watson: “But consider! Count the cost! Your brain may, as you say, be roused and excited, but it is a pathological and morbid process which involves increased tissue change and may at least leave a permanent weakness. You know, too, what a black reaction comes upon you. Surely the game is hardly worth the candle. Why should you, for a mere passing pleasure, risk the loss of those great powers with which you have been endowed? Remember that I speak not only as one comrade to another but as a medical man to one for whose constitution he is to some extent answerable.”

Holmes’s did not seem offended. On the contrary, he put his fingertips together, and leaned his elbows on the arms of his chair, like one who has a relish for conversation.

Holmes: “My mind rebels at stagnation. Give me problems, give me work, give me the most abstruse cryptogram, or the most intricate analysis, and I am in my own proper atmosphere. I can dispense then with artificial stimulants. But I abhor the dull routine of existence. I crave for mental exaltation. That is why I have chosen my own particular profession, or rather created it, for I am the only one in the world.”

Watson: “The only unofficial detective?”  said while raising his eyebrows.

Holmes: “The only unofficial consulting detective, I am the last and highest court of appeal in detection. When Gregson, or Lestrade, or Athelney Jones are out of their depths–which, by the way, is their normal state–the matter is laid before me. I examine the data, as an expert, and pronounce a specialist’s opinion. I claim no credit in such cases. My name figures in no newspaper. The work itself, the pleasure of finding a field for my peculiar powers, is my highest reward. But you have yourself had some experience of my methods of work in the Jefferson Hope case.”

Watson: “Yes, indeed, I was never so struck by anything in my life. I even embodied it in a small brochure, with the somewhat fantastic title of ‘A Study in Scarlet.’ ”

Holmes shook his head sadly.

Holmes: “I glanced over it. Honestly, I cannot congratulate you upon it. Detection is, or ought to be, an exact science and should be treated in the same cold and unemotional manner. You have attempted to tinge it with romanticism, which produces much the same effect as if you worked a love story or an elopement into the fifth proposition of Euclid.”

Watson: “But the romance was there. I could not tamper with the facts.”

Holmes: “Some facts should be suppressed, or, at least, a just sense of proportion should be observed in treating them. The only point in the case which deserved mention was the curious analytical reasoning from effects to causes, by which I succeeded in unravelling it.

Watson  was annoyed at Holmes criticism of a work which had been specially designed to please him. Watson confess, too, that he was irritated by the egotism which seemed to demand that every line of his pamphlet should be devoted to Holmes own special doings. More than once during the years that Watson had lived with Holmes in Baker Street Watson had observed that a small vanity underlay his companion’s quiet and didactic manner. He made no remark however, but sat nursing his wounded leg. Watson had had a Jezaii bullet through it some time before, and though it did not prevent him from walking it ached wearily at every change of the weather.

Holmes: “My practice has extended recently to the Continent,” said Holmes after a while, filling up his old brier-root pipe. “I was consulted last week by Francois le Villard, who, as you probably know, has come rather to the front lately in the French detective service. He has all the Celtic power of quick intuition but he is deficient in the wide range of exact knowledge which is essential to the higher developments of his art. The case was concerned with a will and possessed some features of interest. I was able to refer him to two parallel cases, the one at Riga in 1857, and the other at St. Louis in 1871, which have suggested to him the true solution. Here is the letter which I had this morning acknowledging my assistance.”

Holmes tossed over, as he spoke, a crumpled sheet of foreign notepaper. Watson glanced his eyes down it, catching a profusion of notes of admiration, with stray magnifiques, coup-de-maitres and tours-de-force, all testifying to the ardent admiration of the Frenchman.

Watson: “He speaks as a pupil to his master.”

Holmes: “Oh, he rates my assistance too highly. He has considerable gifts himself. He possesses two out of the three qualities necessary for the ideal detective. He has the power of observation and that of deduction. He is only wanting in knowledge, and that may come in time. He is now translating my small works into French.”

Watson: “Your works?”

Holmes: “Oh, didn’t you know?” he cried, laughing. “Yes, I have been guilty of several monographs. They are all upon technical subjects. Here, for example, is one ‘Upon the Distinction between the Ashes of the Various Tobaccos.’ In it I enumerate a hundred and forty forms of cigar, cigarette, and pipe tobacco, with coloured plates illustrating the difference in the ash. It is a point which is continually turning up in criminal trials, and which is sometimes of supreme importance as a clue. If you can say definitely, for example, that some murder had been done by a man who was smoking an Indian lunkah, it obviously narrows your field of search. To the trained eye there is as much difference between the black ash of a Trichinopoly and the white fluff of bird’s-eye as there is between a cabbage and a potato.

Watson: “You have an extraordinary genius for minutiae.”

Holmes: “I appreciate their importance. Here is my monograph upon the tracing of footsteps, with some remarks upon the uses of plaster of Paris as a preserver of impresses. Here, too, is a curious little work upon the influence of a trade upon the form of the hand, with lithotypes of the hands of slaters, sailors, cork cutters, compositors, weavers, and diamond-polishers. That is a matter of great practical

interest to the scientific detective–especially in cases of unclaimed bodies, or in discovering the antecedents of criminals. But I weary you with my hobby.”

Watson: “Not at all. It is of the greatest interest to me, especially since I have had the opportunity of observing your practical application of it. But you spoke just now of observation and deduction. Surely the one to some extent implies the other.”

Holmes: “Why, hardly,” he answered, leaning back luxuriously in his armchair and sending up thick blue wreaths from his pipe. “For example, observation shows me that you have been to the Wigmore Street Post Office this morning, but deduction lets me know that when there you dispatched a telegram.”

Watson: “Right! Right on both points! But I confess that I don’t see how you arrived at it. It was a sudden impulse upon my part, and I have mentioned it to no one.”

Holmes: “It is simplicity itself,” he remarked, chuckling at my surprise–“so absurdly simple that an explanation is superfluous; and yet it may serve to define the limits of observation and of deduction. Observation tells me that you have a little reddish mould adhering to your instep. Just opposite the Wigmore Street Office they have taken up the pavement and thrown up some earth, which lies in such a way that it is difficult to avoid treading in it in entering. The earth is of this peculiar reddish tint which is found, as far as I know, nowhere else in the neighbourhood. So much is observation. The rest is deduction.”

Watson: “How, then, did you deduce the telegram?”

Holmes: “Why, of course I knew that you had not written a letter, since I sat opposite to you all morning. I see also in your open desk there that you have a sheet of stamps and a thick bundle of postcards. What could you go into the post office for, then, but to send a wire? Eliminate all other factors, and the one which remains must be the truth.

Watson: “In this case it certainly is so,” he replied after a little thought. “The thing, however, is, as you say, of the simplest. Would you think me impertinent if I were to put your theories to a more severe test?”

Holmes: “On the contrary,” he answered, “it would prevent me from taking a second dose of cocaine. I should be delighted to look into any problem which you might submit to me.”

Watson: “I have heard you say it is difficult for a man to have any object in daily use without leaving the impress of his individuality upon it in such a way that a trained observer might read it. Now, I have here a watch which has recently come into my possession. Would you have the kindness to let me have an opinion upon the character or habits of the late owner?”

Watson handed Holmes over the watch with some slight feeling of amusement in his heart, for the test was, as he thought, an impossible one, and he intended it as a lesson against the somewhat dogmatic tone which Holmes occasionally assumed. Holmes balanced the watch in his hand, gazed hard at the dial, opened the back, and examined the works, first with his naked eyes and then with a powerful convex lens. Watson could hardly keep from smiling at Holmes crestfallen face when he finally snapped the case to and handed it back.

Holmes: “There are hardly any data,” he remarked. “The watch has been recently cleaned, which robs me of my most suggestive facts.”

Watson: “You are right,” he answered. “It was cleaned before being sent to me.”

In Holmes heart he accused his companion of putting forward a most lame and impotent excuse to cover Watson’ s failure. What data could he expect from an uncleaned watch?

Holmes: “Though unsatisfactory, my research has not been entirely barren,” he observed, staring up at the ceiling with dreamy, lacklustre eyes. “Subject to your correction, I should judge that the watch belonged to your elder brother, who inherited it from your father.”

Watson: “That you gather, no doubt, from the H. W. upon the back?”

Holmes: “Quite so. The W. suggests your own name. The date of the watch is nearly fifty years back, and the initials are as old as the watch: so it was made for the last generation. Jewellery usually descends to the eldest son, and he is most likely to have the same name as the father. Your father has, if I remember right, been dead many years. It has, therefore, been in the hands of your eldest brother.”

Watson: “Right, so far,” said I. “Anything else?”

Holmes: “He was a man of untidy habits–very untidy and careless. He was left with good prospects, but he threw away his chances, lived for some time in poverty with occasional short intervals of prosperity, and finally, taking to drink, he died. That is all I can gather.”

Watson sprang from his chair and limped impatiently about the room with considerable bitterness in his heart.

Watson:  “This is unworthy of you, Holmes,” he said. “I could not have believed that you would have descended to this. You have made inquiries into the history of my unhappy brother, and you now pretend to deduce this knowledge in some fanciful way. You cannot expect me to believe that you have read all this from his old watch! It is unkind and, to speak plainly, has a touch of charlatanism in it.

Holmes: “My dear doctor,” said he kindly, “pray accept my apologies. Viewing the matter as an abstract problem, I had forgotten how personal and painful a thing it might be to you. I assure you, however, that I never even knew that you had a brother until you handed me the watch.”

Watson: “Then how in the name of all that is wonderful did you get these facts? They are absolutely correct in every particular.”

Holmes: “Ah, that is good luck. I could only say what was the balance of probability. I did not at all expect to be so accurate.”

Watsons: “But it was not mere guesswork?”

Holmes: “No, no: I never guess. It is a shocking habit–destructive to the logical faculty. What seems strange to you is only so because you do not follow my train of thought or observe the small facts upon which large inferences may depend. For example, I began by stating that your brother was careless. When you observe the lower part of that watch case you notice that it is not only dinted in two places but it is cut and marked all over from the habit of keeping other hard objects, such as coins or keys, in the same pocket. Surely it is no great feat to assume that a man who treats a fifty-guinea watch so cavalierly must be a careless man. Neither is it a very far fetched inference that a man who inherits one article of such value is pretty well provided for in other respects.

Watson nodded to show that he followed his reasoning.

Holmes: “It is very customary for pawnbrokers in England, when they take a watch, to scratch the numbers of the ticket with a pinpoint upon the inside of the case. It is more handy than a label as there is no risk of the number being lost or transposed. There are no less than four such numbers visible to my lens on the inside of this case. Inference–that your brother was often at low water. Secondary inference–that he had occasional bursts of prosperity, or he could not have redeemed the pledge. Finally, I ask you to look at the inner plate, which contains the keyhole. Look at the thousands of scratches all round the hole–marks where the key has slipped. What sober man’s key could have scored those grooves? But you will never see a drunkard’s watch without them. He winds it at night, and he leaves these traces of his unsteady hand. Where is the mystery in all this?”

Watson: “It is as clear as daylight,” he answered. “I regret the injustice which I did you. I should have had more faith in your marvellous faculty. May I ask whether you have any professional inquiry on foot at present?”

Holmes: “None. Hence the cocaine. I cannot live without brainwork. What else is there to live for? Stand at the window here. Was ever such a dreary, dismal, unprofitable world? See how the yellow fog swirls down the street and drifts across the dun coloured houses. What could be more hopelessly prosaic and material? What is the use of having powers, Doctor, when one has no field upon which to exert them? Crime is commonplacc, existence is commonplace, and no qualities save those which are commonplace have any function upon earth.

Watson had opened his mouth to reply to this tirade when, with a crisp knock, our landlady entered, bearing a card upon the brass salver.

Landlady Mrs. Hudson: “A young lady for you, sir,” she said, addressing Watson’s companion.

Holmes: “Miss Mary Morstan,” he read. “Hum! I have no recollection of the name. Ask the young lady to step up, Mrs. Hudson. Don’t go, Doctor Watson. I should prefer that you remain.”

1. Detection is, or ought to be, an exact science and should be treated in the same cold and unemotional manner.

Sherlock Holmes does not allow for emotions to come into his method of detection, or his method of reasoning. He tries to keep feelings and emotions outside of he considers to be how detection is actually done or how detection actually ought to be done. Now Holmes is either guided by what detection actually is or what detection ought to be, or both what detection is and what detection ought to be. This appears to be open to being derived from  Is v. Ought and Descriptive v. Normative, or Is and Ought are one and the same and Descriptive and Normative are one and the same. As Joe Friday use to say, “Just the facts, ma’am.”. The Facts, for Holmes, are, or ought to be, treated in a cold and unemotional manner.

2.  Analytical reasoning from effects to causes, by which succeeded in unravelling a fact.

Sherlock will argue from an observation to a cause of that observation. From a single fact, Holmes argues to another, which is what produced the fact before him, what is the facts cause. From the fact that there is smoke, by analytical reasoning, Holmes concludes that there is fire. From the fact that there is red mud on Dr. Watson’s pants, he argues to a cause of the red mud on Dr. Watson’s pants. This fact was noticed by observation. From the facts of scratches and writing, and a certain functional characteristic on the watch that he observed, Holmes reaches a certain cause of those scratches and writing, and certain functional characteristics of the watch.

In the examples that are given in the dialogue, inductive reasoning is being used. Holmes moves from what is known to what is unknown. Holmes moves from the known to the unknown. Holmes moves from the effect, from the known, to the unknown cause. Holmes knows there is red mud on Watson’s pants, but Holmes did does not know where Watson went when Holmes was not with Watson. Holmes, also, did not see Watson walk into any red mud in the time that they were together.

3. The power of observation,  deduction, and a wide range of exact knowledge, (and intuition(?)).

You must be able to use your senses. You must be able to observe in order to notice things. You must have a wide base of exact knowledge. The example of Watson’s clock is one. Holmes notices some scratches on it, and he notices some writing on it, and he also knows the type of watch. The type of watch is based on Holmes wide range of exact knowledge. This wide range of exact knowledge also includes Holmes notices some scratches on it, and he notices some writing on it,  feels the watch in his hand, he focuses his attention to the dials of the clock, he opens the back of the watch and looks at the internal functionings of the watch with his naked eye and than with a magnifying instrument in front of his naked eye. These are the facts of observation that is shown to Holmes by observation.

Holmes have a wide range of exact knowledge, which either comes from his personal experience or from those that he has read in books or other people have said. He knows that jewelry is passed down to the eldest son, the eldest son usually has the same first name as the father, and he knows what  50 years old watches look like. From this exact knowledge he could deduce that the watch is Watson’s brothers. From that wide range of exact knowledge is previous knowledge brought to the situation when make the observations, which is how certain things can stand out to garner ones attention.

Holmes has a wide range of knowledge that is known to be true, and he has these particular observation, data, before him, and these together allow him to deduce something that is not known by the observations, or  data, itself or the wide range of knowledge itself. He does not know that the watch was owned by Watson’s brother and that Watson cleaned the watch before showing it to Holmes. But he knows a certain general principle that was established by enumeration of particular observations by himself or others, and the observations before Holmes now are consistent with those general principles themselves, and so it is another enumeration of that general principle.

All men are mortal (part of Holmes wide range of knowledge). Socrates is a man (observation made by Holmes). So Holems concludes that Socrates is mortal, even though Holmes has not made the observation itself that Socrates is mortal. Holmes concludes this through logical deduction from these known things. But the conclusion that Holmes draws is one that is not known itself by observation. He has not observed that Socrates has died, and so does not know that Socrates is mortal.

4. Eliminate all other factors, and the one which remains must be the truth.

Holmes will eliminate other factors that can lead to different conclusions of the observations before him. Take the example of the ash that comes from different cigars. Holmes had enumerated many experiments with a hundred and forty forms of cigar, cigarette, and pipe tobacco. He noticed that each type of cigar, cigarette, and pipe tobacco, left their own distinct ash. This became a wide range of exact knowledge he obtained.If Holmes did not know all these different possible cigars, cigarettes, and pipe tobacco, and the ash they leave behind, then he would not know what else would be consistent with the ash that Holmes observes. But knowing these things, he can eliminate certain possible types of cigars, cigarettes, and pipe tobacco, because the observation eliminates those causes of the ash. The observation is not consistent with those possible causes, or source, of the ash that is left behind.

Knowing all the possible factors involved in the situation, would allow Holmes to eliminate certain possible causes for what is being observed. Holmes would eliminate what is impossible, because the observation contradicts a cause that is possible in and of itself. Like eliminating that the ash belongs to cigar type x because cigar type x ash is not similar to the ash observed. So whatever else is left would be the truth if it is the only factor left, like cigar y is the only source consistent with the observed ash, and if it is not the only factor left then at least know what is not the possible source of the ash. Cigar types a,b, and c have been eliminated. It narrows the search down further to the cigar, cigarette, and pipe tobacco to be the source, the cause, of the ash observed.

Holmes eliminates possible causes of the effect that is observed, and only one possible cause is correct. The murder smoked a particular type of tobacco product, and that particular tobacco product left behind a certain kind of ash. He eliminated particular tobacco products as the cause of the ash because those causes product different effects than the one observed. So the murder did not smoke those tobacco products. But Holmes himself did not observe what particular tobacco product itself that the murder smoked. He is eliminating a possible unknown cause by a known effect, and how the possible unknown cause is not consistent with the known effect.

5. Some facts ought be suppressed, or not given much attention.

Some observations ought not to be taken attention or pay much attention to. This appears to follow from Holmes saying that emotions that are found to go along with observations ought to be ignored. This is because emotions are not cold and unemotional. There are also other factors that do not play into a possible cause for the observation, which appears to come from ones wide range of exact knowledge, or intuition. The shoes that Watson has on appear to have no causal relation with the watch the Watson presented for Holmes to observe. So Holmes ought to suppress the observation of what shoes Watson has on, or Holmes emotional state in making the observation of the watch.

(This blog post will go through alteration and addition at a later date.)

Posted in Philosophy | Tagged: , , , , , , , , , , , , , , , , | Leave a Comment »

David Hume on Induction

Posted by allzermalmer on May 20, 2012

This is David Hume on the Problem of Induction, and this comes from Treatise of Human Nature: Book I (Of the Understandin), Part III (Of Knowledge & Probability), Sect. VI. Of the Inference from the Impression to the Idea

“It is easy to observe, that in tracing this relation, the inference we draw from cause to effect, is not derived merely from a survey of these particular objects, and from such a penetration into their essences as may discover the dependence of the one upon the other. There is no object, which implies the existence of any other if we consider these objects in themselves, and never look beyond the ideas which we form of them. Such an inference would amount to knowledge, and would imply the absolute contradiction and impossibility of conceiving any thing different. But as all distinct ideas are separable, it is evident there can be no impossibility of that kind. When we pass from a present impression to the idea of any object, we might possibly have separated the idea from the impression, and have substituted any other idea in its room.

It is therefore by EXPERIENCE only, that we can infer the existence of one object from that of another. The nature of experience is this. We remember to have had frequent instances of the existence of one species of objects; and also remember, that the individuals of another species of objects have always attended them, and have existed in a regular order of contiguity and succession with regard to them. Thus we remember, to have seen that species of object we call flame, and to have felt that species of sensation we call heat. We likewise call to mind their constant conjunction in all past instances. Without any farther ceremony, we call the one cause and the other effect, and infer the existence of the one from that of the other. In all those instances, from which we learn the conjunction of particular causes and effects, both the causes and effects have been perceived by the senses, and are remembered But in all cases, wherein we reason concerning them, there is only one perceived or remembered, and the other is supplyed in conformity to our past experience.

Thus in advancing we have insensibly discovered a new relation betwixt cause and effect, when we least expected it, and were entirely employed upon another subject. This relation is their CONSTANT CONJUNCTION. Contiguity and succession are not sufficient to make us pronounce any two objects to be cause and effect, unless we perceive, that these two relations are preserved in several instances. We may now see the advantage of quitting the direct survey of this relation, in order to discover the nature of that necessary connexion, which makes so essential a part of it. There are hopes, that by this means we may at last arrive at our proposed end; though to tell the truth, this new-discovered relation of a constant conjunction seems to advance us but very little in our way. For it implies no more than this, that like objects have always been placed in like relations of contiguity and succession; and it seems evident, at least at first sight, that by this means we can never discover any new idea, and can only multiply, but not enlarge the objects of our mind. It may be thought, that what we learn not from one object, we can never learn from a hundred, which are all of the same kind, and are perfectly resembling in every circumstance. As our senses shew us in one instance two bodies, or motions, or qualities in certain relations of success and contiguity; so our memory presents us only with a multitude of instances, wherein we always find like bodies, motions, or qualities in like relations. From the mere repetition of any past impression, even to infinity, there never will arise any new original idea, such as that of a necessary connexion; and the number of impressions has in this case no more effect than if we confined ourselves to one only. But though this reasoning seems just and obvious; yet as it would be folly to despair too soon, we shall continue the thread of our discourse; and having found, that after the discovery of the constant conjunction of any objects, we always draw an inference from one object to another, we shall now examine the nature of that inference, and of the transition from the impression to the idea. Perhaps it will appear in the end, that the necessary connexion depends on the inference, instead of the inference’s depending on the necessary connexion.

Since it appears, that the transition from an impression present to the memory or senses to the idea of an object, which we call cause or effect, is founded on past experience, and on our remembrance of their constant conjunction, the next question is, Whether experience produces the idea by means of the understanding or imagination; whether we are determined by reason to make the transition, or by a certain association and relation of perceptions. If reason determined us, it would proceed upon that principle, that instances, of which we have had no experience, must resemble those, of which we have had experience, and that the course of nature continues always uniformly the same. In order therefore to clear up this matter, let us consider all the arguments, upon which such a proposition may be supposed to be founded; and as these must be derived either from knowledge or probability, let us cast our eye on each of these degrees of evidence, and see whether they afford any just conclusion of this nature.

Our foregoing method of reasoning will easily convince us, that there can be no demonstrative arguments to prove, that those instances, of which we have, had no experience, resemble those, of which we have had experience. We can at least conceive a change in the course of nature; which sufficiently proves, that such a change is not absolutely impossible. To form a clear idea of any thing, is an undeniable argument for its possibility, and is alone a refutation of any pretended demonstration against it.

Probability, as it discovers not the relations of ideas, considered as such, but only those of objects, must in some respects be founded on the impressions of our memory and senses, and in some respects on our ideas. Were there no mixture of any impression in our probable reasonings, the conclusion would be entirely chimerical: And were there no mixture of ideas, the action of the mind, in observing the relation, would, properly speaking, be sensation, not reasoning. It is therefore necessary, that in all probable reasonings there be something present to the mind, either seen or remembered; and that from this we infer something connected with it, which is not seen nor remembered.

The only connexion or relation of objects, which can lead us beyond the immediate impressions of our memory and senses, is that of cause and effect; and that because it is the only one, on which we can found a just inference from one object to another. The idea of cause and effect is derived from experience, which informs us, that such particular objects, in all past instances, have been constantly conjoined with each other: And as an object similar to one of these is supposed to be immediately present in its impression, we thence presume on the existence of one similar to its usual attendant. According to this account of things, which is, I think, in every point unquestionable, probability is founded on the presumption of a resemblance betwixt those objects, of which we have had experience, and those, of which we have had none; and therefore it is impossible this presumption can arise from probability. The same principle cannot be both the cause and effect of another; and this is, perhaps, the only proposition concerning that relation, which is either intuitively or demonstratively certain.

Should any one think to elude this argument; and without determining whether our reasoning on this subject be derived from demonstration or probability, pretend that all conclusions from causes and effects are built on solid reasoning: I can only desire, that this reasoning may be produced, in order to be exposed to our examination. It may, perhaps, be said, that after experience of the constant conjunction of certain objects, we reason in the following manner. Such an object is always found to produce another. It is impossible it coued have this effect, if it was not endowed with a power of production. The power necessarily implies the effect; and therefore there is a just foundation for drawing a conclusion from the existence of one object to that of its usual attendant. The past production implies a power: The power implies a new production: And the new production is what we infer from the power and the past production.

It were easy for me to shew the weakness of this reasoning, were I willing to make use of those observations, I have already made, that the idea of production is the same with that of causation, and that no existence certainly and demonstratively implies a power in any other object; or were it proper to anticipate what I shall have occasion to remark afterwards concerning the idea we form of power and efficacy. But as such a method of proceeding may seem either to weaken my system, by resting one part of it on another, or to breed a confusion in my reasoning, I shall endeavour to maintain my present assertion without any such assistance.

It shall therefore be allowed for a moment, that the production of one object by another in any one instance implies a power; and that this power is connected with its effect. But it having been already proved, that the power lies not in the sensible qualities of the cause; and there being nothing but the sensible qualities present to us; I ask, why in other instances you presume that the same power still exists, merely upon the appearance of these qualities? Your appeal to past experience decides nothing in the present case; and at the utmost can only prove, that that very object, which produced any other, was at that very instant endowed with such a power; but can never prove, that the same power must continue in the same object or collection of sensible qualities; much less, that a like power is always conjoined with like sensible qualities, should it be said, that we have experience, that the same power continues united with the same object, and that like objects are endowed with like powers, I would renew my question, why from this experience we form any conclusion beyond those past instances, of which we have had experience. If you answer this question in, the same manner as the preceding, your answer gives still occasion to a new question of the same kind, even in infinitum; which clearly proves, that the foregoing reasoning had no just foundation.

Thus not only our reason fails us in the discovery of the ultimate connexion of causes and effects, but even after experience has informed us of their constant conjunction, it is impossible for us to satisfy ourselves by our reason, why we should extend that experience beyond those particular instances, which have fallen under our observation. We suppose, but are never able to prove, that there must be a resemblance betwixt those objects, of which we have had experience, and those which lie beyond the reach of our discovery.

We have already taken notice of certain relations, which make us pass from one object to another, even though there be no reason to determine us to that transition; and this we may establish for a general rule, that wherever the mind constantly and uniformly makes a transition without any reason, it is influenced by these relations. Now this is exactly the present case. Reason can never shew us the connexion of one object with another, though aided by experience, and the observation of their constant conjunction in all past instances. When the mind, therefore, passes from the idea or impression of one object to the idea or belief of another, it is not determined by reason, but by certain principles, which associate together the ideas of these objects, and unite them in the imagination. Had ideas no more union in the fancy than objects seem to have to the understanding, we could never draw any inference from causes to effects, nor repose belief in any matter of fact. The inference, therefore, depends solely on the union of ideas.

The principles of union among ideas, I have reduced to three general ones, and have asserted, that the idea or impression of any object naturally introduces the idea of any other object, that is resembling, contiguous to, or connected with it. These principles I allow to be neither the infallible nor the sole causes of an union among ideas. They are not the infallible causes. For one may fix his attention during Sometime on any one object without looking farther. They are not the sole causes. For the thought has evidently a very irregular motion in running along its objects, and may leap from the heavens to the earth, from one end of the creation to the other, without any certain method or order. But though I allow this weakness in these three relations, and this irregularity in the imagination; yet I assert that the only general principles, which associate ideas, are resemblance, contiguity and causation.

There is indeed a principle of union among ideas, which at first sight may be esteemed different from any of these, but will be found at the bottom to depend on the same origin. When every individual of any species of objects is found by experience to be constantly united with an individual of another species, the appearance of any new individual of either species naturally conveys the thought to its usual attendant. Thus because such a particular idea is commonly annexed to such a particular word, nothing is required but the hearing of that word to produce the correspondent idea; and it will scarce be possible for the mind, by its utmost efforts, to prevent that transition. In this case it is not absolutely necessary, that upon hearing such a particular sound we should reflect on any past experience, and consider what idea has been usually connected with the sound. The imagination of itself supplies the place of this reflection, and is so accustomed to pass from the word to the idea, that it interposes not a moment’s delay betwixt the hearing of the one, and the conception of the other.

But though I acknowledge this to be a true principle of association among ideas, I assert it to be the very same with that betwixt the ideas of cause and effects and to be an essential part in all our reasonings from that relation. We have no other notion of cause and effect, but that of certain objects, which have been always conjoined together, and which in all past instances have been found inseparable. We cannot penetrate into the reason of the conjunction. We only observe the thing itself, and always find that from the constant conjunction the objects acquire an union in the imagination. When the impression of one becomes present to us, we immediately form an idea of its usual attendant; and consequently we may establish this as one part of the definition of an opinion or belief, that it is an idea related to or associated with a present impression.

Thus though causation be a philosophical relation, as implying contiguity, succession, and constant conjunction, yet it is only so far as it is a natural relation, and produces an union among our ideas, that we are able to reason upon it, or draw any inference from it.”

___________________________________________________________________________________________________________________________

This is David Hume on the Problem of Induction from the Enquires Concerning Human Understanding: Section IV. Sceptical Doubts Concerning the Operations of the Understanding, Part II

“But we have not yet attained any tolerable satisfaction with regard to the question first proposed. Each solution still gives rise to a new question as difficult as the foregoing, and leads us on to farther enquiries. When it is asked, What is the nature of all our reasonings concerning matter of fact? the proper answer seems to be, that they are founded on the relation of cause and effect. When again it is asked, What is the foundation of all our reasonings and conclusions concerning that relation? it may be replied in one word, Experience. But if we still carry on our sifting humour, and ask, What is the foundation of all conclusions from experience? this implies a new question, which may be of more difficult solution and explication. Philosophers, that give themselves airs of superior wisdom and sufficiency, have a hard task when they encounter persons of inquisitive dispositions, who push them from every corner to which they retreat, and who are sure at last to bring them to some dangerous dilemma. The best expedient to prevent this confusion, is to be modest in our pretensions; and even to discover the difficulty ourselves before it is objected to us. By this means, we may make a kind of merit of our very ignorance.

I shall content myself, in this section, with an easy task, and shall pretend only to give a negative answer to the question here proposed. I say then, that, even after we have experience of the operations of cause and effect, our conclusions from that experience are not founded on reasoning, or any process of the understanding. This answer we must endeavour both to explain and to defend.

It must certainly be allowed, that nature has kept us at a great distance from all her secrets, and has afforded us only the knowledge of a few superficial qualities of objects; while she conceals from us those powers and principles on which the influence of those objects entirely depends. Our senses inform us of the colour, weight, and consistence of bread; but neither sense nor reason can ever inform us of those qualities which fit it for the nourishment and support of a human body. Sight or feeling conveys an idea of the actual motion of bodies; but as to that wonderful force or power, which would carry on a moving body for ever in a continued change of place, and which bodies never lose but by communicating it to others; of this we cannot form the most distant conception. But notwithstanding this ignorance of natural powers and principles, we always presume, when we see like sensible qualities, that they have like secret powers, and expect that effects, similar to those which we have experienced, will follow from them. If a body of like colour and consistence with that bread, which we have formerly eat, be presented to us, we make no scruple of repeating the experiment, and foresee, with certainty, like nourishment and support. Now this is a process of the mind or thought, of which I would willingly know the foundation. It is allowed on all hands that there is no known connexion between the sensible qualities and the secret powers; and consequently, that the mind is not led to form such a conclusion concerning their constant and regular conjunction, by anything which it knows of their nature. As to past Experience, it can be allowed to give direct and certain information of those precise objects only, and that precise period of time, which fell under its cognizance: but why this experience should be extended to future times, and to other objects, which for aught we know, may be only in appearance similar; this is the main question on which I would insist. The bread, which I formerly eat, nourished me; that is, a body of such sensible qualities was, at that time, endued with such secret powers: but does it follow, that other bread must also nourish me at another time, and that like sensible qualities must always be attended with like secret powers? The consequence seems nowise necessary. At least, it must be acknowledged that there is here a consequence drawn by the mind; that there is a certain step taken; a process of thought, and an inference, which wants to be explained. These two propositions are far from being the same, I have found that such an object has always been attended with such an effect, and I foresee, that other objects, which are, in appearance, similar, will be attended with similar effects. I shall allow, if you please, that the one proposition may justly be inferred from the other: I know, in fact, that it always is inferred. But if you insist that the inference is made by a chain of reasoning, I desire you to produce that reasoning. The connexion between these propositions is not intuitive. There is required a medium, which may enable the mind to draw such an inference, if indeed it be drawn by reasoning and argument. What that medium is, I must confess, passes my comprehension; and it is incumbent on those to produce it, who assert that it really exists, and is the origin of all our conclusions concerning matter of fact.

This negative argument must certainly, in process of time, become altogether convincing, if many penetrating and able philosophers shall turn their enquiries this way and no one be ever able to discover any connecting proposition or intermediate step, which supports the understanding in this conclusion. But as the question is yet new, every reader may not trust so far to his own penetration, as to conclude, because an argument escapes his enquiry, that therefore it does not really exist. For this reason it may be requisite to venture upon a more difficult task; and enumerating all the branches of human knowledge, endeavour to show that none of them can afford such an argument.

All reasonings may be divided into two kinds, namely, demonstrative reasoning, or that concerning relations of ideas, and moral reasoning, or that concerning matter of fact and existence. That there are no demonstrative arguments in the case seems evident; since it implies no contradiction that the course of nature may change, and that an object, seemingly like those which we have experienced, may be attended with different or contrary effects. May I not clearly and distinctly conceive that a body, falling from the clouds, and which, in all other respects, resembles snow, has yet the taste of salt or feeling of fire? Is there any more intelligible proposition than to affirm, that all the trees will flourish in December and January, and decay in May and June? Now whatever is intelligible, and can be distinctly conceived, implies no contradiction, and can never be proved false by any demonstrative argument or abstract reasoning priori.

If we be, therefore, engaged by arguments to put trust in past experience, and make it the standard of our future judgement, these arguments must be probable only, or such as regard matter of fact and real existence, according to the division above mentioned. But that there is no argument of this kind, must appear, if our explication of that species of reasoning be admitted as solid and satisfactory. We have said that all arguments concerning existence are founded on the relation of cause and effect; that our knowledge of that relation is derived entirely from experience; and that all our experimental conclusions proceed upon the supposition that the future will be conformable to the past. To endeavour, therefore, the proof of this last supposition by probable arguments, or arguments regarding existence, must be evidently going in a circle, and taking that for granted, which is the very point in question.

In reality, all arguments from experience are founded on the similarity which we discover among natural objects, and by which we are induced to expect effects similar to those which we have found to follow from such objects. And though none but a fool or madman will ever pretend to dispute the authority of experience, or to reject that great guide of human life, it may surely be allowed a philosopher to have so much curiosity at least as to examine the principle of human nature, which gives this mighty authority to experience, and makes us draw advantage from that similarity which nature has placed among different objects. From causes which appear similar we expect similar effects. This is the sum of all our experimental conclusions. Now it seems evident that, if this conclusion were formed by reason, it would be as perfect at first, and upon one instance, as after ever so long a course of experience. But the case is far otherwise. Nothing so like as eggs; yet no one, on account of this appearing similarity, expects the same taste and relish in all of them. It is only after a long course of uniform experiments in any kind, that we attain a firm reliance and security with regard to a particular event. Now where is that process of reasoning which, from one instance, draws a conclusion, so different from that which it infers from a hundred instances that are nowise different from that single one? This question I propose as much for the sake of information, as with an intention of raising difficulties. I cannot find, I cannot imagine any such reasoning. But I keep my mind still open to instruction, if any one will vouchsafe to bestow it on me.

Should it be said that, from a number of uniform experiments, we infer a connexion between the sensible qualities and the secret powers; this, I must confess, seems the same difficulty, couched in different terms. The question still recurs, on what process of argument this inference is founded? Where is the medium, the interposing ideas, which join propositions so very wide of each other? It is confessed that the colour, consistence, and other sensible qualities of bread appear not, of themselves, to have any connexion with the secret powers of nourishment and support. For otherwise we could infer these secret powers from the first appearance of these sensible qualities, without the aid of experience; contrary to the sentiment of all philosophers, and contrary to plain matter of fact. Here, then, is our natural state of ignorance with regard to the powers and influence of all objects. How is this remedied by experience? It only shows us a number of uniform effects, resulting from certain objects, and teaches us that those particular objects, at that particular time, were endowed with such powers and forces. When a new object, endowed with similar sensible qualities, is produced, we expect similar powers and forces, and look for a like effect. From a body of like colour and consistence with bread we expect like nourishment and support. But this surely is a step or progress of the mind, which wants to be explained. When a man says, I have found, in all past instances, such sensible qualities conjoined with such secret powers: And when he says, Similar sensible qualities will always be conjoined with similar secret powers, he is not guilty of a tautology, nor are these propositions in any respect the same. You say that the one proposition is an inference from the other. But you must confess that the inference is not intuitive; neither is it demonstrative: Of what nature is it, then? To say it is experimental, is begging the question. For all inferences from experience suppose, as their foundation, that the future will resemble the past, and that similar powers will be conjoined with similar sensible qualities. If there be any suspicion that the course of nature may change, and that the past may be no rule for the future, all experience becomes useless, and can give rise to no inference or conclusion. It is impossible, therefore, that any arguments from experience can prove this resemblance of the past to the future; since all these arguments are founded on the supposition of that resemblance. Let the course of things be allowed hitherto ever so regular; that alone, without some new argument or inference, proves not that, for the future, it will continue so. In vain do you pretend to have learned the nature of bodies from your past experience. Their secret nature, and consequently all their effects and influence, may change, without any change in their sensible qualities. This happens sometimes, and with regard to some objects: Why may it not happen always, and with regard to all objects? What logic, what process of argument secures you against this supposition? My practice, you say, refutes my doubts. But you mistake the purport of my question. As an agent, I am quite satisfied in the point; but as a philosopher, who has some share of curiosity, I will not say scepticism, I want to learn the foundation of this inference. No reading, no enquiry has yet been able to remove my difficulty, or give me satisfaction in a matter of such importance. Can I do better than propose the difficulty to the public, even though, perhaps, I have small hopes of obtaining a solution? We shall at least, by this means, be sensible of our ignorance, if we do not augment our knowledge.

I must confess that a man is guilty of unpardonable arrogance who concludes, because an argument has escaped his own investigation, that therefore it does not really exist. I must also confess that, though all the learned, for several ages, should have employed themselves in fruitless search upon any subject, it may still, perhaps, be rash to conclude positively that the subject must, therefore, pass all human comprehension. Even though we examine all the sources of our knowledge, and conclude them unfit for such a subject, there may still remain a suspicion, that the enumeration is not complete, or the examination not accurate. But with regard to the present subject, there are some considerations which seem to remove all this accusation of arrogance or suspicion of mistake.

It is certain that the most ignorant and stupid peasants—nay infants, nay even brute beasts—improve by experience, and learn the qualities of natural objects, by observing the effects which result from them. When a child has felt the sensation of pain from touching the flame of a candle, he will be careful not to put his hand near any candle; but will expect a similar effect from a cause which is similar in its sensible qualities and appearance. If you assert, therefore, that the understanding of the child is led into this conclusion by any process of argument or ratiocination, I may justly require you to produce that argument; nor have you any pretence to refuse so equitable a demand. You cannot say that the argument is abstruse, and may possibly escape your enquiry; since you confess that it is obvious to the capacity of a mere infant. If you hesitate, therefore, a moment, or if, after reflection, you produce any intricate or profound argument, you, in a manner, give up the question, and confess that it is not reasoning which engages us to suppose the past resembling the future, and to expect similar effects from causes which are, to appearance, similar. This is the proposition which I intended to enforce in the present section. If I be right, I pretend not to have made any mighty discovery. And if I be wrong, I must acknowledge myself to be indeed a very backward scholar; since I cannot now discover an argument which, it seems, was perfectly familiar to me long before I was out of my cradle.”

Posted in Philosophy | Tagged: , , , , | Leave a Comment »

Are All Empirical Statements Merely Hypotheses?

Posted by allzermalmer on December 19, 2011

This blog will be based on an article done by W.T. Stace. It is called, Are All Empirical Statements Merely Hypotheses? It appeared in the philosophical journal known as The Journal of Philosophy Vol. 44, No. 2 (Jan. 16, 1947), pp. 29-38.

It is sometimes stated that all empirical statements are only probable. This was stated by those like, and especially by, Rudolph Carnap. One philosopher who disagreed, and said that some empirical statements are certain, was G.E. Moore. Stace shall agree with Moore, but with some qualifications. The statement that will be the exemplar of what is being talked about will be the statement of “This key is made of iron”. Now this statement is a singular statement like x is Y.

“To say that this proposition can never be more than probable means, I assume, that there must always be some doubt as to its truth. The question we have to get clear about is: what is the doubt, or what are the doubts, which those philosophers who say that such a statement can never be more than probable, have in mind?”

Some of the doubts could be as follows for what makes this empirical statement probable: the laws of nature are statistical, we could be deceived by some sort of demons or might be dreaming, or statements that we make rely on memory and our memory could be wrong. None of these things seems to be what has lead some to think that all empirical statements are probable. That is because these doubts are arising from practical doubt because of the frailty of human faculties.

The philosophers, like Carnap, seem to be relying on theoretical/logical doubt. This seems to be based on the logic at which we arrive at empirical truths, regardless of the frailties of particular human beings. They seem to be saying that we arrive at these empirical statements, like “this key is made of iron”, are arrived at by means of induction. And, through the means of induction, we never arrive at certainty by by means of probability.

Stace quotes Carnap on the basic idea of which is to lead to all empirical statements are merely probable. Take the statement that “This key is made of iron”. This proposition will be known as P1. We can test P1 by seeing if it is attracted by a magnet, if it is then we have partial verification of P1. So here is what Rudolph Carnap says, which leads him to state that all empirical statements are merely probable in his book Philosophy and Logical Syntax:

“After that, or instead of that, we may make an examination by electrical tests, or by mechanical, chemical, or optical tests, etc. If in these further investigations all instances turn out to be positive, the certainty of the proposition P1 gradually grows…but absolute certainty we can never attain. the number of instances deducible from P1 is infinite. Therefore there is always the possibility of finding in the future a negative instance.”

Now this is the logical problem that we face. Anytime we perform a new test, and the test is passed, it only adds a degree of probability to the statement that “this key is made of iron”. And the problem, further, is that we can’t completely verify the statement, or be certain of it, because we would have to complete an infinite number of observations. But this is not only practically impossible, it is also logically impossible.

But there is some ambiguity of what Carnap means, because there are two ways that this can be taken. The first thing could be about the different kinds of tests. For we noticed that he brought up the tests that could be done, like magnetic, electrical, chemical, and etc. So the it could be meant that the number of different kinds of test is infinite, which means we would have to make an infinite number of kinds of tests in order to achieve complete verification of the statements truth. But Stace has an objection to this position.

“If an infinite number of kinds of tests of the key were possible, this would imply that the key must have an infinite number of different characteristics or properties to be tested for. But even if an object can have an infinite number of characteristics, it would not be necessary to test for them all in order to identify the object as iron. All we need is to verify the defining characteristics of iron, which are certainly finite in number. and there is, of course, no logical difficulty about doing that.”

Now there is a second possible meaning for which Carnap has in mind. We could do a single test of a defining characteristic like “being attracted by a magnet”, or what other defining characteristics there might be. These tests only make the statement probable because we may find that the key is attracted one time and perform many of the same tests a thousand times in succession and find the same results as the first test. But we can never be sure that an instance will not turn up in the future in which the object will not be attracted by a magnet (problem of induction). “If the same thing happens in the same circumstances in a vast number of times, each time it happens makes it a little more probable that it will happen again, but it can never be quite certain.”

It is true that scientists perform the same experiments, this is the repeatably of the scientific tests. What one scientist is able to do in a test, it has to be reproducible by other scientists around the world. The same experiment can be repeated by the same experimenter over and over, or can be done by other experimenters around the world. But why are experiments repeated? Is it because each fresh instance of a positive result of the same test adds to the probability of the conclusion? It seems not.

Let us assume that we have an object that is to be tested. We want to test whether it is composed of a certain substance, which we can call X. Now let us suppose that there is only one defining characteristic of X which we call A. The scientist is testing for Y. If Y is found it is a sign that the substance is X. Now, is it true that A may be repeated many times. But why?

“It is not because he supposes that a barren repetition of instances of A makes it more probable that the substance is X. It is always, on the contrary, because he has doubts whether he has satisfactorily established by his observations of the presence of A. It is not the validity of the inductive inference from A to X that he is doubting, but whether A is really present…the doubt which the experimenter is trying to exclude is not any logical doubt about induction, but practical doubts arising from difficulties of observation, possible deficiencies in apparatus, difficulty in ensuring that the experiment is made in the exact conditions required, and so on. He is not doubting that the inductive premises will lead to an absolutely certain conclusion. He is doubting whether he has satisfactorily established the inductive premises.”

What is going on is that the scientist procedure is that a single observation is sufficient to establish an inductive conclusion with certainty. But this is only the case provided that the premises have been established. So it is not the inductive conclusion that is being questioned, but it is the premises that are being questioned. As Stace says, “What is implied by the scientist’s procedure is that a single observation or experiment is sufficient to establish an inductive conclusion with certainty, provided the premises have been established. I hold that the scientist is right.”

Stace locates the problem at three points. And this is the problem of how some philosophers have reached the conclusion that all empirical statements are merely probable.

(1.) One of the problems was how philosophers thought that scientists were repeating experiments to try to dispel logical doubts about the validity of induction. What the scientists were doing, in fact, was trying to dispel practical errors in observing or establishing the premises on which an induction rests. The question of probability doesn’t fall within the inductive argument, but outside of the inductive argument.

“That is to say, what is only probable is not that, if A is once associated with B, it will always be associated with B, but that A has actually been found associated with B; not that if a substance has a certain specific gravity it is gold, but that the substance now before me actually has that specific gravity…a natural mistake located the question of probability within the inductive argument instead of outside of it; have extrapolated it from the practical sphere of observation, measurement, and so on, where it actually belongs, to the logical sphere of the inductive inference in which in reality it has no place.”

So the problem is not in the inductive argument itself, but outside of the argument. What is outside of the argument is making sure that you have made an observation that meets with the premises of the argument. This is what constant testing is about, to make sure that the observations are in line with the premises. It is not the argument being questioned, but something outside of the argument that is being questioned.

(2.) Another reason that it seems that it is brought up that empirical statements are probable deals with the view of induction where an application of the inductive principle to a type of cases different from that of the Iron key. This other application is based on generalizing from observations. For example, we generalize from observations of a number from a certain class to the whole class. This means, from observing some white swans, we go on to generalize to the class of swans. From seeing a certain number of swans being white, and not observing any black swans, we go on to say that All swans are white. This will be dealt with a little later on.

(3.) This view seems to follow, as some philosophers think, from what David Hume had to say on the problem of Induction. Hume showed that we can’t “prove” a conclusion in an inductive argument. Because of this, some seem to have imagine that because we can’t prove it, we can at least make it probable. But it doesn’t seem that this follows from what Hume said on the problem of Induction. But Stace does think that something follows from what Hume said on this problem.

Imagine that we have a single instance of A being associated with B, and we’ve ruled out all practical doubts from possible errors of observation or experiment. We now have, logically, two positions that we can take up.

The first is that we can assume the validity of the principle of Induction. So, in this single instance, we can conclude that A is always associated with B, and our conclusion follows with absolute certainer from our two premises of single observed association of A with B and the principle of induction. With these two premises, the conclusion is certain to start with, and so there is no increasing probability or probability at all.

The second is that you may not assume that validity of the inductive principle. Now this means that we follow Hume, which means that there’s no logical connection between the premises and the conclusion of induction. This means, nothing follows from induction, neither certainty nor probability. No matter how many single instances that support our inductive conclusion, the probability never arises above zero. (Karl Popper would agree with this point). There is no connection to say that because the conclusion obtained, that we can say that the probability of the premises rises some more. They are disconnected. It is like having three dots on a sheet of paper. They are disconnected from each other. So when we affirm one, we can’t affirm any of the others because they’re not connected with one another.

“I have affirmed that, given the inductive principle, a single case will prove the inductive conclusion with certainty, I ought to give a formulation to the inductive principle which embodies this…”If in even a single instance, we have observed that a thing of the sort A is associated with a thing of the sort B, then on any other appearance of A, provided the other factors present along with A are the same on both occasions, it is certain that A will be associated with B.””

There is the clause of “provided the other factors present along with A are the same on both occasions.” This forms part of the principle, which comes down to “Same cause, same effect”. There is an example to help make this point clear. If the bell is struck in air then it produces sound. But it doesn’t follow that a bell struck in a vacuum will produce sound. This is because of the clause that was inserted into the principle. The factors aren’t the same, and so they’re not the same type of thing. But it does introduce a new inductive discovery.

There is one obvious objection that one could make to this principle. It could be said that this new interpretation is merely an assumption that is incapable of proof. So if this is a matter of being arbitrary choice of how to formulate it in terms of certainty and probability, then we ought not to assume more than is necessary to justify our sciences and our practice. So someone could say, “it will be quite sufficient for these purposes to assume that, if A is associated with B now, it will probably be associated with B at other times and places. On this ground the probability formulation should be preferred.”

But putting the term certainty in there is not meant to be arbitrary, but it is mean to represent a formulation of the assumption which has been the basis of science and practice. But maybe Stace should be more clear, which is what he tries to do like as follows:

“If you have one case of a set of circumstances A associated with B, and you are quite sure you have correctly established this one association, then, assuming the uniformity of nature, or the reign of law, or the principle of induction-call it what you will- a repetition of identically the same set of circumstances A is bound to be associated with B. For if not, you would have a capricious world, a world in which A sometimes produces B, and sometimes it does not, a world in which the kettle put on the fire may boil today, but freeze tomorrow. And this would clearly be a violation of the principle of induction which you have assumed.”

Now, if you assume the principle of induction, then a single case validates an induction. But now Stace will try to prove his second contention that if you don’t assume the principle of induction, your inductive conclusion aren’t probable at all and there’s no repetition of instances, so no matter how great the number, then the probability is never raised above zero.

To establish this position, Stace will assume that Hume is right. This means, between the premises and the conclusion of an inductive argument there is absolutely no logical connection at all. This means that there is nothing to establish the slightest probability because they’re is no connection between them. So if we affirm one part, it has no connection to another to raise the probability of this part that is connected to what we affirmed. They are so completely disconnected that there’s no logical connection to even bring up probability.

For example, here is what Al-Ghazali said about causality, which is the same position that David Hume took up, and this is based in some ways on the principle of induction. “The affirmation of one does not imply the affirmation of the other; nor does its denial imply the denial of the other. The existence of one is not necessitated by the existence of the other; nor its non-existence by the non-existence of the other.” So when we affirm one thing with induction, like a correct experiment, this in no way can increase any probability when the affirmation of one doesn’t imply the affirmation of the other. How can you raise the probability when what you affirm has no connection to anything else to raise the probability of this other thing? You can’t.

Stace goes on to try to examine the types of cases in which generalize a whole class from a number of instances that are smaller than the whole class. Try to generalize about a whole class of swans from observing a few of the swans that are suppose to make up the whole class. If we observe one swan and it is white,nto conclude that all swans are white, we might be accused of generalizing from one instance. But if we make 10,000 observations, we might think we have a degree of probability to support the generalization. We go on to make observe 1 billion swans and they were white. This might lead us to go on to admit that the hypothesis has become even more probable. So, someone might say to defend the probability view, that how can we deny that we probability and use the probability view of induction?

“But the inductive principle only holds with the proviso, “if the factors present along with A are the same” in subsequent repitition of A. And this case of the swans is simply a case in which it is extremely difficult to be sure that this is so. A in this case means the defining characteristics of the class swan, and B means whiteness. Now different swans will have, along with the defining characteristics A, a number of other characteristics. and these will differ with different individual swans, not to mention circumambient differences of environment. Thus the first case of A you observed was really ACDE, and this was associated with B. The second case was APQR, the third AXYZ. Now, of course, it does not follow from the principle of induction that because ACDE was associated with B, therefore APQR and AXYZ must be associated with B. For we do not have there that exact repetition of the same sets of circumstances which the inductive principle requires.”

To try to remedy the situation that we are in, we constantly repeat observations of this class of swans. Now if we keep making these observations of A, and they’re found to have B, then we think it becomes more and more likely that we have eliminated other certain possibilities, and raise the probability. We want to eliminate some of the accidental characteristics of certain swans. This would be something like they’re size. food they eat, and the climates that they live in. When we rule out sets of circumstances as irrelevant, they become more probable.

The fundamental reason why there is constant repetition of observation on new members of class is that although in theory the association of A with B, once it is observed must always hold, is because in practice we never get our cases of pure A. “We can not isolate the system. It is always mixed up with extraneous circumstances. Thus the doubt which we are trying to dispel by repeated observations has nothing at all to do with Hume’s doubt about the validity of induction…” That doubt can’t be dispelled, no matter now many numerous observations we make. But the doubt that we are trying to get rid of isn’t the logical doubt. The doubt we are trying to get rid of is the practical doubt from the enormous complexity of nature, our frailty of our intellects which are unequal with the task to disentangle the complexities, or the inadequacy of the instruments that we have at our disposal to isolate the system present.

Some, like Carnap, have divided knowledge into empirical knowledge and necessary propositions. Necessary propositions would be those like mathematics and logic. Now the empirical propositions could be considered doubtful because the practical doubts that arise from our human infirmities. But this means that we ought to have the same doubts in concern with mathematics. This is why we have people that check our work in mathematics, to make sure that we made no practical doubts in the process that we followed.

“There is one sense in which mathematical, or, in general, deductive conclusions are certain this may be called the logical or theoretical sense. And there is another sense, which may be called the practical sense, in which they are only probable, since the mathematician or the syllogizer may err in his reasoning. The mathematician may miscalculate, and the syllogizer may make any one of a hundred mistakes. And if practical doubts are not a ground for denying that, in an appropriate sense, mathematics is certain, then practical doubts can not be a ground for denying that, in an appropriate sense, empirical conclusions are uncertain.”

“As it is with mathematical truths, so precisely it is with empirical truths. There is one sense in which an inductive conclusion is certain, namely, the theoretical sense that it follows with certainity from a single observation plus the inductive principle. And there is another sense, the practical one, in which it is probable only, because there may be errors in observation, experimentation, and the like.”

“The statement that empiricial knowledge may be theoretically certain is, of course, subject to the proviso that we accept the inductive principle. If we don’t accept it, then, of course, empirical knowledge is not even probable. It has no validity at all. In no case does any question of probability enter into the matter.”

Posted in Philosophy | Tagged: , , , , , , , , , , , , , , , , , , , , | Leave a Comment »

Refutation of Realism

Posted by allzermalmer on June 28, 2011

This blog is going to be based off an article done by W.T. Stace. The name of the paper is The Refutation of Realism, and it appears in the philosophical journal Mind, Vol. 43, No. 170 (Apr., 1934), pp. 145-155. This article is a play off of G.E. Moore’s article The Refutation of Idealism.

Now, the obvious question would be “What is meant by realist?”. Stace goes on to say, by realist, he means someone who agrees to the assertion that “some entities sometimes exist without being experienced by any finite mind.” Now, this might not be what all realist would agree to, but it is close enough to the very basic idea.

So let us take a look at what a realist might believe. Before me is a book, and I know this because I am seeing it, I am touching it, and I hear it when I slam my hand against it, I am smelling it, and taste it. Now, a realist would believe that the book continues to exist when I put it in a drawer, and I no longer have those experiences of it, and there is no other finite mind experiencing it. Thus, a realist will at least believe that it continues to exist when no one is experiencing it.

Now, there would also seem to be no point in asserting that entities might exist unexperienced, unless they do, as a matter of fact, sometimes exist unexperienced. Now, imagine that the universe has a property, which we call X, as a matter of fact, the universe has no such property, would be useless, and has no contribution to truth. Now, some realist might think that such a belief of the relation between knowledge and object as such, helps them in someway of helping with the belief in things that exist unexperienced by some mind.

Now, it should be stated as clearly as possible, and which is very important. That statement is,  One cannot prove that no entities exist without being experienced by minds. For, it is always possible that they do exist unperceived. However, it is also possible that they do not exist unperceived. Thus, we find that both are equal in their possibility. But, the main point is this: We have not the slightest reason for believing that they do exist unexperienced. And it is from this that the realistic position is groundless, and one that ought not to be believed. And the realistic position is like that of “there is a unicorn on the planet Mars”. We cannot prove that there is not a unicorn on Mars. However, since there is not the slightest reason to suppose that there is one, it is a proposition which we ought not to believe.

Now it will not be held that objects of experience, like a color patch that is green, are “mental”. And so when it comes to the question of if what we experience is only mental, it will be held that this question is meaningless, and this is a form of neutral monism. Now, the position will be as follows: “There is absolutely no reason for assertion that these non-mental, or physical, entities ever exist except when they are being experienced, and the proposition that they do so exist is utterly groundless and gratuitous, and one which ought not to be believed.”

It will be attempted to show that we do not know that any single entity exists unexperienced. It will be inquired how we could possibly know that unexperienced entities exist, even if they do exist unexperienced.

Let us get back to a previous example. Now, at this moment, I am experiencing this book in front of me. But how can I know that it existed last nigh in my drawer, when, as far as I know, no other finite mind was experiencing it? How can I know that it will continue to exist tonight when there is no one in the room? A realist knows, or at least believes, that they continue to exist. Now a question comes up: How could such knowledge, or belief, be obtained and justified?

There are two ways in which it could be asserted that the existence of any sense-objects can be established. They are by sense-perception, and the other is inference from sense-perception. I know of the existence of the book now because I see it. It is part of my sense experience. Now, I am supposed to know of the other side of the moon, which has never been seen, by inference from all the various actual astronomical observations, and so I make an inference from things actually experienced. And, it is also a possible experience. I could fly out to the moon, and go around to the dark side to have a sense experience.

1. It should be obvious that we cannot have sense-perception of things that are not sense-perceptions. For, to have a sense-perception of something that is not a sense-perception would be a contradiction. Both sense-perception and not sense-perception. And, if we were to have a sense-perception, it would be experienced by some finite mind, and so it would not be existing without some finite mind experiencing it.

2. Now inference seems like the most likely candidate for coming to the belief of things existing unexperienced by some finite mind. So how can I pass, by inference, from a particular fact of experiencing the book now, when it is being experienced, to the different particular fact of the existence of the book yesterday or tomorrow, when no finite mind is experiencing it? Now the onus of proof is on those that say things somethings exist when some finite mind is not experiencing. It would be up to them to show how they passed from what is sense-perception to something that is not a sense-perception. So one may sit back and wait for them to show how they came to such a proposition, which means to support their proposition.And Bertrand Russell had something to say about this, “Belief in the existence of things outside of my own biography must, from the standpoint of theoretical logic, be regarded as a prejudice, not as a well-grounded theory.”

Now, such an inference to things existing when some finite mind is not experiencing it cannot be done by an inductive inference. Induction works from what has been observed, what we have experienced, to what will be experienced, but which is currently unexperienced. For example, every morning I have found that the sun rises in the east. This I have experienced. From this, based on an inductive inference, I come to the conclusion that tomorrow morning, which is unexperienced, that I will experience the sun rising in the east.

Now inductive reasoning cannot help me here, since I have never experienced something existing unexperienced, since that is just a contradiction, and not possible. In other words, there is no case where it has been observed to be true that an experienced object continues to exist when is not being experienced. It is, by hypothesis, its existence when not being experienced, cannot be observed. And induction is also about generalization from observed facts, but there is not one single case of an unexperineced existence, since that is a contradiction, which can be the basis of the generalization that entities continue to exist when one is experiencing them.

Now, since induction is ruled out, we are left with deductive inferences. Deduction depends on consistency. Thus, when given P→Q, we can only prove Q if P is admitted. From P→Q , all that can be admitted is that P and not Q are inconsistent with each other, and we cannot hold both propositions, P and not Q, together, though we can hold to P and not Q as separate propositions. Thus, to assert that the book exists now when I am experiencing it, to the existence of the book when no one is experiencing it, together is an internally inconsistent proposition. But, there is no inconsistency when these two propositions are asserted separately. In other words, deductive inferences do not allow us to reach that because things exist when some finite mind is experiencing them, to things existing when no finite mind is experiencing them, is deductively invalid.

Thus we find that we have no sense-perception to support the realist position, and that we cannot use inferences to the realist position, since deduction and induction do not help us.

Now it is not proved that because we cannot make an inference to the existence of things existing unexperienced by some finite mind, that they do not exist unexperienced. For such a way of reasoning would be fallacious. However, because it has not been proved there does not exist things unexperienced, that it shows that they do exist unperceived. For to argue either way would be an argument from ignorance. An argument from ignorance carries these two forms, which is both, respectively, positive and negative.

Positive:If a proposition has not been disproven, then it cannot be considered false and must therefore be considered true.
Negative:If a proposition has not been proven, then it cannot be considered true and must therefore be considered false.

Now that we have no sense-perception that can allow us to assert such a proposition, and we cannot make an inference to such a proposition, we ought not to believe it. For we ought not to believe that there is a unicorn on Mars because we have no sense-perception of it, and we have no inference to reach such a conclusion. It does not mean that it does exist or does not exist, but that we ought not to believe it. Thus, the unicorn are like the existence of things existing unperceived by some mind. And from a logical point of view, the onus of proof is on the realist that asserts that things exist unperceived by some finite mind, and until they keep to their burden, we ought not to believe what they say.

Now some might come to use the causal processes to make an inference to things existing when not experienced. The whole argument of causal sequences continuing on when not perceived is  begging the question. For you are still assuming that things that happen when perceived continue on when not perceived, and that is the thing in question.  If  someone, say, John stays in the room as he builds a fire and keeps it going till it is done, which takes about an hour, he observes a certain sequences of the phenomena. The sequence follows like this, m, n, o, p, q, r,  s, t, u. Now if John leaves the room after it starts, and returns half an hour, he will see it at sequence q. If John leaves the room after that sequences and returns to it in a quarter-hour, he will get the sense experience of s. And on this goes. John will thus ‘infer’ that m,n,o, & p have occurred in his absence and that of any other mind. However, the only way this inference can be made is with the belief that things go on in his absence, or as if he were there. John cannot infer the conclusion of things going on unperceived as they do when perceived, because of his belief in uniform causal sequences rests on belief in the general belief in continuity of nature, i.e. continued occurrence of events when he is not perceiving them. He has to first come to the belief in continued existence when no one is perceiving things before he can believe in uniform causal sequence when not being perceived. Thus, he cannot logically make the inference that he does.

So, like we cannot perceived unexperienced things, so too we cannot perceive unexperienced processes and laws. Also, like we cannot infer from anything which we experience to the existence of unexperienced things, so we cannot infer from any processes and laws we experience the existence of unexperienced processes and laws. And our belief in the processes of causality that happens when we experience it, to it going on when we do not experience it, is based on the belief in the continued existence of things when we are not experiencing it, and so begs the question.

Now some have made some distinction between sense-data and our awareness of sense-data. It is said that Green is not the same as awareness of Green. This is said because of us comparing different sense-data. Say that I experience a green sense-datum and a blue sense-datum. We find that there is some common element between them, and this is awareness. Thus, awareness must be different from green, since awareness also exists in the case of blue, and that awareness is not green. Thus, it is thought that Green exists when we are not aware of Green. But this is not the case.

Whenever we come across green, we find that we have awareness of green, but we also find that green and awareness of green are not the same thing. Thus, there is a difference between X and Y. Yet when we find X, we also find Y. Thus, to say that X goes on existing when Y is not there, is not supported by sense-perception, and now we are stuck with inference, and we come to the same problems. We do not find sense-perception to show that green exists when there is no awareness of green, and we cannot make an inference to it either. Thus, such a distinction between green and awareness of green does not allow us to believe that things exist when unexperienced by some finite mind.

Now, since experience and inferences cannot lead us to the realist position, and all the arguments to such a conclusion are fallacious, we ought not to believe it. However, some would say that it is probably true, and thus we ought to believe it. However, all such reasoning would have to be based on the same types of arguments, and they all come to rely on fallacious reasoning. Also, since both options are possible, we find that they have an equal probability, and one does not have a greater probability than another. Heads and tails both have the same probability. Also, we cannot present an argument to support the realist position, and if we could then we could just as well use the critique presented her to show that it could be even more probable that they do not exist when not experienced by some finite mind.

Now some mind resort to it being an animal faith a primitive belief, or an instinctive belief. To invoke such things to support the realist proposition is to throw up ones hands in defeat, and to admit that one has no rational reasons to support their beliefs. It becomes an unreasoned belief, and has nothing to rely on by fiat. It is to be one who files for bankruptcy, and gets ride of rational grounds for their belief.

So, throughout, we find that the logically correct position is this. We cannot have any reason whatsoever to believe that unexperienced entities exist. We cannot prove that they do not exist. The onus of proof is on those who assert that they do exist unexperienced. We have found that experience does not attest to the existence of unexperienced things, and we have no way of inference to reach it (without fallacious reasoning), and thus we find that it is impossible to reach such a conclusion. Thus, we ought not to believe it, if we are to be rational, like we do not believe in a unicorn on Mars.

But, the way around this is to be explained as it being a mental construction, or a fiction. It is a pure assumption which we invent to simplify our view of the world.

Posted in Philosophy | Tagged: , , , , , , , , , , , , , , , , | Leave a Comment »