allzermalmer

Truth suffers from too much analysis

Posts Tagged ‘Hypothesis’

False Hypotheses & True Predictions

Posted by allzermalmer on June 23, 2016

In logic, a conjunction is a logical connective that connects two separate propositions. For example, say we have the propositions ‘The Golden State Warriors won the Western Conference Championship of the NBA in 2016’ and ‘The Cleveland Cavaliers won the Eastern  Conference Championship of the NBA in 2016’. We can represent each of those propositions, respectively, as P and Q.

The logical connective of conjunction would combine each of these two separate propositions together. Each of these propositions would be known as a conjunct that makes up a conjunction. Conjunct of P and conjunct of Q make up the conjunction of ‘Both The Golden State Warriors won the Western Conference Championship of the NBA in 2016 & The Cleveland Cavaliers won the Eastern Conference Championship of the NBA in 2016’. This can be represented as ‘P&Q’.

A conjunction is only true when each conjunct is true. A conjunction is false when either one of the conjuncts is false or both conjuncts are false. In the example presented, it is true that both teams won the Conference championships in 2016. So the conjunction is a true proposition.

Logic tells us that from false hypotheses, or hypothesis, that true predictions follow from it.  Suppose that P means ‘The Golden State Warriors won the NBA Championship in 2015’ and that Q means ‘The Golden State Warriors won the NBA Championship in 2016’. From these two propositions, we can form the conjunction of ‘Both The Golden State Warriors won the NBA Championship in 2015 & The Golden State Warriors won the NBA Championship in 2016’. This can be represented as ‘P&Q’.

Taking ‘P&Q’ as a hypothesis, we can prove that some propositions follow from that hypothesis. One of these propositions that follow is P.  So from the hypothesis of ‘Both The Golden State Warriors won the NBA Championship in 2015 & The Golden State Warriors won the NBA Championship in 2016’ that it necessarily follows by rules of logic that ‘The Golden State Warriors won the NBA Championship in 2015’.

Suppose ‘P&Q’ then necessarily follows ‘P’.

The hypothesis presented is false, P&Q is false. One of the conjuncts is false, Q is false. One of the conjuncts is true, P is true. So the conjunction is false. But from this false hypothesis, we find that a true conclusion follows from it.

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Different Models of both Knowledge & Epistemology

Posted by allzermalmer on September 20, 2013

One of the differences in epistemology are different theories of knowledge. Renee Descartes helped to present one theory of knowledge, which followed a general form of Rationalism. There is another general form known as Empiricism.

We shall have two Categories and three Truth-values.

Category 1: Cognitive or Cognition
Truth Value: Either Cognition is always true or Cognition is sometimes true & sometimes false or Cognition is always false.

Category 2: Sensory or Senses
Truth Value: Either Senses are always true or Senses are sometimes true & sometimes false or Senses are always false.

Now we can combine both of these categories together to form Both Cognition & Senses, apply the Truth Values, and derive 9 different Models of Epistemology or Knowledge.

Hypothesis *1:
Both cognition is always true & senses are always true.
Both senses are always true & cognition is always true.

Hypothesis *2:
Both cognition is always true & senses are sometimes true and sometimes false.
Both senses are sometimes true and sometimes false & cognition is always true.

Hypothesis *3:
Both cognition is always true & senses are always false.
Both senses are always false & cognition is always true.

Hypothesis 1*:
Both cognition is sometimes true and sometimes false & senses are always true.
Both senses are always true & cognition is sometimes true and sometimes false.

Hypothesis 2*:
Both cognition is sometimes true and sometimes false & senses are sometimes true and sometimes false.
Both senses are sometimes true and sometimes false & cognition is sometimes true and sometimes false.

Hypothesis 3*:
Both cognition is sometimes true and sometimes false & senses are always false.
Both senses are always false & cognition is sometimes true and sometimes false.

Hypothesis *1*:
Both cognition is always false & senses are always true.
Both senses are always true & cognition is always false.

Hypothesis *2*:
Both cognition is always false & senses are sometimes true and sometimes false.
Both senses are sometimes true and sometimes false & cognition is always false.

Hypothesis *3*:
Both cognition is always false & senses are always false.
Both senses are always false & cognition is always false.

These models of knowledge, or epistemology, exhaust all logically possible positions given only these two categories and these three truth values. Some possible subdivisions could be made, especially when either categories, or both, take on the truth value of sometimes true and sometimes false.

One basic idea is that cognition, under Rationalism, would always be true & senses, under empiricism, would always be true.

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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.

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Proof of Disjunctive Syllogism

Posted by allzermalmer on July 28, 2013

anguage

(I) Symbols: Ø = contradiction, → = conditional, and [] = Modal Operator
(II) Variables: p, q, r, p’, q’, r’. (Variables lower case)

Well Formed Formula for Language

(i) Ø and any variable is a modal sentence.
(ii) If A is a modal sentence, then []A is a modal sentence.
(iii) If A is a modal sentence and B is a modal sentence, then A implies B (A→B) is a modal sentence.

* A, B, and C are modal sentences, i.e. upper case letters are modal sentences. These upper case letters are “variables as well”. They represent the lower case variables in conjunction with contradiction, conditional, or modal operator.

So A may possibly stand for p, or q, or r. It may also possibly stand for a compound of variables and symbols. So A may stand for q, or A may stand for p→Ø, and etc.

Negation (~) = A→Ø
Conjunction (&) = ~(A→B)
Disjunction (v) = ~A→B
Biconditional (↔) = (A→B) & (B→A)

Because Ø indicates contradiction, Ø is always false. But by the truth table of material implication, A → Ø is true if and only if either A is false or Ø is true. But Ø can’t be true. So A → Ø is true if and only if A is false.

This symbol ∞ will stand for something being proved.

(1) Hypothesis (HY) : A new hypothesis may be added to a proof anytime, but the hypothesis begins a new sub-proof.

(2) Modus Ponens (MP) : If A implies B and A, then B must lie in exactly the same sub-proof.

(3) Conditional Proof (CP): When proof of B is derived from the hypothesis A, it follows that A implies B, where A implies B lies outside hypothesis A.

(4) Double Negation (DN): Removal of double negation ~~A & A lie in the same same sub-proof.

(5) Reiteration (R): Sentence A may be copied into a new sub-proof.

Proof of Disjunctive Syllogism: Because at least one disjunct must be true, by knowing one is false we can infer tat the other is true.

If either p or q and not p, then necessarily true q.

Premise (1) p v q (Hypothesis)
Premise (2) ~p (Hypothesis)
(3) ~p implies q ((1) and Definition v)
Conclusion (4) q (Modus Ponens by (2) and (3))

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Proof of Modus Tollens

Posted by allzermalmer on July 28, 2013

Language

(I) Symbols: Ø = contradiction, → = conditional, and [] = Modal Operator
(II) Variables: p, q, r, p’, q’, r’. (Variables lower case)

Well Formed Formula for Language

(i) Ø and any variable is a modal sentence.
(ii) If A is a modal sentence, then []A is a modal sentence.
(iii) If A is a modal sentence and B is a modal sentence, then A implies B (A→B) is a modal sentence.

* A, B, and C are modal sentences, i.e. upper case letters are modal sentences. These upper case letters are “variables as well”. They represent the lower case variables in conjunction with contradiction, conditional, or modal operator.

So A may possibly stand for p, or q, or r. It may also possibly stand for a compound of variables and symbols. So A may stand for q, or A may stand for p→Ø, and etc.

Negation (~) = A→Ø
Conjunction (&) = ~(A→B)
Disjunction (v) = ~A→B
Biconditional (↔) = (A→B) & (B→A)

Because Ø indicates contradiction, Ø is always false. But by the truth table of material implication, A → Ø is true if and only if either A is false or Ø is true. But Ø can’t be true. So A → Ø is true if and only if A is false.

This symbol ∞ will stand for something being proved.

(1) Hypothesis (HY) : A new hypothesis may be added to a proof anytime, but the hypothesis begins a new sub-proof.

(2) Modus Ponens (MP) : If A implies B and A, then B must lie in exactly the same sub-proof.

(3) Conditional Proof (CP): When proof of B is derived from the hypothesis A, it follows that A implies B, where A implies B lies outside hypothesis A.

(4) Double Negation (DN): Removal of double negation ~~A & A lie in the same same sub-proof.

(5) Reiteration (R): Sentence A may be copied into a new sub-proof.

Proof of Modus Tollens: 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 p implies q & ~q, then necessarily true that ~p)

Premise (1) p implies q (Hypothesis)
Premise (2) ~q (Hypothesis)
(3) q implies Ø ((2) and of Definition ~)
(4) p (Hypothesis)
(5) p implies q (Reiteration of (1))
(6) q (Modus Ponens by (4) and (5))
(7) q implies Ø (Reiteration of (3))
(8) Ø (Modus Ponens by (6) and (7))
(9) p implies Ø ( Conditional Proof by  (5) through (8))
Conclusion (10) ~p ((9) and Definition of ~)

Shortened version, with some steps omitted, would go as follows.

P (1) p implies q
P (2) ~q
(3) q implies Ø ((2) and Definition of ~)
(4) p (Hypothesis)
(5) q (Modus Ponens by (1) and (4))
(6) Ø (Modus Ponens by (3) and (5))
(7) p implies Ø (Conditional Proof by (3) through (6))
C (8)  ~p ((7) and Definition ~)

Here is an even shorter proof of Modus Tollens, and it only requires the rule of inference of Hypothetical Syllogism:

(1) p implies q (Hypothesis)
(2) q implies Ø (Hypothesis)
(3) p implies Ø (Hypothetical Syllogism by (1) and (2))
(4) ~p (Reiteration of (3) by Definition of ~)

So we have proved that If p implies q and ~q, then ~p is necessarily true.

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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.

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Strong Inference: The Way of Science

Posted by allzermalmer on September 27, 2012

This is a copy of an article from the journal The American Biology Teacher;  Vol. 65, No. 6 (Aug., 2003), pp. 419-424. The article is called Strong Inference: The Way of Science, by Thomas B. Kinraideand R. Ford Denison. You can read the article here.

“Valentine: It may all prove to be true.
Hannah: It can’t prove to be true, it can only not prove to be false yet.
Valentine: (Pleased) Just like science.
– From “Arcadia,” a play by Tom Stoppard

Science teachers and science textbooks commonly introduce students to the scientific method in elementary and junior high school, but the study of scientific method and philosophy can be a life-long endeavor. Our essay concentrates on a particular aspect of the scientific method -the testing of hypotheses. Concepts of hypothesis testing have changed even within the relatively short period of modern science. Specifically, the concept of proof has been abandoned for reasons we shall describe. Although we can not prove hypotheses, we can almost certainly disprove some hypotheses, if they are false.

To describe the modern method of hypothesis testing, we borrow the term “strong inference” from John R. Platt’s Science (1964) essay by the same name. In brief, strong inference is the method of testing a hypothesis by deliberately attempting to demonstrate the falsity of the hypothesis. A hypothesis that repeatedly withstands attempts to demonstrate its falsity gains credibility, but remains unproven. We are confident that our essay reflects the thinking of most scientists that hypotheses are potentially disprovable but not provable. Nevertheless, we qualify these views somewhat, arguing that neither proof nor disproof is certain.

Strong inference is an avenue to knowledge that is systematically applied in cience, but some practice of strong inference has occurred in human endeavors for thousands of years. For example, courts of law in ancient civilizations occasionally used elements of strong inference – facts were assembled from physical evidence and the testimony of witnesses; hypotheses  were developed (only the grand vizier could have stolen the documents); and impossible or illogical consequences of the hypotheses were grounds for rejecting  the hypotheses (an alibi would establish the grand vizier’s innocence) Nevertheless, former and present methods of inference sometimes differ significantly- an ancient magistrate may have awaited a ghostly visitation during which the truth of a case would be revealed; the body of an accused witch may have been examined for incriminating marks; and confessions may have been extracted by torture. [This mixture of strong inference and alternative methods is described in tales of the historical Chinese magistrate, Judge Dee, by the Dutch diplomat and scholar Robert Van Gulik (1976).]

Even today, people rely upon alternative avenues to knowledge that may include intuition, revelation, and adherence to authority. We are reluctant still to use strong inference outside of enterprises that are recognizably scientific, and the application of strong inference to some beliefs may be impossible. Even when strong inference is possible, its application may be uncomfortable, and its application to the beliefs of others may be considered hostile. Challenges to authority and received wisdom may seem disloyal or arrogant. This reluctance to use strong inference follows understandably from the requirement that belief (or hypotheses) be subjected to deliberate attempts to demonstrate the falsity of the beliefs and by formulating and testing competing beliefs. Nevertheless, strong inference can be practiced with civility and can do much to offset our prejudices and natural gullibility.

A Definition of Hypothesis

Because the formulation and testing of hypotheses are at the heart of strong inference, we will present a definition of hypothesis here, however, a detailed discussion of hypotheses will be delayed until some other terms, incorporated in the definition, are considered. For the definition of hypothesis, and most other terms, we have consulted Webster’s Third New International Dictionary, Unabridged (Gove, 1976)

Hypothesis: [An explanatory] proposition tentatively assumed in order to draw out its logical or empirical consequences and so test its accord with facts that are known or may be determined.

Inevitably, the burden of definition is shifted to other words. In the present case, “fact” is one of those words. Strong inference ultimately rests upon facts, and facts and hypotheses are sometimes confused with each other. Therefore, we shall consider first the concept of fact.

The Concept of Fact

Fact: An occurrence, quality, or relation the reality of which is manifest in experience or may be inferred with certainty.

Here, too, the burden of definition is shifted to other words, among them, “experience” and “reality”. To deal with these terms we must concede that science rests upon a few basic assumptions. Science assumes that nature has a reality independent of the human mind, and science assumes that the human mind can grasp the reality of nature. These epistemological issues are rarely considered in the ordinary practice of science.

Manifest Fact & Inferential Fact

The definition of fact indicates the existence of two kinds of fact- manifest fact and inferential fact. Again, some definitions may be helpful.

Manifest: Capable of being easily understood or recognized at once by the mind: not obscure: obvious.

Inference: The act of passing from one or more propositions…considered as true to another the truth of which is believed to follow from that of the former.

Manifest facts are not highly dependent upon inference. We will call a fact that is highly dependent upon inference an inferential fact. To illustrate inferential and manifest facts, consider the case of a forest fire. If the fire occurred recently, then its occurrence is likely to be a manifest fact. It may have been observed by hundreds of people, and newspaper readers and television viewers are certainly being reasonable in accepting the occurrence of the fire as a manifest fact.

What if the fire had occurred 200 years ago? Most scientist would accept as fact (inferential fact) that a fire had occurred in an area if several observations pointed, convergently, toward a fire. These observations might include the absence of any trees in the area older than 200 years (despite the presence of older trees in surrounding areas), the scarcity or absence of old wood on the forest floor, and the presence of an ash layer beneath the recent leaf and twig litter. Perhaps none of these observations was convincing by itself (the ash may have been blown in from another fire some distance away). Convergence of evidence is the clincher.

In some cases, facts and hypotheses may be confused, but confusion may be avoided by remembering that a hypothesis is a candidate explanation, not a candidate fact. The statement “The Earth is spherical” in ancient times was a candidate fact, and in the present age of satellite photographs, and other evidence, the statement may be regarded as a manifest fact. The statement was also a hypothesis in ancient times, but only when used as an explanation for some other observation. Thus the statement “vertical objects cast shadows of different length at different latitudes because the Earth is spherical” is a hypothesis (a candidate explanation) and not merely a candidate fact. If we confuse a candidate fact for a hypothesis, then we may conclude mistakenly that hypotheses are provable.

Scientific Facts are Public

Another feature of scientific facts is that they are public; that is, a fact (especially a manifest fact) is accessible to all competent observers. The issue of competence is sometimes problematical. In science, public accessibility to facts is crucial even though comprehension of the facts is not always easy. The devotees of mystery cults may be entitle to both their own private opinions and their own private facts, but science disallows private facts.

The Concept of Hypothesis

“Science” and “strong inference” are not synonymous. Science is both a method and a body of knowledge. Facts can be compiled and many questions can be answered without the formulation and testing of hypotheses. Natural history inventories (lists of birds, plants, minerals, and other items) play a role in science and in society. The answer to some questions (What is the speed of light?) may require high technical skill but can be answered without the formulation of hypotheses. In some cases, laws of nature may be formulated without the explicit testing of hypotheses. (Laws are descriptive, often quantitative, but not explanatory, statements having a value intermediate between fact and hypothesis. Examples are Ohm’s law [I=V/R], Newton’s law of motion [e.g. F=ma], and the law of conservation of charge.)

Despite the possibility of some success in science without the testing of hypotheses, science attempts to do more than just compile and describe. Science attempts to explain. This requires the formulation of hypotheses in a creative process that may require the investigator to think beyond readily available explanations. A good hypothesis must be explanatory, but it must have another feature too: It must be testable by strong inference. If it is false, it must be possible to show that it is false.

A Case Study of Hypothesis Testing

A textbook that one of us (T.B.K.) assigned years ago as a college professor was The Study of Biology, 3rd Edition (Baker & Allen, 1977). The first two chapters of that book, The Nature and Logic of Science and Testing Hypotheses and Predictions, are excellent.The following case study was taken from that book.

The Pacific salmon Oncorhyncus kisutch hatches in streams in the Northwest, swims to the sea, then eventually, returns to streams to spawn. We may ask, and answer, the question “Do individual fish return to the stream of their birth?” without formulating an explanatory hypothesis. Tagging experiments have confirmed the fact that the fish predominantly do return to their natal streams. In order to determine how the fish do this, we can proceed in one of two ways. We can continue to study the fish, compiling facts in the hope that an answer may emerge. Sometimes “fishing expeditions” such as these can lead to serendipitous results, but eventually strong inference (hypothesis formulation and testing) is usually needed.

Platt, in the Science article cited above, makes an important suggestion: Formulate more than a single hypothesis. With more than one hypothesis, the investigator is less likely to adopt a “pet” hypothesis to which he/she becomes emotionally attached, and the necessary attempt to demonstrate the falsity of the hypotheses is less worrying- perhaps one will survive. Incidentally, the negation of a significant hypothesis is a significant contribution to science.

In our case study, two hypotheses as to how salmon find their way back to their natal streams might be these:

1. Salmon find their way back by using their sense of sight.
2. Salmon find their way back using their sense of smell (detecting dissolved substances from their birth streams).

Hypotheses are formulated on the basis of prior knowledge, and we know that fish both see and smell. The hypotheses just stated were rather obvious possibilities, but the formulation of hypotheses may be very difficult. The observations for which an explanation is sought may be a very strange (divorced from ordinary experience). Sometimes a hypothesis may be formulated that seems very good because it is compatible with almost all of existing knowledge, but not all of it. In that case, we must consider that the hypothesis, however attractive, may be wrong or that some of the accepted knowledge is wrong.

The next step in strong inference is to test the hypotheses. That is done by deliberately subjecting them to jeopardy, that is, by attempting to demonstrate their falsity. In our fish story, each of the two hypotheses has logical consequences that give rise to predictions as to the outcome of certain experiments. The hypotheses and the predictions are often stated together in if…then… statements. It is very important to make these statements explicit. Such a formulation applied to our example may be “if salmon find their way back using their sense of sight, then salmon with shielded eyes (black plastic discs were used in an actual experiment) will predominantly fail to find their birth streams.” The salmon did, in fact, find their way back in experiment, and the hypothesis was thus considered to be false. The alternative was tested after formulating the statement “If salmon find their way back using their sense of smell, then salmon with a blocked sense of smell (benzocaine ointment was used) will predominately fail to find their birth streams.” This prediction came true, and the second hypothesis was regarded as supported, but not proved.

The Impossibility of Proof

The problem is that even false hypotheses may sometimes give rise to correct predictions. For example, consider the false hypothesis that salmon find their way back to their birth streams by the sense of sight. This gave rise to the prediction that sightless salmon will predominantly fail to find their birth streams. This prediction turned out to be incorrect in the experiment cited earlier, but conceivably the prediction could have been correct. Suppose blindfolded salmon were so traumatized by the blindfolding operation that they did not try to return or that they became so confused without their sight that they ignored their sense of smell and swam off randomly from their release site. In such cases the prediction would have been correctly fulfilled. Is the hypothesis in that case “proved?” Certainly not, though the investigators may claim support for their sight hypothesis if they failed to observe the trauma or the confusion.

A logical truth table presented by Baker and Allen, and others, shows the relationship.

According to the table, an incorrect prediction always corresponds to a false hypothesis, but a correct prediction can come from either true or a false hypothesis. Because of these relationships, hypotheses are often regarded as potentially disprovable (falsifiable) but rarely proveable. How then do some hypotheses come to be regarded as true?

A hypothesis is supported, but not proved, when repeated attempts to negate the hypothesis fail, when competing hypotheses are discredited, and when additional facts (not used in the initial development of the hypothesis) are successfully embraced by the hypothesis.

In the case of the fish, the smell hypothesis withstood an opportunity for disproof, and the competing sight hypothesis was disproved. Still, the smell hypothesis is not proved. Perhaps smell plays no role, and a third sense is the key. Perhaps the benzocaine treatment so traumatized the fish that they could not function properly, or perhaps the benzocaine knocked out the third sense. These worried lead to additional hypotheses, predictions, experiments, and facts.

Another way considering the general unprovability of hypotheses is that no hypothesis can be considered proved if an alternative hypothesis, that excludes the possibility of the first hypothesis and is equally compatible with the facts, is possible. Since we can never be sure that we have considered all possible hypotheses, proof remains unattainable.

Earlier, we stated that a hypothesis is a candidate explanation, not a candidate fact. The case of the salmon provides an illustration of the difference. Early on, people may have observed that the salmon in a particular stream were physically similar to each other and different from salmon in another, distant stream. A couple of hypotheses may be stated:

1. Only salmon of a particular body type are able to navigate a particular stream and that is why they look alike.
2. Salmon return to their natal streams to spawn and look alike because they are genetically similar.

The “fact” that salmon do return to their natal streams establishes the truth of the statement “Salmon return to their natal streams,” but this statement was a candidate fact, not a hypothesis, and the second hypothesis remains unproved.

The Uncertainty of Disproof

Although scientists often refer to the disprovability of hypotheses (as we have), we contend that disproof is uncertain also. The reason for this requirement for the prediction of logical consequences in the testing process, but we can never be certain that our predicted consequences are logical. As an example let’s return to one of our if…then… statements. “If salmon find their way back using their sense of smell, then the Red Sox will win the World Series.” If the Red sox failed to win, we should have concluded falsely, that the hypothesis was false.

The Red Sox example used a preposterously illogical prediction, but some illogical predictions are not so obviously illogical, and the problem is not trivial in some cases. Sometimes scientists disagree over the cogency of a predicted outcome, especially in complex situations where variables are hard to control (see The Triumph of Sociobiology by John Alcock [2001] for interesting discussions of some uncertainties and controversies). An outcome that constitutes adequate grounds for the rejection of a hypothesis for one investigator may be viewed as inadequate by another investigator. The problem of the illogical prediction can be illeviated by testing additional predictions and by the public critique of the methods and conclusions. (The initial stage of public critique is the expert “peer review” of scientific manuscripts prior to publication. See the Acknowledgement in this essay.) Despite the uncertainty of disproof, scientists accept the qualified use of terms such as “disproof”, “falsification,” and “negation,” but not the term “proof”.

The Concept of Theory

When a hypothesis has undergone very extensive testing, especially if the testing attacked the hypothesis from many different angels using independent lines of evidence, then the hypothesis may graduate to the status of theory or, together with other hypotheses and principles, become incorporated into a theory. A dictionary definition of theory is this:

Theory: The coherent set of hypothetical, conceptual, and pragmatic principles forming the general frame of reference for a field of inquiry.

The term theory implies that the component hypotheses are very likely to be true and that together are important and comprehensive. Theories, like well-supported hypotheses, give rise to predictions that are consistently correct, but in the case of theories the range of predictions is often wider than the range of predictions for hypotheses. Theories come to provide a conceptual framework for scientific thought. Some examples include The Atomic Theory, The Theory of Evolution, The Germ Theory of Disease, The Theory of Relativity, and The Quantum Theory. Despite their high status, theories are still hypothesis-like (perhaps we could call them metahypotheses), and as such they are necessarily vulnerable. That is, they must be testable, and potentially falsifiable.

Will Strong Inference Always Work?

Some issues that would seem to be accessible by strong inference remain controversial because of emotional involvement, inadequacy of definitions, or a variety of technical difficulties. For example, a few scientists and public policy makers refute to acknowledge that HIV is the causative agent of AIDS, and the causes, and even the occurrence, of global warming remain controversial.

For many people, science is not the only pathway to knowledge. For them, propositions may rest upon personal revelation or upon religious authority, to cite just two additional pathways to knowledge. For the faithful, faith propositions are considered to be truths, not hypotheses. With regard to the term hypothesis, believers and scientists are in agreement. In most cases, neither scientists (many of whom are religious) nor religious believers (some of whom are scientists) consider religious beliefs to be hypotheses; believers because they consider applying the term to religious teachings to be belittling, and scientists because the term hypothesis can be applied only to statements that their adherents are willing to subject to possible disproof.

Although not scientific, faith propositions are not necessarily in conflict with science, but they may be. A tenet of faith that cannot be accessed by strong inference because it is beyond the technical or epistemological scope of science is not in conflict with science. Examples include doctrines that claim consciousness in inanimate objects, a purpose to life, or rewards or punishments after death. Science cannot now address these propositions, although it may be able to do so in the future (formerly, only faith, not science, could address such issues as the cause of disease, the change of seasons, and the formation of stars).

Some faith propositions are clearly in conflict with science. A tenet of faith that can be accessed by strong inference may be, but is not necessarily, in conflict with science. The indigenous religion of Hawaii provides a fascinating case study. At the time of European discovery, Hawaiian society was encumbered by hundreds of taboos whose violation was though to ensure calamity for individuals and society (Malo, 1959). This religion disintegrated quickly as Hawaiians observed that Europeans (and Hawaiians influenced by Europeans) could violate the taboos and live to tell about it. The Hawaiian nobility quickly embraced the religion of the Europeans and ordered the destruction of idols and the abandonment of many taboos. The causes of this religious transition are complex, but the obvious conflict between reality and some of the faith propositions surely played a role.

A Summary of Strong Inference

1. Observed and inferred facts inspire a question.

2. The question inspires one (or preferably more) hypotheses. This is a creative process. Several hypotheses may be proposed, and they need not have a high likelihood of being supported, but a good hypothesis must be an explanatory statement that is testable.

3. The hypotheses are deliberately subjected to jeopardy (falsification) by, first, stating the logical consequences of the hypotheses. Statements in the form “if (the hypothesis), then (the consequences)” are useful.

4. Next, the accuracy of the predicted consequences are tested by the acquisition of new facts from experimentation, or observation, or from the body of known facts not already used to formulate the hypotheses.

5. Incompatibility between prediction and outcome leads to the rejection of hypotheses, and compatibility leads to tentative acceptance. In all cases, repeated incompatibility or compatibility from separate lines of testing is desirable.

6. The hypotheses, together with the facts and the record of the inferential process, are submitted to public scrutiny and may become accepted into the body of public knowledge.

7. An accepted hypothesis typically spawns the acquisition of more facts and the formulation of new hypotheses (perhaps by the critics of the old hypothesis). These ongoing exercises in strong inference may cause the revision or rejection of the accepted hypothesis.”

8. A hypothesis, or more often a collection of complementary hypotheses, may become incorporated into a theory.

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How Science is Done

Posted by allzermalmer on September 23, 2012

This comes from the book Biology 6th edition by Raven and Johnson. It is from page 7 to page 9.

“How do scientists establish which general principles are true from among the many that might be true? They do this by systematically testing alternative proposals. If these proposals prove inconsistent with experimental observations, they are rejected as untrue. After making careful observations concerning a particular area of science, scientists construct a hypothesis, which is a suggested explanation that accounts for those observations. A hypothesis is a proposition that might be true. Those hypotheses that have not yet been disproved are retained. They are useful because they fit the known facts, but they are always subject to future rejection if, in the light of new information, they are found to be incorrect.

Testing Hypothesis

We call the test of a hypothesis an experiment (figure 1.4). Suppose that a room appears dark to you. To understand why it appears dark, you propose several hypotheses. The first might be, “There is no light in the room because the light switch is turned off.” An alternative hypothesis might be, “There is no light in the room because the light bulb is burned out.” And yet another alternative hypothesis might be, “I am going blind.” To evaluate these hypotheses, you would conduct an experiment designed to eliminate one or more of the hypotheses. For example, you might test your hypotheses by reversing the position of the light switch. If you do so and the light does not come on, you have disproved the first hypothesis. Something other than the setting of the light switch must be the reason for the darkness. Note that a test such as this does not prove that any of the other hypotheses are true; it merely demonstrates that one of them is not. A successful experiment is one in which one or more of the alternative hypotheses is demonstrated to be inconsistent with the results and is thus rejected.

As you proceed through this text, you will encounter many hypotheses that have withstood the test of experiment. Many will continue to do so; others will be revised as new observations are made by biologists. Biology, like all science, is in a constant state of change, with new ideas appearing and replacing old ones.

figure 1.4

This diagram illustrates the way in which scientific investigations proceed. First, scientists make observations that raise a particular question. They develop a number of potential explanations (hypotheses) to answer the question. Next, they carry out experiments in an attempt to eliminate one or more of these hypotheses. Then, predictions are made based on the remaining hypotheses, and further experiments are carried out to test these predictions. As a result of this process, the least unlikely hypothesis is selected.

Establishing Controls

Often we are interested in learning about processes that are influenced by many factors, or variables. To evaluate alternative hypotheses about one variable, all other variables must be kept constant. This is done by carrying out two experiments in parallel: in the first experiment, one variable is altered in a specific way to test a particular hypothesis; in the second experiment, called the control experiment, that variable is left unaltered. In all other respects the two experiments are identical, so any difference in the outcomes of the two experiments must result from the influence of the variable that was changed. Much of the challenge of experimental science lies in designing control experiments that isolate a particular variable from other factors that might influence a process.

Using Predictions

A successful scientific hypothesis needs to be not only valid but useful—it needs to tell you something you want to know. A hypothesis is most useful when it makes predictions, because those predictions provide a way to test the validity of the hypothesis. If an experiment produces results inconsistent with the predictions, the hypothesis must be rejected. On the other hand, if the predictions are supported by experimental testing, the hypothesis is supported. The more experimentally supported predictions a hypothesis makes, the more valid the hypothesis is. For example, Einstein’s hypothesis of relativity was at first provisionally accepted because no one could devise an experiment that invalidated it. The hypothesis made a clear prediction: that the sun would bend the path of light passing by it. When this prediction was tested in a total eclipse, the light from background stars was indeed bent. Because this result was unknown when the hypothesis was being formulated, it provided strong support for the hypothesis, which was then accepted with more confidence.

Developing Theories

Scientists use the word theory in two main ways. A “theory” is a proposed explanation for some natural phenomenon, often based on some general principle. Thus one speaks of the principle first proposed by Newton as the “theory of gravity.” Such theories often bring together concepts that were previously thought to be unrelated, and offer unified explanations of different phenomena. Newton’s theory of gravity provided a single explanation for objects falling to the ground and the orbits of planets around the sun. “Theory” is also used to mean the body of interconnected concepts, supported by scientific reasoning and experimental evidence, that explains the facts in some area of study. Such a theory provides an indispensable framework for organizing a body of knowledge. For example, quantum theory in physics brings together a set of ideas about the nature of the universe, explains experimental facts, and serves as a guide to further questions and experiments.

To a scientist, such theories are the solid ground of science, that of which we are most certain. In contrast, to the general public, theory implies just the opposite—a lack of knowledge, or a guess. Not surprisingly, this difference often results in confusion. In this text, theory will always be used in its scientific sense, in reference to an accepted general principle or body of knowledge.

To suggest, as many critics outside of science do, that evolution is “just a theory” is misleading. The hypothesis that evolution has occurred is an accepted scientific fact; it is supported by overwhelming evidence. Modern evolutionary theory is a complex body of ideas whose importance spreads far beyond explaining evolution; its ramifications permeate all areas of biology, and it provides the conceptual framework that unifies biology as a science.

Research and the Scientific Method

It used to be fashionable to speak of the “scientific method” as consisting of an orderly sequence of logical “either/or” steps. Each step would reject one of two mutually incompatible alternatives, as if trial-and-error testing would inevitably lead one through the maze of uncertainty that always impedes scientific progress. If this were indeed so, a computer would make a good scientist. But science is not done this way. As British philosopher Karl Popper has pointed out, successful scientists without exception design their experiments with a pretty fair idea of how the results are going to come out. They have what Popper calls an “imaginative preconception” of what the truth might be. A hypothesis that a successful scientist tests is not just any hypothesis; rather, it is an educated guess or a hunch, in which the scientist integrates all that he or she knows and allows his or her imagination full play, in an attempt to get a sense of what might be true. It is because insight and imagination play such a large role in scientific progress that some scientists are so much better at science than others, just as Beethoven and Mozart stand out among most other composers.

Some scientists perform what is called basic research, which is intended to extend the boundaries of what we know. These individuals typically work at universities, and their research is usually financially supported by their institutions and by external sources, such as the government, industry, and private foundations. Basic research is as diverse as its name implies. Some basic scientists attempt to find out how certain cells take up specific chemicals, while others count the number of dents in tiger teeth. The information generated by basic research contributes to the growing body of scientific knowledge, and it provides the scientific foundation utilized by applied research. Scientists who conduct applied research are often employed in some kind of industry. Their work may involve the manufacturing of food additives, creating of new drugs, or testing the quality of the environment.

After developing a hypothesis and performing a series of experiments, a scientist writes a paper carefully describing the experiment and its results. He or she then submits the paper for publication in a scientific journal, but before it is published, it must be reviewed and accepted by other scientists who are familiar with that particular field of research. This process of careful evaluation, called peer review, lies at the heart of modern science, fostering careful work, precise description, and thoughtful analysis. When an important discovery is announced in a paper, other scientists attempt to reproduce the result, providing a check on accuracy and honesty. Nonreproducible results are not taken seriously for long.

The explosive growth in scientific research during the second half of the twentieth century is reflected in the enormous number of scientific journals now in existence. Although some, such as Science and Nature, are devoted to a wide range of scientific disciplines, most are extremely specialized: Cell Motility and the Cytoskeleton, Glycoconjugate, Journal, Mutation Research, and Synapse are just a few examples.

The scientific process involves the rejection of hypotheses that are inconsistent with experimental results or observations. Hypotheses that are consistent with available data are conditionally accepted. The formulation of the hypothesis often involves creative insight.

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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.”

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Facts, Constructions, and Hypothesis

Posted by allzermalmer on November 10, 2011

This blog will be about a chapter in Walter Terrance Stace’s book calledTheory of Existence and Knowledge. This blog will be based on chapter 7, which is called Facts, Constructions, and Hypothesis.  This chapter is also related to posts on the Construction of the External World, and you can read the first one here.

There were six constructions in constructing the external world. And of these six, they can be broken down into two.  These two are Unificatory Constructions and Existential Constructions.

Unificatory Constructions:  Of the six mental constructions we employed to create the external world, three of them fall under the term of Unificatory Constructions. The second, third, and sixth mental construction were of the Unificatory sort. Here’s all three of them.

2.) That the corresponding presentations of different minds are identical, and that there are not many universes, but only one.

3.) That the presentations of a mind may continue in existence unperceived by that mind, provided that some other mind perceived them.

6.) That the different senses we may perceive the ‘same’ objects, and that the worlds of the different senses are, in general, identical with one another.

The characteristic of these three, and Unificatory Constructions in general, are that they don’t postulate new existence, but reduce the number of existences. For example, we find that we have many different things, but we reduce them to a few things to connect all these things together.

The second construction will identify your purple with my purple. my world with your world, and the private worlds of all minds with one another. This helps reduce the multitude of worlds to one world. Instead of having as many worlds as minds, there’s only one world. From many to one, which is a reduction.

The third construction identifies my purple now with your purple in a later moment. When I look at something, I know it exists through experience. But when I don’t look at something, I don’t know that it exists. With the third construction, following the second, we know that there’s only one world and what I see is similar to what you see. When I don’t see something, but you see it, it still exists and is similar to what I would see when I turn to look at it. It reduces the many successive world to one.

The sixth construction reduces all the different senses to combine into one thing, which would be what we call objects. The bird gives me a visual sense, but this visual sense isn’t the same audible sense of the bird. Neither does the taste or smell. But we combine these different senses to the “same” thing. This reduces the many to one.

Unificatory Constructions rest on two principles.
(1.) Principle of Superfluous Existences: Existences that make no difference to either knowledge or practical activities, and may be treated as if they were non-existent; they’re irrelevant to the mind’s purposes, either theoretical or practical, they can be cut out of the universe.
(2.) They Can’t be Proved: They’re not facts, but serviceable fictions, and they’re not inferences from facts. One unificatory construction can serve as an inference from another construction, like the third construction is an inference from the second construction. One construction can serve as a premise to lead to another construction.

Existential Constructions: Of the six mental constructions we used before, three of them were Existential Constructions. They are as follows..

1.) The presentations of one mind bear to the corresponding presentations of other minds the relation of resemblance.

4.) That presentations may exist when no mind is aware of them.

5.) That there exists ‘things’ or ‘objects’, which are not identical with presentations; and that the presentations are ‘qualities’ of the ‘things’; and that the ‘qualities’ may change while the ‘things’ remain the same.

What is common to these three, and one of the characteristics of some of our mental constructions, is that the imagination will invent the existence of some fictions that aren’t given in experience or infered from experience. We try to model these existence off of our experiences, and they’re made out of the materials of experiences we’ve had. But this asserted existence is never actually experienced, and are presented in a hypothetical type of proposition (If…then).

When we make a hypothetical type of proposition when expressing the existence of something never experienced or inferred from experience, the antecedent is something that we can never perceive it’s existence. This antecedent existence is something that we can never experience, and wasn’t experienced in the first place or inferred from what was experienced in the first place. And these things are mental constructions, or fictions.

Unificatory Constructions and Existential Constructions were employed to help build the external world, and they had two things going for them at their basis. There were six mental constructions used, which broke into unificatory and existential, and it all served for simplicity and consistency.

The first, second, fourth, and sixth constructions were all done for simplicity. With the first, we decide to take other people having perceptions to our own. It’s simpler to think that they’re similar than dissimilar. Both are equally ‘true’ and workable for intellectual and practical action.

With the second, we decide to think that our perceptions are approximately identical and believe in one universe instead of many. This goes from many different worlds for different people, but they’re all part of the one world. The one over many carries some sign of simplicity.

With the fourth, we decided to think we think that things go on existencing when we’re not experiencing it. Instead of having one universe going out of existence when people aren’t experiencing it is, and then having a new universe when experincing it, the same one universe continues on when not experincing it.

With the sixth, we decide to say that all our different senses give us information on “thing”. The world of the different senses become unified. The world of the apple feel, apple sight, apple taste, apple smell, hear it.

The third and fifth construction served for another use besides simplicity. They were used for consistency. The mind created this theory of the common world, which went against the facts that contradicted the theory. Because there’s a difference between our various minds and experiences. The third and fifth construction reconcile the differences with the theory of the common world and get rid of the inconsistency with mental constructions.

“We find again and again in the history of knowledge repetitions of this procedure. The mind, having invented a construction for the purposes of simplification and convenience, meets with new facts which do not square with the constructed belief. It is forced either to retrace its steps,  abandon the ground which it has gained, and give up the construction or even the system of constructions (which may well constitute a large bloch of its scheme of knowledge), or, in order to avoid this, it is compelled to manufacture new constructions or systems of constructions which will reintroduce harmony and avoid contradictions. In this way human knowledge grows as well as by the accumulation of new facts and inferences.”

From the epistemological analysis already set up, there’s two different kinds of existence that should be recognized. It’s (1) factual existence and, (2) constructive existence.

Factual existence is the existence of whatever is, has, or will be actually perceived by any mind, at any time or place. An example is that the existence of the computer while it’s being perceived by you or anyone else is a factual existence. But more explicitly, the existence of a visual presentation called the “computer”, the touch of the thing called the “computer”, and etc, are factual existence. When we say that no one is perceiving the computer, we supposed by the mind to think that it’s still there, it is a constructive existence.

What is actualy being experienced is the factual, which means that having the visual experience of the computer, that has factual existence. But when not touching the computer, it is given a constructive existence. When not tasting it, it has a constructive existence. But we go to think that at all times, whether the computer is experienced or not, there is a ‘thing’ behind the experiences and different from them, and this  is a constructive existence.

The sun rising tomorrow has a factual existence, because it will be actually perceived. The existence of Thomas Jefferson is also factual, because he was perceived. And for epistemology, this is an important distinction between factual and constructive existence. “But for the purposes of all other knowledge it is essential to obliterate and forget it.”

Constructive existence consists of supposing that unperceived things go on existing like they did as when actually perceived. Thus, we have experience of the computer existing when being perceived, and project that type of factual experience into a realm of where we have no experience. Projecting perceived factual existents, into the unperceived constructive existents.

The distinction between constructive and factual existence has only importance for the theory of epistemology, and not with theory or pratice. We can easily go on thinking that the computer exists when we don’t perceive it. But what they are during times when not perceived or if they are, they have no difference to us as practical people. What matters is when it’s there when we turn to it, what else would matter as practical people?

This situations makes no difference to the knowledge of the computers. We know the method of the manufacture of the computers, chemistry, electronics, and physics of operation. Any conceivable knowledge have of the computer remains the same during unperceived existences.

“It is, as we have seen, a logical rule of the mind that it ignores and treats as non-existent superfluous existences, existences which make no difference of any kind either to theory or practice.”

From this, the mind ignores the distinction between factual and constructive existence. We come to lump together all existence together as factual, and this may be regarded as a Unificatory Construction. And the attitude of which the mind takes up in this matter must be regarded as ‘true’.

For the most part, our knowledge has been built on mental constructions. And if we admit this knowledge as knolwedge, and not as false, then we admit constructed beliefs as being composed of truths. So we must take it as true that there’s an independent external world, things exist when no one perceives them, your penny is the same penny as mine, the table you touch is the same as the one that I see. And this forms part of our admitted knowledge of the world.

“These propositions form a part of our admitted knowledge of the world. They are universally accepted as true. Unless we are to do extreme violence to all accepted standards of truth and to all acknowledge conceptions of knolwedge, we must also admit them to be true, and must frame our definition of truth so as to include them.

And these things apply to our common world knowledge. Now let’s consider scientific knowledge to be distinguished from common world knowledge, and we find a similar conclusion as we did common world knowledge (i.e. factual existents and constructive existents).

Scientific knowledge is also composed of mental constructions, like the common world. We should be reminded of the ‘hypothetical’ nature of science. But as has been pointed out earlier, the ‘hypothetical’ aspect is composed of constructions, e.g. atomic theory and electronic theory. If we regard scientific knowledge as true, then we admit that such truth includes constructions.  This admission does not mean that the theories are false.

“We have to take a broad view of knowledge, to regard it in something the same way as we regard the world of art. The world of art is a product of the immense labors of the human spirit. So is the world of knowledge. It has been constructed by countless minds working through countless centuries.”

Truth, therefore, is held to include those constructions which have been built into human knowledge and form permanent parts of it. But this seems to raise a problem: Constructions are fictions, and if all constructions are true, then this destroys the distinction between truth and falsehood altogether. What ever we imagine could claim to be truth, would seem to be allowable. But some constructions are true and some false. (Future blog)

Hypotheses can assert either factual or constructive existences. For example, I now hear a noise behind me, and I conjecture that it’s my cat. I turn around and see the cat doing something with bubble wrap. I conjectured that the cat was behind me doing something to make noises. It’s a hypothesis, and the verification of it was based on me seeing the cat behind me doing something that’s making the noises that I heard. This hypothesis asserts the factual existence of my cat. The cat isn’t a construction but a fact.

Now it’s true that the existence of my visual cat when not being seen is a construction. It could be further said to be true when I say “I believe that the noise is caused by my cat” is not a hypothesis but a construction. But my statement of belief was based on two parts. (1.) My general belief in independent external world existing whether I experience it or not, and  (2.) my belief that among objects of this independent world is my cat which is causing the noise. And once grant an external world, my guess at my cat making the noise is a hypothesis.

At one point there was an invention known as the ether of space, which at the time required to be carrier of the light waves. The ether of space was not only hypothetical, but it was also a construction. It was posited not only the existence of the external world, but it also posited the existence of a new unperceived object.

Hypothesis are as much concerned with factual existence as with constructive existences, and what is usually called the hypothetical nature of science should be called its constructive character.

The character of science is said to be hypothetical, but this can’t mean that all scientific knowledge consists in unverified hypotheses. Hypothesis cease to be hypothesis when it has been verified. It will become known as a theory or a fact. For example, we once found that orbit of Uranus was the way that Newton’s theory was, and we came up with the hypothesis that there was another planet which helped cause the Uranus to be the way that it is, and different from what we thought with Newton’s theory. We eventually came to find this new planet, and this new planet became a fact. So this doesn’t quite to be what is meant by science being hypothetical.

Does this mean science is only concerned with hypothetical propositions? But this seems erroneous. It’s true that science makes very wide use of hypothetical propositions, but they’re intended to advance towards categorical ones.

“Hypothesis is a method of seeking scientific truth. But the truth when found is in no wise hypothetical. Hypothesis is not the end at which science aims-as would seem to be almost implied by such a phrase as ‘the hypothetical character of science’-but merely a means towards its end. And its real ends are the attainment of categorical propositions.”

Let’s use an example, and one dealing with Einstein’s theory and the displacement of Mercury. Einstein frames a hypothetical proposition like this, “If the geometry of space-time is such and such, then the displacement of the orbit of Mercury will be so and so, and rays of starlight passing the limb of the sun will be bent in such and such angle.” We come to know the displacement of the orbit of Mercury, and the bending of the light rays is measured. These facts are found to agree with deductions of the geometry of space-time that was set forth in the hypothetical proposition. And the hypothesis to some extent has been verified. And the hope is to be able to give the categorical proposition ‘The structure of space time is such and such.”

Supposes the scientist has a hypothesis that says that the atom may be described with the characters of mathematical formula like X,Y,Z. It is taken that X,Y,Z is true, and then attempts to deduce known properties of matter as observed in our ordinary life and in experiments. If correct, it shows that hypothesis explains all relevant facts that have been discovered, and if no further tests then it’s probably true. But what is actually hoped is that it is proved true, as far as such proof is possible in science. It is hopped to give the categorical proposition of the nature of the atom actually given is by the formula X,Y,Z. If the hypothesis is proved wrong, then it is hoped to hit the right one and prove the nature of the atom is expressed by the formula of P,Q,R.

So it’s not strictly true to say that scientific knowledge is hypothetical. It aims at being categorical. But it seems that there’s an important truth that science is hypothetical, and that could be that it’s expressing the constructional character of science.

“The essential distinction, then, between hypothesis and construction is that the construction is always a pure creation of the mind, and the existence posited by it, if any, is always a constructive existence; whereas in hypothesis need not possess this character. The existence posited by it may be factual, as is the case with the rat and the planet Neptune. It is true that any hyothesis may sometimes also be itself a construction…So that some hypotheses are also constructions and posit constructive existences. But this is not essential to the character of hypothesis as hypothesis. The existence posited by a construction is always constructive. The existence posited by an hypothesis may be either factual or constructive.”

The results can be summed up as follows:

(1.) A fact is something actually perceived, with qualification that the mind which perceives or knows is itself also a fact.

(2.) Mental constructions are pure creations of the mind and to which no facts correspond.

(3.) Existences posited by hypothesis are either factual or constructive.

(4.) The method of science may be mostly the method of hypothesis, the nature of science truth is not hypothetical. But it’s nature is constructional. And this is probably what is meant to refer to the ‘hypothetical character’ of science.

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