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Truth suffers from too much analysis

Archive for November, 2012

Principles of William of Ockham (Occam)

Posted by allzermalmer on November 18, 2012

These are the basic principles of William of Ockham or William of Occam. This comes from

1. All things are possible for God, save such as involve a contradiction.

In other words, God can do (or make or create) everything which does not involve a contradiction; that which includes a contradiction is absolute non-entity. Ockham expressly bases this principle on an article of faith: ‘I believe in God the Father Almighty’. From this Ockham immediately infers a second principle which is encountered everywhere in his writings:

2. Whatever God produces by means of secondary (i.e. created) causes, God can produce and conserve immediately and without their aid.

Hence any positive reality which is naturally produced by another created being (not of course without the aid of God who is the first cause) can be produced by God alone without the causality of the secondary cause. In other words, God is not dependent on the causality of created causes, but they are absolutely dependent on His causality. This is stated in a more general manner:

3. God can cause, produce and conserve every reality, be it a substance or an accident, apart from any other reality.

Hence God can create or produce or conserve an accident without its substance, matter without form, and vice versa. In order to bring anything under the operation of this principle, it is sufficient to prove that it is reality or entity. These rules or guiding principles are theological in nature, as Ockham does not fail to emphasise. The following is, however, a scientific principle of general application:

4. We are not allowed to affirm a statement to be true or to maintain that a certain thing exists, unless we are forced to do so either by its self-evidence or by revelation or by experience or by a logical deduction from either a revealed truth or a proposition verified by observation. 

That is the real meaning of ‘Ockham’s Razor’ can be gathered from various texts in Ockham’s writings. [Nothing must be affirmed without a reason being assigned for it, except it be something known by itself, known by experience, or it be something proved by authority of holy scripture.’ and ‘We must not affirm that something is necessarily required for the explanation of an effect, if we are not led to this by a reason proceeding either from a truth by itself or from an experience that is certain.’]

It is quite often stated by Ockham in the form: ‘Plurality is not to be posited without necessity’ (Pluralitas non est ponenda sine necessitate), and also, though seldom:  ‘What can be explained by the assumption of fewer things is vainly explained by the assumpition of more things’ (Frustra fit per plura quod potest fieri per pauciora). The form usually given, ‘Entities must not be multiplied without necessity’ (Entia non sunt muliplicanda sine necessitate), does not seem to have been used by Ockham. What Ockham demands in his maxim is that everyone who makes a statement must have a sufficient reason for its truth, ‘sufficient reason’ being defined as either th eobservation of a fact, or an immediate logical insight, or divine revelation, or a deduction from these. This principle of ‘sufficient reason’ is epistemological or methodological, certainly not an ontological axiom.

The scholastics distinguished clearly between a sufficient reason or cause (usually expressed by the verb sufficit) and a necessary reason or cause (usually expressed by requiritur). As a Christian theologian Ockham could not forget that contingent facts do not ultimately have a sufficient reason or cause of their being, inasmuch as God does not act of necessity but freely; but our theological and philosophical, and in general ll our scientific, assertions ought to have a sufficient reason, that is a reason from the affirmation of which the given assertion follows. All created things can be explained ultimately only by a necessary reason, i.e. a cause which is required to account for their existence. For every creature is contingent. The guiding idea of Duns Scotus, to safeguard contingency (servare contingentiam), is present everywhere in the work of Ockham. We can formulate it as follows:

5. Everything that is real, and different from God, is contingent to the core of its being.

If we bear in mind these guiding principles of Ockham, then his philosophical work becomes intelligible as the effort of a theologian who is looking for absolute truth in this contingent world, viz. for truth independent of any of those thoroughly contingent worlds which are equally possible. He is a theologian who views the world from the standpoint of the absolute. Consequently he sees many truths which were called ‘eternal’ dwindling away in the light of eternity, which is God himself. The actual order of creatures remains contingents; the possible order of creatures is above contingency. Hence the tendency of Ockham to go beyond the investigation of the actual order, by asking what is possible regardless of the state of the present universe. What is absolutely possible can never be impossible; and in that sense statements about absolute possibility are always true and free from contradiction, and for that reasons are necessary. Thus the work of Ockham also becomes intelligible- and this is only the converse of the former viewpoint- as the effort of a philosopher who constantly remanded by the theologian in himself that he must not all any truth necessary unless it can be shown that its denial implies a contradiction.

 

 

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Eternal Recurrence: The Heaviest Weight

Posted by allzermalmer on November 15, 2012

“The Heaviest Weight What if some day or night a demon were to  steal into your loneliest loneliness and say to you : ‘This life as you now live it and have lived it you will have to live once again and innumerable times again; and there will be nothing new in it, but every pain and every joy and every thought and sigh and everything unspeakably small or great in your life must return to you, all in the same succession and sequence – even this spider and this moonlight between the trees, and even this moment and I myself. The eternal hourglass of existence is turned over again and again, and you with it, speck of dust!’ Would you not throw yourself down and gnash your teeth and curse the demon who spoke thus? Or have you once experienced a tremendous moment when you would have answered him: ‘You are a god, and never have I heard anything more divine. ‘ If this thought gained power over you, as you are it would transform and possibly crush you; the question in each and every thing, ‘Do you want this again and innumerable times again?’ would lie on your actions as the heaviest weight! Or how well disposed would you have to become to yourself and to life to long for nothing more fervently than for this ultimate eternal confirmation and seal?” The Gay Science 341

 

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Determinism and Predicting Machine

Posted by allzermalmer on November 13, 2012

This is a copy of the article Determinism and Predicting Machine by Daniel Gogol. It appeared in the philosophical journal Philosophy and Phenomenological Research, Vol. 30, No. 3 (Mar., 1970), pp. 455-456

“Determinism is sometimes thought to entail the theoretical possibility of total knowledge. A strongly deterministic position is, that all physical events conform to a set of laws, and that if sufficient data were given about the state of the universe at a given instant, the occurrence or non-occurrence of a given future event could be deduced from these laws. Related to this strongly deterministic position is the question of the theoretical possibility of building a machine to predict the future.

We present an argument whose outcome is that it is impossible for a certain type of predicting machine to exist.

Assume that a machine could exist, called machine M, such that there is some amount of time, t hours, and some distance, d feet, such that the machine would correctly answer any question given it as long as the question had a “yes” or “no” answer and was about the occurrence or nonoccurrence of a physical event within t hours and within d feet of the machine. Assume also that the machine’s answer would consist of some physical event occurring within t hours and within d feet. For example, it might be built to type “yes” or “no”, depending on the correct answer to the question.

Now suppose that the machine were asked the following question: “Will the machine M answer ‘no’ before answering ‘yes’, and at some time during the next t hours?”

Now since this is a question with a “yes” or “no” answer about future physical events occurring within d feet and within t hours, the machine will answer “yes” or “no” within the next t hours. But if it answers “yes”, then the correct answer is “no”, and if it answers “no”, then the correct answer is “yes”. Therefore, by assuming the existence of a machine with certain properties we have been led to a contradiction, so we must reject the existence of such a machine as a logical impossibility.

Of course, the philosophical implications of the impossibility of such a machine are sharply limited. The argument used does not show, for instance, that a machine could not be built which could deduce whether or not any given physical event would occur within 24 hours. But such a machine could not also have the property that it always provided the answer within 24 hours.

Also, our argument does not show that a machine could not be built to answer all but certain special questions, such as the one in our argument. but it would seem that if a complete set of physical laws did exist, such that the answer to all questions of a certain type could be deduced from a sufficient data, then a machine which provides the answers should be theoretically possible, so that the fact that it is not possible destroys some of the plausibility of the idea that such a complete set of physical laws exists. If such a complete set of laws does exist, then it is a “physical” impossibility to build a machine to collect sufficient data and make the necessary deductions fast enough to have the properties of machine M.

Our argument about machine M applies to other possible universes as well as our own, and in different possible universes machine M may be impossible for different reasons. We could divide possible universes into the following two classes:

(1) Those possible universes in which there does not exist a set of physical laws such that any given future physical event can be logically deduced if there is sufficient data about the present physical state of the universe.”

(2) Those possible universes in which there is such a set of physical laws, but it is a physical impossibility to build a machine with the properties of machine M.

 

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Why Science Doesn’t Invoke Metaphysics

Posted by allzermalmer on November 1, 2012

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

or

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

or

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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