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Truth suffers from too much analysis

Posts Tagged ‘Principle of Empiricism’

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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Positivism

Posted by allzermalmer on January 18, 2012

This blog will be based on a paper done by W.T. Stace. It was published in the philosophical journal Mind, New Series, Vol. 53, No. 211 (Jul., 1944), pp. 215-237. It was called Positivism.

During the time of writing this paper, there was a big movement in parts of Europe and eventually came to America, and it was Logical Positivism or Logical Empiricism. This group was known for the principle for which they became infamous and later collapsed. Stace says what he takes the principle to be, and calls it the Positivism Principle.

“A set of words purporting to express a factual proposition P is significant only if it is impossible to deduce or infer from it, in combination if necessary with other premises, some proposition or propositions (at least one) Q^1, Q^2, Q^3…etc., the truth or falsity of which it would be logically possible to verify by direct observation. If no such directly verifiable deductions from P are possible, then the set of words purporting to express P is non-significant, and P is not really a proposition at all, but a pseudo-proposition.”

Now there are some terms in that principle that would need to be clarified. These terms are “significant” and “meaning”. We, in our common speaking, talk of meaning of a sentence and meaning of a word. This will also deal with the difference between significant and meaning. The meaning of a sentence is called significance, because only a sentence can be true or false. The meaning of a word is called meaning, but words can’t be either true or false. This is because meaning of sentences is where the predicate of true or false apply, but those predicates don’t apply to single words like “red”. Sentences have significance, and words have meaning. This forms a big distinction from which the rest of the paper follows.

The difference between significance and meaning are based on a distinction within the genus of semantical meanings. So Stace shall be dealing with the semantical significance of sentences and the semantical meaning of words. And Stace will deal with “deduce or infer” as being a deduction or being a causal inference. So when we make the statement of “P”, it can hold the form of “P→Q”. This will help spell out some of the deduction and causal inference that is going on.

But Stace also quotes the Logical Positivist A.J. Ayer, as he states what is meant by the Positivist Principle.

“Let us call a proposition which records an actual or possible observation and experiential proposition. Then we may say that it is the mark of a genuine factual proposition…that some experiential proposition can be deduced from it in conjunction with certain other premises without being deducible from those other premises alone.”

There seems to be no clear distinction between A.J. Ayer and what W.T. Stace has said as well. And so what Stace would say would also seem to hold for the Positivism Principle.

The Positivism Principle seems to be of the same of the Verification principle, but there is some slight difference from when the original Verification principle was proposed. Schlick was one of the first to propose the Verification principle. Verification was meant to be direct and complete verification, which was the significance of a statement was the method of its verification. It had to be direct and complete verification. But such a principle makes universal statements to be insignificant. For to directly and completely verify a universal statement, you wold have to observe an infinite number of facts, which would have been of the past, present, and future, and all locations. And even singular statements about material objects would be insignificant sine the complete verification would also involve an infinite number of observations. Also, talk of the past wouldn’t be allowed for to be significant.

In order to escape some of these downfalls of what Schlick presented as the Verification principle, it was mean to soften it some, but keep some of the same points. Now, instead of complete and direct verification, the new principle allowed for indirect and partial verification. So we can verify the past occurrence of something by checking the present effect. And this is part of Carnap seems to mean with “testing” the proposition. Stace points out how we come to indirectly and partially verify something.

“What is now required in order to make a statement about the past significant is, not that the facts asserted in the statement should be themselves now observable, but that some of their effects should be observable (indirect verification). And what is required to make a universal proposition significant is not that all the facts which it asserts (an infinite number) should be observable, but that some of them should be observable (partial verification). These are the requirements which are embodied in the positivist principle as formulated in the first paragraph of this article.”

Now with the Positivist principle, and what was originally in the Verification principle which was later modified, seemed to be another principle. In other words, the Positivist Principle seems to be based on another principle. And now see what this other principle is would seem to help cast light on the Positivist Principle. This principle would be called The Principle of Observable Kinds:

“A sentence, in order to be significant, must assert or deny facts which are of a kind or class such that it is logically possible directly to observe some facts which are instances of that class or kind. And to observe some facts which are instances of that class or kind. And if a sentence purports to assert or deny facts which are a class or kind such that it would be logically impossible directly to observe any instance of that class or kinds, then the sentence is non-significant.”

Now let us use an example to see what this principle is trying to get across. Take “Napoleon crossed the Alps”. It is logically impossible for us to now directly observe this particular fact asserted in the sentence. This fact no longer exists, and so we can’t directly observe it. But this particular fact of Napoleon crossing the Alps is also part of the class of “men crossing mountains”, which we can experience. So the point becomes that we might not be able to logically observe all particular members of the class, but it is logically possible for us to observe some of the particular members of that class. Thus, the fact itself might not be observable but it is of the observable kind. This means that if the kind of thing said is unobservable, then we definitely can’t observe the particulars.

So the point becomes, “A sentence is significant if what it asserts or denies is the sort of thing which it is logically possible to observe, even if the particular instance in the sentence is such that it would not be logically possible to observe it.”

Now Stace will maintain that the Positivist Principle implies the Principle of Observable Kinds. But the Positivist Principle might not directly say it. But the Principle of Observable Kinds doesn’t seem to be what the Positivist Principle is saying, or what the Logical Positivist themselves maintain. There seem to be two differences between the two principles: 1. The principle of observable kinds introduces the notion of classes, while, on the other hand, the positivist principle says nothing about classes. 2. The Positivist principle makes use of the concept of indirect verification while the principle of observable kinds contains only concepts of direct verification or observation.

Now the Principle of Observable Kind is based on direct verification, and would seem to go back to that of the Verification principle that was given by Shclick. But this wouldn’t be correct to think that it goes back to the Verification principle. But the Principle of Observable Kinds does make a distinction from that of the Verifiability principle, which is based on that of classes.

“Suppose the proposition to be examined for its significance is P. Then according to the original principle of verifiability the facts asserted or denied in P must themselves be capable of being observed. What the new positivist principle says is that the facts asserted or denied in Q (the proposition or propositions deduced from P), must themselves be capable of being observed. It does not say anything at all about the observability or non-observability of the facts asserted or denied in P. It entirely ignores that question.

Now as was pointed out earlier, P can be replaced with P→Q. So P of the P→Q might not be directly verifiable by experience, or direct experience. But the consequence of it, which is Q, would be of the observable kinds. But now there is a divide between both principles, the original formulation and the later formulation that deals with indirect verification. And this divide is filled with the Principle of Observable Kinds. This is because the original formulation doesn’t state whether the facts stated in P must be observable. Nothing is said on this.

So what is the Positivist to say with this divide? “He ought to say, not that the particular facts asserted in P must be observable (this is what he wished quite rightly to avoid), nor yet that they may be of a wholly unobservable kind; but rather that the particular facts asserted in P, although they cannot be themselves be observed, must yet be of a kind of facts which other instances can be observed. And this is what the principle of observable kinds does say.” Thus, the Principle of Observable Kinds is implied by the new Positivist Principle.

The Principle of Observable Kinds seems to carry some of the same meaning of the Positivist Principle, but would seem to give more gain than that of the Positivist Principle. One of the reasons is that the Positivist Principle is based on the way of the propositions logical consequences, while the Principle of Observable kinds don’t seem to be worried too much about that.

Now A.J. Ayer makes a point in his book The Foundation of Empirical Knowledge, that we can have two different philosophers disagree over a certain point. So take that Philosopher A said that “We do not perceive the table or the chair, we only perceive sense-data which we believe to belong to a  table and a chair.” But Philosopher B says, “No, what we perceive is the actual table and the actual chair”. What Ayer says is that both philosophers disagree with the language, but they agree with the observations. They agree about the color, shape, weight, and about every fat which could possibly be observed. They agree about all possible observable facts, and there is no disagreement between these two philosophers on the facts. Thus, they both disagree over the language and not the facts.

But what do we say, in this position, when they disagree over unobservable facts? This seems to be something that Ayer might have overlooked, and is overlooked by the Positivist Principle.

“For instance, Philosopher A may hold the view that there is a “physical object”, X, which possesses intrinsic qualities which correspond to the perceived qualities of shape, size, color, smell, etc, but which are forever hidden fro us, so that we can never know anything about these intrinsic qualities except the fact of their correspondence to perceived qualities; and that this physical object X stands in a causal relation to our sense-data…Philosopher B may deny that any such object as X exists. He may say that the table or the chair simply is the collection of all the sense-data which (according to A) are caused by it. Thus both of them may admit the existence of the sense-data, and may entirely agree about all their characteristics, which means that they will agree about all the observable facts. But they will assert that they are in disagreement whether x exists or not. X, if it is a fat, is a fact forever unobservable These philosophers will therefore say that they are in disagreement about whether or not there exists an alleged unobservable fact. Mr. Ayer appears to have overlooked this in his argument.”

This seems to be one reason why the Positivist Principle would have many things listed as insignificant. It is more of a difference over language than it is over some actual fact. And thus, for the Positivist, it is only about a way of speaking than some actual facts. For they both contain the same observable kinds.

But now maybe the Positivist principle doesn’t rely on the principle of observable kinds. What might be the case if this isn’t so? Than although the facts stated in Q of P→Q are logically capable of being directly verified, then P itself might states facts which would be logically impossible to observe. And the Positivist principle seems to tell us that this might be the case. For Q tells us that it is observable, but it doesn’t say anything about the observability of P. And there seem to be two cases: (1.) Where P→Q is a deductive argument, and (2.) where P→Q is a cause and effect inference.

Case 1: If P→Q is a deductive argument, then either (A.) Q states some facts as P, either in whole or in part or (B.) Q states some facts or elements of fact which are not asserted in P. (A.) is the view that logical rules are rules of linguistic transformations. (B.) is the view that in the conclusion of a deductive argument there may be some element of fact that may be “new”, i.e. not “contained” in the premises.

If we accept (A.), then it is clear that if Q is of the observable kind then P will be of the observable kind as well. This is because Q states the same thing as P, but in different words. Thus, if Q is observable, then P would also be observable since P is just another way of saying Q. This means P is another way of saying observable kind, which is what Q did as well. Thus, the Positivist principle implies the Principle of Observable Kind.

If we accept (B.) then it doesn’t seem that we can rigorously prove that if Q states observables P must state observables. For p might conceivably be of a different kind from the facts stated in Q. But, what seems to be enough, is that the Logical Positivist themselves held to the linguistic transformations.

Case 2: If P→Q is a cause and effect inference, then it’s certain that facts stated in P cannot be unobservable if the facts stated in Q are observables. This is because inference must rest on a causal law. “The cause C will be the fact stated in P, while the effect E will be the fact stated in Q. For instance, P any state the fact that it rained five minutes ago, while Q states in effect of this rain, namely, that the ground will be wet now. But it is impossible that the causal connection between C and E can have been established except on the basis that E has been observed to follow C. Therefore C, the fact stated in P, must be an observable.”

Thus, from these considerations, it appears obvious that the Positivist Principle does rely on the Principle of Observable Kinds. And the Positivist Principle, if adopted because that is the definition for significance that they choose, it carries no real force. This is because they just freely choose this criterion while someone else can pick whatever else criterion they wish to use for significance. But if they wish for it to carry some meaning about it based on experience, it would have to be shown through some sort of experience. This would be be based on inductive generalizations.

Now we might wonder how did we arrive at this Positivist Principle. Stace has an answer on how he thinks that the Positivist derived their principle.

“I think it is almost certain that positivists believe that their principles are a development of the general principle of empiricism. They call themselves “empiricists”. And thus by implications they claim that, whatever evidence there is to support the general principle of empiricism is also evidence which supports them. They think that,although their position is in some way different from that of the other empiricists (such as Hume)- more “advanced” no doubt- yet it grows out of the same root as does the tree of empiricism., and that therefore the sap which nourishes that tree will also nourish them. This is a very interesting and also a very important claim. And I propose to examine it. the question is: Is positivism a legitimate development of empiricism, and are the grounds which support empiricism also grounds which support positivism?”

Now the Logical Positivist claim that they’re “empiricists”, but we might wonder what type of empiricist they are. They’re seems, in history, to be different types of empiricist, but they haven’t, as Stace says, made it clear what type of empiricists they are. But there does seem to be two different types of Empiricism. (1.) the doctrine that all knowledge is “based upon ” or “derived from” experience, and (2.) the doctrine that all “ideas” are “based upon” or “derived from” experience.

With the first kind, the meaning of the phrase “based upon” or “derived from” seem to be different in (1.) and (2.). With (1.) is that if any proposition is known to be true, it can only be so known because there is empirical evidence for it, or must be empirical grounds for it. John Stuart Mill brought this up and tried to use it to support that 2+2=4 is an empirical generalization and illustrates this kind of empiricism. The (2.) kind is based upon ideas, like that of a “centaur”. The idea is neither true or false. What happens is that we can break down our ides into some basic parts, or that our experiences are built up off of some basic parts like “blue”, “horse”, “human head”, and etc. This is like Hume saying that “complex ideas” are based on “simple ideas”.

It appears that the Principle of Observable Kinds isn’t based on the first type of empiricism. As Stace says, “For the principle of observable kinds professes to be a criterion, not of the truth of propositions, nor of ways of knowing them to be true, but of whether they have significance. But the first kind of empiricism has nothing to do with significance at all, and cannot so far as I can see have any bearing on that subject.”

For whatever the relaations between “being known to be true” and “being significant” may be, they are certainly not the same thing, since a proposition may be significant and yet not known to be true. A significant proposition may in fact be known to be false. The long and short of it is that the first kind of empiricism is a theory about the truth of propositions (more correctly about how their truth can be known) while the principle of observable kinds is a theory about the significance of propositions. And since the two theories are “about” different subjects, one cannot possibly follow from, or be legitimately developed out of, the other.”

Of the first kind of empiricism, which is about the truth of propositions, the Logical Positivist would have seemed to hold this position as well. And the position that they state is that a priori statements are analytic statements, which means they’re not “derived from” experience. This stance follows from the first kind of empiricism, but we’ve also noticed that the significance of a proposition isn’t based on the first kind of empiricism. And all a priori propositions being analytic would follow from the first principle.

Now take the second kind of empiricism. We might wonder if the Principle of Observable Kinds comes from the second kind of empiricism. David Hume, after all, does bring up something that would be similar to that of the second kind of empiricism, “from what impression is that supposed idea derived.” But the Principle of Observable Kinds doesn’t follow from the second kind of empiricism.

The second kind of empiricism dealt with “ideas” being derived from experience. But as was pointed out earlier, the Principle of Observable Kinds is based on sentence significance, and not word significance. The second kind of empiricism is worried about the ideas, like that of “red”. But it is only the sentences that make significance and not the words itself. The second kind of empiricism is strictly concerned from what those experiences come from, like “red”, “sweater”, “blue-jeans”, “tennis shoes”, and etc, but isn’t concerned with whole sentences. The Principle of Observable Kinds is concerned with only whole sentences, like “James wore a red sweater while also having some blue-jeans to match their tennis shoes.” That sentence carries significance.

So it doesn’t look like the Principle of Observable Kinds follows from empiricism as well, in either kind. Thus, since the Positivist Principle seems to be implied by the Principle of Observable Kinds, the Positivist Principle seems to carry no weight when it comes to empiricism. Thus, those who call themselves empiricists and support the Positivist Principle don’t seem to have such a right.

The reason is that the principle of empiricism was stated by David Hume. The idea can be listed as the mind cannot spontaneously generate “simple ideas”, nor create them out of nothing, but has to derive them from “impressions”. These simple ideas would be those things that you can’t break down any further from your experience. For example, you have “red, “hot”, “cold”, “round”, “soft”, “sweet”, “loud”. From these unanalyzable, simple, building blocks, we can create different things from them by combining them in different ways. Giving some basic material, you can combine it in many different ways. But the basic idea is that you can’t create these simple ideas out of nothing, which means that you needed some impression of them.

The principle of empiricism implies nothing on how we form these simple ideas are to be combined into complex ideas. It provides no rules for combination. This means that we are free to combine the simple ideas in any way we would like, at least we have no rules on how to combine them, or at least according to the principle of empiricism. But there could be some laws, like the law of non-contradiction, or incompatible characters cannot be combined in the mode of spatio-temporal coincidence, though they can in the mode of spatial juxtaposition. This second idea is the Principle of Incompatibles. It basically states that the surface of a ball may be red and blue simultaneously if juxtaposed over one another. Also, we might have the laws of syntax to deal with how to combine our ideas. But the point is that none of these ideas follow from the principle of empiricism.

“The principle of empiricism concerns only the origination of simple ideas, nothing else. It tells us: no impressions,then no simple ideas. We may add as part of the principle, if we wish, the fact that certain of our ideas are not simple but are compounded out of simple ideas.”

But sentences are based on some ideas being placed in relation to one another in a certain way, or whatever way since the principle of empiricism does not care. Sentences, it seems, deals with complex ideas. So take a word to be symbolized like “F”. This word is composed of different simple ideas, like a certain color, shape, smell, taste, or sound, to go along with it. So all these different, simple ideas, can be symbolized as m,n,o,p,q. Thus, F=m,n,o,p,q. And sentences are composed of complex ideas which talk about the relations between something like A being B or A being related to B.

Thus, when empiricism isn’t concerned on how we form complex sentences, which is how we form our simple ideas together, it doesn’t imply the Principle of Observable Kinds because that principle relies on sentences or how complex ideas are to be put together. And this would also mean that the Positivist Principle isn’t implied by the principle of empiricism.

“What [the principle of empiricism] tells us is that if a sentence asserts or denies a fact F, which is a complex of a,b,c,d…, then each of these simples, a,b,c,d,…, must be an observable. But what the principle of observable kinds does is to assert that the total complex fact F, or abcd, must as a whole, be an observable. But for this there is not the slightest warrant in the principle of empiricism.”

The main point is that the Positivist have no right to claim to their principle of significance follows from empiricism. And that they’re constriction on propositions is arbitrary on it’s own, and has no standing in the principle of empiricism.

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