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Gordon and Logical Positivism

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Modus Tollens Posted: Mon, Mar 8 2010 11:45 AM

In his essay The Philosophical Origins of Austrian Economics, David Gordon describes how Austrian economics arose in opposition to the German Historical School and then had to counter the logical positivism of the Vienna Circle. Gordon believes that the influence of logical positivism prevents most economists from accepting praxeology and Austrian economics. However, in my view, mainstream economists are often right to reject the Austrian school, particularly when its proponents turn their minds to matters of logic and philosophy. On such matters, Austrian economists too often do more harm than good, and taint good economics with bad philosophy. The section of the essay I wish to focus on is toward the end where Gordon discusses Mises' rejection of the verification criterion:

It is easy to see that Mises' reaction to the verifiability criterion would be the same. Praxeology arrives at truth by deduction. If someone wishes to define "meaning" so that the conclusions of praxeology are empirically meaningless, why should he care? To this an obvious rejoinder suggests itself. The logical positivists did not view their criterion of meaning as an arbitrary proposal, to be dismissed by anyone not sharing the Circle's affinities. On the contrary, they claimed that their position was well supported. Are they correct?

I do not think so. In point of fact, the criterion is worthless, since every statement comes out verifiable under it. Suppose that p is a non-controversially verifiable statement, e.g., "there is a chair in this room." Let us take q to be a statement logical positivists reject as meaningless. A good example is one that Rudolf Carnap held up to ridicule when he called for an end to metaphysics. He cited the following from Martin Heidegger's Being and Time (1927): "The not nothings itself." I shall not attempt to explain this: one can see why Carnap presented it as a paradigm instance of a meaningless statement.

Does the verification principle eliminate it? Surprisingly, it does not. From p, we deduce p or q. (This step is non-controversial.) Assuming that a logical consequence of a verifiable proposition is itself verifiable, (p or q) is verifiable. Further, if p is verifiable, then the negation of p is verifiable; this principle seems difficult to question. Now, consider this argument:

p or q
not -p
______
q

This argument is valid, and each of its premises is verifiable. Then, q is a logical consequence of verifiable propositions, and it, too, is verifiable. Clearly, if the verification criterion cannot eliminate "the not nothings itself," it is not worth very much.

Gordon rightly explains that if p is verifable, then p v q is verifiable. However, his claim that "if p is verifiable, then the negation of p is verifiable" is problematic; the negation of a verifiable proposition is not necessarily verifiable. Gordon argues that “this principle seems difficult to question,” so a charitable interpretation of the claim is that by p he is referring specifically to the proposition “there is a chair in this room.” Assuming this proposition refers to a sufficiently small, well lit room and relatively large, undisguised chair, both the proposition and its negation are verifiable. In contrast, if p referred to the proposition “there is a chair in the solar system,” then ~p would be unverifiable, since while an entire room may be observable, the entire solar system is not (at least not for the purpose of finding a relatively small object like a chair). Gordon asks us to consider this argument:

p v q, ~p |= q

But why? The verified statement in the above argument is ~p, so the verificationist has no business including the formula p v q among his premises. Without verifying p or q independently, p v q is unverified. Gordon seems to be under the impression that both p v q and p can be introduced as premises merely because they are verifiable. A verificationist, meanwhile, would maintain that only premises that have actually been verified (not those that are merely verifiable) are eligible. How might a verificationist have verified p v q to include it among his premises? If p v q has been deduced from the verification of p, then including ~p in the premises is merely a contradiction introduced by Gordon, and if p v q has been deduced from the verification of q, then the premise ~p is irrelevent, because q has already been independently verified.

Although I previous urged a charitable interpretation of Gordon, his later application of the same argument to falsificationism seems to betray a fundamental misunderstanding of logic:

A falsification criterion fairs no better. If p is falsifiable, then (p and q) is falsifiable. Once more, not-p should be falsifiable if p is, though Karl Popper has implausibly denied this. By an argument parallel with that for verification, we conclude that q is falsifiable.

Once more, he states, without qualification, that “not-p should be falsifiable if p is,” but the negation of an existential proposition is logically equivalent to a universal proposition:

~Ex[Fx] =||= Ax[~Fx]

According to Gordon, if p refers to the verifiable proposition “there exists a white swan,” then ~p is also verifiable, but the proposition “there does not exist a white swan,” is logically equivalent to “all swans are non-white.” Therefore, if Gordon’s argument were a valid “criticism” of either verificationism or falsificationism, then he has inadvertantly demonstrated that the universal claims of scientific theories can indeed by verified by observation; rather than undermining the logical positivist program, Gordon would have removed their longest standing obstacle: the problem of induction. Karl Popper's "implausible denial" was simply the application of standard textbook logic; Gordon merely erred by assuming that because the negation of his particular example of a verifiable statement (i.e. "there is a chair in this room") was verifiable, that the negation of all verifiable statements are verifiable--it seems that apriorists can commit the inductive fallacy too!

Gordon's argument is not valid. He betrays a funamental misunderstanding of quantitative logic and misrepresents his opponents' position. Austrian economics deserves better defenders than this, especially from its flagship instititution.

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I find this a little tough to follow...

what is happening here?

Lee Kelly:
p or q
not -p
______
q

is that p double negated ? 

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I apologise, that space between "not" and "-p" is an artifact of my copy-paste from the original source. It is simply not-p, i.e. the negation of p.

I rewrote the same argument lower down in a more symbolic form: p v q, ~p |= q. I wanted to stop using words like "or" for the disjunction and replace it with the symbol "v," because then it would be clearer when I was talking about two individual formulae instead of one, e.g. p or q (two individual formulae) and p v q (a disjunctive formula).

If the p were double negated, then Gordon's argument would be clearly invalid. As the case is, Gordon's little deduction is valid, but his use of it as a argument against verificationism is invalid, or so that is my claim.

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Lee Kelly:
In contrast, if p referred to the proposition “there is a chair in the solar system,” then ~p would be unverifiable, since while an entire room may be observable, the entire solar system is not (at least not for the purpose of finding a relatively small object like a chair)

I'm having trouble understanding the point you are trying to raise. My understanding of positivism is that it only deals with observable, empirical data and explanations. So saying something like 'the whole solar system', wouldn't be an observable and therefore not in the motif of positivism. The solar system could just be short hand for the combination of visible planets and stars but in essence is it not an abstraction? 

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AJ replied on Mon, Mar 8 2010 12:25 PM

Gordon:

p or q
not -p
______
q

Lee Kelly:
If p v q has been deduced from the verification of p, then including ~p in the premises is merely a contradiction introduced by Gordon, and if p v q has been deduced from the verification of q, then the premise ~p is irrelevent, because q has already been independently verified.

I believe your criticism in this sentence is right on target, and fatal to Gordon's argument as presented.

Of course, the whole exercise of trying to "eliminate" meaningless sentences is silly. If they're meaningless to you, they're meaningless to you - what more need be said? Why not also try to "eliminate" meaningless hand gestures as well? Meaningless pictures, meaningless combinations of musical notes, etc.

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does' X is verifiable' mean that particular person p1 could verify whether X if he had powers A,B & C and it was the case that X

or does X is verifiable, mean that there is no purely formal obstruction to anyone verifying whether X, if X

or does it mean something altogether else?

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Hi Andrew,

My point here is that while the negation of the verifiable proposition "there is a chair in this room" is also verifiable, this relation does not hold for all verifiable propositions. In some cases, the negation of a verifiable proposition is not itself verifiable, such as with the proposition "there is a chair in the solar system." While the proposition "there is a chair in the solar system" is verifiable, i.e. it is possible to observe a chair in the solar system, the negation "there is not a chair in the solar system" is unverifiable, since there is no way to observe the entire solar system at once for an object as small as a chair. By binding the proposition to a small space, like a room (as opposed to a star system), and to a relatively large object, like a chair (as opposed to a microbe), it is possible to create a proposition where both it and its negation are verifiable, but this relation does not hold for all verifiable propositions.

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Lee Kelly:
In some cases, the negation of a verifiable proposition is not itself verifiable, such as with the proposition "there is a chair in the solar system."

But to a positivist there wouldn't be such a thing as a solar system or it would only be a short hand term for a collection of viewable planets and stars. It is like atoms, some positivists don't believe in the existence of atoms and merely use them for short hand to remark about how an experiment would turn out.

Lee Kelly:
While the proposition "there is a chair in the solar system" is verifiable, i.e. it is possible to observe a chair in the solar system, the negation "there is not a chair in the solar system" is unverifiable, since there is no way to observe the entire solar system at once for an object as small as a chair. By binding the proposition to a small space, like a room (as opposed to a star system), and to a relatively large object, like a chair (as opposed to a microbe), it is possible to create a proposition where both it and its negation are verifiable, but this relation does not hold for all verifiable propositions.

Thus it would not be an empirical statement because one cannot witness the abstraction known as 'the solar system.'

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AJ replied on Mon, Mar 8 2010 12:34 PM

I'm going to have to echo Nir's questions: does verifiable mean (1) verifiable in principle, or (2) verifiable by "reasonable human capabilities," or something else? 

You (Lee) seem to be interpreting it as (2), but - for instance - "there is not a chair in the solar system" could be said to be verifiable in principle, like if we ever get near-instantaneous solar-system sweep-searching technology or something.

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AJ,

I agree that logical positivists erred by turning their criterion of verification into a criterion of meaning. It seems to have been an attempt to change the rules of rational discourse to banish beliefs and problems that the logical positivists disagreed with or weren't interested in. Dismissing all unverifiable propositions as "meaningless" effectively placed a bouncer by the entrace academia, with strict instructions to not let anyone pass who might disagree with the positivists on fundamental matters of philosophy and knowledge. It was an anti-rational development, because rather than confronting differing opinions head on in peaceable debate, it battened down the hatches and closed off criticism.

However, the criterion of meaning can be extricated from logical positivism with ease. One can still maintain that the criterion of verifiability be applied to seperate science from non-science, and absolute verification can be replaced by degree confirmation. Expecting all these associated philosophical errors to fall with the criterion of meaning is mistaken--each must be confronted in turn as opponents modify their position to past criticism.

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Andrew,

Many different varieties of logical positivism exist. In some extreme variants the very idea of the solar system might be rejected, though I do not believe that is the kind of positivism that many (perhaps some solipsists?) subscribe to. In any case, my example was intended to be illustrative. But even in the case of an extreme form of positivism like you describe, we merely need reduce the proposition from "there exists a chair in the solar system" to "there exists a chair"--with no reference to where or when.

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AJ,

Right, what is verifiable depends on knowledge and technology. For example, physicists can verify that a galaxy is moving away from us at a particular speed, but, of course, that verification is theory-laden, i.e. the truth of the verification is contingent physical theories about light, space, technology, and even our own eyes. This is simply to say that verification is fallible, because it is theoretical all the way down. However, for the purposes of my original argument, none of this of great importance (though interesting in its own right), since there I was concerned more with logic. In logic, we don't concern ourselves too much with our fallibility--we just assign truth-values to variables and see what follows.

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AJ replied on Mon, Mar 8 2010 1:06 PM

Right, keeping this somewhat on topic, I think you've discovered something fairly important. It's simply not favorable to have flawed counterarguments to Austrian theory.

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Lee Kelly:
we merely need reduce the proposition from "there exists a chair in the solar system" to "there exists a chair"--with no reference to where or when.

Again you are missing the empirical nature of positivism. 'There exists a chair"..where? in Platonic heaven? On Earth? In a room?

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Andrew,

A positivist can verify the existence of a chair by observing a chair. Perhaps, so far as a radical positivist is concerned, that chair (and himself) are all that exists in the universe, so that when he looks at the chair he sees everything. In any case, I understand what you're driving at, but 1) I think it is a bit of a straw man (though an interesting exploration of where positivism could lead), and 2) I think it's irrelevent to my argument. The propositions I expressed in English were merely illustrative, since my arguments could have been expressed in purely formal terms. Moreover, I chose to write statements about the existence of a chair to maintain continuity with Gordon's original essay.

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Lee Kelly:
A positivist can verify the existence of a chair by observing a chair. Perhaps, so far as a radical positivist is concerned, that chair (and himself) are all that exists in the universe, so that when he looks at the chair he sees everything. In any case, I understand what you're driving at, but 1) I think it is a bit of a straw man (though an interesting exploration of where positivism could lead), and 2) I think it's irrelevent to my argument. The propositions I expressed in English were merely illustrative, since my arguments could have been expressed in purely formal terms. Moreover, I chose to write statements about the existence of a chair to maintain continuity with Gordon's original essay.

Well correct me if I am wrong but your argument is that  we cannot verify the negation of verification in some circumstance, correct? We can verify that there is a chair in the next room but we cannot verify if there isn't a chair in the solar system because we cannot perceive the whole solar system. However according to Roderick Long, the method of positivism is that the 'meaning of a sentence is its method of verification.' Since we cannot observe the 'the solar system' meaning the actual, full length solar system, we can perceive planets but I don't think that is what you are discussing, then it is meaningless  since it cannot be observed. So the statement that 'we cannot verify that there isn't a chair in the solar system' would be a meaningless statement since one cannot observe the abstraction know as the 'solar system'. 

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AJ:

Gordon:

p or q
not -p
______
q

Lee Kelly:
If p v q has been deduced from the verification of p, then including ~p in the premises is merely a contradiction introduced by Gordon, and if p v q has been deduced from the verification of q, then the premise ~p is irrelevent, because q has already been independently verified.

I believe your criticism in this sentence is right on target, and fatal to Gordon's argument as presented.

Of course, the whole exercise of trying to "eliminate" meaningless sentences is silly. If they're meaningless to you, they're meaningless to you - what more need be said? Why not also try to "eliminate" meaningless hand gestures as well? Meaningless pictures, meaningless combinations of musical notes, etc.

I admit the symbols lost me in the OP.  But "meaningless" means no rationalization has been given.  To state:  'chair in room' is meaningful.  First off, the words are rational, meaning, knowing what a chair is and what a room is and even to know what is meant by "in" is rationalized.  It's not only observed.  There is thought put into this prior to observation.  If that is admitted, then there is an admittance of meaning attached to what is observed:  'chair in room'.  That's of the philosophic school of rationalism, and not of the school of logical positivism.

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Gordon's argument is not valid. He betrays a funamental misunderstanding of quantitative logic and misrepresents his opponents' position. Austrian economics deserves better defenders than this, especially from its flagship instititution.

I wouldn't make sweeping proclamations if I were you.

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Andrew,

A negated existential statement is logically equivalent to a universal statement, i.e. "there does not exist a white swan" is the same proposition as "every swan is non-white." That's all you really need to know.

In any case, a logical positivist can verify the existence of the solar system. If the solar system is defined as sol and its orbiting planets, then a logical positivist need only observe sol and its orbiting planets. He might even claim that he has verified (indirectly, perhaps) that no other planets exist, since he might verify the orbits of the planets and determined that no other major gravitational body is nearby. The specific standards of what counts as a verification in any instance differ among even non-positivists like myself; it is mostly a matter of convention within science. You seem to be more concerned with epistemological positivism rather than methodological positivism, but whatever the case, your comments so far have kinda missed my point (though interesting in their own right).

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Jon Irenicus:
I wouldn't make sweeping proclamations if I were you.
But then what is the internet for? :)

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Lee Kelly:
If the solar system is defined as sol and its orbiting planets, then a logical positivist need only observe sol and its orbiting planets.

That is what I was talking about before as 'solar system' merely being the shorthand for the collection of several planets and stars. 

Andrew Cain:

But to a positivist there wouldn't be such a thing as a solar system or it would only be a short hand term for a collection of viewable planets and stars.

The point is that you cannot view an entity called 'the solar system.' It is an abstraction.You can view Mercury, Venus, Earth, Mars etc etc  which when caballed together becomes the short hand term called 'solar system.'  Positivism is all about the viewable either directly or indirectly. So by saying that is there is a chair in the solar system you are either saying 'Amongst the cabal of planets that are loosely termed the solar system, there is a chair' or the statement is meaningless to the degree that it calls upon trying to view an abstraction which it itself is not observable. 

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Andrew,

The solar system is no more or less an abstraction than Mercury, Venus, Earth, and Mars. After all, we can view, in a single telescope shot, whole star systems no less than we can view planets closer to home. All observation is theory-laden, i.e. is an interpretation. It has all been cobbled together by millions of years of trial and error: evolution, tradition, science. The logical positivist who denies this ends up a solipsist, since it begins with the solar system, moves onto the planets, and soon they don't know whether their friends and familty really exist--we can no more observe the entire lives of our best friends than we can observe the entire solar system.

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Lee Kelly:
The solar system is no more or less an abstraction than Mercury, Venus, Earth, and Mars

Here is the difference. Can you observe 'the solar system'? Can you observe Venus? 

Lee Kelly:
The logical positivist who denies this ends up a solipsist, since it begins with the solar system, moves onto the planets, and soon they don't know whether their friends and familty really exist--we can no more observe the entire lives of our best friends than we can observe the entire solar system.

Again, we're discussing things that are observable. You can observe friends and family. I don't know of any positivist who thinks that the exist of a person depends on whether you are viewing them at every specific moment thus making it such a theory that if a person were to walk into the next room then they would cease to exist. 

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Lee Kelly:
The solar system is no more or less an abstraction than Mercury, Venus, Earth, and Mars.

'X is an abstraction'

a claim about the world that can be falsified?, that can be verified? one wonders............

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Lee Kelly:
All observation is theory-laden, i.e. is an interpretation.

How does a logical positivist observe these "theories"?  What do they look like?

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Andrew Cain:
Here is the difference. Can you observe 'the solar system'? Can you observe Venus? 

Yes, you can.

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scineram:
Yes, you can.

Yes you can to which?

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Andrew Cain:
Can you observe 'the solar system'? Can you observe Venus?
Yes. Astronomers can also look through telescopes and observe other star systems.

The transient arrangement of matter and energy we call Venus is no less an abstraction than the solar system.

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I'm grateful to Lee Kelly for his interesting criticism and hope I may be allowed to reply at this late date, as I have only now seen his post. 

Mr. Kelly notes, following Popper, that there are verifiable statements the negations of which are not verifiable.  "There is a black swan" is verifable, but "No black swans exist" is not, at least on some accounts of verification. No matter how long a black swan has failed to turn up, this does not prove that no black swan exists.  (I ought to say that this conclusion seems to me to depend on a constricted view of verification, but let this pass.)If one takes this point just as its stands, the logical positivist criterion of  empirical meaning at once collapses. Surely no one would wish to claim that the statement "no black swans exist" is meaningless, however unverifiable it may be.  In fact, the positivists did not want to say that such statements were meaningless; and it is only by proceeding as if they were verifiable that the positivist criterion can get off the ground. Otherwise, it eliminates many obviously meaningful statements. In a passage Mr. Kelly is kind enough to quote, I suggested that if a statement is verifiable, its negation is also verfiable. It would have been much better had I made explicit that the negation should be taken as verifiable, in the context of the positivist criterion of meaning.

Mr. Kelly seems to me entirely mistaken when he says "A verificationist, meanwhile, would maintain that only premises that have actually been verified (not those that are merely verifiable) are eligible." That isn't in fact the line verificationists took; when they responded to the argument I offered, which is by no means original with me but quite standard in the literature, they tried to come up with more complicated versions of the criterion that would avoid the problem. To confine meaningful stements to those actually verified would be absurdly to narrow the realm of meaningful statements.

Popper did not propose falsifiablity as a criterion of meaning; and the remarks I offered about falsifiablity apply only if, contrary to Popper, one did attempt to use falsifiablity for this purpose. Once more, it is only that a statement and its negation should be taken as meaningful, in the context of a criterion of meaning. In any case, his demolition of me leaves me unmoved. Mr. Kelly,is a devout Popperian and accordingly believes that Popper, following Hume, has uncovered a crucial flaw in induction. I do not accept this; and I find no problem in taking universal propositions to be verifiable. One has only to abandon the constricted view that   confines verification to universal enumeration.  I also do not think that positivists such as Carnap and Reichenbach who worked on inductive logic had as their principal. aim to refute Popper. To the contrary, they dismissed his views on the topic as eccentric.

I am happy to agree with Mr. Kelly that Austrian economics deserves better defenders than me.

 

 

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David Gordon:
I am happy to agree with Mr. Kelly that Austrian economics deserves better defenders than me.

Don't sell yourself short Mr. Gordon!

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David Gordon,

I had forgotten about this thread. In retrospect, my original post was too harsh and partly mistaken. I thank you for your thoughtful response. I even appreciate the "devout Popperian" jab, since it informs me of how I may be misunderstood. I agree with Popper more than most, that is true, and I am often frustrated with how his views are misrepresented. Perhaps this frustration is sometimes mistaken for devotion.

In any case, on the assumption that a statement and its negation must be verifiable for it to be meaningful, then we get the result you describe. Logical positivists assumed that meaningfulness would, like truth, be transmitted from premises to conclusion, and they were wrong. My incorrect interpretation arose from confusing the set of meaningful statements with its subset of statements that logical positivists accept as knowledge. Certainly, those who do propose falsifiability as an alternaitve criterion of meaning (Popper not being one of them) do fall into the same problem that you describe.

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Classy response Lee.

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