Two Dogmas of Empiricism: Conclusion

By Hanno

Quine argues that "our statements about the external world face the the tribunal of sense experience not individually, but only as a corporate body."(p. 41.) Individual sentences are part of, or implied by, whole theories, and the theories themselves are malleable. Quine cites Duhem as holding the same view. No sentence can be empirically falsified simply because other sentences in the theory can be altered to keep the sentence as 'true.' Let us suppose that we have a theory about how the planets move around the sun, and let us suppose that we predict to see planet x at a particular point in the sky at some time t. We then run the experiment, and discover that the planet does not appear where we thought it would. Is the sentence "planet x at a particular point in the sky at some time t" false? If the positivists are right, the answer must be 'yes.' But maybe the problem is not with the claim about where the planet will appear, but about how light behaves. Then the planet really is there, but we are seeing it in a different place. Science is actually full of just these kinds of examples. Indeed, maybe the observation itself is poorly made. We can even throw out the apparent observation when it conflicts with deeply held theories. In fact, we do so all the time.

On quines view, our theories about the world are radically underdetermined by the data, so that multiple theories explain and predict the same data, whether the theory is about science or history. As he puts it:

"The totality of our so-called knowledge or beliefs, from the most casual matters of geography and history to the profoundest laws of atomic physics and pure mathematics and logic, is a man-made fabric which impinges on experience only along the edges.... the total field is so underdetermined by its boundary conditions, experience, that there is much latitude of choice as to what statements to re-evaluate in light of any single contrary experience. No particular experiences are linked with any particular statements..."

He continues:

"Even a statement...can be held to be true in the face of recalcitrant experience by pleading hallucination or by amending certain statements of the kind called logical laws."

Not only is any statement not falsified by any particular observation, no statement is immune from revision. Even the laws of logic are revisable. We can, for example, give up the law of excluded middle. Some think we should give up the law of non-contradiction. We play with the axioms of geometry, of set theory, and these changes effect the theorems that are then true or false. In short, just as there is no pure synthetic claim, there is no pure analytic claim , either, at least not in the way Kant and others imagines, claims that are true no matter what.

We posit metaphysical entities to account for what we see, like physical objects, and these are not reducible to experiences. The same is true of God and gods. Which metaphysics we adopt is a question for which theoretical framework accounts for our experiences better. But in principle, there is no difference between ontology and natural science.

If asked whether or not sets or numbers exist, Carnap writes that it depends on the linguistic framework we choose, that there is no matter of fact which determines which framework we ought to use. For Quine, the exact same is true of questions in natural science. And we choose our linguistic framework not on the basis of many different reasons, not merely experiential. Hence, conservatism, simplicity, explanatory power, etc., all help choose which theory, and hence which ontology we accept.

Two Dogmas: Reductionism

by Hanno

The second dogma of Empiricism is the view that language is reducible to sense experiences. The original dogma was that the meaning of a term is the copy of a sense impression associated with that term. Thus, one sees a shoe. That is an impression. Then one remembers what they saw, calling it to mind. That is a copy of an impression. The word 'shoe' then means the image called to mind when we think of a shoe.

This fell out of use when Frege convinced everyone that meaning is tied not to terms, but to sentences. The logical positivists then argue that the meaning of any sentence other than a tautology is the method used to verify the truth of that sentence, and that method will come to the occurrence of specific sense impressions. But can all non-tautologies be reduced to sense experiences? Most Logical Positivists assume the answer to be 'yes.' Carnap actually tries to show what such a view would look like, and Quine focuses his critique on Carnap's attempt.

Carnap's view was also a sketch, but a more thorough sketch than any so far. That is, most people assumed the dogma to be true, but Carnap actually tries to do the reduction. His working insight? Using space-time points, the backbone of science, where "quadruples of real numbers"were assigned to sense qualities according to preset rules. The most basic statement forms to which all other sentences were either reducible or nonsensical were "Quality q is at point instant x, y, z, t." If that sensible quality were not there, the basic sentence is false, and more complex sentences were to be built from those basic sentences. Quine argues, however, that "Carnap did not seem to recognize, however, that his treatment of physical objects fell short of reduction not merely through sketchiness, but in principle." Indeed, Quine writes, "... it provides no indication, not even the sketchiest, of how a statement of the form 'Quality q is at point instant x, y, z, t' could ever be translated into Carnap's original language of sense data and logic. The connective 'is at' remains an added undefined connective; the canons counsel us in its use, but not in its elimination." Simply put, we cannot understand the final reduction in the terms the Logical Positivist requires. Their standards of meaningfulness are so high, the best attempt to actually reduce language to sense data, to sense impression, fails, too. Reduction to sense data and logic cannot be the final word in meaningfulness. the only way to do so uses words that are not reducible to either.All the handwaving 'there must be a way to reduce language to experience!' turns out to be just dogma, unsupported beliefs assumed to be true.

Carnap, Quine writes, seems to have accepted this as well. In Carnap's later writings, the whole reductionist project is gone.

What does Empiricism look like without the Dogma? If individual sentences are not the bearer of meaning, what is? How can we understand all knowledge being tied to experience if reductionism is false? That and more next time.

Two Dogmas of Empiricism, part II for real

by Hanno

The best way to read the first part of 2 dogmas is as an attack on the metaphysics of intensions. Logicians make a distinction between the extension of a predicate and the intension of a predicate. Consider a predicate like 'has a kidney.' There is a set of objects which satisfy that predicate, and that set is the extension of the predicate. Some other predicates have the same extension, as, in the classic example, 'has a heart.' The set of objects which have a kidney is identical to the set which has a heart, so the extentions of both predicates is the same. But what it means to have a kidney is different than what it means to have a heart. The meaning of the predicate is called its intension.

So all analytic claims are claims which share not just extension, but intension, i.e. they share meaning. Thus the predicate 'is an unmarried male' and 'is a bachelor' share not just extentions, but meaning, too, i.e. intensions, and because of that the claim 'All bachelors are unmarried males' is an analytic claim. We saw how the Logical Positivists used the distinction between analytic and synthetic claims in their philosophical analysis. But they never show just what these intensions actually are, nor how we can tell when one predicate has the same meaning as another predicate. And as empiricists, this knowledge must either be through logic, or empirical. But Quine in essence shows it can be neither.

Quine exempts from his analysis all truly logical tautologies. Those are statements that are true under all interpretations, from a logical point of view. He also does not object to any explicit definition. So his objection applies only to non-explicit, non-logical assertions of analyticity.

Now the logical structure of 'All bachelors are unmarried men' looks something like '(x)[Bx>(~Mx.Nx)]', where '(x)' is read as 'for all x', and 'Bx' is 'x is a bachelor,' '>' is the material conditional, '~' is the negation, 'Mx' is 'x is married' and 'Nx' is 'x is a man.' Read in its logicese, For any x, if x is a bachelor, then it is not the case that x is married and x is a man.' But this is not a tautology, for we can plug in (interpret) B, M and N in such ways that make it false. For example, if 'B' is 'x is a bat,' 'M' is 'x flies' and 'N' is 'x eats nerf balls,' then the sentence says 'for anything, if it is a bat, then it does not fly and it eats nerf balls,' which is surely false, unless there is something about bats that, really, someone should have told me.


But then it is obvious that all bachelors are unmarried is not known or explained through logic. If not by logic, how? Surely we cannot know the similarity of meaning empirically. If they were known empirically, then we would not know them with necessity or with certainty. A dictionary follows how we use language, and the definitions contained document the meaning of words, but the dictionary could be wrong, and are not necessarily true, or else meanings could never change.

How do we know what the meaning of 'has a heart' is? Answer: only by its extension. But then intension is just a sham, it can carry no philosophical weight. The meanings of predicates are not some entity to be discovered or uncovered. Any knowledge we have of that meaning comes by pointing to the things that have the property, i.e. by exntension. It follows that we can get these radically wrong, as we point to all the red balloons, and say 'balloon.' Then someone points to a red shirt, and we say 'balloon.' We only know what we mean because we have pointed to similar things, but the number of similarities and differences are endless, so we do not know if we latch onto the right similarity, the right difference. So, too, with 'bachelor' and 'unmarried man.' We know these terms by generalizing over the instances we have seen, but we can always be generalizing over the wrong properties.

Except... if we operationally define our terms. If we let how we know whether something or is not of a certain type define that type. Then if the method of verification (or falisfication) is the same, we can know that the meaning is the same. This does not use intensions, but is acceptable by the logical positivists. But can we reduce language, reduce the claims we make in language, to its method of verification? The positivists always assumed the answer was 'yes.' Carnap does is best to show it in his master work, The Logical Structure of the World. But they were wrong to assume it, and Carnaps' works shows vividly why it is impossible. And with that, verificationism, or falsificationism, go out the window.

That story next.

Two Dogmas of Empiricism

By Hanno

T. Furman asked me to write up a description of the classic article "Two Dogmas of Empiricism" by Willard V.O. Quine, perhaps the greatest American born and bred philosopher. From Quine's first classic "Truth by Convention" in 1936 to a slew of classic articles in the '50's and '60's, Quine's work in philosophy and logic shaped a generation. Both of those articles contain criticism of one of the most powerful, lively and influential philosophical movements the Western world has seen, Logical Positivism. Developed by German thinkers in the 1920's and '30's, Logical Positivism had many roots, but contained a criticism of philosophy as it had been practiced before and during the 20's. A collection of like minded intellectuals gathered frequently in Vienna and were called "the Vienna Circle." Many of the thinkers opposed the rise of the Nazi's in Germany, and had to flee when the Nazi came to power both in Germany and in Austria. Some went to England, but many of the most influential went to the USA. These included Gustav Bergman, who landed in Iowa, where he taught two of my professors at the University of Texas, and Rudolf Carnap, perhaps the greatest of the lot, as well as a socialist and pacifist, landed at Harvard, where Quine also taught. Carnap had met Quine earlier, and had already formed a close connection. Quine's criticism of Logical Positivism focuses on Carnap's version. While good friends, they disagreed about many things, yet both influence the other's work, as each responded to the arguments of the other.

Logical Positivism has two primary components, and could only arise after developments in both science and logic. At its head is a belief in empiricism: that all knowledge is to be derived from experience. Empiricism had long had difficulties explaining our knowledge of mathematics. Knowledge of such necessary and universal truths were clearly not empirical. While Hume did not realize the difficulties empiricism faced, and so waved off math as simply being about relations of ideas, and hence simply part of logic, Kant pointed to some difficulties. Kant argued that sentences fall into one four categories based on a matrix of two by two: They are either analytic or synthetic, that is either made true in virtue of the meaning of the parts of the sentences as opposed to sentences which go beyond the content of the subject. In the sentence 'Tigers are mammals,' the subject 'Tigers' does not contain the predicate 'are mammals,' but in the sentence 'Bachelors are unmarried men,' the subject does seem to contain the predicate. We say, that's just what it means to be a bachelor. The other parameter of the matrix is that sentences are either known empirically or a priori. Experience tells us that things are such and such, but not that they must be. Anytime some necessary claim is known, they must be known independent of experience, because experience simply cannot ground necessity.

Math then is the first exception to empiricism for Kant: They are necessary truths, and hence known a priori, but they are also, he argued, not analytic claims. In particular, denying '2+2=4' does not create a contradiction, certainly not until you have a defintion for '2' or '4.' On the face of it, '4' does not contain '2+2.' Denying that the shortest distance between two points is a straight line similarly creates no contradiction, nor does the idea of a line contain 'shortest distance between two points.'

Frege showed, however, that this was the product of not understanding mathematics clearly. In particular, with a more powerful logical system together with naive set theory and clear definitions of what the number one actually is yields a system which answered Kant's problems. In doing so, Frege showed that you could conceive of arithmetic as merely part of logic, and that Hume was right in the end. Notice, Hume was not right, but simply asserting dogmatically, that arithmetic were simply relations of ideas. In the logic of his day, that simply was not true. There was no way to prove most of what mathematicians were studying using Aristotelian logic. Other thinkers soon followed showing that geometry could also be treated as a mere part of logic: Logic plus definitions yields all of math. Principal among these thinkers was Bertrand Russell, and the first effort at this was his classic: The Principles of Mathematics.

This then was one leg of Logical Positivism: Mathematics is simply a part of logic, and following Wittgenstein, logic does not give facts about the world, but simply describes our use of certain symbols. In other words, since mathematics does not describe any real truths, it is not a serious objection to empiricism. It is this view that Quine takes to task in "Truth by Convention."

The other side of Logical Positivism is empiricism. Actual questions about how the world is must be tried to experience. Now again, Hume had stated that the meaning of a word is the combination of sense impressions. Though Hume does argue for this claim, the argument is not very good. Indeed, his argument against the idea of 'cause' is a case and point: Hume argues that all words must be tied to sense impression to have meaning, and that cause is not tied to an impression, so that the word 'cause' has no meaning. But early he tells us that his view that all words are tied to sense impressions rest on an argument: show me a word that is not tied to an impression, and it is up to me, if my view is right, to show how it actually is tied to an impression. He proceeds to do just that with God, for example. By the time he gets to cause, his believe that the meaning of a word is a combination of sense impressions is dogma. There he declares that the word 'cause' is meaningless because there is no impression from which to derive the idea of cause, and hence the word has no meaning.

But it is dogma that is doing real philosophical work. Now Frege, in his work on logic, argued that the meaning of words is a red herring, that the real source of meaning was the sentence. Words only have meaning in the context of a sentence, and thinking of words as the primary barer of meaning creates confusion. You start to think that properties are real things, when in fact properties are incomplete ideas that become complete when in a sentence. Frege coached to "never ... ask for the meaning of a word in isolation, but only in the context of a proposition." (Foundations of Arithmetic). Wittgenstein accepts that, and the positivists also accept that as well.

No longer would it matter if each term in a sentence is tied to a sense impression, but whether the sentence as a whole is tied to experience. But to which experiences? That part the positivists differ, but the most memorable of them was the verificationist principle of meaning. This can be fleshed out in two ways, the first less specific than the second. In general, verificationism holds that a sentence is meaningful if and only if it is either a proposition of logic (a tautology) or if there is some sense experience which could lead one to accept it as true. For claims about the world, this is especially important, and they used this principle to banish bullsh*t from philosophy. If a sentence cannot in principle be verified by experience, then the sentence was not really a proposition at all, but a pseudo-proposition. It sounds like it says something, but it does not. So claims about causal connections are legitimate if there is some experience which would lead someone to accept or reject the claim, even if the idea of cause is not a copy of an impression. Other claims, like "The Absolute enters into, but is itself incapable of, evolution and progress," are meaningless. No one has the slightest idea what experience would lead one to accept such a claim.

But why would verificationism be true? The basic idea is that it is irrational to argue about things that in principle no reason or experience can show to be either true or false. That cleave is a chasm: either reason has something to say (and hence logic will clear the air) or experience has something to say (science) or the claim is meaningless, a pseudo proposition. Used in the hands of a master, this doctrine becomes an executioner's blade, slicing heads off.

What shows us that claims are meaningless, however, if neither reason nor experience can undermine it? Answer: if the meaning of the sentence itself is its method of verification! Then it follows that a sentence that has no method of verification, if not a tautology, is meaningless. And now you can see the work done by Logicism, the view that mathematics simply is a branch of logic: if that were not true, then math, too, would be banished as a pseudo proposition, something so wholly absurd, no one would accept it.

These are then the two dogmas of empiricism: that statements can be divided into analytic claims on the one hand and synthetic claims on the other, and that sentences mean their method of verification (or falsification).

Quine will show the second claim to be false. He will use that to undermine the first claim. And that will dull the edge of the executioner's axe.