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.