Book notes on Ayer

(Originally written September 10, 2006 in Book 8)

VII. 2 An Empiricist Critique of A priori Knowledge

AJ Ayer (1910 - 1989)
-Oxford University
-Argues against synthetic a priori knowledge because all supposed synthetic a priori truths are reducible to tautologies or as an analytical truths

This is a section from Ayer's early work: Language, Truth and Logic

How can empiricists account for necessary truths? Truths of empirical nature cannot ever be proven logically necessary. This, although appears to lead to utter skepticism, doesn't force one there. It is not irrational to hold beliefs that are not logical certainties; what is irrational is to search for certitude where there can be none and to demand certainty when probability will suffice.

The trouble empiricists face is dealing with necessary truths like mathematics and logic. The empiricist must deal with it in one of two ways:
1) He must state that they are not necessary truths and somehow account for their apparent universal nature.
Or, 2) He must state that they have no factual content and account for their truth, practical use, and surprising nature.

If one or two is unsatisfactory, then we are obliged to abandon empiricism and become rationalists.

Or if we opt out of rationalism we will have to adopt Kantian theory despite epistemological difficulties.

If empiricists show either 1) or 2) then, 'we shall have destroyed the foundations of rationalism'.

Mill adopted the theory that truths of logic and mathematics are not necessary truths. He held that these were inductive generalizations based on a huge amount of instances. The large number of instances was what Mill said made us think that they are necessary. He held that they were similar to empirical hypotheses, only much more probable.

Ayer does not think that this is at all acceptable. "In rejecting Mill's theory, we are obliged to be somewhat dormant" (Pojman, 371).

The Irrefutability of the Propositions of Mathematics and Logic

The truths of logic and mathematics are tautologies. If we state that any one is wrong then we contradict ourselves.

Any instance in which we think that we have an empirical situation that seems to refute a logical or mathematic truth we find error in our empirical judgment, not in the logical or mathematical truth.

The Nature of Analytic Propositions

Ayer gives an account of Kant's definitions of analytic and synthetic propositions, but contends that he does not succeed in making the distinction clear.

Kant does not give one straightforward criterion for making the distinction between Analytic propositions and synthetic propositions. He employs a psychological criterion for synthetic propositions and a logical criterion for analytic propositions and takes the criterions equivalence for granted.

Ayer defines an analytic proposition as one whose validity depends entirely on the definition of the symbols it contains; and, synthetic propositions when its validity is determined by facts of experience.

Analytic propositions never provide us any information about matters of fact. Thus, no experience can refute analytic propositions.

Analytic propositions therefore are devoid of factual content. They say nothing. "We are not suggesting they are senseless in the way that metaphysical utterances are senseless" (Jones, 382).

Linehan - Bitchsmack! Cheap shot. Though fairly strong. I admit that it stings.

Linehan - AJ Ayer has made me wary of synthetic propositions. Could I prove that there are only analytic propositions and everything is contained in the definition of the objects? i.e. The physical object 'apple'. An analytic judgment (Ayer's definition) would be that "This apple is an apple". A synthetic proposition would be "This apple is red". Could I reasonably argue (if I hold that there are forms) that the object apple in our mind is one that contains the notion of "red", "sweet/tart", "Grannysmith/other breed", etc. I don't know if I could make it plausible, but I am attracted to this theory.

Ayer - Analytic tautologies give us a way to explicitly state what we mean. It gives us clarification, but not any additional knowledge.

The Propositions of Geometry

While geometry seems the most plausible area for there to be a priori synthetic knowledge, the invention of non-Euclidean geometry has proven this wrong.

The self-evident principles of Euclidean geometry have been shown to be reducible to tautologies.

Geometry is not a study of space, though geometry can be used to reason about space.

Since geometry is analytic we can reject Kant's notion of space being synthetic a priori; since arithmetic is analytic we can reject Kant's notion of time being synthetic a priori.

We have a priori knowledge of necessary truths; they are all tautologies.

How can tautologies be surprising?

They are surprising because our intellects are not as superior as we believe they are.

Complex tautologies can easily surprise us because we are not as smart as we think.