**CHAPTER IV OF
LANGUAGE,
TRUTH, AND LOGIC**

**CONTENTS OF LECTURE**

1 The synthetic *a priori*

2 Analyticity

Here we discuss: (1) the positivist dismissal of the synthetic
*a priori*, and (2) the positivist account of analyticicity.

Ayer characterizes analytic truths in this manner,

A proposition is *analytic* if and only if it follows
logically from a meaning characterizing definition.

If you want a good idea of what Ayer had in mind, think of your high-school geometry. You start with some very general definitions concerning point and line, etcetera, and then by following strictly logical reasoning you prove any geometric statement you want to prove. In Ayer's time, massive world-historical advancements in logic were beginning to be wrought such that something like this method was beginning to be fruitfully applied to all areas of mathematics (though many of its limitations of this method yet to be discovered), and the idea caught hold in other areas of thought.

Once Ayer gives the above characterization of analyticity, he needs to characterize the meaning-characterizing definitions and the logical inference rules. His (and other positivists') idea is that the logical deductive inference rules are guaranteed as valid in virtue of the meanings of words such as ``and,'' ``or,'' ``not,'' ``if - then,'' ``all,'' and ``some.''

Then, the initial definitions that corespond to (say in the case of Euclidean Geometry) the postulates of Euclidean geometry for example, are considered to be true in virtue of linguistic convention. The initial definitions are in some sense considered to be stipulative; they stipulate what we take the meaning of the terms occuring in the definitions to amount to.

Finally, Ayer has the task of trying to show how analytic truths such as these can be useful in our general theorizing about the world. For example, a lot of mathematics is part of our physical theories. If this mathematics is just the result of stipulating meaning of the mathematical terms by picking definitions and then following the logical consequence relation, it is very unclear why, say, calculus is such an intergral part in describing the world with physics.

Note that ethical judgments occur nowhere in Ayer's boxes. In Chapter 6 he argues that ethical statements are not even meaningful.

Also notice that scientific laws are now considered to be synthetic/a-posteriori by Ayer.

For Ayer the synthetic truths will be those which are not analytic, but are still meaningful by the principle of meaningfulness given above. This brings us to Chapter 5 of Ayer's book.