Verification Principle: to be have meaning, a statement must either be (1) logically true or false in virtue of language alone or (2) (in principle) empirically verifiable as a result of sense experience, e.g. observation, with or without the use of instruments, experiment and the like.

Analytic/Synthetic Distinction: This distinction tracks the difference between (1) and (2) above.  Analytic propositions, e.g. “All bachelors are unmarried,” are true in virtue of language alone and their negations are self-contradictory. They don’t say anything about the world outside language and hence, unlike synthetic statements, are not “factually significant.” Synthetic statements, by contrast, make factual claims about the world outside of language, which can be confirmed or disconfirmed by sense experience. Kant’s characterization of the distinction may be in a rough and ready way intuitively correct but Kant was wrong in thinking that there are statements which are synthetic but a priori, in particular, truths of mathematics.

Hume’s Fork: “If we take in our hand any volume...let us ask, Does it contain any abstract reasoning concerning quantity of number? No. Does it contain any experimental reasoning concerning matter of fact and existence? No. Commit it then to the flames.” The idea is, if it isn’t (1) math or Ayer would add, logic understood in the broadest sense to include philosophical analysis or (2) science/common sense facts about the world, it’s trash. Math is problematic because it doesn’t appear to be obvious or trivial but we don’t want to chuck it (along with bad metaphysics, theology, etc.) so Ayer mounts a defense to show that mathematical truths, though not obvious or trivial, are indeed ultimately true by definition.

The Linguistic Turn: Philosophy properly done doesn’t, and can’t, compete with science, including psychology, or common sense since it isn’t about the same subject matter but rather is about language. It includes the analysis of scientific and ordinary discourse and the exposure of pseudo-problems arising from the misleading character of surface grammar which gives rise to bad metaphysics. The paradigm of philosophy as it should be done is Russell’s Theory of Descriptions: Russell exposes the misleading subject-predicate form of sentences involving definite descriptions which leads bad metaphysicians to assert the existence of non-existent objects and gives the correct analysis which allows us to avoid commitment to such items.

Rational Reconstruction: Most of the great philosophers of the past were not doing bad metaphysics most of the time but good philosophy and their claims can be rationally reconstructed as the analyses of various kinds of talk.

Phenomenalism: This is the doctrine that all empirical statements can be cashed out, without change so to speak, in terms of statements about experience (phenomena, “ideas”). Later in Language, Truth and Logic, Ayer will and rationally reconstruct and defend J. S. Mill’s phenomenalism—a model of how Great Philosophers who appeared to be doing metaphysics can be rehabilitated. Although Mill, misleadingly, talks about objects as “permanent possibilities of sensation” suggesting that he was talking about the nature of material things, his account can readily be reconstructed as the analysis of talk about physical objects into subjunctive conditionals about what observers would experience under appropriate conditions. Commitment to the existence of “external objects” wholly independent of experience is bad metaphysics.