The Elimination of Metaphysics
The central thesis is that any genuine proposition must either be a tautology or be empirically verifiable. For Ayer all meaningful propositions must be concerned with empirical matters of fact or be purely analytic. If a proposition is neither analytic or empirical Ayer,
hold(s) that it is metaphysical, and that being metaphysical, it is neither true nor false but literally senseless.(LTL, p.9)
Literal significance is a property of a proposition in virtue of it being capable of being true or false, propositions that do not satisfy this criteria cannot be considered either true nor false. This has some rather drastic consequences, following Wittgenstein mathematics and logic are totally vacuous and consist of nothing more than a body of tautologies. All propositions regarding supra-empirical issues (e.g Theology, Ethics) are considered senseless. With Ayer also claiming that the verification principle can provide solutions to many of the outstanding problems of philosophy.
The Roots of Ayer's Positivism
Ayer see's the roots of Logical Positivism lying in the psychological empiricism offered by the British empiricists most notably David Hume, who wrote:
If we take in our hand any volume: of divinity or school of metaphysics, for instance; let us ask, Does it contain any abstract reasoning concerning quantity or number? No. Doe it contain any experimental reasoning concerning matters of fact or real existence? No. Commit it then to the flames: for it can contain nothing but sophistry and illusion. (Hume, Enquiry Concerning Human Understanding)
For Ayer 'this is but a rhetorical version of our own thesis that a sentence which does not express either a formally true proposition or an empirical hypothesis is devoid of literal significance?'(LTL, p.40). But Ayer differs from Humean empiricism in that his claim is not a psychological one (all ideas are derived from sense impressions) but rather it is based on a criterion of significance. Which seeks differentiate between the meaningful and sentences with no literal significance.
For Ayer the function of philosophy lies in the analysis and clarification of our language, providing definitions in use and clarifying troublesome concepts. This seems very anti philosophy but the whole field of knowledge is exhausted by the sciences and such role secures a place for philosophy in the scientific world. Ayer takes great effort to stress the analytic nature of philosophy holding that many of what are considered the great philosophers were mainly concerned with analysis.
The Verification Principle
The tool used in order to differentiate between meaningful propositions and those devoid of literal significance is the verification principle. The first formulation of the principle is stated as:
'We say that a sentence is factually significant to any given person, if and only if, he knows how to verify the proposition it purports to express - that is, he knows what observations would lead him, under certain conditions, to accept the proposition as being true or reject it as being false' (LTL, p.16)
Ayer then distinguishes between propositions that in principle verifiable and those that can be in practice verified. A proposition can only be verified in practice if one is in a suitable position to verify it. But this seems to rule out meaningful statements so Ayer introduces the concept of being verifiable in principle. A proposition is verifiable in principle if:
'I do know what observations would decide it for me, if as is theoretically conceivable, I were once in the position to make them.'(LTL, p.17)
What exactly does in principle mean for Ayer? Well Ayer offers up the example of the dark-side of the moon which had not been observed at the time of publication. A statement about the dark side of the moon would be literally significant if you could state how you might go about verifying such a proposition.
Strong Vs. Weak Verification
Ayer also sets out two notions of verification, propositions can be either strongly or weakly verified. Strong verification is only possible 'if, its truth can be conclusively verified in experience'(LTL, p.18) The class of propositions which can be strongly verified is relatively small. For example, general propositions such as 'arsenic is poisonous' cannot be conclusively verified, since such general propositions are designed to cover an infinite number of cases. This seems to lead to propositions only being strongly verifiable are ones concerning our direct phenomenal experience. It also seems to rule out propositions about the remote past can never seem to be strongly verified.
Propositions can be weakly verified 'if it is possible for experience to render it possible'(LTL, p.18). The notion of weak verification allows a much larger number of propositions to be literally significant. We can see the proposition arsenic is poisonous can be verified as experience can lead us to conclude that it is highly probable and it also seems to allow through propositions about the remote past to be meaningful if we can conclude it was probable for them to have occurred.
The Second Formulation
Ayer offers a second formulation of the verification principle in Language, Truth and Logic which somewhat differs from the first formulation offered in the book. A proposition that consists of an actual or possible observation is considered an 'experiential proposition'.
'the mark of a genuine factual proposition, not that is should be equivalent to an experiential proposition, or any finite number of experiential propositions, but simply that experiential propositions can be deduced from it in conjunction with certain other premises without being deducible from those propositions alone'(LTL, p.20)
This second formulation seems to address concerns about propositions not being possible verified without reference to other propositions. A proposition such as salt is soluble can be counted as an experiential proposition because together with other propositions, it allows us to deduce other experiential propositions.
Ayer addressed some of the terminological issues that were raised regarding the first edition in an Introduction to the 1946 edition. Propositions are clearly true or false but not all sentences express propositions. The criterion of significance seems to imply that these sentences express nothing and therefore are not literally significant. Ayer replies that we could avoid the problem by simply applying the verification principle to all sentences. But there is utility in talk about propositions.
Problems with the Initial Formulation of the Verification Principle
A more serious problem for Ayer is that the verification principle as outlined in the main text of Language, Truth and Logic is far too liberal. The principle can be shown to let patently metaphysical sentences through. Take this example:
S1: The Absolute Is Lazy
S2: If the Absolute is Lazy, this is white
O: This is white
Under this formulation S1 comes out as factually significant.
In the 1946 Introduction (now the Appendix in UK editions of the Book), Ayer reformulates the verification principle in order to avoid this problem. A statement is directly verifiable only when it is an observation statement and in conjunction with one or more observation statement it entails at least one observation statement that is not deducible from these premises alone. You can see how this avoids the Absolute is lazy example, as no observation statement is deducible from S1 or S2.
A statement is indirectly verifiable, when in conjunction with other premises it entails at least one directly verifiable statement which isn't deducible from the premises alone and these other statements do not include statements that aren't either analytic or directly verifiable, or capable of being independently verified. S1 is not indirectly verifiable as it is not analytic, verifiable or capable of being established independently.
But even this reformulation wasn't enough to establish the verification principle as a criteria for literal significance, as Alonzo Church pointed out.
S: Either (not-O1 and O2) or (O3 and not-N)
O1, O2, and O3 are observation statements and N is any statement whatsoever (for example the absolute is lazy)
S in conjunction with O1 entails O3, So S is directly verifiable