A.J. Ayer, answered from the texts and cited to the page.
Tautologies are propositions that agree with every possible distribution of truth and falsehood among the elementary statements from which they are constructed.1 Because they exclude no possible state of affairs, they say nothing whatever about the world; their content is, so to speak, zero.2 The simplest illustration makes this vivid: to be told that it is either raining or not raining is to be told nothing at all about the weather.3
Compare this with being told that it is raining, or even that it is not raining — both of those statements make a claim upon the facts, one that could be confirmed or denied by looking out of the window. The tautology makes no such claim; it is compatible with every condition and therefore rules out none. The propositions of logic are all tautologies in this sense, and if the reduction of mathematics to logic succeeds, so are the propositions of mathematics.4
This is precisely why they are necessary and certain: they cannot be confuted by experience because they make no assertion about the empirical world.5 They record our determination to use words in certain ways, and any denial of them would be self-contradictory, since the denial would itself presuppose the very conventions it was attempting to overthrow.6
This result disposes of Kant's transcendental aesthetic rather economically. Kant supposed that the propositions of geometry and arithmetic were synthetic — that they told us something about the world, specifically about the forms of our intuition — and that this explained their necessity. But if they are tautologies, they are analytic, not synthetic, and the Kantian apparatus becomes superfluous.7
The necessity belongs to them not because they track some deep structure of space, time, or mind, but because denying them would be self-stultifying. Tautologies are not therefore trivial in any pejorative sense. Their tautological character is often far from obvious, and the work of formal logic consists largely in bringing out implications that are concealed in what we already, in a sense, know.8
the meaning of the more complex statements which can be constructed out of them is constituted by the selection of truth distributions with which they agree or disagree.Logical Positivism, pp. 23–24
If, on the other hand, we are told a tautology, no possibility is excluded but they all remain open. Consequently, we learn nothing about reality from the tautology... Tautologies, therefore, are empty. They say nothing; they have, so-to-speak, zero-content.Logical Positivism, p. 155
It is raining (here and now) or it is not raining.Logical Positivism, p. 155
On this view, all the truths of logic are tautologies; and if Russell and Whitehead succeeded in their attempt to show that mathematics is reducible to logic, so are the truths of mathematics.Logical Positivism, pp. 23–24
the reason why they cannot be confuted in experience is that they do not make any assertion about the empirical world.Language, Truth and Logic, p. 83
We cannot deny them without infringing the conventions which are presupposed by our very denial, and so falling into self-contradiction. And this is the sole ground of their necessity.Language, Truth and Logic, p. 83
our view that the propositions of arithmetic are not synthetic but analytic leads us to reject the Kantian hypothesis that arithmetic is concerned with our pure intuition of time... they are without exception analytic propositions, or, in other words, tautologies.Language, Truth and Logic, p. 83
The only way in which they can add to our knowledge is by enabling us to derive one statement from another: that is, by bringing out the implications of what, in a sense, we know already.Logical Positivism, pp. 23–24