Though I have given special attention to the issue of induction in other places , regarding the Baconian and even Humean understanding of the subject, A.J. Ayer’s discussion is just as equally interesting. Of course, though his attention to the subject is brief, A.J. Ayer’s discussion on the problem of induction in his notable book Language, Truth and Logic (1936) is something I want to draw a particular exposition over. To begin, Ayer defines the problem of induction as:
[ … ] the problem of finding a way to prove that certain empirical generalizations which are derived from past experience will hold good also in the future. 
Ayer suggests from the beginning that it is a “superstition” to regard natural science as logically unrespectable until philosophers have solved the problem of induction. In other words, the problem of induction isn’t (nor should it) be a real problem. The optimistic attitude Ayer has towards science is seen throughout his reevaluation of the discipline of philosophy, particularly rejecting the view that philosophers should be concerned with the matter of “first principles”, or (even) taking a “bird’s-eye view” of reality-as-a-whole.
However, before we go about a continuation of Ayer’s philosophic approach, in regards to Ayer’s idea of how we go about explaining things it is important to note his spirit of scientific methodology.
A.J. Ayer’s Empiricism
Ayer thought that a given theory must fit the facts; or, that any given method must fit a criterion under the framework of empirical testability. As Ayer states, “[t]he criterion which we use to test the guaranteeing of apparent statements of fact is the criterion of verifiability.”  He continues:
We say that a sentence is factually significant to any given person, if, and only if, he knows how to verify the proposition which it purports to express – that is, if he knows what observations would lead him, under certain conditions, to accept the proposition as being true, or reject it as being false. If, on the other hand, the putative proposition is of such a character that the assumption of its truth, or falsehood, is consistent with any assumption whatsoever concerning the nature of his future experience, then, as far as he is concerned, it is, if not a tautology, a mere pseudo-proposition. 
This is understood in light of Ayer’s previous commitment to the elimination of metaphysics as having no literal significance under the empiricist’s framework – although it should be noted (see Ayer 1952: 71) that Ayer considers himself to be advocating a “form of empiricism” since he sees philosophy as predominately a “logic of science” and distinctively analytic (see p. 46 and pp.71-72). Thus, Ayer’s position can best stated to say that he renders all a priori truths (e.g., truths of logic and mathematics) as analytic propositions, or tautologies .
All knowledge begins with sense-experience – though, as he recognizes alongside Kant, it does not arise from sense-experience (see p. 74) – and that “there can be no a priori knowledge of reality” . Thus, by the criterion of verifiability, Ayer only allows for two type of propositions:
- (1) Analytic Propositions: A statement that is purely definitional, or true by definition (e.g., a square circle is false).
- (2) Synthetic Propositions: A statement that is verifiable, or able to be confirmed by the senses (e.g., the chicken is raw).
With these two criterions, “no sentence which purports to describe the nature of a transcendent god can possess any literal significance” . It is why Nathan Nobis in his essay on Ayer’s ethical position suggests that “A.J. Ayer [ … ] advocated ethical emotivisms, non-cognitivist understandings of the meanings of moral terms and functions of moral judgments” . Ayer in his furthering of the criterion of verifiability not only attempted to do away with the supposed “literal significance” of metaphysical propositions, but also theological and ethical ones.
The Justification of Induction
Ayer goes on to say that the assumption that the problem of induction is a genuine problem rests on two ways of approaching it: attempting to deduce the proposition which one is required to prove by a
- (1) Formal Principle or
- (2) Empirical Principle.
Ayer regards (2) as begging the question, since “in the latter case one simply assumes what one is setting out to prove” . This is a respectably notable point, namely, that even as Ayer suggests himself, the solve the problem of induction – or account for the uniformity of nature – via empirical explanation is to beg the question. However, in respect to (1) Ayer suggests that it commits “the error of supposing that from a tautology it is possible to deduce a proposition about a matter of fact” (p. 49).
Formal propositions or tautologies according to Ayer carry no real meaningful content, so, any attempt as to deduce anything from them will ultimately fail . However, Ayer provides optimism to the case by suggesting that “the only test to which a form of scientific procedure which satisfies the necessary condition of self-consistency is subject, is the test of its success in practice” . In other words,
We are entitled to have faith in our procedure just as long as it does the work which it is designed to do – that is, enables us to predict future experience, and so to control our environment.
However, though Ayer admits that this does not give us a logical guarantee of its success, “it is a mistake to demand a guarantee where it is logically impossible to obtain one. (1952, 50) This may even be according to d’Espagnat 2007 consistent with a general realist perspective regarding the scientific overview. In his analysis, d’Espagnat identifies two key elements that realists tend to agree upon in some way or another :
- (1) The notion of reality per-se;
- (2) A representation we build up of independent reality.
In respect to (1), the hypothesis that we can “say something true” about this independent reality may at first sight seem like a kind of truism, but the fact that we have dreams “already convincingly shows” that this independent reality is quite far from actually being one. d’Espagnat goes on:
In fact the hypothesis in question is one of those that, like induction and so on, are quite often intuitively assumed true (and maybe rightly so) without being scientifically provable. To try to make it plausible is, of course, quite legitimate; [ … ] [b]ut it cannot be proved correct. 
-  You can see my post The Nature and Limitations of Science at https://philosophicaugustine.wordpress.com/2013/04/26/the-nature-and-limitations-of-science/
-  A.J. Ayer, Language, Truth and Logic (Dover Publishers: 1952) p. 49
-  Ibid., p. 35
-  Ibid.
-  Ayer writes on p. 77, “The principles of logic and mathematics are true universally simply because we never allow them to be anything else. And the reason for this is that we cannot abandon them without contradicting ourselves, without sinning against the rules which govern the use of language, and so making our utterances self-stultifying.”
-  Ibid., pp. 86-87
-  Ibid., p. 115
-  Nathan Nobis, Ayer and Stevenson’s Epistemiological Emotivisms (Croatian Journal of Philosophy, vol. IV, no. 10: 2004) p. 61
-  Ibid., p. 49
-  Ayer writes on p. 87, “tautologies, though they may serve to guide us in our empirical search for knowledge, do not in in themselves contain any information about any matter of fact.”
-  Ibid., p. 50
-  Bernard d’Espagnat, On Physics and Philosophy (Princeton University Press: 2006) p. 24
-  Ibid., p. 24, emphasis mine.