as a typical epistemological problem concerning the possibility of knowledge in general. This proof is not intended to provide a way out to the problem of infinite regress as it is usually conceived, i.e.
For a criticism of Lear’s position, see Scanlan (1983). Lear (1980, 15-34) describes this argument as a “compactness proof”.
A proper proof is offered only in APo I 19-22. In APo I 3, Aristotle states this foundationalist solution without presenting an argument in its favour. If 〈 Π, c 〉 is the complete demonstration of c, the set Π is finite because there is a subset of Π that contains only indemonstrable truths, from which the other premises in Π and, consequently, c are demonstrated. The philosopher prefers to deny the common assumption, held both by the sceptics and by the proponents of circular demonstration, that all scientific truths are demonstrable. In that case, however, if 〈 Π, c 〉 were the complete demonstration of c (in the sense we have just defined), c itself would be a member of Π, which is unacceptable for Aristotle (see APo I 2, 72b32-73a6). In APo I 3, Aristotle rejects a potential solution to this challenge, according to which demonstrations would proceed “in a circle and reciprocally” ( APo I 3, 72b17-18). If p i is not a member of Φ (the set from which it is demonstrated), every scientific truth would be demonstrated from different and more basic premises, which makes Π infinite and impossible to survey with thought ( APo I 3, 72b10-11).
Now, if each p i is itself demonstrable, there must be, for each p i, a subset of Π, Φ, such that 〈 Φ, p i 〉 would be the complete demonstration of pi. Let us say that the ordered pair 〈 Π, c 〉 is a complete demonstration in this sense, where Π is a set of premises p 1, p 2, …, p n and c is the conclusion the scientist intends to explain. If so, our scientific understanding of the conclusion would remain inaccurate or incomplete unless the demonstration takes the form of a complex argument in which the premises are themselves properly explained. Now, suppose that the categorical premises from which a given truth is explained require a causal explanation as well. a deductive argument that produces scientific knowledge, which means that its premises must reveal the causal explanation of the conclusion ( APo I 2, 71b9-19). Nevertheless, he does recognize the need to face a particular sceptical challenge in APo I 3. Aristotle does not present a systematic account of a broader concept of knowledge, nor is he interested in convincing sceptical readers of the possibility of knowledge in general. The main object of the treatise is ἐπιστήμη ἅπλῶς, as defined in APo I 2, 71b9-12, a distinguished kind of knowledge peculiar to expert scientists. Even though the Posterior Analytics (hereafter, APo) is concerned with ἐπιστήμη, commonly translated as ‘knowledge’, its doctrine can hardly be classified as an epistemology stricto sensu.
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