This article sketches, and works to motivate, a controversial approach to Posterior Analytics II.19. But its primary goal is to recommend a novel solution to one particular interpretive aporia that’s especially vexed recent scholars working on Post. An. II.19. The aporia concerns how to understand the enigmatic "ē ek pantos" ( “or from all...”) in the genealogical account of foundational knowledge at II.19 100a3-9. Our proposed solution to the aporia is discussed in connection with a number of larger philosophical issues (...) concerning Aristotle’s theory of epistēmē. (shrink)

Aristotle contrasts episteme and doxa through the key notions of universal and necessary. These notions have played a central role in Aristotle’s characterization of scientific knowledge in the previous chapters of APo. They are not spelled out in APo I.33, but work as a sort of reminder that packs an adequate characterization of scientific knowledge and thereby gives a highly specified context for Aristotle’s contrast between episteme and doxa. I will try to show that this context introduces a contrast in (...) terms of explanatory claims: on the one hand, episteme covers those claims which capture explanatory connections that are universal and necessary and thereby deliver scientific understanding; on the other hand, doxa covers the explanatory attempts that fail at doing so. (shrink)

In Posterior Analytics 71b9 12, we find Aristotle’s definition of scientific knowledge. The definiens is taken to have only two informative parts: scientific knowledge must be knowledge of the cause and its object must be necessary. However, there is also a contrast between the definiendum and a sophistic way of knowing, which is marked by the expression “kata sumbebekos”. Not much attention has been paid to this contrast. In this paper, I discuss Aristotle’s definition paying due attention to this contrast (...) and to the way it interacts with the two conditions presented in the definiens. I claim that the “necessity” condition ammounts to explanatory appropriateness of the cause. (shrink)

This article offers a reconstruction of an argument against infinite regress formulated by Aristotle in Posterior Analytics I 22. I argue against the traditional interpretation of the chapter, according to which singular terms and summa genera, in virtue of having restrict logical roles, provide limits for predicative chains, preventing them from proceeding ad infinitum. As I intend to show, this traditional reading is at odds with some important aspects of Aristotle’s theory of demonstration. More importantly, it fails to explain how (...) his proof is connected to a defence of the existence of ultimate explanations, a connection that must be the case if I 19-22 is advancing a foundationalist way-out to a sceptical challenge raised in I 3. (shrink)

In this article, the author attempts to explicate the notion of the best known Talmudic inference rule called qal wa-omer. He claims that this rule assumes a massive-parallel deduction, and for formalizing it, he builds up a case of massive-parallel proof theory, the proof-theoretic cellular automata, where he draws conclusions without using axioms.

In Prior Analytics 1.27–30, Aristotle develops a method for finding deductions. He claims that, given a complete collection of facts in a science, this method allows us to identify all demonstrations and indemonstrable principles in that science. This claim has been questioned by commentators. I argue that the claim is justified by the theory of natural predication presented in Posterior Analytics 1.19–22. According to this theory, natural predication is a non-extensional relation between universals that provides the metaphysical basis for demonstrative (...) science. (shrink)

Three distinctly different interpretations of Aristotle’s notion of a sullogismos in Prior Analytics can be traced: (1) a valid or invalid premise-conclusion argument (2) a single, logically true conditional proposition and (3) a cogent argumentation or deduction. Remarkably the three interpretations hold similar notions about the logical relationships among the sullogismoi. This is most apparent in their conflating three processes that Aristotle especially distinguishes: completion (A4-6)reduction(A7) and analysis (A45). Interpretive problems result from not sufficiently recognizing Aristotle’s remarkable degree of metalogical (...) sophistication to distinguish logical syntax from semantics and, thus, also from not grasping him to refine the deduction system of his underlying logic. While it is obvious that Aristotle most often uses ‘sullogimos’ to denote a valid argument of a certain kind, we show that at Prior Analytics A4-6, 7, 45 Aristotle specifically treats a sullogismos as an elemental argument pattern having only valid instances and that such a pattern then serves as a rule of deduction in his syllogistic logic. By extracting Aristotle’s understanding of three proof-theoretic processes, this paper provides new insight into what Aristotle thinks reasoning syllogistically is and, moreover, it resolves three problems in the most recent interpretation that takes a sullogismos to be a deduction. (shrink)

I discuss an important feature of the notion of cause in Post. An. 1. 13, 78b13–28, which has been either neglected or misunderstood. Some have treated it as if Aristotle were introducing a false principle about explanation; others have understood the point in terms of coextensiveness of cause and effect. However, none offers a full exegesis of Aristotle's tangled argument or accounts for all of the text's peculiarities. My aim is to disentangle Aristotle's steps to show that he is arguing (...) in favour of a logical requirement for a middle term's being the appropriate cause of its explanandum. Coextensiveness between the middle term and the attribute it explains is advanced as a sine qua non condition of a middle term's being an appropriate or primary cause. This condition is not restricted either to negative causes or to middle terms in second‐figure syllogisms, but ranges over all primary causes qua primary. (shrink)