William Wians claims that he read my Knowledge and Demonstration: Aristotle’s Posterior Analytics. Unfortunately his review failed to spell out the content of my argument, despite the mention of the “string of assertions that might hang together well enough on their own terms”. Therefore I would like to provide this information.
My Knowledge and Demonstration has a very specific aim: it offers an alternative to the widespread interpretation which plays down the importance of syllogistic logic for Aristotle’s theory of knowledge. It attempts to show that the central position of syllogistic inferences in Aristotle’s theory of demonstration is a necessary consequence of the concept of knowledge underlying this theory. The five chapters of my book together with the conclusion form one long argument in support of this thesis.
The structure and aim of this argument are clearly presented in the introduction and in the opening paragraphs of each chapter. The length of my book, which Wians considers a shortcoming, is determined by its aim and argumentative structure. Each of the “dizzying number of topics” with which my book deals is a step in the argument that answers the question concerning the role of syllogistic logic in Aristotle’s theory of demonstration. As a result, my discussion of these topics is confined to substantiating the claims that lead to my final conclusion. Detailed discussion of the secondary literature is presented only when it is needed to support my argument. Knowledge and Demonstration is less ambitious than Wians expects it to be: it does not aim to provide exhaustive accounts of particular topics such as induction, intellect, mathematical objects, and Greek mathematics. Nor does it aim at any detailed account of the vast literature on these topics. I had hoped that by limiting the scope of my discussions of the secondary literature, I would make the structure of my argument more comprehensible. The absence of a description of this argument in Wian’s review may suggest that my book is not short enough.
Wian’s review focuses on my interpretation of Aristotle’s account of induction and intellect in the Posterior Analytics II.19. His treatment of this discussion ignores its role in the argument presented in the book. As I say in the introduction, the first two chapters deal with the question whether Aristotle’s account of the first principles accords with the formal structure of syllogistic inference. Its primary aim is to show that Aristotle’s hypotheses are predicative propositions of the form A is B and not existence claims as it is commonly held. My interpretation of Posterior Analytics II.19 paves the way for this discussion. It opens with a distinction between two senses of the term arche : one that refers to the intellect and the other to the immediate propositions that serve as the premises of demonstration. This distinction is introduced in order to answer the question whether Aristotle’s first principles are terms or propositions. I argue that the intellect grasps terms or, as Wians correctly says, the form of the thing, whereas the immediate premises are propositions formed on the basis of this intellectual apprehension but are not identical with it. The distinction between the intellectual apprehension of terms and the formation of the immediate premises has the advantage of rendering Aristotle’s account of first principles compatible with his theory of syllogism. As Wians does not present this discussion in its argumentative context, he overlooks this advantage.
Wians’ brief description of the last two chapters of Knowledge and Demonstration is unfortunately inaccurate. My fourth chapter is not aimed at discussing the discrepancy between Aristotle’s theory of knowledge and scientific practice. It aims rather to show that Aristotle’s treatment of the objects of knowledge accords with the underlying presuppositions of his theory of syllogism. These presuppositions are presented in my third chapter, where I show that Aristotle’s logic, unlike modern logic, is not based solely on truth values but also on the relations of subordination and coordination between syllogistic terms. The main evidence to this effect is found in Aristotle’s discussion of syllogisms from false premises, where Aristotle determines the conditions under which a true conclusion is to be drawn from false premises. In modern logic, by contrast, the truth value of a conclusion drawn from false premises cannot be determined. In chapter IV I show that Aristotle forms his account of mathematical objects in accordance with this notion of syllogistic entailment. My discussion of the relationship between the theory of demonstration and scientific practice is a corollary of my discussion of syllogistic reasoning and the object of knowledge. It shows that the discrepancies between Aristotle’s mathematical examples and Euclid’s proofs can be explained in terms of his conception of mathematical objects.
In contrast to Wians’ report, my fifth chapter is not aimed at exploring the difference between knowledge of the fact and knowledge of the reason why. As explained in the introduction, the fifth chapter examines the relationship between Aristotle’s concept of knowledge and the demonstrative procedure leading to this knowledge. It is in this context that I draw the distinction between perceptual and conceptual understandings. The main point of this distinction is in response to the question whether Aristotle’s theory of demonstration presents a theory of knowledge or a theory of explanation. Although Aristotle’s notion of episteme seems to be closer to our notion of understanding, I claim that it would be historically more adequate to interpret episteme as a conceptualization, attained through syllogistic inferences. This conceptualization leads from perceptual understanding, which is knowledge of the fact to conceptual understanding, which is knowledge of the reason why.
Wians misleadingly compares my attempt to construe Aristotle’s theory of demonstration in the light of his conception of substance to Richard McKirahan’s insightful account of predication. However, the linkage I suggest between Aristotle’s theory of demonstration and his conception of substance concerns not the theory of predication but instead the epistemic implications of his notion of substance. I argue that Aristotle’s notion of knowledge is developed as a counterpart to his theory of substance. According to Aristotle, knowledge of substances is attained through definitions. The theory of demonstration shows how a similar mode of cognition applies to the objects of knowledge, although these are syntactically and ontologically attributes rather than substances. Perhaps Wians’ treatment of this issue is due to his curious conviction that my book ends on page 130. My discussion of the relationship between Aristotle’s conception of substance and the theory of demonstration begins on page 143.
In the absence of a full and accurate presentation of its content, Wians’ evaluation of my book seems to represent a matter of taste. Wians prefers long books that approach ancient texts first and foremost from the standpoint of the secondary literature. My book, I admit, is short and based on different methodological assumptions.