Atoms, complexes, and demonstration: Posterior analytics 96b15-25

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Abstract

There is agreement neither concerning the point that is being made in Posterior analytics 96b15–25 nor the issue Aristotle intends to address. There are two major lines of interpretation of this passage. According to one, sketched by Themistius and developed by Philoponus and Eustratius, Aristotle is primarily concerned with determining the definitions of the infimae species that fall under a certain genus. They understand Aristotle as arguing that this requires collating definitional predictions, seeing which are common to which species. Pacius, on the other hand, takes Aristotle to be saying that a genus is studied scientifically through first determining the infimae species that fall under that genus. This interpretation attributes to Aristotle a distinction between primary and derivative subjects. I argue for Pacius’s interpretation, defending it against Barnes’s objections.

Introduction

Like much of the philosophy of science presented in the Posterior analytics, APo. 2.13 96b15–25 is concise to the point of near unintelligibility. There is agreement neither concerning the point that Aristotle is making nor the issues that he intends to address.1 There are two reasons why the passage is so obscure. First, as in much of the APo., Aristotle uses technical language. But the terms that he uses have multiple senses, and there are not enough clues to clearly determine which sense any of them have. Second, the passage appears to be out of context. Again this is not unusual for the APo., much of which appears to be a sheaf of unrelated notes. But because the passage is so difficult, commentators have strained to find ways to link the passage to what is discussed in what precedes and follows: the hunt for definitions. As we shall see, what results is a family of interpretations that are endorsed by most commentators. I believe that these are mistaken. In the present paper I show why this is so, how the passage is to be interpreted, and why this is important.

I shall argue that most commentators are wrong in taking the passage to concern the use of the method of division to determine the definitions of the infimae species falling under a genus. Rather, Ross is correct in taking the passage to lay out the explanatory relations that hold among the definitions of simple subjects and those predicates that are demonstrated to hold of composite subjects, built out of the simple ones.2 In Goldin (1996) I have argued at length that the clarification of the relations between simple subjects, composite subjects, and their kath’ hauta sumbebēkota (demonstrable attributes) is a main theme of APo. 2.8–10. I have shown how Aristotle there distinguishes between simple subjects, which are the proper subject matter of the sciences, and derivative subjects, which are identified with the demonstrated attributes, which are studied by determining how they follow from the definitions of the simple subjects. I believe that the same point is being made here. The passage confirms the interpretation I have put forward of 2.8–10.

I begin by presenting an interpretation-free translation, and indicating the terminological ambiguities on which a choice of interpretation must rest. I then take up each of these points in turn, and argue for my interpretation. I then review without supporting argument what I take to be the gist of 2.8–10, and show how Aristotle is making much the same point here. I conclude with both a full translation and a paraphrase, which show how the text is to be understood.

Section snippets

APo. 2.13 96b15–25 is as follows:

The following translation steers clear of commitment on any controversial point, and as such is unintelligible:

When someone is dealing with a certain whole, one must divide the genus into the primary things that are atomic in kind. For example, one must divide number into triad and dyad, and then in this way one must try to get the definitions of them. For example, one must try to get the definitions of straight line, circle, and of right angle. After this,

1) What does Aristotle mean when he tells us that, when dealing with some whole, one must divide the kind under consideration into the primary things atomic in kind?

However we interpret the details of the passage, Aristotle is discussing how to ‘get definitions’ and ‘study attributes’. Definitions are the principles of demonstration. Hence at least part of what Aristotle is discussing is the securing of the principles of demonstration. Throughout the APo., Aristotle has stressed that different

An interpretation of this difficult passage must be assembled from these various options. It must meet the constraint of making one or more points consistent with the demonstrative theory sketched elsewhere in APo. Two more features of an interpretation would strengthen it. Aristotle ought to be making an interesting point, and the point ought to make some sense in its present context (though the Apo. is full of parenthetical notes that do not seem to be placed where they are for any clear

Among major commentators, Barnes alone has presented an argument against Pacius’s interpretation. He makes two points. The first misunderstands Pacius’s point; the second is successful against Pacius but not against my adaptation of Pacius’s account.

Barnes first focuses on point 1a. As we have seen, for Pacius the atoms are those infimae species on the basis of which other kinds are built, as all of the other numbers are built up from the dyad and triad. Barnes’s objection does not focus on the

I begin with what I take to be the Aristotle’s understanding of the distinction between simple and complex subjects studied by the sciences. I present this without supporting argument, for which I refer the reader to Explaining an eclipse.

Aristotle takes the objects of scientific understanding to be propositional, that is, they are expressed in logoi in which one term is predicated of another. Scientific understanding of a proposition comes about through showing how it follows syllogistically

Conclusion

I conclude with a rendering of 96b15–25 which supplies what Aristotle’s terse Greek leaves out, and presents the meaning of the passage as I understand it.

When someone is dealing with the whole body of facts dealt with by a science, one must begin by dividing the genus into the infimae species. For example, in order to approach the task of working through the science of arithmetic as a whole, one must divide the genus number into the species triad and dyad, and then in this way one must try to

Acknowledgements

I owe thanks to Arun Iyer for editorial help, to Richard Tierney for comments and discussion, and especially to an anonymous referee for this journal for suggestions and questions.

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