Aristotle’s Posterior Analytics, I.4: Aristotle’s phrase “said of all” (kata pantos)
I would like to comment on this section (for the text, see “A” below) of Aristotle’s Posterior Analytics, I.4 by way of arguing that the truth conditions [see note (1) below] of Aristotle’s inferences, and especially their necessity, may be related to the four questions of Posterior Analytics, II.1-2. How this works will be clarified in what follows. If successful, this analysis will show exactly how the question of existence in II.1-2 is related to the question of essence.
Aristotle opens his discussion of conditionals and necessity with an account of what is meant by “said of all”. It should be made clear at the outset that when Aristotle says “said of all” in this context he really does mean to say that there are universals that hold absolutely, or as he says, not at one time but not at another (73a29). This is important to recognize since it allows for a clearer vision of how necessity will ultimately be related to Aristotle’s notion of essence and ousia. Indeed, as will become more apparent, ousia should be understood as based upon just such a foundation.
In this regard, much can be gleaned from taking a close look at Aristotle’s examples at the beginning of Ana. Post. I.4. Consider the following:
(a) If animal is in every case implied by man [kata pantos anthropou], [then] if it is true to say “this is a man”, then it is also true to say “this is an animal”…..
(b) …and if there is a point in every line, and so forth. (73a30-33)
Clearly, both examples follow a certain pre-established format: first (with regard to (a)) there is the universal claim (either B is said of A in every case, or all B’s are “in relation to” A’s, or better still, “imply” B’s (to translate kata)); then there is the conditional, “if p, then q” ( as above) [note 2 (see below)]; lastly, (now looking at (b) there may be isolated out from the second step the further stipulation that q must follow from the truth of p: p implies q iff p is true.
What Aristotle means by “said of all” in the first step has already been discussed above. The second two steps will prove more interesting. It is not merely the simple fact that one thing may be said of another in every case that interests Aristotle; it is rather, as I would like to point out, the existential ground of truth of such conditionals. This brings us to a discussion of the relationship between this text and Posterior Analytics II.1-2.
Posterior Analytics I.4, II.1-2, existence as a truth condition, and ousia.
Of particular significance for the purpose of comparing I.4 and II.1-2 is the fact that steps 2 and 3 immediately above require that that sort of conditional that will fulfill all the steps must be one that admits of modus ponens (note 3). In other words, q must follow from the truth of p. Only if p is true will q necessarily follow. If q will necessarily follow, it can be inferred that in terms of the modern truth table for conditionals, only the first line (T/T/T) will fit all of Aristotle’s steps. As will be seen further on, the deducibility of q from p fits nicely with the Aristotelian notion of ousia as a ground for predication.
Now, the next thing to consider is what it is that grounds the truth of q as necessarily following from p in the examples. The most obvious and best candidate is the existence of the subject of the antecedent: for only if a man exists can it be inferred that an animal must necessarily exist. The ground for necessity here is nothing more than the mere existence of the subject in question. In keeping with the classical characterization of the Posterior Analytics as being concerned with the “matter” of propositions as opposed to their form, one can see in the present case that nothing contemplated here would be considered in a purely formal discussion of conditional inference. Rather, we are, as was mentioned in the introduction, contemplating the ousia of things as a ground of necessity.
Now the link between existence (ei esti) and essence (or what answers to the question, “what is it?” or ti esti) can be made clear at this point as well as the connection with Posterior Analytics II.1-2 following a distinction: where the subject of the consequent clause is an attribute of the subject of the antecedent clause, it may be taken to be an essential attribute and as constitutive of the essence of the antecedent subject; where, on the other hand, the consequent follows based upon a cause-effect relationship (note 4), the relationship may be characterized as essential-accidental according to the third and fourth modes of perseity (note 5). Here of course, we are concerned with a subject-attribute relationship. Where modus ponens can be applied to such a relationship, there one may the attribute to be constitutive of the essence of the subject of the antecedent clause.
This insight may be applied to the four questions of Posterior Analytics II.1-2. The four questions, it may be recalled are: whether 1) A is a fact and 2) what the reason for that fact might be; one may also ask 3) whether a thing exists and 4) what the essence of the existent thing happens to be. Without the foregoing example and explanation, it might be difficult to see the full significance of the existential question (apart from the existence of God perhaps), or how such a question relates to the question of essence. It is clear how 1) and 2) are related; but it is less immediately apparent from the context of II.1-2 how 3) is immediately connects with 4). The foregoing discussion reveals the secret to this mystery (note 6). This is especially important since Aristotle never gives any clear example of such a relationship in Posterior Analytics II.8 where he takes up the subject of the relationship between demonstration and definition, but instead gives examples involving cause-effect relationships involving thunder and an eclipse. This analysis serves the additional purpose of providing this missing piece to the puzzle of the Posterior Analytics.
(1) For a brief explanation of the notion of what is “truth conditional” click here.
(2) A short explanation of mp is here
(3) An efficient-material as opposed to a formal/final causal relationship is meant here of course.
(4) To be taken up in successive essays.
(5) The analysis above can also be applied to Posterior Analytics I.x.
Text A: Since the object of pure scientific knowledge cannot be other than it is, the truth obtained by demonstrative knowledge will be necessary. And since demonstrative knowledge is only present when we have a demonstration, it follows that demonstration is an inference from necessary premisses. So we must consider what are the premisses of demonstration-i.e. what is their character: and as a preliminary, let us define what we mean by an attribute ‘true in every instance of its subject’, an ‘essential’ attribute, and a ‘commensurate and universal’ attribute. I call ‘true in every instance’ what is truly predicable of all instances-not of one to the exclusion of others-and at all times, not at this or that time only; e.g. if animal is truly predicable of every instance of man, then if it be true to say ‘this is a man’, ‘this is an animal’ is also true, and if the one be true now the other is true now. A corresponding account holds if point is in every instance predicable as contained in line. There is evidence for this in the fact that the objection we raise against a proposition put to us as true in every instance is either an instance in which, or an occasion on which, it is not true. Essential attributes are (1) such as belong to their subject as elements in its essential nature (e.g. line thus belongs to triangle, point to line; for the very being or ‘substance’ of triangle and line is composed of these elements, which are contained in the formulae defining triangle and line): (2) such that, while they belong to certain subjects, the subjects to which they belong are contained in the attribute’s own defining formula. Thus straight and curved belong to line, odd and even, prime and compound, square and oblong, to number; and also the formula defining any one of these attributes contains its subject-e.g. line or number as the case may be.