Aristotle’s four modes of perseity (Posterior Analytics I.4). Introduction (II) “said of all” as a criterion for necessary attributes.

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.

Preliminarlies 

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.

Aristotle’s four modes of perseity (Posterior Analytics I.4): Introduction (I)

[The reader may wish to read text A below before turning to the following remarks]

As a general introduction to Aristotle’s four modes of perseity, the first thing to be considered (other than where to find them (in Posterior Analytics I.4)) might be what their name indicates about the role they play in Aristotle’s system.

The basics

The phrase “modes of perseity” and the idea of one term applying to another “per se” comes down to us from medieval Latin sources as a rather accurate way to convey what was meant by Aristotle’s phrase “kath’ hauto”.  Both phrases express the concept of one thing applying to another “of itself”.  Aristotle means by this phrase to indicate a necessary relationship between two terms.  An example will serve to clarify what is meant here.

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Consider Aristotle’s phrase, “point belongs (of itself) to line”.  There are two ways to understand this phrase: in one way, the relationship does not seem to be a necessary one: for, (it might be said) there may or may not be a line for a point to belong to; but, if, on the other hand, Aristotle is taken to mean that if there does happen to be a line, one can infer that there is a point, the necessity of the one applying to the other becomes immediately apparent (since, by definition, lines are made up of points).  This relationship can (and should) be considered as a conditional:

If there is a line, then there is a point.

Notice that there are two clauses: an “if” clause and a ”then” clause.  For ease of reference, I will refer to these as “antecedent” and “consequent” respectively.

Now, it may be wondered in some corners whether a conditional properly applies to Aristotle’s text here.  On this point, notice that Aristotle himself sometimes speaks of the subject of the antecedent clause (“line”) as the “subject”, and the subject of the consequent clause (“point”) as what is predicated of the subject (cf. 73b6ff.).  Now, obviously, one cannot go around saying “a line is a point”. The phrase Aristotle regularly uses is “belongs to” to express the relationship he is after.    This relationship seems most clearly understood as a conditional relationship.  “Belonging to” really is not the same thing as “being predicated of”: a point may belong to a line but not be predicated of a line or a line predicated of a point.  The argument need not be complex to show what Aristotle very likely has in mind.  In view of the tendency to think of all such relationships as predicative ones (especially if one reads the texts in translation) it seems important to make this clear.  This phrase might even be better expressed as “belongs necessarily to” to hit squarely upon the type of relationship Aristotle wishes to highlight in this chapter. 

Metaphysical considerations about this relationship

With these points out of the way, it should also be said, by way of introduction, that necessity is here contrasted with belonging (to a subject) accidentally.  This contrast should remind the reader that what Aristotle has in mind as the ground of the kind of inference given above is ultimately the thing, the subject-ground (hypokeimenon) to which a given attribute is said to belong necessarily.  It is because of what a line is, for example, that it necessarily includes a point.  What might be called the “ontological” aspect of a thing (our understanding of its being in the world as a systematically structured being) is always intertwined with the logic of the terms presented.  The conditional above further exemplifies this perspective.

This point helps to bring out the way in which Aristotle understands the role of ousia in such contexts.  Aristotle would urge that when we consider the necessary relationships we may perchance discover in language, we must distinguish those that are genuinely indicative of an ontologically well-grounded relationship from those that are not (1).   Logical relationships that indicate necessary ontological  relationships should be set apart from those that might be considered as merely fortuitous connections of language (2).  Those of the former kind (such as appear in the example above) ought, moreover, to be evaluated with respect to their source, and that source is always the things themselves that act and are acted upon in the world.

If one asks what the grounding factor is in things that we are looking for when we attempt to discover necessary relationships, the Aristotelian response would be that it is ousia.  ousia  may be thought of as what it is in a thing that underlies the necessary connections among the things (including events) we hope to explain.  It is in this ousia of things that Aristotle hopes to discover what grounds the appearances of our experience for which we seek an explanation.  It is no longer the aim of the philosopher, at this stage in the development of scientific thought, to discover such explanations in “the gods”, for instance; rather, experience itself is meant to serve as the basis for its own explanation.  Far from being an “occult entity” of some kind, ousia seems most sensibly regarded as a way of describing a thing from an ontological point of view, of the kind discussed above.

To return to the distinction between what is necessary and what is accidental as it applies directly to I.4, it is only the truly necessary connections we might discover that indicate something about the “nature” of a thing that coincides with the notion of its having an ousia.  The modes of perseity have the function of clarifying what such genuine connections might look like when they are discovered.  They present a logical criterion for such connections that allows them to be joined to other bits of knowledge. (3)

Finally, it should be seen that the clarification of the role of ousia as a source of necessity is the underlying subtext of I.4.  What he has to say about it in I.4 is of great significance for Aristotle’s overall characterization of knowledge and of what it means to know something (4).  ousia is the ultimate building block of Aristotle’s ontology (here understood as a broader schema of the way in which the being of things in general reveal themselves to us in their systematic inter-relations).  Such an ontology will have its basis not in general ideas such as “substance”, or “quality”, or “quantity”, but in the being in the world of basic entities.  The conditional above illustrates this: the fact that whenever there is a line there is also a point indicates something necessary or essential about the structure of the being of a thing; the fact that it is true in every case indicates that the relationship is a systematic one that may be used to further characterize its relationship to other things in a regular, consistent way.  Such systematic relationships are the basis for what is meant by episteme in its braodest sense: the systematic arrangement of regular and consistent relationships that yield a body of knowledge, or a “science”.

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(1) Consider the first chapter of Aristotle’s Categories in this light.

(2) For example, “cat” and the kind of “cat” one might meet on the streets of Milwaukee happen to be connected by language, but the connection is not one that Aristotle would consider to be grounded in the ousia of a thing.  They are homonyms, two things that happen to have the same name, but are substantially different.

(3) For example, one bit of knowledge, that there is a line, yields another, that there must be a point.  From the fact that there is a triangle, one may infer the existence of a line and a point.

(4) More will be said about this in further posts, particularly about the way that existence and necessity tie together to yield ousia.

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Some texts for consideration:

A) The opening paragraph of Posterior Analytics, I.4: 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’ [ousia] 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. 

B) The opening chapter of Aristotle’s Categories, and the first remarks Aristotle makes on Substance (ousia) (see part 5):

Part 1 

Things are said to be named ‘equivocally’ when, though they have a common name, the definition corresponding with the name differs for each. Thus, a real man and a figure in a picture can both lay claim to the name ‘animal’; yet these are equivocally so named, for, though they have a common name, the definition corresponding with the name differs for each. For should any one define in what sense each is an animal, his definition in the one case will be appropriate to that case only. 

On the other hand, things are said to be named ‘univocally’ which have both the name and the definition answering to the name in common. A man and an ox are both ‘animal’, and these are univocally so named, inasmuch as not only the name, but also the definition, is the same in both cases: for if a man should state in what sense each is an animal, the statement in the one case would be identical with that in the other. 

Things are said to be named ‘derivatively’, which derive their name from some other name, but differ from it in termination. Thus the grammarian derives his name from the word ‘grammar’, and the courageous man from the word ‘courage’.

Part 5 

Substance [ousia], in the truest and primary and most definite sense of the word, is that which is neither predicable of a subject nor present in a subject; for instance, the individual man or horse. But in a secondary sense those things are called substances within which, as species, the primary substances are included; also those which, as genera, include the species. For instance, the individual man is included in the species ‘man’, and the genus to which the species belongs is ‘animal’; these, therefore-that is to say, the species ‘man’ and the genus ‘animal,-are termed secondary substances. 

It is plain from what has been said that both the name and the definition of the predicate must be predicable of the subject. For instance, ‘man’ is predicted of the individual man. Now in this case the name of the species man’ is applied to the individual, for we use the term ‘man’ in describing the individual; and the definition of ‘man’ will also be predicated of the individual man, for the individual man is both man and animal. Thus, both the name and the definition of the species are predicable of the individual. 

With regard, on the other hand, to those things which are present in a subject, it is generally the case that neither their name nor their definition is predicable of that in which they are present. Though, however, the definition is never predicable, there is nothing in certain cases to prevent the name being used. For instance, ‘white’ being present in a body is predicated of that in which it is present, for a body is called white: the definition, however, of the colour white’ is never predicable of the body. 

Everything except primary substances [ousia]is either predicable of a primary substance or present in a primary substance [ousia]. This becomes evident by reference to particular instances which occur. ‘Animal’ is predicated of the species ‘man’, therefore of the individual man, for if there were no individual man of whom it could be predicated, it could not be predicated of the species ‘man’ at all. Again, colour is present in body, therefore in individual bodies, for if there were no individual body in which it was present, it could not be present in body at all. Thus everything except primary substances [ousia] is either predicated of primary substances [ousia], or is present in them, and if these last did not exist, it would be impossible for anything else to exist.

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