Aristotle’s Posterior Analytics, I.4


The Modes of Perseity in Aristotle’s Posterior Analytics, I.4

ozu tracks

Introduction

[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.

Argument

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”.   “Of itself” as a translation of kath’ hauto requires some explanation and defense.    An example will begin to clarify what is meant here.

Consider Aristotle’s phrase, “point belongs (of itself) to line”.  There are three ways to understand this phrase: in one way, what Aristotle seems to have in mind is that “point” is a term that belongs properly to “line” in the sense that it does not belong properly to any other predicate.  For example, it might be said that “point” might belong to all sorts of things, including triangles, squares or other shapes.  But here one can see that in order to belong to any of those other things a point must first belong to a line.  The way Aristotle’s first two examples proceed, that line belongs to triangle and point belongs to line might be said to provide some additional support for thinking that this was Aristotle’s intention.  kath’ hauto belong of themselves to their subject in this sense.  Further examples Aristotle lists of kath’ hauto predicates that are usually translated as pertaining to a second sense in which a thing can be an essential attribute (i.e. a kath’ hauto predicate) serve to reinforce this impression: odd or even belong “of themselves” to line in the sense that there is no other thing they are properly predicated of, as is the case with “straight” or “curved” when said of “line”. 

In another sense, it seems in keeping with Aristotle’s text to say that there is a way to understand kath’ hauto predicates as distinct from “said of all” generic ones by the fact that Aristotle’s examples list cases in which kath‘ hauto predicates are costitutive of the being of the thing they are predicated of.  For example, in the case of line, a line cannot exist without also having a line; in the case of number, being a number at all presupposes being odd or even; and one can have a line only if one has a straight or a curved one.  Support for this view may be found in the fact that Aristotle says very clearly not only that all such terms belong to a definitory account of “what the thing is”, but says that point is related to line, and line is related to triangle in the sense that, “the ousia of line and triangle is [consituted] of those things” (cf. 73a35-37). 

It should be noted that this second way of considering kath’ hauto predicates does not align as neatly with those in the second sense as it does those in the first: “odd or even” and “straight or curved” do indeed constitute the essence of “number” and “line”, but not quite in the same sense as points consitute a line.  “Straight” and “curved” are more like types of lines, whereas a “point” is not a type of line.   

Finally, in a third way, Aristotle may be taken to mean that if there is (in some sense) a line, one can infer that there is a point.  Here the necessity of one term applying to the other becomes immediately apparent (since, by definition, lines are made up of points).  Only if there is a point, can there be a line, and this is confirmed especially by the second way of understanding the phrase kath’ hauto.  This relationship can 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. 

Moreover, “belonging to” 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 long winded or 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 ultimately due to the particular kind of being or ousia a line has, 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.

Introduction-2: 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 (1) 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.  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 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” ( (Ǝx) (Mx→Ax) as above); lastly, 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.

Introduction-3: 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 (2).  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 (3), the relationship may be characterized as essential-accidental according to the third and fourth modes of perseity (4).  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 (5).  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.

Introduction-4: Aristotle’s four modes of perseity: posterior analytics I.4

 

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Perseity and Identification

{The texts in Aristotle’s corpus relevant to the following discussion have been placed at the end of the essay for ease of reference}

The general way in which the notion of persiety can be characterized has been explained above  (See Introduction I and II ).  Part 1 in the present series emphasized the difference between necessary and accidental connections, while Aristotle’s “said of all” was explored in part 2 as a criterion for necessity.  What remains to be seen is the way in which each of these two discussions help to situate the notion of an essential attribute, and prepare the way for a deeper understanding of the role that kath’hauto (per se) predicates play in Aristotle’s larger schema for organizing knowledge.

Argument

What I would like to argue, as a preliminary matter, is that kath’hauto predicates indicate that one term is related to another in such a way that it may be said to be entailed by the very existence (or being) of another thing.  Thus, in the example given above, “point” bears a kath’hauto or per se relationship to “line” because it is one of the conditions necessary for there to be a line.  (See Note* below)  But the true importance of the role such predicates play, is that they serve to anchor one term to another, thus enabling a schema for identifying a certain subject/substance as one thing or another.  As will be seen, this has the further consequence that kath’hauto predicates help to give “atomic” subjects their atomicity.

In keeping with Aristotle’s recommended procedure for exploring a subject, we will proceed from what is better known to us toward a formulation that will be more intelligible in itself.  I will proceed to show how the identification of smallpox sorts with Aristotle’s overall scheme for identifying a thing as something or other, and in the process, make clear the role that kath’hauto predicates play within this framework. 

In brief, my contention will be that they can be viewed as a necessary term or as a conjuction of necessary terms that are sufficient to identify a particular subject.  The precise way in which they are sufficient will have to be worked out as we proceed.  If all that I am about to say is correct, it will show the way in which Aristotle’s theories of research and syllogistic proof are actually quite compatible with modern scientific methods.  As will become clear, it is by emphasizing the role of identification in having an account of a thing that the theory of demonstration can come to be seen as useful for the purposes of scientific research.

The smallpox example

Suppose that you are a nurse working in a hospital.  One day someone comes into the hospital with the following symptoms: flu-like symptoms, including a headache, vomiting, and high fever.  Moreover, there are the beginnings of a kind of rash in the patient’s mouth, and the patients complains of a backache and overall fatigue.  What can be concluded from these symptoms?  Not much in the way of identifying their precise cause, since they could apply to many causes.  It is always possible that even all the syptoms together, which are the symptoms of smallpox, might not be enough to conclude that the patient has smallpox.  It could be the case, for example, that the rash in the patient’s mouth is due to an infection of some kind that is totally unrelated to the other symptoms.

These symptoms could be said to be the necessary conditions for having smallpox.  Note that these conditions/symptoms are not even sufficient when taken together or conjunctively to make an identification.  What is lacking are the truly characteristic markers that will yield such an identification according to which one can make a determination that what is before us is smallpox and not something else.

There are two ways that such an identification might be made.  One way would be to wait until further symptoms present themselves, such as the characteristic pustules that can yield a positive diagnosis.  Another way might be to give the patient a blood test whereby the virus that causes smallpox, variola major, can be identified.  In the case of the former method, the patient will become highly contagious and in 30% of cases death occurs.  Moreover, in the initial stages of the formation the characteristic pustules the disease may be mistaken for chickenpox.  These potential problems make it a much better idea to take a blood test.  The identification of variola major requires another set of conditions and chararcteristic markers, and the fact of identification will suffice for our purposes.

The Variola Major virusVariola Major

Now let’s apply this story about the identification of a virus to Aristotle’s tools for identification.  Aristotle’s tool kit includes such items as properties, predicates that are “said of all” or “in every case” of their subject, essential predicates (kath’hauto/per se predicates), generic predicates, and accidents.  Let’s consider these in order from least to best in terms of their capacity for identifying a subject.

Aristotle’s tool box

Accidents In terms of identification, true accidents serve very little purpose if any at all.  They are the attributes of a thing that may or may not belong to a subject.  They may be said to have various grades, from those that appear in many instances but not all to those that are purely fortuitous, such as being “next to a pillar” when said of a man (an example that appears in Renaissance texts).  Here I mean to speak of accidents in the strict sense, as those that may belong to a thing but by themselves indicate very little or nothing about what a thing is.  (I)  These would apply to the purely accidental features that a patient would present.  Perhaps the patient has a broken leg: in this case, since having a broken leg is unrelated to having smallpox, it is purely accidental.  It cannot be considered a symptom, and nothing can be inferred from it.

Properties Properties, again, come in various grades.  In the strict sense, a property is an attribute that belongs to one kind of thing and not another in every case.  Thus, properties play a comparatively important role in the identification of a thing although he says that they do not indicate the essence of a thing.  But Aristotle goes further and provides a criterion for property-hood.  The ability to learn grammar is a property of man (i.e. it applies to “man” alone and in every case) if and only if the following two propositions are both true:

(1) If x is a man, then x is able to learn grammar.

(2) If x is able to learn grammar, then x is a man.

(2) is more likely to be acceptable to readers than (1).  Sometimes, an attempt is made to resolve skepticism about (1) by appealing to the notion of the nature of a thing: that cases that do not fit are merely unnatural accidents.  I propose to clarify this somewhat by adding that one might think of a predicate such as “able to learn grammar” along the same lines as one can think of the predicate “living being”: not all things that are “man” are actually living beings, although it is a class of things that “man” may be said to belong to by nature. (II)  If one were to think of a typical member of the species homo sapiens and to try to find an attribute of that species that distinguishes it from any other, the ability to learn grammar, might (in the 4th Century BC at least) count as such a distinguishing mark. In the story above, the rash that appears in the mouth is a characteristic mark of smallpox. Chickenpox, by contrast, breaks out over the skin.  Hence, since smallpox breaks out first in the throat and mouth while chickenpox never does, the initial rash in the mouth may be thought of as a property of smallpox relative to chickenpox.  This is not quite the essence of smallpox, for which the virus, variola major seems a better candidate due to its priority.

Predicates that aresaid of all” were discussed above (III).  The main point to be remembered for our purposes here is that they are necessary conditions.  The fact that one predicate is said of another in every case means that one term is implied by another.  For example, since “point” may be said to belong to “line” in every case, “point” is implied by “line”.  It is important to note that such predicates are not essential predicates but only necessary ones.  Thus, although they directly precede Aristotle’s discussion of perseity in I.4, they are not the same as per se predicates.  They correspond to all the symptoms of smallpox in the smallpox example, since they signify the presence of smallpox in every case, although they are not sufficient by themselves to do so.

Generic predicates are those that are predicated as answering to the question, “what (sort of thing) is it?”, and thus characterize the ousia (or substance) of a subject.  They may be thought of as predicates that are said of a species in such a way that they fall in the same category as the species and are not accidents.  In terms of identification, they again mark necessary but not sufficient conditions.  For example, if there is a man there is necessarily an animal (or mobile being, or substance); but if there is an animal, there is not necessarily a man.

Finally, we come to kath’hauto-1 predicates.  Kath’hauto-1 predicates are essential attributes and hence indicate the presence of a certain subject in every case.  Unlike properties, Aristotle does not go as far as saying that they are convertible with their subject.  For this reason, they seem far more sound in terms of their logic than properties.  In this case, these would seem to correspond either to the characteristic pustules that smallpox produces, or to the variola major virus that causes smallpox.  Each can be construed as fitting the constraints Aristotle’s “line and point” example in I.4 provides, since in every instance where there is an instance of smallpox there is either the variola major virus or else the characteristic pustules.  Moreover, they fulfill the requirement that the implication “where there is smallpox there is variola major” must hold, although the converse might not hold in every case (this is also true of the line and point example).  Finally, it may be seen that variola major is related to smallpox in such a way that it could be said to be part of its definition.  Some kath’hauto attributes may be said to be kath’hauto in such a way that they are also part of the explicit definition of a thing although this need not actually be the case.  They may, in particular belong to the genus-differentia paradigm for definitions that Aristotle uses quite frequently in the corpus.

A final comment on this particular case should probably be made before moving on.  There is an order of priority among these elements that begins with kath’hauto attributes and extends to all the necessary conditions/symptoms.  Aristotle makes use of the notion of ontological dependency to establish this priority as a causal priority.  In this case, since, apparently, the presence of the variola major virus is the underlying cause of all the symptoms, the virus must first be present if they are to arise as symptoms of smallpox.  Moreover, the presence of variola major gives the symptoms a unity; it unites them to some underlying entity that makes them attributes of some particular kind of thing and not simply a collection of accidents. (III)  Hence, although one could perhaps make do with simply mentioning variola major to convey the idea of what kind of condition the patient is in, a full account would have to include the symptoms and could not omit them.

All these components may be arranged together on the following chart for ease of reference:

Synthesis

As the chart suggests, the search for a proper diagnosis/identification of a thing can be thought of as reducible to the project of apprehending an attribute that will serve to distinguish the thing in question from all other things. Let’s take a closer look at how this works:

There is a sense in which one must already know what one is looking for when one is attempting to identify a thing as something else (IV).  This is because identification fundamentally involves relating some present experience to pre-existing knowledge.  It means, in other words, being able to identify some particular before us as one that ought to fall under some concept (Aristotle gives an extended discussion of this aspect of what it means to know in the introductory chapter to the Posterior Analytics (I.1)).  In yet other words, it means, in an ideal case, that one has the tools to identify something in a “scientific” manner, which means being able to distinguish it from everything else.  This means having a knowledge of its essence.

Understanding the books of the Analytics as being basically about identification and creating patterns for identification bears on the question of what Aristotle’s intention was for them.  This has been debated somewhat recently, especially with regard to book I of the Posterior Analytics.  It has been said by some that demonstration is a tool for discovery.  I do not think this is correct.  The countervailing view propounded by Jonathan Barnes is that it is rather a didactic tool to be used in a school setting.  The view I am arguing for, that it is basically a pattern for identification, is compatible with this view, but gives its range of application a broader scope and shows how it may be of service to scientists working in the field.

Before moving on to the next section, which will continue the present synthesis, let’s take stock now of what has yet to be shown.  It remains to be seen whether Aristotle himself actually used the sort of schema for identification presented above.  This will be shown by taking account of what Aristotle says in Posterior Analytics II.13.  Furthermore, having shown Aristotle’s own process of identifying an object to be consonant with the method of the chart, it will become a much simpler to show that Aristotle’s whole theory of syllogism and demonstration may be related to the project of identifying an object.  Lastly, the overall objective of characterizing kath’hauto attributes will finally be fully realized when both these objectives have been achieved.

————————————————

Note*: I would like to suggest that the logic for conditions for being or existing in cases involving things that mathematical objects can be understood in terms of conditional statements.  Thus, in a statement like “if there is a line, then there is a point” the conditional should be read as saying “if there were a point, there would be a line”.  Thus, we can talk intelligibly about the conditions for existence in a hypothetical sense.  At present I dont have any other textual support for this reading than the text itself, which seems to require such an interpretation in order to account for this way of speaking about such objects.

(I) See the discussion of essence vs. accident in the first article in this series here.

(II) I think there are genuine problems for Aristotle when it comes to his example and to his formulation of properties in general.  It is sometimes said in defence that Aristotle’s notion of a species is not that of a set, but this too will not square with his criterion or with other criteria that appear in his corpus.  Aristotle is serious when he means “said of all” or “true in every instance“.  It seems that he could have made do with (2) alone and treated the fact that the ability to learn grammar applies only to man as an empirical fact.

(III) On the points of both priority and unity the reader may wish to see Aristotle’s Metaphysics, Book Z, chapter 17.

(IV) Consider this in relation to “the problem of the Meno”.

———————————————————————–

Posterior Analytics I.4 on kath’hauto attributes in the first and second senses of perseity:

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.

Text on demonstration as relevant to identification (recognition of the particular as falling under some concept): (Posterior Analytics, I.1)

All instruction given or received by way of argument proceeds from pre-existent knowledge. This becomes evident upon a survey of all the species of such instruction. The mathematical sciences and all other speculative disciplines are acquired in this way, and so are the two forms of dialectical reasoning, syllogistic and inductive; for each of these latter make use of old knowledge to impart new, the syllogism assuming an audience that accepts its premisses, induction exhibiting the universal as implicit in the clearly known particular. Again, the persuasion exerted by rhetorical arguments is in principle the same, since they use either example, a kind of induction, or enthymeme, a form of syllogism. 

……..

If he did not in an unqualified sense of the term know the existence of this triangle, how could he know without qualification that its angles were equal to two right angles? No: clearly he knows not without qualification but only in the sense that he knows universally. If this distinction is not drawn, we are faced with the dilemma in the Meno: either a man will learn nothing or what he already knows; for we cannot accept the solution which some people offer. A man is asked, ‘Do you, or do you not, know that every pair is even?’ He says he does know it. The questioner then produces a particular pair, of the existence, and so a fortiori of the evenness, of which he was unaware. The solution which some people offer is to assert that they do not know that every pair is even, but only that everything which they know to be a pair is even: yet what they know to be even is that of which they have demonstrated evenness, i.e. what they made the subject of their premiss, viz. not merely every triangle or number which they know to be such, but any and every number or triangle without reservation. For no premiss is ever couched in the form ‘every number which you know to be such’, or ‘every rectilinear figure which you know to be such’: the predicate is always construed as applicable to any and every instance of the thing. On the other hand, I imagine there is nothing to prevent a man in one sense knowing what he is learning, in another not knowing it. The strange thing would be, not if in some sense he knew what he was learning, but if he were to know it in that precise sense and manner in which he was learning it.

Topics, I .5 where Aristotle presents the elements of his ontological “tool box”:

We must now say what are ‘definition’, ‘property’, ‘genus’, and ‘accident’. A ‘definition’ is a phrase signifying a thing’s essence. It is rendered in the form either of a phrase in lieu of a term, or of a phrase in lieu of another phrase; for it is sometimes possible to define the meaning of a phrase as well. People whose rendering consists of a term only, try it as they may, clearly do not render the definition of the thing in question,because a definition is always a phrase of a certain kind. One may, however, use the word ‘definitory’ also of such a remark as ‘The “becoming” is “beautiful”‘, and likewise also of the question, ‘Are sensation and knowledge the same or different?’, for argument about definitions is mostly concerned with questions of sameness and difference. In a word we may call ‘definitory’ everything that falls under the same branch of inquiry as definitions; and that all the above-mentioned examples are of this character is clear on the face of them. For if we are able to argue that two things are the same or are different, we shall be well supplied by the same turn of argument with lines of attack upon their definitions as well: for when we have shown that they are not the same we shall have demolished the definition. Observe, please, that the converse of this last statement does not hold: for to show that they are the same is not enough to establish a definition. To show, however, that they are not the same is enough of itself to overthrow it. 

A ‘property’ is a predicate which does not indicate the essence of a thing, but yet belongs to that thing alone, and is predicated convertibly of it. Thus it is a property of man to-be-capable of learning grammar: for if A be a man, then he is capable of learning grammar, and if he be capable of learning grammar, he is a man. For no one calls anything a ‘property’ which may possibly belong to something else, e.g. ‘sleep’ in the case ofman, even though at a certain time it may happen to belong to him alone. That is to say, if any such thing were actually to be called a property, it will be called not a ‘property’ absolutely, but a ‘temporary’ or a ‘relative’property: for ‘being on the right hand side’ is a temporary property, while ‘two-footed’ is in point of fact ascribed as a property in certain relations; e.g. it is a property of man relatively to a horse and a dog. That nothingwhich may belong to anything else than A is a convertible predicate of A is clear: for it does not necessarily follow that if something is asleep it is a man. 

A ‘genus’ is what is predicated in the category of essence of a number of things exhibiting differences in kind. We should treat as predicates in the category of essence all such things as it would be appropriate tomention in reply to the question, ‘What is the object before you?’; as, for example, in the case of man, if asked that question, it is appropriate to say ‘He is an animal’. The question, ‘Is one thing in the same genus as another or in a different one?’ is also a ‘generic’ question; for a question of that kind as well falls under the same branch of inquiry as the genus: for having argued that ‘animal’ is the genus of man, and likewise also of ox, we shall have argued that they are in the same genus; whereas if we show that it is the genus of the one but not of the other, we shall have argued that these things are not in the same genus. 

An ‘accident’ is (i) something which, though it is none of the foregoing-i.e. neither a definition nor a property nor a genus yet belongs to the thing: (something which may possibly either belong or not belong to any one and the self-same thing, as (e.g.) the ‘sitting posture’ may belong or not belong to some self-same thing. Likewise also ‘whiteness’, for there is nothing to prevent the same thing being at one time white, and at another not white. Of the definitions of accident the second is the better: for if he adopts the first, any one is bound, if he is to understand it, to know already what ‘definition’ and ‘genus’ and ‘property’ are, whereas the second is sufficient of itself to tell us the essential meaning of the term in question. To Accident are to be attached also all comparisons of things together, when expressed in language that is drawn in any kind of way from what happens (accidit) to be true of them; such as, for example, the question, ‘Is the honourable or the expedient preferable?’ and ‘Is the life of virtue or the life of self-indulgence the pleasanter?’, and any other problem which may happen to be phrased in terms like these. For in all such cases the question is ‘to which of the two does the predicate in question happen (accidit) to belong more closely?’ It is clear on the face of it that there is nothing to prevent an accident from becoming a temporary or relative property. Thus the sitting posture is an accident, but will be a temporary property, whenever a man is the only person sitting, while if he be not the only one sitting, it is still a property relatively to those who are not sitting. So then, there is nothing to prevent an accident from becoming both a relative and a temporary property; but a propertyabsolutely it will never be

Metaphysics VII.17:

“Let us state what, i.e. what kind of thing, substance should be said to be, taking once more another starting-point; for perhaps from this we shall get a clear view also of that substance which exists apart from sensible substances. Since, then, substance is a principle and a cause, let us pursue it from this starting-point. The ‘why’ is always sought in this form–’why does one thing attach to some other?’ For to inquire why the musical man is a musical man, is either to inquire–as we have said why the man is musical, or it is something else. Now ‘why a thing is itself’ is a meaningless inquiry (for (to give meaning to the question ‘why’) the fact or the existence of the thing must already be evident-e.g. that the moon is eclipsed-but the fact that a thing is itself is the single reason and the single cause to be given in answer to all such questions as why the man is man, or the musician musical’, unless one were to answer ‘because each thing is inseparable from itself, and its being one just meant this’; this, however, is common to all things and is a short and easy way with the question). But we can inquire why man is an animal of such and such a nature. This, then, is plain, that we are not inquiring why he who is a man is a man. We are inquiring, then, why something is predicable ofsomething (that it is predicable must be clear; for if not, the inquiry is an inquiry into nothing). E.g. why does it thunder? This is the same as ‘why is sound produced in the clouds?’ Thus the inquiry is about thepredication of one thing of another. And why are these things, i.e. bricks and stones, a house? Plainly we are seeking the cause. And this is the essence (to speak abstractly), which in some cases is the end, e.g. perhaps in the case of a house or a bed, and in some cases is the first mover; for this also is a cause. But while the efficient cause is sought in the case of genesis and destruction, the final cause is sought in the case of being also. 

“The object of the inquiry is most easily overlooked where one term is not expressly predicated of another (e.g. when we inquire ‘what man is’), because we do not distinguish and do not say definitely that certain elements make up a certain whole. But we must articulate our meaning before we begin to inquire; if not, the inquiry is on the border-line between being a search for something and a search for nothing. Since we must have the existence of the thing as something given, clearly the question is why the matter is some definite thing; e.g. why are these materials a house? Because that which was the essence of a house is present. Andwhy is this individual thing, or this body having this form, a man? Therefore what we seek is the cause, i.e. the form, by reason of which the matter is some definite thing; and this is the substance of the thing. Evidently, then, in the case of simple terms no inquiry nor teaching is possible; our attitude towards such things is other than that of inquiry. 

“Since that which is compounded out of something so that the whole is one, not like a heap but like a syllable-now the syllable is not its elements, ba is not the same as b and a, nor is flesh fire and earth (for when these are separated the wholes, i.e. the flesh and the syllable, no l

 

 
 
 
Introduction 5

At the end of the prior section, I promised to bring together the smallpox example with Aristotle’s Posterior Analytics II.13 and to show how both approaches lead to a vision of Aristotle’s Analytics as being concerned with identification schemata.

Aristotle describes a sequence both in Posterior Analytics II.13 and in Topics II.2 for hunting down the attributes that belong to the definition of a thing according to which one begins with some atomic species that serves as the “target” of one’s inquiry and then proceeds to ask what its proper genus might be.  If, for example, the atomic species to be defined is the number 3, then one might naturally begin by taking “number” to be the genus to which it belongs.  Next, after deciding upon a genus, one generates successive lower genera by a process of division.  For example, one can divide numbers generally into odd and even, then into prime and not prime, and finally according to the different senses in which a number can be prime: those that are either (a) not measurable by number (see (I) below), or (b) not composed of numbers (for example, 7 is composed of the primes 2 and 3).  This set of genera apply uniquely to 3 conjunctively: that is, they are disjunctively necessary attributes, but are conjunctively sufficient to identify the number 3 uniquely, or in other words, to pick out its essence. (II)

Here it is easy to pick out the elements present in Aristotle’s tool box: the role of genus is to set a certain perameter to the subject matter, which is here “number”; attributes “said in every instance of their subject” pertain to all the successive divisions/differentia/more specific genera or attributes and relate in this case to “odd” or “even” numbers; and kath’hauto attributes pertain to every instance of their subject matter in such a way that they might be incuded in the defining formula of the thing, and here apply to the attribute of being prime.

But Posterior Analytics II.13 helps to reveal more than this about kath’hauto attributes.  They are not simply attributes that belong to their subject in every instance or are included in its definition in a way that may coincide with belonging in the account of what it is considered in a broad sense; they may be characterized, moreover, as those attributes that make certain atomic subjects atomic.  Atomic subjects are species-terms that are reached at the end of a process of division.  They are, hence, “a-tomos”, literally, non-divisible.  Kath’hauto attributes belong to atomic subjects in such a way that they characterize such subjects as being what they are specifically (they are not particulars but species) and not something else.

Democritus
Democritus

In Posterior Analytics II.13, kath’hauto attributes coincide with the lowest common differentia that characterizes the subject one was attempting to reach by division.(III)  In the case of the number 3, what is kath’hauto is the combination of both senses in which a thing can be prime along with the other attributes, including most notably, that of being odd, which distinguishes 3 from 2.  Here a small problem arises that should not detain us for long.  In the case of this example, it appears that the lowest differentia does not do the work of identifying 2 from 3 all on its own, as we would expect the differentia of a genus-differentia definition (one in which the last differentia does serve to pick out an atomic species uniquely) to do.  Hence, the last attribute is not kath’hauto of itself, but only the combination or conjunction of necessary attributes turns out to be sufficient to identify the species 3.  One must think of the conjunction as applying kath’hauto.  Nevertheless, one should not conclude that the method Aristotle has described here is incompatible with discovering a genus-differentia type definition.  Indeed, Aristotle seems to assume that it does almost explicitly in II.13 at 96b22-25, 97a10-14, and 97a20-23.

What does this procedure accomplish?  I have argued above (III) that the end result is to create a paradigm for identification.  What is smallpox? Variola Major.  How may it be identified? By its symptoms.  What is 3?  A odd number that is prime in both senses listed.  Aristotle summarizes the procedure for creating a identification paradigm by listing three directives one must: (a) select attributes that are in the “what is it” of a subject (i.e. all the attributes that would be included in a definitive account of the subject in question); (b) arrange those attributes in order of (ontological) priority; and (c) make sure that the selection is complete.  Only one thing remains to mention: that the attributes selected in (a) must all be such that they fall within one genus.

Three tpyes of badger within the genus "meles"
Three species of badger within the genus “meles”

With a paradigm for identification in place, one is also able to identify particulars that “fall under” the concept/species/kind in question as falling under that concept/species/kind.  In order for such identification to be sure or well founded for scientific purposes, prior knowledge is required of the kind that the paradigm schema can provide.  Moreover, a paradigm for identification that yields an organization of facts into a schema that shows their ontological priority and posteriority relative to one another can likewise yield the elements of a demonstration. This is a further result, since such identifying elements are also the elements of a definition, and a conclusive demonstration is merely a re-arrangment of the elements found in the definition of a thing.(v) This approach may also help to explain why Aristotle says in Posterior Analytics II.8 that demostration does not prove but only makes manifest the essence of a thing.

Clearly, this is the role of demonstration relative to the results of founding such a paradigm.  It perhaps serves to show in a concise format exactly how the elements in such an identification schema are related to one another.  In the case of kath’hauto attributes, it is through them that other necessary attributes may be shown to belong to a specific kind of subject.  On my reading it thus serves as a concise way to relate facts about a kind of thing within a deductive schema that is the end result of a dialectical kind of division.  The true importance of demonstration is to establish such identification paradigms as may result from the process of dialectical division as founded upon logical necessity.

—————————————————

(I) 1 was considered to be the measure of number since it was the starting point of number, but not a number itself: hence 3 is not measurable by “number” but only by the combination of a number (2) and the measure of number itself (1) and is therefore not prime in this latter sense.

(II) This example follows Aristotle’s description at Posterior Analytics II.13 96a24 ff.

(III) One might recall here the project taken up in the Symposium of “finding the angler”.

(IIII) See the prior article in this series here.

(v) See Posterior Analytics II.10 93b37-94a2.

 

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