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Themes from Aristotle

24/2/2020

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3 Comments

Joe M

24/2/2020 11:14:51 am

COMPARING THE CATEGORIES OF KANT AND ARISTOTLE

Aristotle has ten categories (introduced at ch 4): Substance, Quantities, Qualities, Relation, "When" (Times), "Where" (Places), Position (spatial orientation?), Having (a category for the miscellaneous, it seems), Acting and Being-Acted-Upon.

We should tidy this up a bit, before comparing with Kant. First, I'm going to ignore two of Aristotle's categories—Position, which seems to mean the orientation of a thing at a given place and time (eg whether a person is sitting down or standing up), which can be reduced to space, with a sufficiently fine-grained conception of space; and Having, which seems a grab-bag meant to include disparate notions. Second, we need to add some extra notions—in particular, various Opposites (ch 10), of which most relevant are things opposed as contraries (11b34, so that it is impossible for something A to be both F and G, where F is not the negation of G, eg red and green, noting that red is not the same as not-green), privation and possession (12a26, what we can call "internal contradictories", so that, for something A that exists, we oppose A's being F with its being not-F), and affirmation and denial (13a36, or "external contradictories", so that we contrast the truth and falsity of the statement "A is F", noting that one way of its being false is when "A" does not refer to anything).

Kant has twelve categories (and their associated judgments), divided into four groups of three. Again, it will be useful to ignore the last group, Modality (consisting of Possibility, Existence and Necessity), since as Kant himself notes (B266) these categories concern more the modes of our knowing objects rather than the objects themselves. Further, we need to add some the "special" categories of Space and Time.

Here is a table that matches these up:

(1) Quantity: Totality (Universal judgments), Plurality (Particular), Unity (Singular)

• Kant's group Quantity = Aristotle's category Quantity.

There are some differences. Aristotle divides all quantities into discrete (eg counting numbers) and continuous (eg features of geometric things), while Kant thinks of the fundamental notions of quantities are All, Some, and One. Kant does mention something like Aristotle's distinction when he talks about "extensive magnitudes" (B203), which are those understood to be the combination of discrete parts, and "intensive magnitudes" (B208), which a those coming in degrees of perception, presumably continuous.

But is Aristotle entitled to talk about quantities, or numbers more generally, and especially continuous quantities? This is an important question, since, these days, numbers are usually understood as Platonic entities, and continuity is defined in terms of actual infinities (ie, limits of series), both of which Aristotle will deny.

(2) Quality—Reality (Affirmative judgments), Negation (Negative), Limitation (Infinite).

• Kant's Reality = Aristotle's Quality, since Kant's category is expressed in Affirmative judgments ("Socrates is white").
• Kant's Negation = Aristotle's opposition of affirmation and denial, since Kant's category is expressed as an external negation ("It is false that A is F").
• Kant's Limitation = Aristotle's opposition of possession and privation, since Kant's category is expressed as an internal negation ("A is not-F").

(3) Relation—Substance & Accident (Categorical), Cause & Effect (Hypothetical), Community (Disjunction)

• Kant's Substance & Accident = Aristotle's Substance & all Aristotle's remaining categories, which attribute what are accidental properties to the substance (= things "present in but not said of" that substance).
• Kant's Cause & Effect = Aristotle's Acting & Being-Acted-Upon, though, with further reading, I guess we will find out that Aristotle's thoughts on causation are more extensive than this.
• Kant's Community = Aristotle's notion of contraries, since Kant's category is expressed as a Disjunction, this being a statement of the form that exactly one of P, Q, R, etc, is true.

(4) Time and Space—these clearly correspond to Aristotle's When and Where.

Joe M

24/2/2020 01:58:14 pm

ARISTOTLE ON NUMBERS, AND SETS AND RELATIONS

"There are three things on the table"—How does Aristotle understand this statement, and what (if any) does that imply about other things he says?

Discussing the category of Having, Aristotle says that things can Have a Quantity (15b17), and so, since Three is a quantity, there must be /something/ that has the quantity Three. In particular, there must be some /one/ thing that has that quantity. So, in addition to there being the individual things on the table—"This one, this one, and this one"—there must also be the aggregate of them—to wit, "The things on the table".

So we have: "The things on the table are three". Now, if we had the sentence "This ball is white", then we would say that Whiteness (an accidental universal) is said-of this particular instance of whiteness (an accidental particular), which is present-in this ball (a primary substance). Similarly, if we use that as a model, then we should say that Three-ness (and accidental universal?) is said-of this particular instance of three-ness, which is present-in this aggregate (a primary substance?). But is this quite right?

First, is Three-ness an accidental universal merely present-in this aggregate? So far as I can tell, an accidental universal is a property that happens to apply to various things, even though they could have existed with its applying to them. Thus, Whiteness is an accidental universal merely present-in the ball, since the white things could all have been not-white, and this ball could have been not-white. But do aggregates merely happen to be three, and could the aggregate we are talking about have not been three? The answer has to be No to both questions, since if this aggregate had a different number then it would have been a different aggregate, and the same applies to any other aggregate that is actually three in number.

Second, is this aggregate a primary substance? It seems the answer has to Yes. For "The things on the table" is not said-of or present-in anything. It follows that, if there is some /one/ thing referred to by "The things on the table", then it will have to be a primary substance, albeit composed of other primary substances. This is consistent with Aristotle's approach. In another context, he agrees that wholes are still substances even though they have parts (3a30), so we too can say that aggregates are substances even though they have members, albeit that the members are prior in existence to the aggregate (14a25).

In sum, we should say that Three-ness (a natural universal) is said-of this particular instance of three-ness (a natural particular), which is said of the aggregate of the things on the table (a primary substance). Aristotle seems committed to the existence of aggregate substances, or what are otherwise called sets or classes.

An important application of this is that he can talk about relations in a more modern manner. Aristotle's actual view is that, while there are relational predicates (ie, as items of language), there are no relational properties (ie, as metaphysical existents). Thus, while there are sentences of the form "Brian is taller than Joe", they should be understood as "Brian is tall, compared to Joe", since there is no relational property of being-taller-than but only the one-place property being-tall, which is applied in a relative manner.

However, even assuming that all properties are one-place, Aristotle could still think that there are relational properties. For he is committed to the existence of aggregates, and, in my view, he is also committed to the existence of /ordered/ aggregates. (There are two ways this might be so: (i) he will want to say things like "Leonidas came third in the race", and for that he will need to place the runners as a whole in some order, and so think of them as an ordered aggregate; (ii) he will allow that some things are parts of others which are in turn parts of others, so he should allow that some aggregates are members of other aggregates (eg the set of cliques at the party), in which case the notion of, say, an ordered pair <a,b> can be defined in the usual manner, as {{a},{a,b}}.) But if Aristotle can use the notion of an ordered aggregate, then he can understand sentences of the form "Brian is taller than Joe" to be attributing the /one-place/ property of being-taller-than to the /ordered/ aggregate <Brian,Joe>. The relational predicate corresponds to a one-place property because its subject is a single thing, which happens to be an ordered pair.

net worth link

5/10/2022 09:08:35 pm

Thank you! This helps me a lot.

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