Tag Archives: being

More Questions Surrounding Infinite Regress

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In the last post I was puzzled as to why in the very beginning of Lamda 3, Aristotle has chosen to say that, “if not only bronze comes to be round but also the round comes to be and the bronze comes to be,” then there will be an infinite regress as a consequence.  (Dhananjay has some helpful and clarifying things to say in the comments.)

After these things, [one must observe] that neither matter nor form comes to be, I mean the ultimate ones.  For everything undergoes change as something and by something and into something.  The by something is the initiating mover, the something is the matter, and the into which is the form.  Therefore they continue into an infinite regress, if not only bronze comes to be round but also the round comes to be and the bronze comes to be.  Indeed, these must stop. (My translation, Metaphysics 1069b35-1070a4) (1).

Note that I have changed the unwritten subject in the last line to, “Indeed, these must stop,” on the basis of Dhananjay’s translation.  This gives better sense, and “these” must refer to the round and the bronze.

On a related note, is the “Indeed, these must stop” simply a restatement of the first sentence, “After these things, [one must observe] that neither matter nor form comes to be, I mean the ultimate ones“?  That is, are the ultimate ones, usually translated as “proximate [form and matter]” simply the stopping point, from which (working backward as we are in the context of a supposed infinite regress) all change will occur?

More broadly, is the term τὰ ἔσχατα, “the proximate form and matter” simply a stipulation of definition?  On reflection I think the answer is no, for there is a argument for why this is so, by both explaining the necessary elements of the process of change, and of course, the infinite regress itself.

Are 1070a2-3, ὁ χαλκός and τὸ στρογγύλον, (bronze and the round) examples of 1069b35, ἡ ὕλη οὔτε τὸ εἶδος (matter and form)?  This seems to clearly be yes, but does little, for me, to clarify the intent of the first sentence in the passage.

Perhaps most intriguingly to me, why in the sentence, “For everything undergoes change as something and by something and into something” is the order subject, agent, form (SAF) while in the next, explanatory sentence, “The by something is the initiating mover, the something is the matter, and the into which is the form,” the order is agent, subject, form (ASF)?

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Notes:

(1) Μετὰ ταῦτα ὅτι οὐ γίγνεται οὔτε ἡ ὕλη οὔτε τὸ εἶδος,   (35)
λέγω δὲ τὰ ἔσχατα. πᾶν γὰρ μεταβάλλει τὶ καὶ ὑπό
(1070a) τινος καὶ εἴς τι· ὑφ’ οὗ μέν, τοῦ πρώτου κινοῦντος· ὃ δέ, ἡ
ὕλη· εἰς ὃ δέ, τὸ εἶδος. εἰς ἄπειρον οὖν εἶσιν, εἰ μὴ μόνον
ὁ χαλκὸς γίγνεται στρογγύλος ἀλλὰ καὶ τὸ στρογγύλον
ἢ ὁ χαλκός· ἀνάγκη δὴ στῆναι.

Another Infinite Regress in Aristotle

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After these things, [one must observe] that neither matter nor form comes to be, I mean the ultimate ones.  For everything undergoes change as something and by something and into something.  The by something is the initiating mover, the something is the matter, and the into which is the form.  Therefore they continue into an infinite regress, if not only bronze comes to be round but also the round comes to be and the bronze comes to be.  Indeed, there must be a stopping point (My translation, Metaphysics 1069b35-1070a4) (1).

This is how Lamda 3 begins.  Focus for a moment on the infinite regress which Aristotle offers as a consequence of this first paragraph. What line of reasoning is Aristotle following here?  Certainly if bronze has to come to be before it even serves as the subject of a transition into a bronze statue, then the process is pushed back one step.  But why should this be an infinite regress.  In other contexts, Aristotle uses eis apeiron to mean infinite regress, so I think it is solid to interpret it as such here.  

I believe that Aristotle is here already assuming a substratum or hypokeimenon. The idea of a substratum, or underlying thing, would seem to serve at least two purposes.  The first would be to explain the persistence of a thing through change and over time.  Secondly to avoid having to explain the antecedent coming to be of something in order to serve as the subject of a change.  It is perhaps this second idea that is motivating Aristotle’s infinite regress.  I will try to develop this idea in a second post.

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Notes:

(1) Μετὰ ταῦτα ὅτι οὐ γίγνεται οὔτε ἡ ὕλη οὔτε τὸ εἶδος,   (35)
λέγω δὲ τὰ ἔσχατα. πᾶν γὰρ μεταβάλλει τὶ καὶ ὑπό
(1070a) τινος καὶ εἴς τι· ὑφ’ οὗ μέν, τοῦ πρώτου κινοῦντος· ὃ δέ, ἡ
ὕλη· εἰς ὃ δέ, τὸ εἶδος. εἰς ἄπειρον οὖν εἶσιν, εἰ μὴ μόνον
ὁ χαλκὸς γίγνεται στρογγύλος ἀλλὰ καὶ τὸ στρογγύλον
ἢ ὁ χαλκός· ἀνάγκη δὴ στῆναι.

Aristotle’s Categories: 10-Fold Division of Being

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(See here for the previous posts on the Categories: Chapter 1, Chapter 2, Chapter 3)

In this fourth chapter of the Categories Aristotle introduces a second division of being, classifying “things said without combination.”  When considered in their most elemental form, if they can be, on Aristotle’s view things will be organized into these 10 types of categories.  In J.A. Ackrill’s considered opinion Aristotle arrived at these categorial classifications, “by observing that different types of answer are appropriate to different questions.” [2]  However he discovered this system of classification, he introduces them very briefly by exampling them with 2 or 3 instances.

Each of the things said without combination signify either substance (ousia)[1], or quantity (poson), or quality (posos), or relation (pros ti) or where (pou) or when (pote) or being in a position (keisthai) or having (echein) or doing (poiein) or being affected (paschein). And substance is, to speak generally, for example a man, a horse; and quantity for example, two cubits long, three cubits long; and quality is for example, white, grammatical; and relation is for example, double, half, greater; and where is for example, in the Lyceum, in the market; and when for example is yesterday, a year ago; and being in a position for example, reclining, sitting; and having for example, having shoes on, being armored; and to do for example, cutting, burning; and to be affected for example, to be cut, to be burnt.

In any affirmation though, none of the things mentioned is said by itself; rather in the combination of these with each other an affirmation comes about. Each affirmation seems either to be true or false, but none of the things said without combination is true or false, for example man, white, runs, wins (translation mine, Categories, 1b25-2a10). [3]

So we have rather straightforwardly, a classification that looks like this:

Substance (ousia) example: horse, man
Quantity (poson) example: two cubits long, three cubits long
Quality (posos) example: white, grammatical
Relation (pros ti) example: double, half, greater
Where (pou) example: in the Lyceum, in the market
When (pote) example: yesterday, a year ago
Being in a position (keisthai) example: reclining, sitting
Having (echein) example: having shoes on, being armoured
Doing (poiein) example: cutting, burning
Being affected (paschein) example: to be cut, to be cut

It should be noted that when Aristotle both earlier and in this chapter spoke of “things said without combination,” he must have intended this to mean the objects to which the words refer.  We can be confident of this because he gives as an example of one his categories, which are by definition said without combination, “in the Lyceum” which is two words in Greek.  Yet, on the supposition that Aristotle was referring to linguistic terms alone, of course using two words is an example of combination.  Thus, Aristotle must be referring to the concrete items for which these terms are merely used as designations.

It is mnemonically suggestive that 8 of the 10 categories begin with the letter p (Greek π).  This might be similar to the journalistic admonition to remember the “W questions,” i.e. who, when, why, where, what.  If so, this might cynically incline us to believe that these categories were chosen because they were easily accessible to Aristotle.

In the second half of this passage, Aristotle wants to emphasis that while these categorial uses are building blocks, they are not of any use when discussing truth or falsity.  We cannot discover the truth value of “horse.” In order to make it truth-evaluable we must say, “horse is white” or “horse is grammatical,” for example.

Some interpretative questions:

Is “in accordance with no combination” κατὰ μηδεμίαν συμπλοκὴν used by Aristotle as a circumlocution to avoid adding another predicate, i.e. things that are without combination are either, etc.?

Why does Aristotle preface his introduction with “to speak generally” ὡς τύπῳ εἰπεῖν about substance (or maybe all the categories, it seems ambigious)?  Is this just to say the examples he is about to give are not exhaustive, typical, or that we should refrain from inferring too much from limited examples?

Does Aristotle want us to understand, in the second paragraph, translating more literally, “In no affirmation is each of the things mentioned predicated of itself?”  Viz. “Horse is horse”  If this is so, what does this mean for how he intended his theory of predication to be employed, since we are excluding this meaning?

 

REFERENCES:

[1] Could be translated ‘being.’
[2] Aristotle’s Categories and De Interpretatione, Oxford, 1963, pg. 79
[3] Τῶν κατὰ μηδεμίαν συμπλοκὴν λεγομένων ἕκαστον ἤτοι (25)
οὐσίαν σημαίνει ἢ ποσὸν ἢ ποιὸν ἢ πρός τι ἢ ποὺ ἢ ποτὲ ἢ
κεῖσθαι ἢ ἔχειν ἢ ποιεῖν ἢ πάσχειν. ἔστι δὲ οὐσία μὲν ὡς
τύπῳ εἰπεῖν οἷον ἄνθρωπος, ἵππος· ποσὸν δὲ οἷον δίπηχυ,
τρίπηχυ· ποιὸν δὲ οἷον λευκόν, γραμματικόν· πρός τι δὲ
(2a.) οἷον διπλάσιον, ἥμισυ, μεῖζον· ποὺ δὲ οἷον ἐν Λυκείῳ, ἐν
ἀγορᾷ· ποτὲ δὲ οἷον χθές, πέρυσιν· κεῖσθαι δὲ οἷον ἀνάκειται,
κάθηται· ἔχειν δὲ οἷον ὑποδέδεται, ὥπλισται· ποιεῖν δὲ οἷον
τέμνειν, καίειν· πάσχειν δὲ οἷον τέμνεσθαι, καίεσθαι.

ἕκαστον δὲ τῶν εἰρημένων αὐτὸ μὲν καθ’ αὑτὸ ἐν οὐδεμιᾷ κατα- (5)
φάσει λέγεται, τῇ δὲ πρὸς ἄλληλα τούτων συμπλοκῇ
κατάφασις γίγνεται· ἅπασα γὰρ δοκεῖ κατάφασις ἤτοι
ἀληθὴς ἢ ψευδὴς εἶναι, τῶν δὲ κατὰ μηδεμίαν συμ-
πλοκὴν λεγομένων οὐδὲν οὔτε ἀληθὲς οὔτε ψεῦδός ἐστιν,
οἷον ἄνθρωπος, λευκόν, τρέχει, νικᾷ. (10)