Tag Archives: Ancient Greek Philosophy

The Four Predicables: Property

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And a property is that which does not make evident the essence of a thing, but it belongs to the thing alone and can be predicated reciprocally of the thing, for example a property of a human is a natural capacity toward grammar. For if he is a human, he has the capacity of grammar, and conversely, if he has the capacity of grammar, he is a human. For no one says that a property is that which is able to belong to another thing, such as sleeping belongs to the human. Not even if the thing happened to belong to it alone for a certain time. And if one of these things would be called a property, it will not be called a property purely, but a temporary property or a property in relation to something else. For, “Being on the right,” is a temporary property, and “Being two-footed,” happens to be a property in relation to something else, such as man is two-footed with respect to a horse or a dog. And it is obvious that of the things able to belong to another thing, none of them are able to be predicated reciprocally. For it is not necessary, if something sleeps, that it is a human. 1
 Topica 102a18-30

After the introduction of “definition,” which is the essence of something, Aristotle transitions to the idea of what a “property” is. Possibly one of the motivations leading Aristotle to discuss property secondly is that there is a common misconception that the property of something simply is its essence. But Aristotle has told us that the essence of something is its definition, not a property. Man, he informs us, has as one of his properties, the ability to understand grammar. But this is only a property insofar as it can be uniquely said of an individual human being as well, and in addition can be mutually said in reverse: i.e. A man is grammar-capable, the one who is grammar-capable is a man.

As one “proof” of his conception, Aristotle, as he often does, seems to appeal to the common opinion and sense of his listeners: “No one says ‘sleeping’ is a property of the human.” In the background of this comment lies the latent idea that people implicitly only attribute properties if they appear to belong uniquely to some one thing. Not only must a property belong to that thing alone, but it must always belong to it. If not, in Aristotle’s eyes, it is merely a temporary or quasi-property. He gives as examples the relative property “being on the right,” relative because it depends on a temporary relation of space and can change. Similarly, “bipedal,” as a biological categorization, is a term created to distinguish it from other animals which have 4 feet.

Near the end of his discussion Aristotle returns to the idea that properties must apply reciprocally to the things they are properties of, and shows the absurdity of disagreeing. “If something sleeps, it is a man,” is absurd. Although one could understandably (and mistakenly) think that sleep is a property of man, the possibility can be tested by “flipping” the subject and predicate and deciding if what ensues is nonsense.

1
Ἴδιον δ’ ἐστὶν ὃ μὴ δηλοῖ μὲν τὸ τί ἦν εἶναι, μόνῳ δ’
ὑπάρχει καὶ ἀντικατηγορεῖται τοῦ πράγματος. οἷον ἴδιον
ἀνθρώπου τὸ γραμματικῆς εἶναι δεκτικόν· εἰ γὰρ ἄνθρωπός (20)
ἐστι, γραμματικῆς δεκτικός ἐστι, καὶ εἰ γραμματικῆς δε-
κτικός ἐστιν, ἄνθρωπός ἐστιν. οὐθεὶς γὰρ ἴδιον λέγει τὸ ἐν-
δεχόμενον ἄλλῳ ὑπάρχειν, οἷον τὸ καθεύδειν ἀνθρώπῳ, οὐδ’
ἂν τύχῃ κατά τινα χρόνον μόνῳ ὑπάρχον. εἰ δ’ ἄρα τι
καὶ λέγοιτο τῶν τοιούτων ἴδιον, οὐχ ἁπλῶς ἀλλὰ ποτὲ ἢ (25)
πρός τι ἴδιον ῥηθήσεται· τὸ μὲν γὰρ ἐκ δεξιῶν εἶναι ποτὲ
ἴδιόν ἐστι, τὸ δὲ δίπουν πρός τι ἴδιον τυγχάνει λεγόμενον,
οἷον τῷ ἀνθρώπῳ πρὸς ἵππον καὶ κύνα. ὅτι δὲ τῶν ἐνδεχο-
μένων ἄλλῳ ὑπάρχειν οὐθὲν ἀντικατηγορεῖται, δῆλον· οὐ γὰρ
ἀναγκαῖον, εἴ τι καθεύδει, ἄνθρωπον εἶναι. (30)

The Four Predicables: Definition

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Aristotle, in Topica 1.IV, discussed the basis of propositions and problems, the later of which are merely the former recast in question form.  A proposition is assumed to be of the form, “A is an X.”  Thus, we have the traditionally assigned term, “predicable,” that is, something which can be predicated of a thing.  For example, “John is a two footed animal” or “Man is capable of learning to type” are two propositions and each subject, “John” and “Man” has something predicated of it, respectively a “two footed animal,” and “capable of learning to type.”  Whether Aristotle has intended to exhaustively account for all predicables, that is, attributes which are said to be about some thing “X”, we do not know.  It does appear though, that this four-fold division into definition, property, genus and accident is able to suffice for all practical purposes.
Let us look now at all the first predicable, definition.

One must speak about what definition is, what a property is, what a genus is, and what an accident is.  A definition is a phrase which signifies the essence.  A phrase is either given in exchange for a word or a phrase in exchange for another phrase.  For it is possible for one of the things being signified to be defined by a phrase.  When people make a proposition by assigning a name by some way, it is obvious that they do not give the definition of a thing, since every definition is a kind of phrase.  Indeed one must consider such a thing “definitional”, such as, “the seemly is noble.”  And likewise, “Whether perception and knowledge are the same thing or different?”  For most of the effort concerning definitions is whether something is the same or different.  Simply let all those things be called “definitional” which come under the same method as definitions.  That all the things just said are such, it is obvious from these.  When we are able to argue that things are the same or different, we are also able to undertake this same way regarding definitions.  For pointing out that things are not the same, we will have destroyed the definition.  The thing just said cannot be said in reverse though.  For it is not sufficient for proving a definition to point out that something is the same; though it is sufficient for demolishing a definition to point out that something is not the same.[i]  Topica 101b36-102a17 

We might have expected Aristotle to have given us a clear and detailed definition of “definition,” since it this idea, at least from the time of Socrates, that appears to be the starting point for philosophical discourse.  Aristotle is stinting as often, however, and we do not quite receive as full an explanation as we had wished.

Aristotle begins by pointing out that a definition is necessary and sufficient to describe the essence of something.  Because it sets up the minimal conditions of what something is, a definition cannot be as simple as a single word.  A definition must be a phrase.  For example the phrase, “A flat-surfaced, 4 legged object,” could correspond, as a definition, to the word, “table.”  Likewise, “[A table is] a flat-surfaced, 4 legged object,” could be used in place of another phrase, such as, “horizontally raised plane.”  We could alternatively, for instance, say, “a horizontally raised plane” is a “flat-surfaced, 4 legged object.”

When something is merely a copulative pairing, such as, “x is y,” Aristotle prefers to call it “definitional” (horikos) rather than properly a definition (horos/horismos).

Aristotle makes the fascinating point that much of the time and effort in coming up with definitions involves determining similarities and differences between two things.  Furthermore, by giving either an example or a counterexample I can prove or disprove a definition.  If I maintain that a, “horizontally raised plane” is, in fact, a “table,” such a designation may be insufficiently determinative of the “essence” of the thing in question.  Thus the phrase, “horizontally raised plane” is insufficient for demonstrating a given definition, at least by the method of providing examples.  Another way of saying this is that if I point out objects which are really tables, they would also match the description of “horizontally raised plane.”  That an actual table happens to match up with my definition of table might in fact be a mere coincidence, owing to the broad and accommodating definition I have offered.  As Aristotle correctly puts it, therefore, you cannot prove a definition in this way.  On the other hand, however, one could disprove a definition by offering a counterexample.  “Horizontally raised plane” also includes things such as desks, cabinets or even geographical landmarks such as plateaus.  Because of the imprecision in this case (perhaps flat-out error in another example of a definition), the definition of a table as a, “horizontally raised plane” has been refuted.  Thus counterexamples have proved the definition incorrect.

 


[i] Λεκτέον δὲ τί ὅρος, τί ἴδιον, τί γένος, τί συμβεβηκός.
ἔστι δ’ ὅρος μὲν λόγος ὁ τὸ τί ἦν εἶναι σημαίνων, ἀποδίδο-
(102a.) ται δὲ ἢ λόγος ἀντ’ ὀνόματος ἢ λόγος ἀντὶ λόγου· δυνατὸν
γὰρ καὶ τῶν ὑπὸ λόγου τινὰ σημαινομένων ὁρίσασθαι. ὅσοι
δ’ ὁπωσοῦν ὀνόματι τὴν ἀπόδοσιν ποιοῦνται, δῆλον ὡς οὐκ
ἀποδιδόασιν οὗτοι τὸν τοῦ πράγματος ὁρισμόν, ἐπειδὴ πᾶς
ὁρισμὸς λόγος τίς ἐστιν. ὁρικὸν μέντοι καὶ τὸ τοιοῦτον θετέον, (5)
οἷον ὅτι <τὸ> καλόν ἐστι τὸ πρέπον. ὁμοίως δὲ καὶ τὸ πότερον
ταὐτὸν αἴσθησις καὶ ἐπιστήμη ἢ ἕτερον· καὶ γὰρ περὶ τοὺς
ὁρισμοὺς πότερον ταὐτὸν ἢ ἕτερον ἡ πλείστη γίνεται δια-
τριβή. ἁπλῶς δὲ ὁρικὰ πάντα λεγέσθω τὰ ὑπὸ τὴν αὐτὴν
ὄντα μέθοδον τοῖς ὁρισμοῖς. ὅτι δὲ πάντα τὰ νῦν ῥηθέντα  (10)
τοιαῦτ’ ἐστί, δῆλον ἐξ αὐτῶν. δυνάμενοι γὰρ ὅτι ταὐτὸν
καὶ ὅτι ἕτερον διαλέγεσθαι, τῷ αὐτῷ τρόπῳ καὶ πρὸς τοὺς
ὁρισμοὺς ἐπιχειρεῖν εὐπορήσομεν· δείξαντες γὰρ ὅτι οὐ ταὐτόν
ἐστιν ἀνῃρηκότες ἐσόμεθα τὸν ὁρισμόν. οὐ μὴν ἀντιστρέφει γε
τὸ νῦν ῥηθέν· οὐ γὰρ ἱκανὸν πρὸς τὸ κατασκευάσαι τὸν ὁρι- (15)
σμὸν τὸ δεῖξαι ταὐτὸν ὄν. πρὸς μέντοι τὸ ἀνασκευάσαι αὔτ-
αρκες τὸ δεῖξαι ὅτι οὐ ταὐτόν.

 

Thinking of Thought in the Thought of Aristotle’s God Part 3/3

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“Indeed in some situations knowledge is the important thing, while in the productive arts without matter the substance and the essence are the important thing, while in the theoretical arts logic and the thought are the important thing.  Therefore, because the thing being thought and the intellect are not different, in so far as they possess no matter, the same thing will be the case, and thought is one thing in the thing being thought.

 Yet surely difficulties remain, if the thing being thought is composite.  For there would be change in the parts of the whole intellect.  In fact, that which does not possess matter is entirely indivisible.  In the same way the human intellect is indivisible, or at least a composite creature in a certain time is indivisible (for being well does not consist in this time or that time, but the best is in the whole of life, because it is something else), in this way the mind itself is from itself for the extent of eternity.”  (Metaphysics 1075a1-10) 1

Part 1       Part 2

Aristotle has to this point (Metaphysics 1074b15-1075) arrived at the following conclusions about nous, beginning from the premise that it is the most divine and honorable thing (from which idea nous is necessarily also an actuality, not a potentiality):  1)  It thinks 2) It thinks about the same thing 3) It thinks about the same thing all the time 4) It thinks about the most divine and honorable thing 5) It thinks about itself, since it is the most divine and honorable thing.

As my last post ended, I perhaps unskillfully made the decision to cut Aristotle’s text at a point which would allow for three somewhat equal sections, and thus three posts.  In order to rectify that division I have to “restitch” the last part of that section and the first part of this section.  As section 1074 closed, Aristotle had proved that a mental state itself and the object of that state can be, but are not necessarily, the same thing.  As 1075 begins Aristotle says that in some sciences the thing being thought is the knowledge.  Thus in Aristotle’s sense, it can be equally said that knowledge is the thing being thought.  He appeals to the productive and theoretical sciences for his examples.  A productive science builds or produces an end product.  This product could be a physical good, but it could also be a “product” like rhetoric.  Thus, in Aristotle’s words, in the case of a “productive science without matter” such as rhetoric, to think of the thing is to actually produce the thing itself.  The act of conceiving a good speech is to actually possess a good speech, even though one may still need to deliver it.  Likewise, as both nous and the object of nous’ thinking are also “without matter,” they are one and the same thing.  Yet Aristotle brings up another potential difficulty if we understand the object of thought to be composite (suntheton).  For nous itself would change insofar as at different times it would think about different parts of this composite, and thus it would change (a change of state) from thinking about X to thinking about Y.  However, nous has already been described as that which always thinks about the best thing, and never changes from such a state. Thus, we seem to have a contradiction in the nature of nous if we say that nous (1) always thinks about the same thing and (2) thinks about a composite thing.

Aristotle answers this difficulty by pointing out that the totality of the things composing a thought, if indeed it is composite, nevertheless is a thing separate from each of its constituents.  Indeed the whole is greater than the sum of its parts.  By analogy with an argument Aristotle makes in the Nicomachean Ethics wherein he states that happiness is achieved by the totality of a life lived in accordance with the virtues, he similarly presses the point here that the thought of nous is a unified, coherent and separate entity different from the mere elements that individually constitute it.  Just as we may accurately speak of a “single” life, we can speak of a “single” thought, because both of these are of a qualitatively different nature than just a collection of virtues or thoughts, respectively.

 

1 ἢ ἐπ ̓ ἐνίων ἡ ἐπιστήμη τὸ πρᾶγμα, ἐπὶ μὲν τῶν ποιητικῶν ἄνευ ὕλης ἡ οὐσία καὶ τὸ τί ἦν εἶναι, ἐπὶ δὲ τῶν θεωρητικῶν ὁ λόγος τὸ πρᾶγμα καὶ ἡ νόησις; οὐχ ἑτέρου οὖν ὄντος τοῦ νοουμένου καὶ τοῦ νοῦ, ὅσα μὴ ὕλην ἔχει, τὸ αὐτὸ ἔσται, καὶ ἡ [5] νόησις τῷ νοουμένῳ μία. ἔτι δὴ λείπεται ἀπορία, εἰ σύνθετον τὸ νοούμενον: μεταβάλλοι γὰρ ἂν ἐν τοῖς μέρεσι τοῦ ὅλου. ἢ ἀδιαίρετον πᾶν τὸ μὴ ἔχον ὕλην—ὥσπερ ὁ ἀνθρώπινος νοῦς ἢ ὅ γε τῶν συνθέτων ἔχει ἔν τινι χρόνῳ (οὐ γὰρ ἔχει τὸ εὖ ἐν τῳδὶ ἢ ἐν τῳδί, ἀλλ ̓ ἐν ὅλῳ τινὶ τὸ ἄριστον, ὂν ἄλλο τι)— [10] οὕτως δ ̓ ἔχει αὐτὴ αὑτῆς ἡ νόησις τὸν ἅπαντα αἰῶνα;