November the 5th.
Minutes.
ON Topics I.
(I use the english translation of the Loeb edition)
The main subject the Topica deals with is syllogistic reasoning, i.e. its main features and constituting elements. He (Aristotle?) starts immediately by drawing a distinction between dialectical and contentious reasoning (ἐριστικὸς συλλογισμός). Συλλογισμός and συλλογίζεσθαι are compound words formed through assimilation: συν- and -λογισμός and συν- and λογίζεσθαι. They mean reasoning. A reasoning can be identified when it finishes. When someone says something we do not quite fully understand we might ask how he came to that conclusion. He could have jumped or rushed into it. He could also have thought about it thoroughly.
A reasoning is a way of applying certain rules to combine more elemental structures. These elemental structures are phrases or declarative sentences which are either affirmative or negative, existential or universally formulated.
Take for instance A and B in the “modus ponens” (A implies B. A. Therefore, B) and in the “modus tollens” (A implies B. Not B. Therefore not A) and take A, B and C in the hypothetical syllogism (If A, then B. If B, then C. Therefore, if A then C). A, B and C can be premises. B and C can be conclusions. B can be both a premise and a conclusion.
A, B and C isolated are however the elemental structures, each of which may be represented through a phrase or a declarative sentence. If A, B and C are sentences of the type “S is P”, “S is not P”, “Some S’s are P”, “Some S’s are not P”, “Every single S is P” or “There is no S that is P”, we need to know how they arrive at? their meaning, their reasoning basis, and whether they are true sentences or false ones.
Before we can move on to investigating how we formally deduce a true conclusion from some premises, the proper function of the συλλογισμός and συλλογίζεσθαι, we need to isolate the λόγος structure as its elementary and basic feature. The ΣΥΝ does not apply if we do not arrive first at a sentence, the elementary logical meaning structure.
Aristotle begins his investigation about what our opinions of (or thoughts about) things are grounded upon.
Text 1:
So “[in order to grasp dialectical reasoning] we need to find a method of investigation (μέθοδον) whereby we shall be able to reason from
opinions that are generally accepted (ἐξ ἐνδόξων) about every problem propounded to us (περὶ παντὸς τοῦ προτεθέντος προβλήματος). When we hold to a λόγος, there is nothing we can say that will contradict it (μηθὲν ἐροῦμεν ὑπεναντίον.)” Top. 100a18-242
Our concern is with the logical elementary structure, the λόγος. So we skip to A. IV.
Text 2. “First, then, we must see the parts of which our inquiry consists. Now if we were to grasp (a) with reference to how many, and what kind of, things οἱ λόγοι take place, and with what materials they start, and (h) how we can become well supplied with these, we should have sufficiently won our goal. Now the materials with which οἱ λόγοι start are equal in number, and are identical, with the subjects on which reasonings, συλλογισμοί, take place. For arguments start with 'propositions' (γὰρ οἱ λόγοι ἐκ τῶν προτάσεων) while the subjects on which reasonings take place are 'problems' (περὶ ὧν δὲ οἱ συλλογισμοί, τὰ προβλήματά ἐστι.). Now every proposition and every problem let us know (πᾶσα δὲ πρότασις καὶ πᾶν πρόβλημα δηλοῖ) either a peculiarity (ἴδιον) or genus (γένος) or an accident (συμβεβηκός).” Top. 101b11-19.
Text 3.
“The specific generic difference (διαφορά γενική) should be ranked (τακτέον) together with the genus (ὁμοῦ τῷ γένει).” Top. 101b18-19.
Aristotle is now ready to state the elementary formal features that constitute a λόγος. These are: “definition, ὅρος, peculiarities?, ἴδιον, genus, γένος, and incident (accident?), συμβεβηκός.” Before getting into a detailed analysis, let us briefly sketch the path Aristotle takes. His aim is to define what syllogistic reasoning is. He presents several ways of how reasoning takes place. He then zooms in on λόγος as the elemental structure of meaning. A λόγος may be a πρότασις, a sentence, S is p, which can be modified to a problem: whether S is p or not or whether it is or is not the case that S is p. It can also be the conclusion of a reasoning, a combination of several προτάσεις.
The terminus technicus λόγος is a sentence of the type: S is p. The question is how soundly S is thereby defined. The issue is not only to determine what are the grounds for us understanding that this is the case. A) It is the opinion of the majority. B) It is the opinion expressed by the experts. C) it is an axiom. D it is the result of a demonstration. What we are trying to determine is the kind of statement that catches the essence of something. Catching the “what it means to be the sort of thing this thing is”
To define something is to say what is particularly idiosyncratic about it. Now this something may for sure have some idiosyncratic characteristics which do not necessarily define it. They serve to momentarily help us identify this something or someone out of many others things that are very similar. We will go into this later. For the time being let us say that this is a property something or someone has at a particular time and in relation to others. This property is circumstantial, depending upon either time or a given relationship or connexion with others. So when I want to get someone’s attention, I tell another person to call me that guy over there, sitting on the right side of someone else, etc., etc. I do not even refer to my friend by his name, let alone saying who he is for me, a friend, an acquaintance or whatever.
On the other hand “what is peculiar, ἴδιον, to something means or signifies what it takes to be the thing that it is. What characterizes something in its peculiarity, what the thing has of its own, its ownness, is a definition: ὅρος. So “An animal that walks on two feet” is the definition, ὁρισμός, of “man”. “A man’s being a walking man on two feet” is what it takes for an animal to be a man, or for something to be someone.
Text 4
“A 'definition', ὅρος, is a phrase, λόγος, signifying, σημαίνων, a thing's essence, τὸ τί ἦν εἶναι. It is rendered (ἀποδίδοται) 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.” Top. 101b37-102a1.
Text 6
“It is sometimes possible to define what conveys meaning by a phrase as well (τῶν ὑπὸ λόγου τινὰ σημαινομένων ὁρίσασθαι). Those whο give an explanation (τὴν ἀπόδοσιν ποιοῦνται) with only a designation (ὀνόματι) clearly do not render a definition of the thing in question ([ὁ] τοῦ πράγματος ὁρισμός), because a definition is always a phrase of a certain kind (πᾶς ὁρισμὸς λόγος τίς ἐστιν.).”
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