5. Formalism (IV); Session Dec. 16, 2014

[Today we are all with the school in Peshawar attacked by this horrible crime. Logic has only very limited access to fundamentalist religion & faith. Where there’s no reason there is no logic. But since the term λόγος also stands for ‘speech’ (4.2.2), it’s even more for us today, all over the world, to support the voice of reason. My little share in this may be this seminar here. That’s certainly not much! But let’s continue with it nevertheless]:

5.1 The ‘Syllogism of Words’ (SoW), of which we spoke at the end of the last session, is, or can be, of things too.

5.2 But while the ‘Syllogism of Things’ (SoT) deduces statements about things from things, SoW deduces meanings from meanings.

5.3 Meanings of words that designate or signify things. But not all words designate things. Words in purely formal deductions do not.

5.4 Or so it’s customarily assumed. Recall the distinction between form & content of previous sessions (2.6 ff., 3.5 ff., 3.9 ff., 3.10.4 ff.).

5.5 However, the meaning of this distinction itself is not at all clear.

5.6 Even the deduction of statements about things from things (5.2) is, of course, from statements (!) about things.

5.7 Thus it’s statements either way, that is, in both SoW and SoT.

5.8 And it’s statements that are either formal or have material content; never ‘things.’

5.9 Logic then inquires into the relationships among terms & statements, whether they be about terms & statements, or about ‘things.’

5.10 For the classification of terms Aristotle used the term Categories (κατηγορίες).

5.11 In peripatetic & scholastic scholarship the Categories were fraught with ontological connotations (4.3.1 ff.). That’s not over yet.

5.12 Most scholars today, however, take the categories as predicables, viz. as terms that classify terms (usually more or less following Kant, Critique of Pure Reason B 107 f., who had “Prädikamente,” that is, ‘Predicaments,’ according to the Cambridge Edition of Kant’s Works; see also Prolegomena, § 39: Plus “Prädikabilien”).

5.13 Aristotle’s Categories list types of predicates, i.e., types/kinds of expressions/terms that can be predicated of something.

5.14 These categories are: Substance/Essence (what), Quantity (how much, how large), Quality (what sort of thing), Relation (half, double, greater than), Location (where), Time (when), Position (also: posture, stance, attitude), State/Condition/Possession (how circumstanced), Action/Activity, and Passivity/Affection.

5.14.1 Aristotle names somewhat different categories at different times and different places:

5.14.2 Compare Categories 1b25-2a4 with e.g. Topica 103b20-25 & Metaphysics 1003b5 ff.

5.15 Generally, though, Categories in Aristotle are somewhat highest genera in the game of predication.

5.16 That is, each category designates one possible relationship between predicate & subject.

5.17 That is, some predications say of their subject ‘what it is,’ others what it is like, again others how much or how heavy it is, etc.

5.18 Accordingly, Aristotle is quickly to note: None of the category terms has any truth value, viz. is true or false (Categories 2a5 ff.).

5.19 Truth values can only be generated by combination of these terms to statements. That’s especially true for Substance.

5.19.1 Take the word ‘tree.’ There’s nothing true or false in the term itself. Only when we combine it with other predicates we get a statement that can be true/false (and like before in 5.8: Only statements can be true or false; never ‘things;’ cf. Metaphysics Bk VII, ch 4).

5.19.2 For example: This tree is a plant (substance) which is green (quality) and stands on a hill (location). [For those metaphysicians or ontologists among us who are searching for a ‘deeper’ sense of Substance than a plant; see Metaphysics 1032a19].

5.20 With this in hand, there is no need to speculate metaphysically about substance, or so-called substantial forms (4.3.2 ff).

5.21 Nor do we need an ontology of ‘abstract entities.’ We can safely leave it to the natural sciences to develop the resp. genera.

5.22 And as Aristotle himself noted: Existence (or Being) is not a genus; Metaphysics 998b21-24.

5.23 Nor is ‘existence’ a predicate; we come back to this when we study Kant on logical formalism (for those already curious: see Critique of Pure Reason B 626 f.).

5.24 This does not mean that we don’t need any philosophy at all! Philosophy is first & foremost an endeavor about words & interpretation.

5.25 And philosophy in the analytic tradition has dealt with just this: With the semantics & syntax of (scientific) language.

5.26 Here then are we back to the Syllogism of Words. It’s about the logical operations of conjunction, negation & conditionals.

5.27 And last, but not least, about quantification; the ontological philosopher’s “everything” when universally quantifying over ‘things.’

5.28 As you might have guessed then, the conditions of the Syllogism of Words are the preconditions of the Syllogism of Things.

5.29 This will be our program. In the next few sessions, however, we’ll be still concerned with some history (e.g. Descartes, Kant, Frege).