I'm reading Ray Monk's biography of Wittgenstein and, on a scathing book review of Wittgenstein's, Monk writes,

There follows a list of such mistakes, which are, for the most part the weaknesses of traditional (Aristotelian) logic customarily pointed out by adherents of Russellian mathematical logic - for instance, that it assumes the copula 'is' (as in 'Socrates is mortal') with the 'is' of identity ('Twice two is four'), and so on.

I was wondering if somebody could explain these criticisms to somebody who has never studied philosophy?

  • See also the related post: Wittgenstein criticizes Coffey's work The science of logic Commented Mar 20, 2018 at 14:55
  • J, Hintikka has strongly opposed the received view about the differences in use of 'is' and even said plainly that it is wrong. Two of his papers: (1984) * Semantical games, the alleged ambiguity of ‘is’, and Aristotelian categories*, Synthese, vol. 54, p. 443–68; (1979) * “Is”, semantical games, and semantical relativity*, J. of Phph. Logic, vol 8, p.433–68.
    – sand1
    Commented Mar 20, 2018 at 20:09

1 Answer 1


"is" in modern logic has different translations, according to the context:

(i) identity: "Socrates is the teacher of Plato".

(ii) membership: "Socrates is mortal", that means that the individual Socrates belongs to the set (or class) of mortals.

(iii) inclusion: "French are Europeans", that means that the set (or class) of French is included into (is a subset of) the set of Europeans.

Aristotelian Logic (based on the syllogism) is based on the grammatical relation of predication: Socrates is human, Plato is not a horse, horses are animals, humans are not horses:

One major difference between Aristotle’s understanding of predication and modern logic is that Aristotle treats individual predications and general predications as similar in logical form: he gives the same analysis to “Socrates is an animal” and “Humans are animals”.

  • Why do you say "grammatical relation" and simply not, e.g., "logical relation"?
    – Geremia
    Commented Mar 20, 2018 at 17:46
  • This strikes me as more or less right, although it's worth emphasizing that what distinguishes (i) - (iii) is that distinct expression types flank 'is' in each case: singular terms in (i); a singular term and a predicate in (ii); and two predicates in (iii). Commented Mar 20, 2018 at 18:34

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