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4. Formal Logic / A. Syllogistic Logic / 3. Term Logic

[Sommers's modern updating of syllogistic logic]

5 ideas
18904 'Predicable' terms come in charged pairs, with one the negation of the other [Sommers, by Engelbretsen]
     Full Idea: Sommers took the 'predicable' terms of any language to come in logically charged pairs. Examples might be red/nonred, massive/massless, tied/untied, in the house/not in the house. The idea that terms can be negated was essential for such pairing.
     From: report of Fred Sommers (Intellectual Autobiography [2005]) by George Engelbretsen - Trees, Terms and Truth 2
     A reaction: If, as Rumfitt says, we learn affirmation and negation as a single linguistic operation, this would fit well with it, though Rumfitt doubtless (as a fan of classical logic) prefers to negation sentences.
18895 Logic which maps ordinary reasoning must be transparent, and free of variables [Sommers]
     Full Idea: What would a 'laws of thought' logic that cast light on natural language deductive thinking be like? Such a logic must be variable-free, conforming to normal syntax, and its modes of reasoning must be transparent, to make them virtually instantaneous.
     From: Fred Sommers (Intellectual Autobiography [2005], 'How We')
     A reaction: This is the main motivation for Fred Sommers's creation of modern term logic. Even if you are up to your neck in modern symbolic logic (which I'm not), you have to find this idea appealing. You can't leave it to the psychologists.
19053 Logic would be more natural if negation only referred to predicates [Dummett]
     Full Idea: A better proposal for a formal logic closer to natural language would be one that had a negation-operator only for (simple) predicates.
     From: Michael Dummett (Presupposition [1960], p.27)
     A reaction: Dummett observes that classical formal logic was never intended to be close to natural language. Term logic does have that aim, but the meta-question is whether that end is desirable, and why.
13916 Term logic uses expression letters and brackets, and '-' for negative terms, and '+' for compound terms [Engelbretsen/Sayward]
     Full Idea: Term logic begins with expressions and two 'term functors'. Any simple letter is a 'term', any term prefixed by a minus ('-') is a 'negative term', and any pair of terms flanking a plus ('+') is a 'compound term'. Parenthese are used for grouping.
     From: Engelbretsen,G/Sayward,C (Philosophical Logic: Intro to Advanced Topics [2011], 8)
     A reaction: [see Engelbretsen and Sayward for the full formal system]
18907 Term logic rests on negated terms or denial, and that propositions are tied pairs [Engelbretsen]
     Full Idea: That terms can be negated, that such negation is distinguishable from denial, and that propositions can be construed syntactically as predicationally tied pairs of terms, are important for the tree theory of predication, and for term logic.
     From: George Engelbretsen (Trees, Terms and Truth [2005], 2)