David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Philosophical Psychology 6 (4):423 – 440 (1993)
Following an earlier paper (Wetherick, 1989), the analysis of syllogistic reasoning via the medieval doctrine of “distribution of terms” is pursued and completed. The doctrine was not originally presented as an explanation of syllogistic reasoning but turns out to furnish one. It is shown that: It is impossible to assert two propositions having a distributed middle term in common without, at the same time, tacitly asserting the valid conclusion, if any. When the middle term is distributed but no valid conclusion follows, this is a consequence of the distributional status of the subject and predicate terms. When the middle term is not distributed the propositions have nothing but a name in common. The logic of Spencer Brown (1969) is employed to show that logic is implicit in the behaviour of any organism that survives by making distinctions (e.g. between prey/non-prey; predator/non-predator). It is suggested that animal organisms answer this description by definition. Cognitive structures have evolved in the human organism so as to permit the conversion of habitual associations into universal propositions thus allowing formal logic and mathematics. This view appears to require a reversion to psychologism in logic, the consequences are considered and judged acceptable.
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Guy Politzer, Jean‐Baptiste Henst, Claire Delle Luche & Ira A. Noveck (2006). The Interpretation of Classically Quantified Sentences: A Set‐Theoretic Approach. Cognitive Science 30 (4):691-723.
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