Within the categorical syllogism, ordinary language represents the ordinary flow of inference. Two premises are given; there is a plash of insight, and one step undertaken. The mind hops right along, not quite knowing where it is going but getting there nonetheless. On the right, a checklist does its work. The logician's clamp retains its force of old, but the inferential steps involve no more than the substitution of symbols for symbols, with the anchor of inference embedded in identities. Inference now proceeds from one identity to the next; no plash of insight is involved, only the solid satisfying ratcheting sound of symbols being substituted for symbols.
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