Journal of Philosophical Logic

, Volume 42, Issue 2, pp 391-407

First online:

The Syllogistic with Unity

  • Ian Pratt-HartmannAffiliated withSchool of Computer Science, Manchester University Email author 

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We extend the language of the classical syllogisms with the sentence-forms “At most 1 p is a q” and “More than 1 p is a q”. We show that the resulting logic does not admit a finite set of syllogism-like rules whose associated derivation relation is sound and complete, even when reductio ad absurdum is allowed.


Syllogisms Proof theory Logic and natural language Computational complexity