%0 Journal Article
%T Impossible Extensions and the Logic of the Concepts
%J Philosophy
%I University of Tehran
%Z 2008-1553
%D 2012
%\ 02/20/2012
%V 9
%N 2
%P 163-184
%! Impossible Extensions and the Logic of the Concepts
%K verity-propositions
%K Ibn-Sina
%K Al-Khunaji
%K Al-Abhari
%K impossible extensions
%K second-order logic
%R
%X A controversy among the Muslim philosophers about the domain of the extensions was that is the subject of the verity-propositions contained the impossible extensions or only all of the actual and possible ones. From Ibn-Sina to Al-Khunaji, there are explicit texts to the former view; but later logicians, starting with Athir Al-Din Al-Abhari, were inclined to the latter. In this paper, we attampt to support Ibn-Sina and Al-Khunaji's view versus Al-Abhari's. For this, we take the extensions as sets of concepts. If an extension is a set of inconsistent concepts we'll regard it impossible and name its logic ‘the logic of the concepts’. For systematizing the logic, we introduce a semantics similar to that of predicate logic and construct a formal system in the first-order language. We show that the logical system can be collapsed to a fraction of the second-order logic, concluding that Ibn-Sina and Al-Khunaji's view can be supported by the second-order logic.
%U https://jop.ut.ac.ir/article_35806_a8763564064a04fad8b0400d3d881c1b.pdf