TY - JOUR
ID - 35806
TI - Impossible Extensions and the Logic of the Concepts
JO - Philosophy
JA - JOP
LA - en
SN - 2008-1553
Y1 - 2012
PY - 2012
VL - 9
IS - 2
SP - 163
EP - 184
KW - verity-propositions
KW - Ibn-Sina
KW - Al-Khunaji
KW - Al-Abhari
KW - impossible extensions
KW - second-order logic
DO -
N2 - 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.
UR - https://jop.ut.ac.ir/article_35806.html
L1 - https://jop.ut.ac.ir/article_35806_a8763564064a04fad8b0400d3d881c1b.pdf
ER -