TY - JOUR
ID - 24932
TI - The Cube of Opposition: the Interrelations of Infinites
JO - Philosophy and Kalam
JA - JITP
LA - en
SN - 2008-9422
AU - Fallahi, Asadollah
AD -
Y1 - 2012
PY - 2012
VL - 45
IS - 1
SP - 123
EP - 143
KW - Conversion
KW - Cube of Opposition
KW - Infinite proposition
KW - Obversion
KW - Square of Opposition
DO - 10.22059/jitp.2012.24932
N2 - Some contemporary logicians have introduced a new simple method of logical consequences and reduced all immediate arguments to Conversion and Obversion. By dint of positive and infinite terms, one of the logicians, Reza Akbari, increased the four traditional quantified propositions to 32 ones: the 4 well-known positives, 4 subject-infinites, 4 predicate-infinites, 4 two-sided-infinites, and the same 16 with ‘A’ and ‘B’ in which converted. Akbari, also, stated among some of the 32 propositions the interrelations: the opposition square, conversion, conversion by contradiction, obversion, inversion, and two new relations: “contraposition of the subject” and the “unknown”. This theory extending the classical 4-quntified-theory can be named “32-quntified-theory”. In this paper, I show that the 32 propositions are equivalent four-by-four, hence, we can reduce the 32 propositions to 8 ones and their relations to the six: equivalence, implication, inconsistency, inclusive ‘or’, exclusive ‘or’ and none (which is the same as Akbari’s “unknown”. By this, I decrease the perplexities of the theory and express so easily and elegantly the relations between the eight in a cube similar to the “Square of Opposition,” which I call the “Cube of Opposition.”
UR - https://jitp.ut.ac.ir/article_24932.html
L1 - https://jitp.ut.ac.ir/article_24932_be877ce2655aa84818d81eb2d7f88045.pdf
ER -