The schoolman, in the fourth book of his Commentary of Aristotle's Metaphysics a commentary which is full of the most ingenious and original views, not only asserts to the law of Identity a coordinate dignity with the law of Contradiction, but, against Aristotle, he maintains that the principle of Identity, and not the principle of Contradiction, is the one absolutely first.
12.
Enumerated and championed by Graham Priest, who was heavily influenced by Richard Routley, this strategy forms the notion of " noneism . " In short, assuming there exist infinite possible and impossible worlds, objects are freed from necessarily existing in all worlds, but instead may exist in impossible worlds ( where the law of contradiction does not apply, for example ) and not in the actual world.
13.
But afterwards, in every row the output q is compared to the now-independent input p and any inconsistencies between p and q are noted ( i . e . p = 0 together with q = 1, or p = 1 and q = 0 ); when the " line " is " remade " both are rendered impossible by the Law of contradiction ~ ( p & ~ p ) ).
14.
In his investigation he comes back now and then to the three traditional laws of thought, singling out the law of contradiction in particular : " The conclusion that the law of contradiction is a law of " thought " is nevertheless erroneous . . . [ rather ], the law of contradiction is about things, and not merely about thoughts . . . a fact concerning the things in the world ."
15.
In his investigation he comes back now and then to the three traditional laws of thought, singling out the law of contradiction in particular : " The conclusion that the law of contradiction is a law of " thought " is nevertheless erroneous . . . [ rather ], the law of contradiction is about things, and not merely about thoughts . . . a fact concerning the things in the world ."
16.
In his investigation he comes back now and then to the three traditional laws of thought, singling out the law of contradiction in particular : " The conclusion that the law of contradiction is a law of " thought " is nevertheless erroneous . . . [ rather ], the law of contradiction is about things, and not merely about thoughts . . . a fact concerning the things in the world ."
17.
Starting from these eight tautologies and a tacit use of the " rule " of substitution, PM then derives over a hundred different formulas, among which are the "'Law of Excluded Middle K'1.71 "', and the "'Law of Contradiction K'3.24 "'( this latter requiring a definition of logical AND symbolized by the modern ?" : ( p ?" q ) = def ~ ( ~ p ?" ~ q ) . ( PM uses the " dot " symbol ?% for logical AND ) ).
