:EXAMPLE : Here Hegel embarks on a critique on one of the most basic assumptions of classical logic, the Law of Identity, usually expressed as A = A . Although superficially the immediate truth of this proposition cannot be denied, further reflection reveals that nothing absolute can be derived from it.
22.
:" "'Law of Identity . "'[ Hamilton also calls this " The principle of all logical affirmation and definition " ] "'Antonius Andreas "': The law of Identity, I stated, was not explicated as a coordinate principle till a comparatively recent period.
23.
:" "'Law of Identity . "'[ Hamilton also calls this " The principle of all logical affirmation and definition " ] "'Antonius Andreas "': The law of Identity, I stated, was not explicated as a coordinate principle till a comparatively recent period.
24.
Subsequently to this author, the question concerning the relative priority of the two laws of Identity and of Contradiction became one much agitated in the schools; though there were also found some who asserted to the law of Excluded Middle this supreme rank . " [ From Hamilton LECT . V . LOGIC . 65-66]
25.
In metaphysics, Butchvarov is perhaps best known for his work on the identity theory of universals and on the nature of informative identity statements ( that is, statements of the form " a = b "-- as opposed to instances of the law of identity, that is, statements of the form " a = a " ).
26.
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.
27.
:: : this is the crux of my'objection'. it is not aimed at cantor's diagonal argument in demonstration of uncountable entities ( note : not sets ), but at our importing the intuitive sense of'individual constituents'of the entities in question . it is one thing to say that a countably-infinite entity ( such as the set of natural numbers )'contains members with individual ontological basis', but quite another to suggest the same applies for an uncountable entity such as the continuum, in which through finitary process only a sparse subset can be differentiated . it would occur to me that the Aristotelian laws of identity and excluded middle do not appertain to what remains of the reals after the removal of the its definable elements . as such, it is inappropriate to speak of this entity as comprising individual self-same elements . talk ) 04 : 49, 7 December 2010 ( UTC)
