at1with0 wrote:Transformation of statements into all of their tautologically- equivalent statements or perhaps some form of consequence closure?
Some people might argue that the Law of Identity is flawed:
X = X
because it it tries to make the statement that a thing is itself ...but in doing so, it generates an error because two different X's are required to be separated by the equals sign. The two X's are actually NOT the same thing as they both exist in different spatial and temporal coordinates.http://en.wikipedia.org/wiki/Tarski%27s ... ty_theorem
http://www.science.uva.nl/~seop/archive ... scernible/
Tarski's undefinability theorem, stated and proved by Alfred Tarski in 1936, is an important limitative result in mathematical logic, the foundations of mathematics, and in formal semantics. Informally, the theorem states that arithmetical truth cannot be defined in arithmetic.
The theorem applies more generally to any sufficiently strong formal system, showing that truth in the standard model of the system cannot be defined within the system.
The Identity of Indiscernibles
The Identity of Indiscernibles is a principle of analytic ontology first explicitly formulated by Wilhelm Gottfried Leibniz in his Discourse on Metaphysics, Section 9 (Loemker 1969: 308). It states that no two distinct substances exactly resemble each other. This is often referred to as `Leibniz's Law' and is typically understood to mean that no two objects have exactly the same properties. The Identity of Indiscernibles is of interest because it raises questions about the factors which individuate qualitatively identical objects.
We can summarize the argument simply by saying that two things are equivalent if and only if they both have the exact same properties.
Yes, the law of identity appears to be an assertion but not a self evident truth unless further clarification is used.
X is not equal to not-X
is more of a self evident truth
This would agree with a fractal basis of reality and a plausible isomorphism between abstract and concrete