The Black Vault

Does that mean truth is random?

at1with0 wrote:Does that mean truth is random?

Truth is an invariance principle

Invariant upon what type of transformation?

at1with0 wrote:Invariant upon what type of transformation?

What indeed...

Transformation of statements into all of their tautologically- equivalent statements or perhaps some form of consequence closure?

Maybe there are different types of truths?
I mean, why not?
one's that depend on perception...one's that depend on the variable setr up at the time
and ultimate truths
Why does it have to be an either/or thing?
Westerners can get trapped into dualistic thinking.

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

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.

http://www.science.uva.nl/~seop/archive ... scernible/

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

hmm..
that's true..and it supports the argument that everything is unique and special
"no two snowflakes"
and the like

I mean two..implies..well..two..equivalent..but still two..seperate

"One is one and all alone and ever more shall be so"

bionic wrote:Maybe there are different types of truths?
I mean, why not?
one's that depend on perception...one's that depend on the variable setr up at the time
and ultimate truths
Why does it have to be an either/or thing?
Westerners can get trapped into dualistic thinking.

Usually, I just consider the ultimate truths to be what I'd call true. Tho one can say "I perceived X" and be ultimately true about that.

khanster wrote: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.

I thought that truth was defined in order to prove that statement about truth. What "truth cannot be defined" means is that there is no first order formula that "generates" truth like 1+1=2.

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

touche

But what is more "self evident" just might be what's more apparently obvious. Some people would say that X=X is more apparently obvious.