Wednesday, February 20, 2013

How to know a=b b=c a=c is true?


How to know a=b b=c a=c logical principle of equivalence is true?

In argument, if premises A=B and B=C, you can apply the logical principle of equivalence to conclude that A=C.

"Define a word by repeating the word itself in the definition." is The Error of Circular Definition.

Likewise, the use of premises and conclusions to prove the logical principal is a Circular Error.

Without committing such an error, how to know the logical principle of equivalence is true?

Additional Details

Oh, Come On!, don't be so narrowed to avoid the big picture in this question.
How do you know the 'must all be identical' part in your comment is true?
How do you prove the principle without using what principle can prove?

@Curtis Edward,
Please do not divert from the main question.
You proved an example "apples" by using the logical principle, but why do you believe that the logical principle itself is true?

Dear true wisdom,

The 3 answers so far do not address the question in full.

Lack of complete answers to the question imply, the products of current education system are adamant, not to accept the baseless nature of logical principles, where the said system is assumed to base upon.

If logical principles cannot be proven on solid grounds (without Circular Error), can the applications/ conclusions based on such logical principles be valid? no

Even the existence of 'space' justification has Circular Error: point is defined using line and line is defined using point.…
"All definitions are ultimately circular in nature since they depend on concepts which must themselves have definitions, a dependence which can not be continued indefinitely without returning to the starting point."

It is fair to say, the belief in Space in Space-Time continuum is unscientific+illogical and is a result of ignorance.

Should we consider 'Aristotelian logic' to be super-mundane like freedom 'nibbana' in Buddhism?


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