Induction & Tautologies

[Leafy]

videogames101 seems to think the proposition

Originally posted by Aristotle
A=A

is an inductive statement. Is it inductive or deductive?

 

[videogames101]

Hmmm, in all known cases X=X is true, but in order to find thta out we attempt say 1=1, and without checking every case, we use induction to assume X=X is true.

 

[Leafy]

No, a tautology is true under any variation. That's why it's an abstraction - the variable "A" in A=A is a placeholder for any possible value. That's how you can know that A=A without checking every "case" or valuation.

 

[videogames101]

Originally posted by: Leafy
No, a tautology is true under any variation. That's why it's an abstraction - the variable "A" in A=A is a placeholder for any possible value. That's how you can know that A=A without checking every "case" or valuation.

2x=x is also an abstraction, but that doesn't make it true for all cases.