On 6/18/2015 1:10 PM, John Clark wrote:
On Thu, Jun 18, 2015 at 1:51 PM, meekerdb <[email protected] <mailto:[email protected]>> wrote:> This is gitting muddled. '2+2=4' is a tautology if the symbols are given their meaning by Peano's axioms or similar axiom set and rules of inference. If the symbols are interpreted as the size of specific physical sets, e.g. my example of fathers and sons, it's not a tautology. In an equation, ant equation, isn't a tautology then it isn't true.
An equation is just a sentence. A tautology is a declarative sentence that's true in all possible worlds. 2+11=1 in worlds where addition is defined mod 12. That's why an equation alone can't be judged to be a tautology without the context of its interpretation.
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