Absolute certainty and universal truth.

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Mefiante (August 17, 2012, 15:58:49 PM):
Well yes, S' = P → P is a tautology (i.e. trivially true) irrespective of the truth-value of P. However, the meaning of S' (as opposed to its logical truth-value) is, as said, an awkward restatement of P. If, moreover, P is an axiom or a theorem then P is true in addition to S'.

The more general case of S = P → Q is discussed more fully in the post I linked to earlier.

The trick is in being fully aware of the distinctions between truth-value, logical validity and meaning. A logical argument can be both true and logically valid (by being sufficiently general) but nonetheless without meaning because meaning will usually lie in particular instances of it.

Hermes (August 17, 2012, 16:30:03 PM):
Thanks. This was just an aside.

Have a nice weekend. ;)


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