Absolute certainty and universal truth.

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.

'Luthon64