Is Peirce's law valid? Could anyone help me see how Peirce's law ((P→Q)→P)→P  is valid?
It seems to me that from (P→Q), P need not follow.
e.g: assume p=pigs can fly, q=1+1=2
Then if (if pigs can fly → 1+1=2) then pigs can fly
since the first part is a valid inference (1+1=2) is always true how can P follow?

$$((P \implies Q) \implies P) \implies P$$
$$((\text{Pigs can fly} \implies 1+1=2) \implies \text{Pigs can fly}) \implies \text{Pigs can fly}$$
$$((\text{False} \implies \text{True}) \implies \text{False}) \implies \text{False}$$
$$(\text{True} \implies \text{False}) \implies \text{False}$$
$$\text{False} \implies \text{False}$$
$$\text{True}$$
