False of course implies true, but the deductions are supposed to be in reverse. So a chain of deductions could be P <= P' <= true where P is the original goal.
This interpretation is not compatible with the text of the article:
> If you need a quick refresher on logical True and False, here it is: The logical proposition True simply represents something that is true, like the statement 1 < 5. Any true statement like that by definition implies True. If we can start from an assumption and perform a series of logical deductions and reach True, then we know our original assumption is True, that it is provable. Conversely, any statement we know or can prove to be wrong (such as "bananas are a myth") implies False. If we can reach False at the end of a series of logical deductions from an assumption, our assumption is incorrect.
Showing that P implies False is a valid way to show that P is false itself. But showing that P implies True isn't a way to show that P is true. If you run things in the other direction, showing that P is implied by True really is a valid way to show that P is itself true, but showing that P is implied by False is not a way to show that P is false -- everything is implied by False.
> If you need a quick refresher on logical True and False, here it is: The logical proposition True simply represents something that is true, like the statement 1 < 5. Any true statement like that by definition implies True. If we can start from an assumption and perform a series of logical deductions and reach True, then we know our original assumption is True, that it is provable. Conversely, any statement we know or can prove to be wrong (such as "bananas are a myth") implies False. If we can reach False at the end of a series of logical deductions from an assumption, our assumption is incorrect.
Showing that P implies False is a valid way to show that P is false itself. But showing that P implies True isn't a way to show that P is true. If you run things in the other direction, showing that P is implied by True really is a valid way to show that P is itself true, but showing that P is implied by False is not a way to show that P is false -- everything is implied by False.