#### Comment Preferences

• ##### Infinitude of facts or one fact? (5+ / 0-)

On page 398, toward top, Tortoise says the statement that "two numbers which are bigger than 29 can't have a product equal to 29" summarizes an infinite number of facts. He goes on, "...when you say '29 is prime', you are actually stating an infinite number of things."

Achilles objects, says it seems like one fact to him. (Me, too.)

T says, "That's because an infinitude of facts are contained in your prior knowledge."

Not sure I get the distinction here -- or, really, why it's important. The prior knowledge about numbers bigger than 29 not multiplying to 29 seems obvious enough to be one fact. But apparently it's helpful to separate out all the facts that go into it ...

Anyway, since this seems to be a basic point of the section, once more I'm feeling a little lost.

• ##### It's about what you need to check(7+ / 0-)

to be sure you are right.

If the statement summarizes an infinite number of facts, you can never be sure it is correct, unless you use some form of induction.  If it is a finite number of facts, then you can check them all.

Induction is notoriously hard to get into formal systems, or into computers.

• ##### Oh, ok ...(3+ / 0-)
Recommended by:
plf515, Joffan, ArthurPoet

... so it's needed to characterize the kind of problem.

Thanks.

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