# Justification of the mathematical definition of logical validity?

Discussion in 'General Philosophy' started by Speakpigeon, Apr 18, 2019.

1. ### SpeakpigeonValued Senior Member

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LOL.
Know what you're talking about before you say anything definitive.
EB

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3. ### arfa branecall me arfValued Senior Member

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I know what I'm talking about. I now have little idea what you're talking about. At the same time, I have little interest.

Knock yourself out trying to convince anyone there's a problem with correct or proper logic. Nobody really cares.

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5. ### SarkusHippomonstrosesquippedalo phobeValued Senior Member

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I understand what "correct" means, thanks. That you continue to say that the definition is either correct or not implies that you think such a descriptor is meaningful in this context. To say that something is not the correct definition implies that there is a correct definition. Whereas the conclusion from JamesR's comment is not that the definition is "not the correct" one, but that the descriptor of "correct" is not applicable.
Your language implies that you think there is a correct definition. Do you?

As for justification for the most common understanding of logical validity, truth preservation is the usual justification. And I think it is worded with reference to what is impossible so as to be falsifiable. But I do not know for sure.

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7. ### Write4UValued Senior Member

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Interesting discussion.....

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8. ### SpeakpigeonValued Senior Member

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Blah-blah-blah.
EB

9. ### SarkusHippomonstrosesquippedalo phobeValued Senior Member

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Wow, trolling your own thread. Way to go!

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10. ### YazataValued Senior Member

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The 'if-then' relationship in 'if A, then B' seems intuitively obvious, but it remains rather mysterious when people try to make better sense of it. It's still an active topic of discussion and controversy among philosophical logicians. And it's important, since the 'if-then' relationship seems to lie at the base of the rest of logical inference.

The thread topic may or may not be the question of why one should accept the Frege-Russell theory of material implication that's seemingly taught in every logic textbook today. (It's hard to know since the thread-starter refuses to explain what he means.)

In fact it isn't universally accepted, since it remains a topic of intense discussion. But it is the account of logical implication that's taught in beginning logic classes, so it's what everyone is first exposed to. The controversies are only introduced later. See the SEP article on Indicative Conditionals below:

https://plato.stanford.edu/entries/conditionals/

Concerning the Frege-Russell truth-functional account, the SEP says (what follows is quoted from the article):

It is a strikingly simple theory: "If A, B" is false when A is true and B is false. In all other cases, "If A, B" is true. It is thus equivalent to "~(A&~B)" and to "~A or B"...

If "if" is truth-functional, this is the right truth function to assign to it: of the sixteen possible truth-functions of A and B, it is the only serious candidate. First, it is uncontroversial that when A is true and B is false, "If A, B" is false. A basic rule of inference is modus ponens: from "If A, B" and A, we can infer B... Second, it is uncontroversial that "If A, B" is sometimes true when A and B are respectively (true, true), or (false, true) or (false, false). "If it's a square, it has four sides", said of an unseen geometric figure, is true, whether the figure is a square, a rectangle or a triangle. Assuming truth-functionality --- that the truth value of the conditional is determined by the truth values of its parts --- it follows that a conditional is always true when its components have these combinations of truth values.

(Me again.) I think that there are other more technical arguments in favor of truth-functional logical systems as well, such that they can be proven consistent and so on. Of course there are counter arguments as well, that the SEP article outlines. We saw one difficulty with "material implication" in an earlier thread with the problem of "explosion", where a false premise seemingly implies any conclusion at all. (Hence motivating some versions of paraconsistent logic, which introduce their own problems.)

Last edited: May 6, 2019
11. ### BeaconatorValued Senior Member

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Noboby has ever fit math to philosophy.

I think the closest we have is risk assessment analysis and the movie "along came Polly"