# 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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Do you know of any proper justification by any specialist of mathematical logic, e.g. mathematicians, philosophers and computer scientists, that the definition of logical validity used in mathematical logic since the beginning of the 20th century would be the correct one?
Here is the definition:
EB

3. ### James RJust this guy, you know?Staff Member

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39,421
What do you mean by "correct one"?

This is a matter of accepted usage, or convention, not "correctness".

What other "ones" are you comparing to?

5. ### SpeakpigeonValued Senior Member

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I know what I mean and I don't need to explain. The question is whether any professional logicians ever offered such a justification. The justification would specify its own standard of correctness.
You mean it's like driving on the right side, each country with its own convention? You must be kidding. You think we would all have our own arbitrary logic without whatever teaching we get?
That's the question. You tell me.
EB

7. ### billvonValued Senior Member

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21,640
Well, since you are asking for an answer, you kind of do need to explain.

exchemist and sideshowbob like this.
8. ### James RJust this guy, you know?Staff Member

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You do if you want anybody else to know what you mean.

I didn't say it is arbitrary. The formal definition of validity reflects our experience of how the world works in practice. But, as a definition, it is a specific formalisation of that experience. By convention, this is the one we usually use. The reason is that nobody has suggested one that "works" better.

I can't read your mind. It's your thread. If you think there's some other definition of validity that would work better, it's up to you to explain yourself. I don't see the point in playing your guessing game.

9. ### SpeakpigeonValued Senior Member

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I don't know of any logician who would justify the mathematical logic's definition of validity on the ground that it "reflects our experience of how the world works in practice". Maybe a quote would help.
Also, it's definitely not our experience. It's contrary to our experience.
Yeah, it's a convention. An arbitrary one. One that mathematicians had to settle on because they don't understand logic.
If you don't know of any justification by any specialist of mathematical logic that mathematical logic is correct, then so be it. I don't know of any. Apparently no one does.
EB

10. ### SpeakpigeonValued Senior Member

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No, you just need to understand the question. It's a simple question. The word "correct" is in all English dictionaries, if you know what that is.
EB

11. ### billvonValued Senior Member

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In that case, the answer is simple as well - yes.

12. ### SpeakpigeonValued Senior Member

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Excellent. I knew you could do it. Good lad.
I don't believe you.
EB

13. ### arfa branecall me arfValued Senior Member

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I know of at least one justification (although whether it's "proper", I can't really say).
Which is that, according to the definition of validity you posted, if an argument is valid or not then an argument is correct or not.

I can't think of anything else that might be relevant. Except that trying to add the terms "proper", or "correct" to the term "valid", is probably unnecessary. Perhaps even just confusing, because the term "valid" is good enough already. I suppose I can say though, that the use of valid arguments in logic (and so in mathematics) is correct, maybe proper as well.

However, valid arguments are all you need in logic. It isn't necessary to prove that this is correct or proper; in fact that seems to introduce a lack of concision (is a valid argument correct? is it proper? who cares?).

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15. ### wegsMatter and Pixie DustValued Senior Member

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Correct premises don't always lead to sensible conclusions. Like the spider monkey example in your link. That would seem obvious. These types of arguments are sometimes helpful, but not always. Doesn't seem like a sustainable model, because the entire argument can be manipulated. We see this type of thing displayed in news reporting, all the time.

16. ### arfa branecall me arfValued Senior Member

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Any term you might want to connect to logic and logical arguments (propositions, etc), will have to be about the structure.

Everything is about structure, and how structure is defined. Therefore logic must have a structure, and terms like "valid", "proper", "correct", "a contradiction", etc must address this somehow. Or how else does it make sense? A structureless logic sounds like a contradiction right off the bat.

The structure of statements, in ordinary language, is a part of this overall structure in the logic addressed by SP's quote--a logic of the existence of arguments which are or are not valid. So it has a binary characteristic, this structure I haven't defined very much, yet.

17. ### James RJust this guy, you know?Staff Member

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And I told you there is no "correct" here, only convention.

18. ### SpeakpigeonValued Senior Member

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Good, that's the only answer that was needed.
Then we all agree here that the definition of logical validity as used in mathematical logic since the beginning of the 20th century is not the correct one.

I sort of knew it.

EB

19. ### SarkusHippomonstrosesquippedalo phobeValued Senior Member

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10,387
You are either being deliberately dishonest or stupid. Difficult to say for sure yet. Following JamesR's point, if there is no "correct" (as in the issue of correctness is meaningless) and only convention, then it is disingenuous to say that it "is not the correct one" in a manner that assumes that correct/incorrect is meaningful.
So I'll go with you being deliberately dishonest.

20. ### SpeakpigeonValued Senior Member

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That you don't understand what "correct" means in this context is irrelevant. I do. That you are even incapable of understanding what it means is proof you don't know any justification that the definition would be correct.
EB

21. ### arfa branecall me arfValued Senior Member

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You seem to be the only person on the planet who has this understanding of a justification for valid forms of argument in logic. But if everyone agrees on what a valid logical argument is, isn't that agreement enough justification for using valid arguments? I mean, it's like arguing that "3" needs a justification for being the correct symbol to use . . . (??)

Since no-one can agree with your claim, or agree that there's a problem here as you also seem to be implying, that is, there is no agreement, why should anyone bother even considering what you say?

22. ### SpeakpigeonValued Senior Member

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???
Seriously, you think I'm the only one?!
Do you know of Aristotle? The Stoics? The Scholastics? All these people spent time on and wrote books on what a valid argument is supposed to be.
But we don't. Even mathematicians don't. There are more theories of logic in mathematical logic alone that I care to know.
Yeah, we all agree that the Sun moves in the sky and comes around every day. So, why bother with Copernicus' claim?!
First, don't make stuff up.
I asked a simple question without claiming there was any problem.
You don't know the answer? Fine, move along.
I'm interested in the answer, not in any irrelevant comment of which you have the secret.
EB

23. ### arfa branecall me arfValued Senior Member

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There's no agreement on what a valid logical argument is? Mathematicians don't agree either?

Who's making up stuff here?