Validity of a simple logical argument

Discussion in 'General Philosophy' started by Speakpigeon, Jan 23, 2019.

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Is the argument valid?

Poll closed Feb 22, 2019.

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45.5%

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1. SpeakpigeonValued Senior Member

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It's not an argument, it's a statement. So, it's not valid or invalid. It could be true or false provided it would be a logical statement. And it's not.
EB

3. SpeakpigeonValued Senior Member

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Most paradoxes aren't usually logical contradictions to begin with. A paradox that would be proven a true proposition or valid argument definitely wouldn't be a logical contradiction.
If you start from the definition of validity as given here, there's not paradox. What there is is a simple contradiction (not a logical contradiction) between your intuition about the argument and what the definition of validity seems to imply about the validity of the argument.
EB

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1,123
EB

7. SpeakpigeonValued Senior Member

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So, as to votes, it seems that those who seem to be a bit more knowledgeable about mathematical logic, i.e. the method of logic issued at the beginning of the 20th century from the notion of truth-table and particularly from the definition of the material implication, all voted "valid". Those who seemed to be less knowledgeable on that appear to have voted according to their intuition.
Those who voted "valid" are indeed in full agreement with the notion of logical validity as defined in mathematical logic to coincide with the truth table of the material implication.
Those who voted "not valid" are in full agreement with classical logic, i.e. logic as initially defined by Aristotle's theory of syllogisms, whereby validity is assessed differently from mathematical logic.
EB

8. BaldeeeValued Senior Member

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Interesting, in that I was taught that Classical logic arose in mid 19/20th century, and that it is classical logic that uses the definition of valid that results in your argument being valid.
I appreciate that you qualify your use of the term, but probably best to refer to it as something like Aristotelian logic, to avoid confusion?
I also don't think Aristotelian logic would consider the argument as being "invalid" per se, but quite possibly rather as simply not being an argument at all.
It certainly wouldn't satisfy anything he regarded as a syllogism.

9. SpeakpigeonValued Senior Member

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I guess it is a matter of appreciation.
If any formal theory qualifies as "classical logic" today, it should conform to Aristotle's theory of syllogism.
That's the misery of modern classical mathematical logic that it has to call itself "classical logic", meaning essentially "two valued" theory of formal logic, so as to try and preserve the valuable connection with logic as understood since the classical times of Aristotle, and so as to distinguish itself from other modern theories of mathematical logic that are more adventurous and hence non-classical.
The expression "classical logic" will be understood as referring to modern classical mathematical logic by people who have been taught this way. Yet, modern classical mathematical logic is obviously part of the modern theory of formal logic born in the 20th century. So, classical logic would be part of modern logic? Not in my book. I call classical logic any theory of formal logic that would conform to Aristotle.
I think the confusion is created from the start by modern classical mathematical logic itself. It's not classical, in the sense I explained above, and it doesn't even seem logical, as demonstrated here. It should be called, it should have been called from the start, by people like Russell, "material logic", since it is based on the material implication, or more accurately "theory of formal material logic". I think this qualifies as the hijack of the century.
And, it's also clear that Aristotle himself would have deemed the argument here not valid, as clearly the premises don't make the conclusion true. Simple.
So, if words still mean anything, classical logic can only refer back to Aristotle.
Sometimes, you have to reclaim.
EB

10. arfa branecall me arfValued Senior Member

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7,696
Well, perhaps Aristotle is happy with the conclusion here.

11. Quantum QuackLife's a tease...Valued Senior Member

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23,281
ok, (how I see it)
Premise:
For the following statement to be true it must be false
"This statement is false"
Conclusion:
The statement is both true and false simultaneously - aka a paradox

The statement is a self referencing argument...with premise, argument and conclusion self contained with in the statement.

Ever heard of the saying "True lies".
=====
Bob is a human
humans are animal
Squids are animals
therefore
Squids are human.

a truly invalid conclusion... yes?
but a valid argument all the same...
=====
All statements are false
It is true all statements are false
Therefore,
This statement is false ( self referencing "true" statement)

12. SarkusHippomonstrosesquippedalo phobeValued Senior Member

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9,558
The statement may be both true and false simultaneously, or considered neither true nor false, but it is not in and of itself an argument. It is a statement.
No, the argument is invalid - suffers from an undistributed middle.
And the conclusion is not in and of itself valid or invalid, merely true or false. Validity applies to arguments, not statements.
The conclusion is a version of the classic Liar's Paradox. And the argument is valid (per the definition previously given) because the premises are contradictory. You could have put any conclusion you wanted and it would still have been similarly valid.

Was there a point to these arguments?

13. Quantum QuackLife's a tease...Valued Senior Member

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23,281
yes, I am learning about the language/definitions used when discussing these things... thanks...

14. parmaleeperipatetic artisanValued Senior Member

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3,194
I'm not entirely sure that your first formulation is incorrect. It is with respect to classical logic, yes, but... I'm sure that I've encountered it before in relation to some logical system, I'll just have to figure out where. It's been more than a couple of decades for me, as well.

15. RainbowSingularityValued Senior Member

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7,218
and the conclusion is false

where is the stated conclusion ?

16. parmaleeperipatetic artisanValued Senior Member

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3,194
For Aristotle, wouldn't the premises not being true in the first place render the argument not valid? Whereas, for Frege, that would have no determinancy on the validity of the argument? And is this how you are demarcating classical logic?

17. SpeakpigeonValued Senior Member

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1,123
To call this statement "argument" is misleading. It's not a logical argument.
The statement doesn't contain parts you could identify as premises and conclusion.
Nothing like a logical argument.
It's just a paradoxical statement, therefore illogical.
You can indeed as you do here produce an argument based on this statement:
This is a logical argument but clearly not a valid argument.
Assuming the premise true doesn't compel the conclusion to be true.
There's also no unique formalisation of the argument so you couldn't possibly prove validity formally.
Conclusions are not valid or invalid but true or false and here it's not valid.
No.
The statement "This statement is false" is neither true not false. Problem solved.
EB

18. SpeakpigeonValued Senior Member

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1,123
In which cases, it's not a logical statement.
If it is both true and false, or neither true nor false, then it can't be processed logically.
There is no suggestion of distribution here.
See?
I guess that what you mean is that "This statement" in the premise and the conclusion does not necessarily refer to the same statement. If you accept that both in the premise and in the conclusion "This" refers to the statement of which it is part, then we merely have to independent statements, so the truth of the premise doesn't compel the truth of the conclusion., so the argument is not valid.
That's paradoxical and not what logic says. The truth of the premise doesn't compel the truth of the conclusion, therefore the argument is not valid.
EB

19. SpeakpigeonValued Senior Member

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Exactly.
Rainbows like colours.
EB

20. SpeakpigeonValued Senior Member

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You're welcome.
EB

21. SpeakpigeonValued Senior Member

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It's the notion of logical validity as it is used since Aristotle.
Modern "classical" mathematical logic tweaked the definition of validity to make it compatible with the truth-table definition of the material implication, which, as it's name clearly suggests, is not the logical implication.
EB

22. SpeakpigeonValued Senior Member

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Clearly, Aristotle himself would have baulked at any argument with necessarily false premises. But remember he was the one who started the ball rolling so you can't expect him to have formalised or even articulated all there is to say on the subject.
So, all we can do is interpret his thinking.
As per the conventional interpretation of Aristotle, the validity of a syllogism is not decided on whether the premises are or not actually true. Instead, you just assume them true and decide for yourself if that somehow compels the conclusion to be true as well. In the case of the argument here, that's not the case since the last premise assumed true contradicts the conclusion, as Write4U correctly observed and probably why Quantum Quack and RainbowSingularity voted "not valid".
That's simple and it exactly fits with our intuition. The aficionados of modern "classical" mathematical logic here, like Sarkus, Yazata and Baldeee, all suppress the expression of their intuition so as to comply with the dogma they submit to even though it doesn't make sense. That is unfortunately something human beings can choose to do.
EB

23. SarkusHippomonstrosesquippedalo phobeValued Senior Member

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9,558
Relevance?
Relevance? How does that stop it being a statement rather than an argument? Answer: it doesn't, so you're being irrelevant.
Yes there is, quite clearly:
To quote again the argument from QQ to which this comment related:
"Bob is a human
humans are animal
Squids are animals
therefore
Squids are human."

If you can't see how this is a rather classic example of a case of an undistributed middle (if you ignore the irrelevant first premise) then you need to revisit your textbooks.
You seem to be mistaken as to which argument from QQ is being referred to as having the undistributed middle. Please re-read my post more carefully.
The definition of valid previously given, and to which was referred: something is valid "if, and only if, it is impossible for (all) the premises to be true and the conclusion at the same time to be false".
According to this his argument is valid, as it contains contradictory premises, and per that definition any argument with contradictory premises satisfies the requirements for validity (since at no point can all the premises be true). The conclusion from such premises can be anything at all, even the version of the Liar's Paradox that QQ gave.
So the argument is valid per that definition, as stated.