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May 4th, 03:47 AM   #21
Lomax
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Hello TheYangist,

Quote:
Originally Posted by TheYangist
Principio [sic] principii ignores the question of the truth of the premises, and so it cannot reliably be the basis for sound argument.
So is the following syllogism invalid?

1. All men are cats
2. All cats are mammals
C. All men are mammals

I suspect that, while it is unsound, it is still formally valid. Is it not?

Lomax
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May 4th, 04:03 AM   #22
the.yangist
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Quote:
Originally Posted by Lomax
Hello TheYangist,



So is the following syllogism invalid?

1. All men are cats
2. All cats are mammals
C. All men are mammals

I suspect that, while it is unsound, it is still formally valid. Is it not?

Lomax
Valid, yes. Sound, no.
 
May 4th, 04:18 AM   #23
Lomax
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Hello TheYangist,

Would you thus regard the syllogism as a fallacious argument form?

Lomax
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May 4th, 08:28 PM   #24
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Quote:
Originally Posted by Lomax
Hello TheYangist,

Would you thus regard the syllogism as a fallacious argument form?

Lomax
Only if you claimed it was sound.

All examples of question-begging involve the logical rule of simplification, but that does not lead me to accept the tautology of (A & B) ⊃ A as a legitimate reason for the propositions A and B being true, and thus the argument sound.

I treat principio principii arguments in exactly the same way.
 
May 5th, 02:04 PM   #25
Phix
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Quote:
Originally Posted by Martin
Greetings, Phix.



I see what you mean, and I agree; yet, I think my claim (that P --> P is a petitio principii) holds: perhaps not all circular arguments look like P --> P, but P --> P is circular.

M. Manzano
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Yes, I suppose it is, but it is a very rare form of the fallacy that we wouldn't often find where fallacy theory gets employed. Even in a formal language, the form P --> P is called reflexsive and not circular. Anyhow, I was merely disputing your claim that the fallacy was not actually a fallacy.
 
May 5th, 02:12 PM   #26
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Greetings, Phix.

Quote:
Originally Posted by Phix
Yes, I suppose it is, but it is a very rare form of the fallacy that we wouldn't often find where fallacy theory gets employed. Even in a formal language, the form P --> P is called reflexsive and not circular. Anyhow, I was merely disputing your claim that the fallacy was not actually a fallacy.

Okay.

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May 5th, 02:16 PM   #27
Martin
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Greetings, the.yangist.

Quote:
Originally Posted by the.yangist
The issue of relevancy isn't one of syntax or deduction rules, but one of fact.

What I mean by "...does not involve relevancy to the facts being stated" is that the state of affairs to which p refers does not affect the truth or falsehood of the statement that 'p |- p.'

A1.) Martians live on Mars.
AC.) Therefore, Martians live on Mars.

B1.) I live on Earth.
BC.) Therefore, I live on Earth.

According to the syntax, both statements are derivable from the available premises. A1 is false, and since it is false, it can imply whatever I want and still be valid....

C1.) Martians live on Mars.
CC.) Therefore, humans are mortal, the center of the Earth is hollow, etc., etc.

However, soundness is a stronger criterion than validity because it demands that the premises are not only able to deduce the conclusion, but also true. Principio principii ignores the question of the truth of the premises, and so it cannot reliably be the basis for sound argument. Assuming that a principio principii argument is sound is to already assume the truth of a premise which is equivalent to the conclusion, thereby defeating the main purpose of the argument, which is to demonstrate proof of a statement in doubt by deduction from true premises.

I thought of putting it another way (like one way placed above). Even if the conclusion is true of a principio principii argument, we cannot be certain if the premises, one or more of which are the same as the conclusion, are true, because both would derive the conclusion anyway. Assuming that you take C to be true, and it to be the same as premise(s) {1...n}, then you cannot be sure that {1...n} is true because, whether {1...n} is true or false, it is still enough to prove the conclusion. But again, this is a trick of validity, which is not sufficient for soundness.
I see what you mean now, and it is not that I do not agree with you. But if you check out again the OP, I was considering the case when v(p) = 1, and then we have a sound argument: valid and with true premises. I was not assuming "that a principio principii argument is sound" per se, but only such case, and that is why I can not see irrelevance in the argument (p --> p, with v(p)=1). I hope I made myself clear.

M. Manzano
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May 7th, 04:57 AM   #28
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Quote:
Originally Posted by Martin
Greetings, the.yangist.



I see what you mean now, and it is not that I do not agree with you. But if you check out again the OP, I was considering the case when v(p) = 1, and then we have a sound argument: valid and with true premises. I was not assuming "that a principio principii argument is sound" per se, but only such case, and that is why I can not see irrelevance in the argument (p --> p, with v(p)=1). I hope I made myself clear.

M. Manzano
"No le pregunta el manzano al haya cómo crecer"
W. Blake
Deductively, principio principii is not at issue for true premises. It only becomes a fallacy when such an argument is used to claim that the premise is true, specifically a relevancy fallacy, since it confuses, "p is true," with, "p can be proven from itself."
 
May 7th, 07:03 PM   #29
Martin
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Greetings, the.yangist.

Quote:
Originally Posted by the.yangist
Deductively, principio principii is not at issue for true premises. It only becomes a fallacy when such an argument is used to claim that the premise is true, specifically a relevancy fallacy, since it confuses, "p is true," with, "p can be proven from itself."
Okay, consider this:
1. 2+10=12
C. 2+10=12
In the argument above I can not see irrelevance neither semantically nor syntactically. Plus, the argument is sound, yet, it is a petitio principii.

M. Manzano
"No le pregunta el manzano al haya cómo crecer"
W. Blake
 
Yesterday, 09:41 AM   #30
Phix
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Quote:
Originally Posted by Martin
Greetings, the.yangist.



Okay, consider this:
1. 2+10=12
C. 2+10=12
In the argument above I can not see irrelevance neither semantically nor syntactically. Plus, the argument is sound, yet, it is a petitio principii.

M. Manzano
"No le pregunta el manzano al haya cómo crecer"
W. Blake
Martin,
Say that it is agreed that your argument is a circular argument. What of significance follows from that? The mere fact that it is sound but also a fallacy does not say much. Indeed, one could argue that the fallacy is employed mainly because circular arguments end up being sound.
 


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