Freethought & Rationalism Archive

ex-xian · 05-10-2003, 08:18 AM

Quote:

Originally posted by John Page
Thanks - I would go a bit further though and say that incoherent statements (ones that imply a causal relationship where none exists) are untrue. This is as opposed to seem intuitively untrue.

This is taken from the website Scorpion referenced above. It explains everything better than I could hope to.

Quote:

Only somewhat counter-intuitive

After saying all this, it is important to note that material implication does conform to some of our ordinary intuitions about implication. For example, take the conditional statement, "If I am healthy, I will come to class." We can symbolize it, H => C. The question is: when is this statement false? When will I have broken my promise?

There are only four possibilities:

H--C--H=>C
T--T---?
T--F---?
F--T---?
F--F---?

In case #1, I am healthy and I come to class. I have clearly kept my promise; the conditional is true.
In case #2, I am healthy, but I have decided to stay home and read magazines. I have broken my promise; the conditional is false.
In case #3, I am not healthy, but I have come to class anyway. I am sneezing all over you, and you're not happy about it, but I did not violate my promise; the conditional is true.
In case #4, I am not healthy, and I did not come to class. I did not violate my promise; the conditional is true.

But this is exactly the outcome required by the "paradoxical" material implication. The compound is only false when the antecedent is true and the consequence is false (case #2); it is true every other time.

ex-xian · 05-10-2003, 08:24 AM

Quote:

Originally posted by John Page
Doesn't it halve the work since only tautologies would be true?

Well, the way proofs generally work is like this (ignoring proof by contradiction or contrapositive): If the statement is a conditional, "If S then P" you assume the truth of S, then proceed logically to prove that P logically follows.

To prove a biconditional, S iff P, you first prove if S then P as above, then you prove if P then S. You do it this way because iff works both ways...kind of like an equal sign. There are other more elegant ways to prove iff statements in some cases, but this is generally how it's done.

John Page · 05-10-2003, 08:28 AM

Quote:

Originally posted by Dr. Retard
Artificial languages don't square with the natural languages they're derived from. So what?

Thanks for clearly and succinctly explaining how propositional logical analysis can be used to imply things that aren't true. I never quite twigged that difference before.

As to the "so what?", surely the issue is which language to use to end up with an accurate understanding of what reality is and how it works. If the universe is deterministic, then any system of representing the universe that ignores cause and effect is incoherent. Is this true?

Cheers, John

Scorpion · 05-10-2003, 08:35 AM

Sorry, can't resist this

Quote:

If the universe is deterministic, then any system of representing the universe that ignores cause and effect is incoherent. Is this true?

Depends.

A: Universe is deterministic
B: Any system of representing the universe that ignores cause and effect is incoherent

A->B is then true in all cases except in case that universe is determistic and some system of representing the universe that ignores cause and effect is not incoherent.

Next question

-S-

John Page · 05-10-2003, 08:38 AM

Quote:

Originally posted by ex-xian

This is taken from the website Scorpion referenced above..... For example, take the conditional statement, "If I am healthy, I will come to class."......
In case #3, I am not healthy, but I have come to class anyway. I am sneezing all over you, and you're not happy about it, but I did not violate my promise; the conditional is true.
In case #4, I am not healthy, and I did not come to class. I did not violate my promise; the conditional is true.
[/B]

But the proposition makes no claim as to what will happen if you are not healthy. Consequently, the analysis completely ignores the "If", the result being the same as for the proposition "I will come to class".

Cheers, John

Dr. Retard · 05-10-2003, 08:49 AM

Quote:

Originally posted by John Page
As to the "so what?", surely the issue is which language to use to end up with an accurate understanding of what reality is and how it works. If the universe is deterministic, then any system of representing the universe that ignores cause and effect is incoherent. Is this true?

Thanks for the nice words.

I don't think a system needs to get involved with cause and effect in order to play a valuable role in representing a deterministic universe. Take geometry. Nothing about cause and effect there. But we can sure use it, quite profitably, in our models of physical reality.

John Page · 05-10-2003, 08:51 AM

Quote:

Originally posted by Scorpion
A->B is then true in all cases except in case that universe is determistic and some system of representing the universe that ignores cause and effect is not incoherent.

Next question

....so in the case that the universe is non-deterministic it is true that (some system of representing the universe that ignores cause and effect is not incoherent)
and it is true that (some system of representing the universe that ignores cause and effect is not incoherent.)

Now that's incoherent! Therefore, a non-deterministic universe is necessarily incoherent. True?

Cheers, John

John Page · 05-10-2003, 09:01 AM

Quote:

Originally posted by Scorpion
In my opinion causal relationships are over and beyond the logical framework. You can not decide within a logical system what actually *is* a causal relationship...

But I could re-state the LOI to be "If a proposition is not true this causes it to be false" and LNC to be "A proposition cannot be caused to be both true and false". How about the exlcuded middle "Something causes a proposition to be either true or false".

Thus, the axioms of this logical system assume or imply causal relationships. Systems of logic, in turn, must be caused by a process of mind. True?

Cheers, John

Scorpion · 05-10-2003, 09:58 AM

<cryptic AD&D reference>Scorpion wields a torch since he suspects that what he is facing will regenerate damage delivered by ordinary weapons</cryptic AD&D reference>

Quote:

....so in the case that the universe is non-deterministic it is true that (some system of representing the universe that ignores cause and effect is not incoherent) and it is true that (some system of representing the universe that ignores cause and effect is not incoherent.)

Err... you said "it is true that (some system of representing the universe that ignores cause and effect is not incoherent.)" twice, I suppose one of those was supposed to be "it is false that..."? Otherwise I can't even begin to understand where you're getting at?

Second, I don't see how...

Quote:

Therefore, a non-deterministic universe is necessarily incoherent. True?

...this could be inferred from anything that was said above?

-S-

Clutch · 05-10-2003, 10:05 AM

Weird! I'm on a half-hour break in a relevance logic conference!

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05-10-2003, 10:05 AM	#30
Clutch Veteran Member Join Date: Oct 2001 Location: Canada Posts: 3,751	Weird! I'm on a half-hour break in a relevance logic conference!

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