John Page

Hmmm, in the closed system of logic you are free to invent your own rules, however, causality is the only reason logic is able to operate in the first place - otherwise no coherence.

Anyway - I'm going to wait a while as the posts are crossing.

Cheers, John

ex-xian

What you're saying is this:
X <=> (~X=>P)
T-------F--T
----------T

That is, X is logically equivalent to, If X is false, then P is true. The problem is that you are trying to make a conditional say something about the antecedent. It's called affirming the consequent. Just because the consequent is true, that has no bearing on the truth of the antecedent.

If it rains, the street will be wet. Just because the street is wet, it doesn't mean that it rained. Perhaps a hydrant blew and caused the street to be wet. You example affirms P and tries to make that affirm X which is negated in the conditional. You can't do that.

As for the legal example, the statement "if the moon is made of green cheese, ex-xian is a murderer" would exculpate me. You're still trying to make a conditional imply causation. If S, then P only means, it is not the case that S is true and P is false. It does mean that S causes P to happen.

Scorpion

I'd like this since it would allow me to achieve practical immortality.

If I'm shot in the heel with a poisoned arrow, I will die =

Iff I'm shot in the heel with a poisoned arrow, I will die =

If I'm not shot in the heel with poisoned arrow, I will not die.

Now if this is not a valid reason to rig the interpretation of standard logic, what is?

-S-

ex-xian

But all us math majors would be pretty upset. Every conditional proof would have to be treated as a biconditional. That doubles the work!

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.

A basic faith statement for example: "If I believe in god then god exists".

Cheers, John

John Page

Correction accepted! My use of iff was screwed up. I'll try and salvage my main point in that the statement is meaningless (and therefore false under propositional logic) unless there is a one-way cause and effect relationship. Without such a realtionship it would seem that everything is true!

Cheers, john

John Page

OK, I give in....

"If I'm not shot in the heel with poisoned arrow, I will not die from being shot in the heel by a poisoned arrow.

Cheers, John

Dr. Retard

The only reason these statements have the air of paradox about them is because "if", the English conjunction, is used differently than "if", part of the "if-then" logical operator. English sentences like "If it's raining outside, then Jerry is wet" often express meanings like, "It's raining outside, and all the rain will cause Jerry to be wet". This would be false if it were not in fact raining outside. Notice the expressed idea that Jerry's wetness is caused by the rain. If Jerry's wet because he's taking a shower, then English speakers tend to reject the sentence as false.

But the "if-then" of logic is different. By its rules, "If it's raining outside, then Jerry is wet" is true whenever it is not raining outside.

Artificial languages don't square with the natural languages they're derived from. So what?

John Page

Doesn't it halve the work since only tautologies would be true?

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 and what is not, for example it is logically possible that my God belief actually does cause its existence. What John Page seems to be trying to do here is to make the tool to do things that should be done by the user before or after having used the tool.

-S-