Scorpion

Sorry, of course, that was sloppy use of language from my part. Obviously logical causal relations are not beyond the logical framework.

Depends on if you consider logical systems to be created by minds or discovered by minds (i.e. does logic exist independently of minds)... but I fail to see the relevance to this topic?

-S-

the_cave

The concept of "cause" is a notoriously difficult one to express in logic, and much work continues to be done on the subject by philosophers.

Logic can still help us in the "real world" by demonstrating which arguments are invalid and which ones are valid. We can then dispense with the invalid arguments. The problem then is to select from the valid arguments, which is where things start to get knotty.

You're right, simple "if-then" statements need more to hold up in places like courts of law. But that doesn't mean they aren't logically valid--it just means that our everyday notions of truth and falsity are not that simple.

Ensign Steve

Thank you guys so much. This is as interesting as it was the first time I learned it in logic. I dig paradoxes. You are all so eloquent at explaining this complex material, especially concerning the logical/natural language barrier. I'm actually getting it! Now, let's see if I can retain any of it this time around.

John Page

Scorpion:

Sorry, something seems to be interfering with my brain waves today. Anyway, I cut and pasted and forgot to take the "not" out.
In fact, no, it should have been:

"....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 incoherent)
and it is true that (some system of representing the universe that ignores cause and effect is not incoherent.) "

So I suggested the conclusion "Therefore, a non-deterministic universe is necessarily incoherent. True?" becauase it is not coherent to have something that is both coherent and inhoherent.

Normal service will be resumed as soon as possible.

Cheers, John

John Page

Necessarily?

Clutch

Classically logical validity just tracks covariance in truth-value; ie, under what conditions must a consequence (call it C) be true? There's nothing in that about the causal conditions for C, and quite rightly, since C may be a statement about numbers, classes or what have you, for which causal conditions are misplaced.

Relevance logic imposes stronger conditions than mere covariance, but these again do not amount to any sort of causal notion, for the same reason just explained.

Clutch

John, no -- contingently. Break's over; back to the talks!

Scorpion

You still have some holes in that (with negating statements with all/some quantors) but I'll leave them to you to find since I know where you were getting at. You were essentially saying that (correct me if this formalization isn't what you had in mind) from

1) A->B
2) ~A

it follows that

3) B & ~B

I don't have the foggiest idea how you arrive to this conclusion but there certainly isn't any rule in standard logic that allows such inference - the closest thing to that I can think of is

4) B v ~B

or, to put it in words:

"in the case that the universe is non-deterministic
it is true that (any system of representing the universe that ignores cause and effect is incoherent) OR
it is false that (any system of representing the universe that ignores cause and effect is incoherent.) "

...so would you like to elaborate this?

Furthermore,

"Therefore, a non-deterministic universe is necessarily incoherent."

Neither A or B says anything about the coherence of the universe (deterministic or not) - B only states something about the coherence of a system representing the universe. If you want to infer something about the coherence of the represented universe from B, you also need something like

C) The universe is coherent iff the system representing it is coherent

...and even if you had this AND the first premise ("if universe is non-determistic, it is true..." etc.), I still can't understand how the incoherence of a non-determistic universe would follow.

-S-

John Page

1. Something must cause a proposition to be true or false, though. e.g. the logical truth or falsity is a result of (is caused by) the application of the system of logic being considered. For the case to be otherwise, truth could just be random.
2. The conditions for C (vs. ~C) are comparison with a set of conditions through a truth telling process.
3. Why does it make any difference what the subject of the proposition is (numbers, classes etc.)? The appearance of classes is caused by analysis of aggregated sense data within the mind/brain. Numbers are classes of things defined as homogenous through a process of quantification. Three oranges belongs to the class of things that have threeness and to the class of things that are orange-like. Classes comprise defining charateristics so I'm confused why you say that for them "causal conditions are misplaced."

Hope this is relevant.

Cheers, John

John Page

OK, let me try again.
Here's the truth table(cut and pasted from ex-xian's post on page 1):
A B A=>B
-----------------
T T T
F T T
F F T
T F F

~A: Universe is nondeterministic

What I observed is that A=>B when ~A, irrespective of B or ~B, (lines 2 and three of the table) which is why I (tried to) put their meanings into words thus:
It follows you are correct in stating:
I simply read this from the table - where am I going wrong?

Cheers, John

BTW, The reason I chose B as "a system of representing the universe" is that logic is such a system so B is testable, whereas the coherence or incoherence of the universe itself would remain moot.

PS. Hope I'm still coherent - long day at work and I'm tired.

Cheers, John