circular reasoning ok sometimes?

[phiwum]

How do we know that the axioms of logic are more certain?

We we deduce (and observe) that logic "works", or presuppose it?

It is closer to an analytic truth. If, for instance, the connective "&" means anything like what we take conjunction to mean, it simply must be the case that "(P & Q) implies P".

It is not merely probable that this is the case, just as it's not merely probable that a triangle has three interior angles. The logical axioms are not some sort of observations of regularities that have been true up 'til now, but rather they specify how we use the connectives.

To try to view it your way is to suppose that we somehow were using "and" and noticed that whenever (P & Q) was true, P happened to also be true. Thus, we concluded that this was probably true in every case, and our confidence grew with each new confirmational observation. But even now, we would have to admit that there's a non-zero probability that "(P & Q) implies P" is false.

On my reading, that's simply nonsensical. To entertain a possibility that (P & Q) is true while P is false is simply to misunderstand what & (and implies) means.

What do you think is the probability that a closed, rectilinear three-angled figure (i.e., a triangle) has more than three angles? Similarly, what is the probability that P & Q is true, but P is false? If the answer to either of these is 0, then you must admit that our confidence in these facts is not due to experience.

 

[ynot]

[FONT=Verdana, sans-serif]This thread is just going around in circles.[/FONT]

 

[kellyb]

What do you think is the probability that a closed, rectilinear three-angled figure (i.e., a triangle) has more than three angles? Similarly, what is the probability that P & Q is true, but P is false? If the answer to either of these is 0, then you must admit that our confidence in these facts is not due to experience.

It is due to my cognitive experience.

Observation (the foundation of science) is also a cognitive experience.

"Faith" is likewise a cognitive experience, but it just happens to do a poor job of predicting the future, or serving as a basis of technological advancement, unlike science.

 

[phiwum]

It is due to my cognitive experience.

Observation (the foundation of science) is also a cognitive experience.

"Faith" is likewise a cognitive experience, but it just happens to do a poor job of predicting the future, or serving as a basis of technological advancement, unlike science.

You previously claimed that we have confidence in logical axioms due to observation. Now you have changed the claim to cognitive experience, and add that observation is a kind of cognitive experience.

So far as I can tell, cognitive experience doesn't mean much here. If you thin that axioms of the sort that we're talking about count as "confirmed by cognitive experience", then stipulation is a form of cognitive experience, because these axioms stipulate how the logical connectives are used.

In any case, it seems that you no longer claim logic is confirmed by observation. Is this correct? If so, fine. I won't argue whether "cognitive experience" accounts for the axioms, because it appears to be a slippery term that does whatever you want. Just so long as we agree that induction has nothing to do with establishing the axioms of logic, we may leave it here.

 

[phiwum]

It is due to my cognitive experience.

Observation (the foundation of science) is also a cognitive experience.

"Faith" is likewise a cognitive experience, but it just happens to do a poor job of predicting the future, or serving as a basis of technological advancement, unlike science.

Out of curiosity, why didn't you answer my questions?

What do you think is the probability that a closed, rectilinear three-angled figure (i.e., a triangle) has more than three angles?

Similarly, what is the probability that P & Q is true, but P is false?

If "appeal to cognitive experience" is anything like induction, the answer to the above two questions must be greater than 0.

 

[kellyb]

Out of curiosity, why didn't you answer my questions?

What do you think is the probability that a closed, rectilinear three-angled figure (i.e., a triangle) has more than three angles?

Similarly, what is the probability that P & Q is true, but P is false?

If "appeal to cognitive experience" is anything like induction, the answer to the above two questions must be greater than 0.

I'd say the probability is close to zero, at least.

Is "appeal to cognitive experience" a "thing" or a fallacy or something?

 

[phiwum]

I'd say the probability is close to zero, at least.

Okay. I'd say that it is precisely zero, just as the probability of finding a married bachelor is also precisely zero. I don't need to take a survey and check. And I don't need to look at various three-angled rectilinear figures to confirm that such things have three angles.

Is "appeal to cognitive experience" a "thing" or a fallacy or something?

"Appeal to experience" is just another expression for inductive reasoning. I simply adapted that term to describe your reference to "cognitive experience" -- though it's still a bit of a mystery what you mean by that.

 

[wakawakawaka]

(D) logic is justified by observation

This is the whole crux of science. We're not all sitting around chatting on the internet on computers via the magic of presuppositional faith in physics. We can observe that the technology works.

heh love that jab at that presup nonsense, anyways have you seen Lisle's blog and some of the posts on his blog? is it head banging and absurd as i think it is?