John Page

No, just a flawed definition of truth.

Cheers, John

Clutch

As usual, suddenly everyone is an expert in logic.

First, what do folks mean by "arbitrary" in this case? I understand this to mean something like, "not relevantly preferable over other options", or "chosen over other options for no good reason". For some inferences, the choice of what logic to employ will hence be arbitrary, and for other inferences not, depending on the whether the difference between logics was relevant to the inference. (For a simple modus ponens, the choice between classical and intuitionistic logic will appear arbitrary.)

Second, why are folks getting worked up about what is and isn't tautologous without any specified working definition of the term? The idea that tautologies are defined independently of choice of logic is dubious; so the idea that we can decide which logics are better by asking which logics include tautologies as axioms is correspondingly dubious.

Third, who said that quantum logic gives up identity, non-contradiction and excluded middle? Did I misunderstand that? QL is just a classical logic that does not include distributivity over conjunction as a rule of inference. Ie, from (P or (Q and R)), you cannot infer ((P and Q) or (P and R)). Logics that give up Excluded Middle are intuitionistic, while those that give up non-contradiction are usually called "dialethic" -- neither of these models quantum reasoning. (Notice, too, that in none of these cases does "giving up" mean "denying" -- it just means that the respective principles are not valid rules of inference.)

Keith Russell

John:

OK, you think 'A is A' is a 'flawed definition of truth'.

First, I wasn't aware that 'A is A' was a definition of truth. Why do you believe that it is?

Second, if 'A is A' is a definition of truth, and a flawed one at that, what do you recommend as a superiour definition of truth?

And, thirdly, why?

Keith.

John Page

Posted with an ironic grin.
That's what it was being bandied about as - I somewhat agree with clutch in that tatologousness is defined in the context of a logic truth functional statements. (Apologies clutch if this isn;t what you were getting at).
The same one as in the "?Absolute Truth?" thread. A truth results from a mind process. The word truth is used to describe what is accurate in comparison with something else.
Truth is subjective - what kind of truth were you looking for?

Cheers, John

Dominus Paradoxum

Hmm. If truth is subjective, then is it subjective because you think it is subjective? Because if it's subjective independenty of whether you think it's sujective or not, then it turns out to be objective after all. On the converse, if truth is only subjectively subjective, then while truth might be subjective for *you*, it would be objective for me. But if it is objective from that point of view, then it would not be objective beacuase of that point of view (since that's what "objective" means), thus, it wouldn't really even be subjectively subjective for *you*, though it would certainly seem that way. But what if truth were subjective and you didn't believe it was subjective? What would that be like?

John Page

FYI I subscribe to the theory that nothing is absolutely subjective or absolutely objective (these are analagous to infinitely small and infinitely large).

Truths have different degress of subjectivity depending on how widely they have been tested, how many observations and viewpoints have been taken etc. This is where my idea of an infinitely valued system of logic comes from....

Cheers, John

Adrian Selby

I'm sorry for not interjecting with comments of my own, I genuinely found myself to be thinking about logic, and with theists who have asked me to prove logic exists 'in the world' (I found this seemed quite an inappropriate thing to ask,) it did bring me back to half baked thoughts on how it is a law of logic is said to exist. I was thinking that it was merely a tool that arose out of a consistency of experience, and that in thinking how it might avoid a skeptical charge that one associates with induction generally, I was interested in a defence of it (perhaps only as a side effect) from Kripke's thoughts on the synthetic a priori.

Clutch's comments are most illuminating with regard to 'logics'. I knew there was more to it than I thought

Thanks to all so far for giving me food for thought.

ex-xian

Hi all...just read this thread and wanted to add my two cents...

Regarding quantum mechanics, I think it would be accurate to say that new logics were invented to work with the mathematics of quantum physics. The theories of linear algebra (especially matrices) had been invented for awhile when von Newmann recognized that they have applications in doing quantum mechanics.

On arguing against logic--Martin Gardner quoted a person whom I can't recall who remarked that those who argue against logic need to take care to see if they use reason to argue against reason. My Logic 1 professor knew a fellow teacher who had an eastern bent that argued, using reason, that reason didn't always apply to reality or metareality, thus justifying his eastern mindset.

Regarding the arbitrariness of logic, I think it is key to remember Kurt Godel's incompleteness theorem. He proved that any axiomatic system will give rise to propostions that cannot be proved within that system. In other words, you have to start somewhere. Whether it's logic or mathematics, certain assumptions are taken for granted, but I don't think this lessons the strength of formal systems. It seems that logic is based on the reasoning portion of the brain. People who have that part of their brain damaged are unable to deal with simple formal rules. And mathematics maps onto the real world. When it doesn't seem to, new mathematics are invented that incorporate the anomolies. In many cases, the theoretical math is invented before a practical application is found, as was the case in quantum mechanics.

Lastly, about tautologies. I'm taking a class in predicate calculus and symbolic logic this upcoming semester. From my previous work with truth tables, doing logic is a matter of finding tautological strings of symbols. If it is a tautology, then the logical statement is considered to be true. As far as it being information empty, I'm not sure what that would mean. I know that in teaching mathematical proofs, the first thing you do is teach the students certain logical tautologies and then formulate a proof based on that structure.

and that's all I have to say about that

Dominus Paradoxum

Not everyone believes that formal logic can capture human reasoning. See Blanshard's "Reason and Analysis" for some good arguements for that perspective.

ex-xian

Dominus Paradoxum wrote

Quote:

Not everyone believes that formal logic can capture human reasoning. See Blanshard's "Reason and Analysis" for some good arguements for that perspective.

Yeah, I didn't mean to imply that I thought it captured it completely. Logic and mathematics and such are human inventions, but I guess I would say that they are based on empirical observation or theoretical standards that seem to always apply.

As was remarked above, Aristotle made some mistakes in his logic of predication. We now recognize this and have even classified those fallacies and incorporated them into our logics. My opinion is that mathematics, logic, physics, whatever are close approximations to reality, but are always subject to improvement.