lifegazer said:
... Let me draw your attention, Tom, to the part of your statement that I have underlined: "Logic determines what reasoning is valid, and what reasoning is not valid."
... I would dispute this as explained in my first statement, above.
It is reason which has constructed the system of logic which, supposedly, determines what reason is and is not valid. Systems of logic, like mathematics, are a construct of the reason which is innate within mankind.
Of course, anyone would agree that what we call "logic" was formulated by reasoning. But that does not change the fact that there is both valid and invalid reasoning, and that logic equips one to tell the difference between the two.
With that in mind, let's contemplate another related statement of yours: "First, the prescriptive laws of reasoning (aka logic) cannot be proven "right" within the system of logic itself.".
... Here, you contend that all constructs of reasoning (logical systems) cannot be proven right within those systems themselves.
The first thing I want to say about this, is that it automatically challenges your own statement - for if we cannot prove that systems of logic are "right", then we cannot prove whether this logical statement of yours is right either... for it too is a construct of the reasoning which posited it. So, it's another self-defeating statement.
First, it's not self-defeating if you look at the most basic rules of logic (from which the more complicated ones are proven), which I would contend are self-evident. Thomas posted a link to those rules in his post; you can see for yourself. All the rules represent abstractions of statements that one would encounter in arguments.
For instance, a statement of the form:
p or q
is true if either or both of the component statements are true, and false if and only if both are false.
Does that really require a proof?
Second, I was making a vague reference to incompleteness with that comment you noted. But even though it is the case that sufficiently powerful systems are either incomplete or inconsistent, it is not the case that we cannot prove statements in those systems,
and neither is it the case that we cannot prove that the statement was proved in that system.
That is, not all propositions are undecidable in second- and higher-order logic. In fact, I can't think of any proposition that is relevant to ontology that would be plagued by this, because "The Goedel Sentence" is a statement whose paradoxical character arises from its syntactical form, not about anything that exists.
Third, while there is no proof of every basic building block of logic (which is impossible, as an infinite number of arguments would have to be constructed), we
can prove which inferences are invalid, by counterexamples.
The second thing I want to say about this, is that all constructs of reason are challengeable. This is not to say that they are always wrong - but they are definitely challengeable. Thus, you cannot simply preach/quote established/ancient logical systems or statements as the basis of your proceeding logic and expect me to agree with you because "Mister Important said this 300 years ago (or whenever), therefore I am right and you are wrong."
There's nothing for me to go on here.
Do you have a challenge to logic to present?
Thirdly, it's impossible to refute the concept of absolutes, because to do so is an absolute statement itself.
The main point of my second post discussed this in detail, which you evidently have not gotten to yet.
Lastly, though constructs of reason are questionable in themselves (though not necessarily wrong), there is no argument which can challenge the potency of reason itself. It is entirely possible that reason alone could fathom the nature of existence
There is an argument that can challenge the ability of humans to determine absolute truths about existence. In fact, it's the argument that I made in my 2 opening posts. Sure, we can "fathom" existence, but that is not the same thing as discovering truths about it with certainty.
I'll ask you the same thing that I asked you at Physics Forums (same thread I linked you to before):
What is this "superlogic" that can determine not only validity, but also
truth values of statements with certainty?
Edit for afterthought: Since reason is not a system of logic but is the essence of all systems of logic, it (reason) is not even challenged/bracketed by your aforementioned statement ("First, the prescriptive laws of reasoning (aka logic) cannot be proven "right" within the system of logic itself."). I.e., your statement challenges constructs/systems of reason, but not reason herself.
I'm not challenging reason itself, I'm saying that there are limits to what reasoning can do by itself. As I said, the rules of logic codify what constitutes
valid reasoning. Since there are limits to the tools we have by which to form sound arguments, and since reasoning doesn''t get any better than "sound", then it follows that there are limits to reasoning itself.
You're right about one thing:
Logic is not a
challenge to reason. It is a formalization of the rules that make reasoning
as good as possible.
edit: fixed a quote bracket