esk@wucs.UUCP (Paul V. Torek) (03/21/85)
>From me (>>) and Rich Rosen (>) {ihnp4 | harpo}!pyuxd!rlr >> "Rational" has a narrower meaning than that. It may be a vague >> word, but you can't stretch it that far -- talk about Humpty-Dumpty-ism. >Hardly. If by rational, you imply something about decision-making processes, >well, don't rivers and rocks make "decisions" about which way they will flow >and fall? Quite rational, they way they make those "decisions"... No it isn't rational, that's the whole point. Only a Humpty-Dumpty would describe the processes in rivers and rocks as "rational". > Can you prove that [logic] is truth-preserving? Especially when the > definition of truth and falsehood, concordance and contradiction, are > fundamental to the notions of logic. Yes, you can prove that logic is truth-preserving, though of course you have to use logic to do it because you have to use it to prove *anything*. And of course a proof is not likely to win any *new* adherents to logic. > Oh? The notion of proof involves making no assumptions either way about the > validity/falsehood of a notion, and showing that, based on other assumed or > proven givens, it MUST be so. Try doing that for logic... The notion of proof involves making no assumptions about the *truth*/falsehood of a statement. Logical laws are rules of inference however, not statements, and neither true nor false. So using them does not assume truth/falsehood of anything, yet it allows us to evaluate certain things which *are* statements *about* logic, such as that it's truth-preserving. No doubt you are asking how rules of inference are supposed to be evaluated; the answer is that they can be checked against each other or against the meanings of certain logical connective words (it is part of the meaning of "if ... then ..." that it can be used in a Modus Ponens argument). Beyond that, validation is neither possible nor necessary. >> Read again what I said (edited [now twice], but meaning unchanged): >> Carroll ... shows ... that reason is not a premise but rather the >> way of getting from premises to conclusions. > THIS, what you've just said, is a premise! Prove it! (That's the whole > point here.) That reason is not a premise? That follows from the fact that it's a rule of inference, which is different. That it's rules of inference? That's what Carroll proved, that reason's function is not performed by treating it as a premise. --The aspiring iconoclast, Paul V. Torek, ihnp4!wucs!wucec1!pvt1047 Don't hit that 'r' key! Send any mail to this address, not the sender's.
rlr@pyuxd.UUCP (Professor Wagstaff) (03/23/85)
>>Hardly. If by rational, you imply something about decision-making processes, >>well, don't rivers and rocks make "decisions" about which way they will flow >>and fall? Quite rational, they way they make those "decisions"... [ROSEN] > No it isn't rational, that's the whole point. Only a Humpty-Dumpty would > describe the processes in rivers and rocks as "rational". [TOREK] Didn't the water make a rational decision to go flow in the direction of the rest of the river? Didn't the rock make a rational decision by deciding to fall downward and not work against the gravitational force? What's that you say? They're NOT deciding? How can you say that? In what way are the rock's processes of decision different from ours? (I think we actually get to this later.) >>Can you prove that [logic] is truth-preserving? Especially when the >>definition of truth and falsehood, concordance and contradiction, are >>fundamental to the notions of logic. > Yes, you can prove that logic is truth-preserving, though of course you > have to use logic to do it because you have to use it to prove *anything*. > And of course a proof is not likely to win any *new* adherents to logic. If you use the method to "prove" the truth-preservingness of the method, you have proven NOTHING. > The notion of proof involves making no assumptions about the *truth*/falsehood > of a statement. Logical laws are rules of inference however, not statements, > and neither true nor false. Why? Because you say so? Because you take them as givens! You say that they are neither true nor false simply because you cannot prove that either way. I agree with you about the nature of logic, Paul, but the point is not that you don't have to prove them, it's because they are *defining* certain terms. One has to get all the way back to the very nature of what assumptions underly the definitions. >>>Read again what I said (edited [now twice], but meaning unchanged): >>> Carroll ... shows ... that reason is not a premise but rather the >>> way of getting from premises to conclusions. >>THIS, what you've just said, is a premise! Prove it! (That's the whole >>point here.) > That reason is not a premise? That follows from the fact that it's a rule > of inference, which is different. Solely because you say so? It's not "different", except in the way I describe above (i.e., its basis in definitions). > That's what Carroll proved, that reason's function is not performed by > treating it as a premise. What Carroll showed was the paradox of trying to prove logic with logic. NOT that you have no reason to do so. He's probably spinning in his grave after hearing your contention that he was trying to show that reason shouldn't be treated as a premise! It's funny that you interpret it that way---it seems to highlight your assumptions about logic. (I never thought I'd be arguing THIS side of the logic issue!) I'm reminded the scene in Annie Hall when Alvy Singer pulls Marshall McLuhan out from behind a billboard to tell some pompous buffoon that he's got his (McLuhan's) notions all wrong. (Not to imply that you're a pompous buffoon.) "Why can't real life be like this?" -- "Which three books would *you* have taken?" Rich Rosen ihnp4!pyuxd!rlr