Noah
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quote:
ORIGINAL: Chaingang
quote:
ORIGINAL: Noah
Logical exploration itself conducted with modest good sense can lead us to see that logical exploration has a finite range of useful application. It isn't logical to apply the tools of logic beyond this range.
Please state the limits of logic. It is not enough to assert that there are limits. What are they, specifically?
"Elwood?"
How did you know what the girls down in Cuernavaca call me? But that’s just for short, if you’ll pardon the expression. My full name in Spanglish is El Wood Mas Mucho Grande, of course.
And yeah, it does shank to my left so the name is sort of over-determined.
Now was that an attempt at condescension or a reference to the Blue's Brothers or what?
Seriously now, Chain, if it indicates that you read condescension toward you into my post, I sincerely apologize for giving that impression. I respect your ideas and I take you seriously.
If it was supposed to be a pet name you have to buy me dinner first.
If you’re just being rude well then fuck you and your Mom.
I'll figure instead that you were just joshing.
On to business.
The arguments I referred to as classic included both the ones I cited explicitly--in favor of God's existence--as well as those claiming to prove that God does not exist, plus the classic "refutations" of the classic "proofs" both ways.
I didn't dispense with any of them in a general way. I explicitly gave them their due as I see it. Their due is considerable, a lot of good and a lot of bad, to put it bluntly.
You are right that in a limited sense I was dispensing with them. But I dispensed with the arguments against in the very same bathwater as the arguments in favor. That was the subject of my post: that the classic arguments on both sides fail on the same terms.
I'm not sure how you got the impression that I was supporting things like the Teleological Argument or the Ontological Argument as establishing the existence of God. Heaven forbid.
Er, I mean: hogwash.
As for the specific limits to the range of useful application of logical analysis, well there are many, of course, and they are of various kinds. Some which any child can recognize on their face, some which it took the greatest logical minds of recent generations to work out, and some which turn up quite clearly with just a little investigation.
I'll point first to the resonances between Turing's formal showing of Undecidability, Gödel's formal showing of Incompleteness, and Tarski's formal showing of Indefinability in their respective areas of application. Since Russell has been quoted around here recently I'll also point to resonances between those three theorems and what is known as Russell's Paradox in set theory and the various attempts by Russell (together with Whitehead) and others through the years to dispense with that.
I'm not sure what motivated your request but, just in case, I hope you see that my acknowledgement of limits to the useful application of logical analysis isn't some wooly-headed new age mumbo jumbo. I know a bunch of logicians including one the most often cited logicians in the logic literature today. I can't imagine any of them or any of their student's for that matter, demanding specifics to support a claim as self-evident as that there are limits to what you can accomplish with logic. And of course I detailed which limit I was relying on with the whole Monopoly discussion in my previous post so I'm not sure why you're asking for the same information again.
Now for those who don't care to take a bunch of graduate level seminars in order to appreciate the point about Tarski and those guys, and who furthermore don't have top-notch logician drinking buddies like I do to walk you through it (I doubt I could have grasped even the little bit I know without their powerful help) let me offer the following example.
The following example isn't meant to illustrate Tarski and Turing et al; please don't misunderstand. Rather it is pretty commonsense illustration of a limit to the range of application of logical analysis; one which I believe everyone here can appreciate with no need for stretching..
How about if I ask you for a complete truth-functional analysis of the following assertion:
"I am lying."
For the benefit of those who don't care to take a stab at it I'll point out that:
if that assertion is true then it is false
and
if that assertion is false it is true
So I ask you to logically analyze it for its truth value. Is it true? Or false? I presume you believe in the law of the excluded middle so as a truth claim it has to be one or the other.
The analysis cannot be completed. This points--from this side of the line, so to speak, to a limit to the useful application of logical analysis.
If you think this is a trivial example then you are at odds with some of those who have done the most to advance the study of logic, who have taken this sort of thing very seriously indeed.
If you want to make a claim like:"There, you see, you said that quite logically; logic therefore applies even to that which logic can't apply to." Then I will thank you for admitting that your point is what logicians call--in a technical sense--trivial, and based on a vague colloquial sense of th word "logic"--though it might be important to you. And I'll buy the next round .
You and I agree that Logic is a splendid tool. It has powers which we might even describe as unbounded in some senses, but like any other tool it does have its limitations.
The saying goes that when your only tool is a hammer, all your problems start looking like nails. Along the same lines, if one anoints logic as the tool which is applicable to all matters (not that you did so, quite,) well all matters start looking like logical problems. But they aren't, of course.
For a very powerful exploration of the overall notion limits to the range of application of logic I recommend Tractatus Logico-Philosophicus by Wittgenstein, preferably in the Pears and McGuinness translation unless you read German at that level (I don't read German at all but I've met Pears through a mutual friend and he struck me as a good sort; wine drinker as I recall but it happened in the previous century so don't quote me on that. It should go without saying that anyone with Guinness in his name is undeniably trustworthy; I came too late to the party to meet Wittgenstein--by several years) And if you want to be thorough get his later book too which has huge, important objections to many things offerred in the Tractatus.
No one will dispute that it is beyond the limits of logic to, say, make a cup of coffee. Silly of me to say, right? Not even germane. It was just so patently obvious that it almost utterly didn't warrant saying, you're right.
And in fact no one will dispute that logic will be enormously useful in countless matters associated somehow with making coffee.
The single point that such an apparently silly observation as mine could have here is to highlight the ... come on now ... undeniable truth that there are challenges which can't be met via logical analysis. Is the God question one of these? Or not?
The question of whether God exists looks and feels to us Children of the Enlightenment like something which falls into the bailiwick of logical analysis, at first. But then again the question of how to draw (or mathematically formulate) a triangular circle seems at first to fall into the bailiwick of Geometry, too.
It doesn't of course. The issue of the triangular circle must be resolved linguistically. It looks mathematical, and specifically geometrical. Indeed careers might rise and fall based upon attempts to derive a formula for triangular circles, or a mathematical proof that no such formula exists. Not that I'd let my kid go to the schools where those careers would play out.
Never mind that, though. By looking carefully at the triangular circle question we can see that it isn't really any sort of question in mathematics at all. It is rather a string of words masquerading as a mathematical question. Mathematical Nonsense.
Maybe some Monk will get mileage out of the triangular circle "idea" as a koan or something. It is surely a useful example to use in a discussion of what are and aren't actually addressable questions. So it isn't baldly without meaning like "5te56g~`54{6ee qwqw" (given without context or instruction.) Still the question of the triangular circle lacks any sense of the very kind someone in my example would want to rely on it for.
Similarly, we can see that the issue of the existence or non-existence of God is a string or words (a thousand miles long!) masquerading as a logical analysis. Logical analysis can no more "decide" the issue of God's existence than geometry can give you a formula for a triangular circle; any more than the rules of Monopoly wield yield a proof of the existence of Charles Darrow, their creator.
That doesn't praise or shame logic. It just recognizes how things stand.
It only takes one small step beyond the formal territory of geometry to point out that the definitions of the terms circle and square obviate the (attempted) question. But linguistical analysis is not a formal part of any system of geometry itself, any more than a rules discussion by the governing body of baseball counts as a play in a baseball game.
We can disqualify something like the Paradox of the Stone in a way similar to that in which we disqualified the Trianular circle, or "surmount" it by making the argument eat it's tail, citing: "The Paradox of the Paradox of the Stone".
In fact the Paradox of the Stone can itself be seen as a linguistic critique of the classical definition of God as all-powerful.
This is a crucial point, by the way. It illustrates something that logical analysis in the general area of Theology CAN productively do.
I think you and I can probably agree on this important limited usefulness of logic in regard to arguments about God's existence. Anytime someone posits a crap argument as a proof of God's existence, logical analysis can show in what way that argument failed to establish the truth of God's existence. This in no way, however gets at the underlying issue about God/no God; not one way or the other.
If I come up with a shitty theory to prove that you exist and LAM is kind enough to logically refute my theory for me--to show its logical shortcomings, that is--he sure hasn't proved that you don't exist, has he?
Logic, of course, operates on assertions, not facts.
Similarly, any time anyone posits a crap argument to disprove God's existence (the Argument from Evil, say, or the Paradox of the Stone) logical analysis can be employed to demonstrate that that argument failed to establish the non-existence of God.
All the while, the underlying issue of God's non/existence rests comfortably undisturbed.
Either of these strictly critical (destructive rather than constructive) applications of logic to Theological theories can be seen as a noble undertaking in the sense that it is often well and tidy to take one's opponent on his own ground, so to speak. Neither effort in the end says fuck-all about whatever being or non-being people are talking about when they are using words like God.
Anyway if we can now agree that the power of logic is not unbounded we can return to what I feel was a modest assertion on my part. If the subject at hand is the existence or non-existence of that which created all things, and if logic is a thing, well how in the heck can one expect logical analysis to tell that tale?
You'll note that I didn't just do a logical proof. I just gave a little verbal map which shows that you can't get there from here,
For illustration please see the Monopoly example.
If on the other hand one says something like: "Whether or not there is or was a creator, the truth of claims regarding the existence of a Creator will and always have have been bounded by logical constraints." then a whole bunch of other problems arise for you.
In this case you are then assigning--like it or not--a sort of priority to logic distressing similar to that which theists enjoy trying to assign to God. This puts you squarely in the sights of the sort of gambit Russell was quoted by LAM as making against the Teleological argument.
To paraphrase
quote:
If everything must have a logical explanation, then the existence of logic must have a logical explanation. If there can be anything without a logical explantion, it may just as well be the God as logic, so that there cannot be any validity in any logical argument against the existence of God.
... unless you are prepared to give a logical proof of how logic has to be able prove whether its creator existed--without being viciously circular, of course, which would be illogical.
Like LAM--but with a different purpose--I'll invoke that perhaps apocryphal Hindu myth and ask what turtle Logic is standing on the back of in a universe which allows a tool to give final adjudication on questions of it's own origin, unless the tool is a Magic 8 Ball?
Finally. I have no doubt whatever that others here know a shitload more about the subject of logic than I do and I welcome and solicit any corrections or clarifications anyone wants to offer. Me I'm just another Bozo on the logic bus.
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