Does anyone want an argument?
Posted by: Not For Me on 13 December 2004
Well?
DS
OTD - The Upbeats - Slit
*** And all the little children said "Nang Nang Nang ***
DS
OTD - The Upbeats - Slit
*** And all the little children said "Nang Nang Nang ***
Who would have thought that Russia with the Worlds largest Gold Reserves, as well as the Worlds third largest Oil Producer, also is the biggest Wine maker on Earth to-boot ?
FRitz Von Welli'llbe
FRitz Von Welli'llbe
Thank you for that, Our Mat would be proud of you, he's never wrong either. I enjoyed re-watching "The Game" last night with M. D. & Sean Penn, very good müwie.
Fritz Von Didyouknowafemaleswaniscalledabic ?
Fritz Von Didyouknowafemaleswaniscalledabic ?
John,
I've probably missed something but I'm running out of time, so this will have to do.
Merry Christmas!
quote:I don't know what "self-provable" means, I'm afraid, and I am certainly not aware that Godel's theorem demonstrates the impossibility of creating a logical foundation for mathematics. If so then why are mathematicians working on the logical foundations of maths? AFAIK Godel's theorem merely imposes on any self-consistent axiomatic system the limitation that there can exist propositions whose truth cannot be derived from the axioms - or that there can be no algorithm that can decide the truth of every proposition.
Godel's theorem basically amounts to "no system is self-provable", and it also demonstrated that creating an entirely logical foundation to mathematics was an inherent impossibility (Russell tried and failed).
quote:Obviously, nobody ever thinks in terms of proving the axioms of an axiomatic system (although you could always have a system with some unneccessary, provable axioms).
Both of which seem very obvious to me; any axiomatic system will never be able to "prove" the axioms, since to do so would require you to go outside the particular system; where there is no axiomatic foundation to use.
quote:Because, as you say yourself:
Originally posted by J. A. Toon:quote:This is precisely the sort of attitude that my previous points allude to!
As for philosophical problems, most of the ones I have come across have been meaningless (IMO) ones about the relationship between maths and its "meaning" or its "reality", which (IMO) should be confined to previous centuries
How could the relationship between maths and "reality", and its "meaning" __possibly__ be dismissed as something to be confined to previous centuries?....
quote:Continuing the second quotation:
Mathematics has no meaning in itself; it is simply a system of symbols that enable you to construct arguments/theories that have the benefit of being highly concise and can be neatly operated on following logical rules.
quote:It is easy to ask difficult questions that we cannot answer - e.g. "Where did the universe come from?" but I argue that (beyond being a vague expression of our sense of wonder) question such as this are literally meaningless without a theory in which the universe can literally have come from somewhere [whatever that means]. I place questions such as "Does the universe follow the laws of mathematics?" in the same category.
.... In my opinion these sorts of questions are among the most important and most difficult questions around; the fact that they are so extremely difficult that even after thousands of years we are still grappling with them only reinforces their importance.
quote:Aha! You've given me a chance to criticise your logic: I can't be simultaneously deliberately misleading and unaware that it poses a problem. I win a point - yay!
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To use an analogy, a box that comtains nothing cannot be said to be nothing simply because it contains nothing. And a box that contains a box that contains nothing does not contain nothing: it contains a box that contains nothing. So, clearly, a box that contains a box that contains nothing is not the same as a box that contains nothing. I cannot see how that this, in itself, poses a problem of either meaning or philosophy.
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I think this analogy is deliberately misleading, and the reason you can't see that it poses a problem is because you're making precisely the types of assumptions that mathematicians tend to criticise others for making, yet they make themselves all the time.
quote:I'm afraid I cannot see the relevance of this. My analogy is severely limited in scope, since a box cannot contain itself, whereas a set can. But the fact that I referred to physical objects is irrelevant: I referred to objects that - within the scope of the example you gave - satisfy the same rules.
You're loading it with an existential permanence that is simply not there by appealing to people's perceptions of a commonly known object. The definition inherently does not have such an existential grounding
quote:. Whether or not that is the case depends on what rules we choose for sets. I cannot understand why you see a philosophical difficulty in the example you provided. I don't deny that there is/was a problem with set theory, which is why I went on to mention Russell's Paradox, so it's not as if I was ignoring the issue.
The empty set does not refer to an "empty box" at all -- it does not refer to an actual existential thing-in-itself. It is simply a placeholder that refers to a set that contains nothing. It denotes the presence of nothing; nothing more. The empty set is nothing in itself; it simply denotes nothing in reference to the presence of other (mathematical) entities.
Therefore it is not like an empty box inside another box; rather it is like a defined empty nothing inside another defined empty nothing, viz. Nothing.
I've probably missed something but I'm running out of time, so this will have to do.
Merry Christmas!
I think this whole conversation points to one seemingly obvious conclusion:-
mathematicians can produce very impressive conclusions to otherwise intractible problems; the trouble is...they only make sense to other mathematicians.
JR
mathematicians can produce very impressive conclusions to otherwise intractible problems; the trouble is...they only make sense to other mathematicians.
JR
O.k., well maybe it's time for an open problem. I'm sure we're all tired of debating the Continuum Hypothesis. So let's move on to the "P=NP?" question
Remember, there's a million dollars at stake here....
Remember, there's a million dollars at stake here....
quote:Oh no they don't!
Originally posted by JonR:
...the trouble is...they only make sense to other mathematicians.
JR
...At least not to this ex-would-be mathematician...
[Once I've finished my degree I would take the advice for mathematicians that Berlin Fritz gave me some months ago - if only I could remember what it was
].quote:
Originally posted by Deane F:
...and anyway, how can a tree be a tree and have the qualities of "browness" and "greenness" while simultaneously being "large" and "willowy" and still be just a "tree"?
Ahhh - I know! Mereological nominalism will solve this conundrum! But hang on, if I make "heaps" of things I'll run into problems. Drat.
There must be an answer.
But didn't Mr Adams (RIP) propose that the answer is useless without a proper understanding of the question?
The problem could be logic. Maybe. If the problem has arisen from forcing my layer of logic over the world how can I possibly expect logic to solve the problem.
Oh dear, that seems to be too logical a thought...
Err...
Is it time to go to work in New Zealand, then?
JR
JR
The problem of inherence and predication seems an ideal place to look for the absurdity of philosophy.
It is evident to any child that a tree can be one thing and many at the same time. "It just is many things and one thing" <child says giving a perplexed "are you an idiot or something" look to the philosopher who has explained the "problem" to the child>
Language, or any other method of modelling the world, will manufacture conundrums.
BTW, I don't work. My wife does.
I stay home and care for my father-in-law.
Deane
quote:
Originally posted by J. A. Toon:
It seems inconsistent to me to state that there is logically only one way to contain "nothing" (as if nothing is some firmly definable entity), and yet that this can be different from a set containing other sets of nothing(s). Whether you have many "nothings" or one "nothing" in the totality of a "nothing-space" (whatever the hell that would be; nothing!), i.e. our set-space, ultimately it is just a nothing.
So the statement that you can have something defined as "containing" something that itself contains nothing and therefore _is_ nothing (since it cannot be viewed as a "container") seems meaningless to me.
The problem of inherence and predication seems an ideal place to look for the absurdity of philosophy.
It is evident to any child that a tree can be one thing and many at the same time. "It just is many things and one thing" <child says giving a perplexed "are you an idiot or something" look to the philosopher who has explained the "problem" to the child>
Language, or any other method of modelling the world, will manufacture conundrums.
BTW, I don't work. My wife does.
I stay home and care for my father-in-law.Deane
quote:
Originally posted by Nime:
Objection! Argumentative!
The objection is sustained!
Are recent low post counts related to not wanting to spend hard earnt ? cash on one's own internet bill, in preference to the usual firms one ? I think, yes, innit.
Fritz Von Nothingnewtherethentightgits
Fritz Von Nothingnewtherethentightgits
quote:
Originally posted by Berlin Fritz:
Are recent low post counts related to not wanting to spend hard earnt ? cash on one's own internet bill, in preference to the usual firms one ? I think, yes, innit.
Fritz Von Nothingnewtherethentightgits
O B J E C T I O N , Mr Fritz!!
Before you have another superiority attack
, I'll have you know that I am at work today and, whilst we're on the subject, I was at work yesterday as well!!Umm....so there.
JR