Clayton, Bertrand Russell and Gottlob Frege would disagree with you. But, I’m sure you’ll say that they aren’t worth reading. Or that I’m name dropping. =P Have fun in your “adult thread” about nothing of value to anyone.
No. Entertaining an unlikely hypothesis for an extended period of time is not mental masturbation. It’s just grown-up thinking.
Trying make other people feel too small to think by themselves, trying to inculcate needless self-doubt in others, pretending to be working to solve provably unsolvable problems (such as discovering The Perfect Language)… these are mental masturbation and they are some of the primary occupations of modern philosophy. Philosophy has always been liable to angels-on-pinhead debates. Contemporary philosophy leaves all prior philosophy in the dust on this count.
Clayton -
Malachi,
Glad your expressing an interest. Without further ado:
Godel proved that a rich enough system will contain true but unprovable theorems.
He certainly never claimed that every system may have hidden contradictions lurking inside it.
There are published proofs that the axioms of set theory including the axiom of choice and the continuum hypotheses, about as rich a system as you can get, are consistent. You can work on them for all time and never ever find a contradiction in them.
As for mathematicians aplenty being around, do you live on Gilligan’s Island? Or is there a college or university within driving distance? Where I live which is pretty much in the sticks, there are several major unis in the area.
Oh boy. Here we go with the Godel crap again. Please specify what, in my post, you think is incorrect. I will note ahead of time that there is one (intentional) omission for the sake of brevity: that my statements are only true of formal systems capable of describing the natural numbers and the elementary arithmetic operations. But for some reason, I don’t think that’s your hangup.
I have just one question for you: Is it possible or is it not possible for a given consistent formal system (definitions and axioms) to prove that it is, itself, consistent? Can consistent F prove “F is consistent” for any given formal system F? Yes or no?
Clayton -
So, I was right? Russell, Frege; worthless?
Mathematics is as close to a universal language as we can get (and we don’t even have it all figured out yet! - not that it would matter because you actively encourage people to stop looking while claiming that you “love philosophy”). Oh yeah, tell me again that “purposive action presupposes causality” because it does not. You won’t respond anyway…
…for God’s sake scientists use binary on gold plates on satellites in hopes that if aliens find it they can deduce what our communications to them will/would be…but no you keep telling people to look for Babel as the ‘universal language’ since formalization is “impossible.”
Duh! No one is disagreeing with this. The point, if you’d have even glanced at ANY of the links I’ve provided (especially the Davidson essay on Logical Form) is to disassociate words from syntax. This requires constructing symbolic language which involves “logic” and will present “truths.”
So, what? You and Mises, then? Leaving poor Russell in the dust? No wonder there are so many books published investigating your threads on the MIses forums…
You should doubt yourself.
By not reading or even engaging in the thought process of the "better’ minds out there, while criticising them, you want man to live in a state of perpetual ignorance. Well, of course, unless it is your atrocious “a priori deductions” involving the mindset of people you don’t know and will never meet (yes, your asinine geopolitics/conspiracy ramblings. Well, and David Icke).
I think there are a lot of dumb people on this forum that you have fooled into thinking you are some profound thinker. No one can prove you wrong either because the claims you make don’t have any foundations. Seriously, if you run with some of the BS you drone on about when it comes to conspiracies (which we partly agree on) you’ll never know if what you think about particular situation is right or wrong, but you’ll continue to make more and more claims with no evidence for or against it…then you call Russell and Frege sophists? People who use “logic” to the best of their ability? I mean, what world do you live in?
You have no apparent familiarty with modern philosophy - which, by the way, includes Descartes who discovered the link between algebra and geometry and Kant who provides the foundation for Misesian methodology (ahem, a priori categories). But yeah, they were always just jacking off inside their minds…
Also, I’m not even sure you know what “modern” and “contemporary” philosphy is…Russell is a contemporary philospher, and Frege pioneered analytic philosphy…
Now, where is my book searching for the language of Babel…oh, here it is…those damn Sumerians…
I’m familiar with both. Make your specific points in plain English, or is that too much to ask? If there is a particular quote from either that you would like me to answer, please cut and paste it. If it’s an extended argument, then surely, you must be able to summarize it in your own words, assuming you yourself actually understand whatever the hell argument you’re trying to challenge me with.
I cannot read every PDF you link me to. I have a day job and it is not babysitting you.
It is no such thing. Mathematics is a wholly human language and is no better or worse than any other domain of human language.
WTF?
SD is.
Oh boy.
Why? Because there are people out there who get paid to claim they sit around and read, think and write all day who are telling me I should doubt myself?
Says who? I read very eclectically.
You have reversed the case in fact. I am not the one exhorting people to doubt themselves. That’s you.
Don’t doubt yourself. Have some fortitude. Go forth and conquer everything you desire to conquer with the utter confidence that the entire Universe is your playground. Do not succumb to timidity and fear based on the verbal intimidation of people who want you to believe they are smarter than you are. Anyone who reads philosophy from a position of self-doubt is not actually discovering anything in what he reads, he’s simply trying to allay his insecurity with the comforting words of disembodied father figures that he perceives to have a greater grasp on reality than he himself has.
You mean like the a priori deduction that the Queen of England is a baby-eating succubus? I stand by that claim!
I have no interest in getting anyone to think of me one way or another. Whatever conclusions people reach are their own. I simply write down what I think. I swore off trying to “persuade” people a long time back because it’s a hindrance to genuine truth-seeking.
LOL, no. I said you were engaging in sophistry.
I misspoke with the word “modern” - I meant contemporary (this is the usual meaning of “modern”… only in philosophy does it mean a bygone era… *sigh).
Clayton -
I have just one question for you: Is it possible or is it not possible for a given consistent formal system (definitions and axioms) to prove that it is, itself, consistent? Can consistent F prove “F is consistent” for any given formal system F? Yes or no?
I figured that is where your mistake lies. You see, there is more than one way to skin a cat. You may try using F to prove itself consistent, or you may try something else. Godel proved that a rich enough system may not be able to prove itself consistent, but that does not slam the door on every possible proof there is.
The modern understanding is that we are human beings. We think using common sense, as sharpened by millenia of geniuses such as Aristotle at al. We then study a system F. We are certainly not inside the system F. We are people, not symbols on a page. We can then prove that, although F cannot prove itself consistent, we can prove F is consistent using our common sense, if we are clever enough.
An example is Paul Cohen, who proved that the axioms of set theory, the axiom of choice, and the continuum hypothesis, all of them together, are consistent. You will never find that they contradict each other. Again, they cannot prove themselves consistent [meaning the set of all valid conclusions of those axioms does not contain the statement that they are consistent], but Paul Cohen can, and did.
Now one might think that he would be considered a laughing stock by the mathematical community for saying something wild like that. But no, he won a Fields Medal and a national Medal of Sciences for that result.
Godel explicitly covers the omnipresent fact that while one cannot use system G to prove that system G is consistent, one can use system F to prove that system G is consistent. Of course this relies on the consistency of system F, which can never be completely established, for reasons familiar to us all. You must have very little respect for us, if you think we would be caught by such an elementary fallacy.
We need to begin saving your posts for posterity. In what way is the human cognitive process not analogous to a “rich enough system”?
Malachi,
So you would strip Paul Cohen of his Fields Medal and National Medal of Sciences, because he did not prove anything according to you. He just had no respect for anyone, and somehow caught them all in an elementary fallacy, totally pulling the wool over their eyes. And he did it around 1965, so he has been pulling the wool over everyone but Malachi’s eyes for 50 solid years. After all, he proved that a system F, [= the axioms of set theory and the axiom of choice and the continuum hypothesis] is consistent, but little did he know that Malachi would catch him red handed making a newbie mistake. Uh huh.
I respect everyone here to the extent that I discuss things with them as if they will not be fooled by sophistry.
Tell you what, Malachi, and everyone else who has doubts, get on the bus and ask your local mathematician. Make a field trip of it. Report back on your researches.
I would say that you have combined assumption begging, strawman, and non sequitur into one sentence, surely this is intentional. Youre not actually arguing in good faith now, are you?
I HAVE.
You choose to respond to other things that I say…
I’m not about to “sum up” Frege’s arguments in the two papers because of the amount of information there is to condense. You just insist on denying the usefulness of symbolic logic without actually reading the reasoning behind it…one needs to do away with the ambiguity of natural langage and formalizing it with symbols is a difficult but necessary way to do just that (this is Russell’s point, summed up).
But, I did sum up Russell and Davidson (AND i put links in there…) and you responded to neither.
Bullshit. Expression of mathematics vary, but the conclusions (truths) of those expressions are universal. You’re familiar with geometric proof, yes? You say you know Frege, but if you did you’d know his proofs…or at least the one in Sinn und Bedeutung.
That is about the response I’d expect. You’re a a liar.
Exactly. You aren’t familiar with Frege OR Russell. You can’ t be bothered to even consider something that is against your “a priori “truth” seeking worldview” (which is just ridiculous to even type out…) You’re familiar with F.A. Hayek, right? geez…
See, B. Russell and/or G. Frege and/or D. Davidson and/or L. Wittgenstien…they will inform you to a world that you unreasonably deny.
Your “thinking” seems to me to be stubborness and your inability to respond to the actual points that I am making seems to indicate that you are lying about much of what you say.
Well, I’m telling them to start with some kind of footing. YOU are the one who should doubt yourself. You’re like a fat girl brimming with confidence…why? You know you’re beautiful…no matter what they say…
Riiight. Like I said one needs to have footing to start running.
I bet you do. Actually, I was referring to your imbecilic ramblings that you didn’t respond to in the other thread about geopolitics. (India will support the US vs. Iran?!?! - where’d you learn that? I mean when did you ‘a priori deduce’ it? Seriously, what grounds does your deduction have other than the superficial notion that hey are a US ally??!?!?)
But, you insinuate that I am merely following the lead of the people I read? So…I don’t know how trying to get people to read things that they aren’t familiar with is sophistry. Sophistry lies in pretending that you know the geopolitical strategies of countries that you have never been to without reading a lick of information about it…then not responding when people call you out on it.
No, you seem to percieve a difference here…
So, now I think you are lying. Straight lying.
And you call me a sophist…
I would say that you have combined assumption begging, strawman, and non sequitur into one sentence, surely this is intentional. Youre not actually arguing in good faith now, are you?
Oh dear. You are diverting attention from the ideas being discussed by engaging in personal attacks. Let’s stick to the topic. Just as I ask the mad bicoiners, I ask you here: Summarize my position and show me where exactly I am wrong.
I’ll help you take the first step. I am engaging in reductio ad absurdum, and pointing out that you are not disagreeing with me, but with Paul Cohen and the whole mathematical community. Tell me why your objection does not invalidate every consistency proof ever offered in the literature. In particular, why does it not invalidate his proof, which is universally honored and accepted.
In what way is the human cognitive process not analogous to a “rich enough system”?
- Your question is a red herring, irrlevant to the topic at hand. Answer the objection to your argument. Why does it not invalidate every consistency proof?
There are several interesting mistakes hidden in your quoted question, but this is not the place to explore them. Let’s put the red herring to bed, if you’ll excuse the mixed metaphor.
Dont think I would want to waste a real mathematician’s time with your sophistry, since Its easily debunkable here. Consistent with Godel, Cohen went outside of the system F by introducing a new technique, ramified forcing. That still doesnt violate Godel’s theorems, which is probably why you felt the need to go back and embellish your post with more nonsense. Are you the only person who thinks that Cohen disproved Godel, or are there others?
Your argument is that I am wrong because cohen disproved godel. I have demonstrated that this is not the case, by observing that cohen indeed does expand the formal system in order to prove its subsystem correct. Your move, Dave.
Because Cohen expanded the system used for the proof. What part of that do you not understand?
Dont think I would want to waste a real mathematician’s time with your sophistry, since Its easily debunkable here.
Oh, I know you personally will never go to someone who might teach you something. My intention was to hint to other readers that if they want to know the truth, they have an easy way to find out.
Consistent with Godel, Cohen went outside of the system F by introducing a new technique, ramified forcing .That still doesnt violate Godel’s theorems…
Thank you for admitting I am right. You have just stated very clearly that one can prove a system consistent.
…which is probably why you felt the need to go back and embellish your post with more nonsense.
Yes, I understand that my posts are at times incomprehensible to you, to the point of seeming nonsensical. i can live with that.
Are you the only person who thinks that Cohen disproved Godel…
You need a scorecard to remind you who the players are. Clayton is the one who claimed all systems might contain hidden contradictions that we will never know about. This is false, and reveals a deep ignorance fo mathematics. In particular, Paul Cohen’s theorem is an instance, one of many , of mathematicians proving a certain system F contains no hidden contradictions.
So I was asserting, correctly, that Cohen disproves Clayton.
You, on the other hand, claimed that Malachi disproves Paul Cohen. You did not grasp that you are saying that, so I pointed it out to you. You are welcome.
Your argument is that I am wrong because cohen disproved godel.
No. That Cohen disproved Clayton.
My move is to point you here: https://forum.freecapitalists.org/t/philosophy-help/25342/58
You strawmanned both Clayton and myself, likely because you know youre wrong. Clayton asserted that a system cant prove itself. You sidestepped and said that Cohen disproves Clayton. He doesnt, and you have misrepresented Cohen as well.
given that system G is consistent, yes. But we already knew that. This is consistent with Godel.