can i know something not proven?

the classic a priori statement is 1+1=2; from there you can go anywhere into the infinite #s you have never seen or heard but you kow that 538+450 is 938 even if you neve knew that before and its truth/validity is uncontestable. that's a place to start with a priori.

 

Log in or Sign up to hide all adverts.

For Tyler

Thank you. I believe that the above statement is the very basis of philosophy, yet it is the one thing that so many people fail to understand. Every man, woman and child on this planets KNOWS something. So why is everyone not in agreement? Yeah, thats right.....

 

Log in or Sign up to hide all adverts.

Hi
Please see my post.
D Man

 

Log in or Sign up to hide all adverts.

Re: For Tyler

Is that a fact? Are you certain? To understand is to know. What you're describing isn't philosophy. It literally means nothing, the second you try to apply or integrate it.
Humans are fallible thus can disagree or even contradict themselves, but that's all the more reason to pursue knowledge, giving up is defeatism, the end, not a basis for anything.
3 blind men feel an elephant, one feels trunk, one feels body, one feels ears. 3 very different interpretations of what an elephant is. All 3 correct. Why? All 3 are consistent with experience. All 3 derive logically from reality. If the blind men are rational and compare data, they might arrive at an idea of what the elephant really looks like. If they say, "well, truth is relative. for me elephants might be long and narrow like snakes, for you they might be big and round like a hippo. we can never know anything. let's agree to disagree" what do they learn? nothing. they invalidate each other's as well as their own experience. End of philosophy, end of knowledge, end of everything.

 

i think river-wind offered a pretty good refutation of the idea of 1+1=2 being a-priori in a post under the thread 'does 1+1=2': **"Don't confuse the real world system that these numbers stand for for the numbers themselves, now! If the world blows up tomorrow, and all the humans on it die, then one earth scrap + one earth scrap still = two earth scraps according to our definition. But there won't be anyone around to discuss it, so why does it matter? We are talking about proxy values here. Numbers don't exist in reality without objects to associate them to. People(or other cognitive creature of your choice) define that association, using the properties of the real world object in question."**
A more comprehensive study on objective knowledge without a-priori can be found in Ayn Rand's _Introduction to Objectivist Epistemology_ and notably in the accompanying essay by Leonard Peikoff on the flaws of analytic-synthetic dichotomy.
Their treatment solves the problems of JS Mills and others which is the problem of universals. But I haven't grasped this comprehensively enough to condense it into a short statement yet. All I know is that before I read IOE, I considered myself terrible at math and almost failed my last math class in high school. Afterwards, I was able to integrate my knowledge of math and philosophy and music and experience and I made a B+ in my first math class in college. Viva la self-actualization!

Please Register or Log in to view the hidden image!

 

At the end was Leonard on Ayn's team? Altho I havent read the IOE it would be interesting to note wherein she crosses the lib/conservative line. With her laissez Faire sp? approach to economics i am sure she is conserative. What does that have to do with philosophy? take John Kerry for an answer..Epistemology non facet est for him.
DMan

 

Yeah, Peikoff as student of Rand. You might also be interested that Alan Greenspan was one of her pupils in the old days. Laissez Faire is right

Please Register or Log in to view the hidden image!

She goes more in depth with that aspect of her philosophy in Capitalism: the Unknown Ideal. She rejects both the Liberals and Conservatives as two sides of the same coin- materialism and mysticism (theological or social mysticism=replace "God" with "society"). She condemns the conservatives as being worse than the liberals because of their failure to defend capitalism and their foundation in religious altruism. I once saw someone quote her as saying "Now we've got to save capitalism from the goddamn capitalists!" hehe.
But I'm new to the philosophy, and I come to this board partially to clarify and refine my understanding of these concepts, so definitely best to go to the primary source!
As far as philosophy as necessary and encompassing all aspects of life, I like Peikoff's position, "Philosophy is not a mere bauble for the intellect." There are no "floating abstractions" in Objectivism. These are the result of what Rand called "the fallacy of the stolen concept" adressed thoroughly in IOE but a possible analogy might be something like the cartoon character sawing off the tree branch that he's standing on, expecting not to fall with the tree.

 

Thanks. I'll put it on my list to read. I've wanted to but have always found an excuse, but after your reply I am headed to half.com for a copy.
DMan

 

It has been mathematically proven that we can know things that are not provable, unless I've misunderstoof Goedel (which is quite possible).

In fact the whole significance of Goedel's first theorum rests on that that a sentence can be known to be true but nevertheless be provably unprovable. This is one of the tricks of consciousness.

Penrose 'Shadows of the Mind' argues this as follows:

2. Penrose's Argument
2.1 The basic contradiction for Penrose is this: Assume that the reasoning powers of some mathematician, say Penrose himself, are completely described by some formal system F. What this means is that for every mathematical statement S in the language of F that Penrose finds to be "unassailably true", S is a theorem of F, and vice-versa. We will further assume that Penrose knows that F describes his reasoning.

2.2 According to Penrose, the belief that F describes his own reasoning entails a belief in the soundness of F. (Penrose justifies this, saying "It would be an unreasonable mathematical standpoint that allows for a disbelief in the very basis of its own unassailable belief system.")

2.3 By Gödel's theorem, since F is sound, then G(F), the Gödel statement for F, must be true, but not a theorem of F. Therefore, since Penrose believes that F is sound, he must conclude that G(F) is "unassailably true". So there is something (namely, G(F) that Penrose finds unassailably true, but which is not a theorem of F. This contradicts the assumption that F completely describes the reasoning powers of Penrose (including his knowledge that F has this property.)

2.3 (Reviewer) So, the Gödel argument doesn't prove that human reasoning must be noncomputable - it only proves that if human reasoning is computable, then it must either be unsound, or it must be inherently impossible for us to know both what our own reasoning powers are and to also know that they are sound.

This is why Goedel's theorums are often connected with arguments for supreme beings or for cosmic consciousness. Whether they should be or not is hotly debated. They do at least show that we can prove that we can know things which cannot be mathematically or scientifically proven.

Sorry this is long but I happened to have the quote handy.

 

Could you explain further why G(F) is not a theorem of F? >>According to Penrose, the belief that F describes his own reasoning entails a belief in the soundness of F. >> Isn't this G(F) as a theorum of F? I might not fully understand the definition of "theorum".

 

This is the bit that interested me about the way Penrose looks at it. If F describes/models the totality of Penrose's reasoning system then he cannot ever know that G(F) is true, since it is undecidable in F yet he does know it's true. Therefore he has reasoning powers beyond those described by F, the larger system in which G(F) is deduced to be true.

Penrose therefore takes G(F) to be a theorum from outside F. Whether he is right to do this (and whether I've got this right) is not quite clear to me. It seems to me G IS a theorum in F, it's just an undecidable or contradictory one. This may be the reviewers fault, since Penrose's point comes out the same in either case - namely that - "This contradicts the assumption that F completely describes the reasoning powers of Penrose (including his knowledge that F has this property.)"

In other words it seems to me this point is true whether or not G is a theorum of his reasoning system.

It's a slippery topic.

 

Oh, I think I see the flaw in it. It's just context dropping. The whole thing seems to forget the most fundamental of all mathematical principles- A=A. A thing is itself- A belief system is that belief system. You don't need any wider context as long as it's all self contained and non-contradictory. I'm sure if I really got into it there are all sorts of subtle mathematical technical errors that would shed light on the real root of their error. But the whole thing just sounds like Kantianism to me, which just couldn't possibly be refuted any further it's so deep in its grave. Yet I know a lot of pedantic type people still buy into it for psychopathological reasons. Frustrating for young people like me who could care less about nonsense besides as material for jokes. ? I see so many honest people seriously struggling with those kinds of riddles, and actually almost assasinated intellectually. Therefore I see philosophers who try to pass those ideas off as serious science as misanthropic sadists one and all.
They want so much to make the simple businessman or factory worker who earns her/his living and has a little family and is content be somehow inferior just because they haven't read this or that book, or whatever- there always has to be some "mystical revelation" (some higher context) that only they know about, or that nobody can know so give into fate. That's always been a scam to gain power without earning it. Bah-fooey!

Please Register or Log in to view the hidden image!

 

A perfect(almost) definition of a Liberal!

 

lol, I know, it describes so many people in our culture! Look at it this way too- Said businessman hasn't done enough just to have integrity, just to excell at whatever work he does, just to have a close, affectionate relationship with his family and always get his friends out of jams when they need help. These deeds are as filthy rags. He's been selfish, for all of these things are only for his own earthly benefit. If only he will abstain from the fleshly pleasures of this world, and give up his dreams and goals of earthly happiness for treasures in heaven, if only he will sacrifice his own wife and children just a little to help the crack-family down the street (for he's but a humble sinner just as they are), if only he will give 10% of the money he's earned to.. say.. the church [hint,hint], God will bless him tenfold. How? Somehow. But his kids need braces! They'll get them in heaven.
Not enough businessmen content with the arrangement? Say they're doing better than 10% returns in the stock market? We've got to make them do it to save their immortal souls! That's what government is for, right, a conscience with a gun. : )
We're doing them all favor, boys, they just don't realize it's for their own good! Duty, patriatism, and immolation; these three and the greatest of all is immolation.

 

You have me scratching. I see nothing wrong being successful in business or the stock market. What is your point? I fit the first part of your description but when you got to filthy rags I lost the thread.What am I missing?
D Man

 

Bold Standard - It would help if you could make it clear what youre talking about. Was this rant about businessmen supposed to relate to my post in someway? What is 'context dropping'? And what do you mean about not needing a wider context as long as it's 'self-contained and non-contradictory'. Do you disgree with Goedel?

 

oh, sorry, I forget sarcasm doesn't translate to text on the internet. I was attempting to show the conservative side of the context dropping scam. My position is that a person who looks out for her/his own, is independent and has integrity is of the highest caliber of virtue. But there are a lot of interest groups and politicians who want to claim a right to the property of people like that, and the only way to do that is to impose vices on them that they don't actually posses, and the only place to find those vices, since they clearly do not exist in reality, is in the supernatural realm. The liberals don't care if it's not in reality cause they just think reality is all relative, the conservatives don't care if it's not in reality because this reality doesn't matter, it's materialism and mysticism which are the same thing basically=collectivism.
The alternative would be contextualism, the context being objective reality as perceived by individual humans on earth.
Oh, and a silly but confusing mistake I made was implying tenfold=10% it would be 1,000% I guess that would be stock in an aids vaccine or something.

Please Register or Log in to view the hidden image!

 

Yeah, it's supposed to relate, if I've understood Goedel correctly based on what you've said. He seems to be saying f can't be a theorum of f(x) or whatever because in order for this to work, you would have to have some way to know that the whole system was true, and you could never know that unless you left the context, in other words, validated it from the context of a wider system.
So I would definitely disagree with that, if I've grasped what you're saying- because f(x)=f(x), in other words, unless there are contradictions inherant in the system itself, fully integrated and as it stands relative to reality, then the system is true. Who then determines what's real and what's not? Nature determines this, yet it is the responsibility of each individual to observe reality and apply logic to those observations, integrate them into concepts, integrate those concepts into a metaphysical view of existence, and that into moral values, and that into goals, then actions etc etc.
I apologize that I'm not proficient enough in math to speak of this strictly in mathematical terms. I'm not primarily a mathemetician, but I believe the same rules as apply to math apply to everything, so that's how I can most naturally verbalize it.

 

OK - but I've lost the thread a bit. This was about whether we can know things that aren't proven. I think I was pointing out that there aren't many things that we've proven for sure, and physical existence isn't one of them.

 

Oh, no, we can't know something without evidence. Faith isn't knowledge, it's an epistemelogical package deal that smuggles potential falsehoods in with possible unverified truths. Emotions aren't a form of cognition. We know that which has to be true in our context.