William James: Proof Proves Nothing

[Architeuthis Dux]

Anyone familiar with Willaim James' critique of "vicious intellectualism?"

James says that concepts are static, incomplete abstractions that are at best only useful analogies of dynamic reality. The corrolary is that reality cannot be completely described or captured by concepts.

"Proof" therefore is essentially nothing save a series of concepts that explains reality to your satisfaction.

But in the final analysis, what you have is not the guaranteed truth, but only the satisfaction.

 

[full-time-climb]

""Proof" therefore is essentially nothing save a series of concepts that explains reality to your satisfaction."

There is joy and satisfaction that comes from choosing a "concept". And anything "new" often appears "wrong" at first. It is hard to have a new idea if everything we think is filtered by our past experience.

I would like to chat with William James.

John

 

[Canute]

James if great. But people have been saying that reality cannot be conceptualised for millenia. A concept is a metaphor, it can never be more.

 

[quartodeciman]

Proof means deduction from presumed assumptions and former results, or induction from statistical results on specific cases. So proofs are not final, only more or less convincing.

But if James' pragmatic criteria were to be taken completely at face value, then psychologists and sociologists would be the only arbiters of scientific value. It pays to assume that specific truths can be approached, even if finality cannot be assured. It is also worthwhile continuing to pursue alternatives even after open-and-shut results seem to be at hand.

It is a wise saying: "Follow those who earnestly seek truth and retreat from those who claim they have it all."

 

[Kakorot]

yes, you cannot prove anything. Once you "prove" something, it becomes a memory, and everything that exists could have been created an instant ago, and your "proof" is just a memory that could have been created. So it may not have existed at all. You can never know. Since you can never truly prove anything.

 

[Les Sleeth]

I think to understand James' statements about proofs one has to take into account the change philosphy was undergoing at the time. After centuries (millenia really) of a priori rationalization James, following in the footsteps of Locke and others, insisted reality is known not through reason, but through direct experience. In his Essay on Radical Empircism he writes, “Nothing shall be admitted as fact except what can be experienced at some definite time . . . everything real must be experienceable somewhere, and every kind of thing experienced must somewhere be real. "

If we accept that experience is the most direct route to knowing reality, and reality is the "truth," then experience gives us truth while reason becomes the process of interpreting, calculating, and devising applications from what area of the truth (i.e., reality) has been experienced. Further, if one understands experience as one thing, and reason as another, then one must accept that each realm has its own methods of validation.

The concept of "proof," then, is understood to be a validation process for the realm of reason. A proof is not required to give us truth but rather to provide a test for the logical interconnections and conclusions used in interpreting, as well as predicting where to look for, experience.

 

[Canute]

Nicely put. With a bit of background added it would make a useful 'sticky'.

 

[Mentat]

Originally posted by Kakorot
yes, you cannot prove anything. Once you "prove" something, it becomes a memory, and everything that exists could have been created an instant ago, and your "proof" is just a memory that could have been created. So it may not have existed at all. You can never know. Since you can never truly prove anything.

Really? Prove it!

Just kiddin'. My real question is, can you ever prove that you can't prove anything?

In postulating that nothing is provable, you create a nasty paradox out of the simple fact that your statement cannot be proven by virtue of it's own correctness. Conversely, if you assume that the statement is not correct, then there must be some statements that are provable, and you are back where you started from.

 

[Canute]

Originally posted by Mentat
Just kiddin'. My real question is, can you ever prove that you can't prove anything?

Anything can be proved or disproved given the right system of proof. But all such proofs are relative and therefore uncertain in absolute terms. This much is provable.

 

[Zero]

There's no need for an absolute proof of anything...if you can get 99% of it right, you'll be ok, generally speaking.

 

[Canute]

I suppose that depends how you define 'ok'.

 

[Zero]

Originally posted by Canute
I suppose that depends how you define 'ok'.

I define it as practical or useful. If 99% of the right thing will do the job as well as 100%, then why quibble over that 1%?

 

[hypnagogue]

Absolute vs. relative is not a difference in degree, but in type. It is possible in principle to be 100% right using a relative truth, provided you carefully consider the relations involved. Relative truth simply implies that a proposition's truth value is modulated with respect to some variable, whereas an absolute truth is constant with respect to all variables.

 

[Canute]

Zero

Yes but if 99% of a proof will do the job then why not 98%?

I agree that usually we have to make do. But surely usefulness is nothing to do with proof, or even with what is true.

 

[Canute]

Originally posted by hypnagogue
Absolute vs. relative is not a difference in degree, but in type. It is possible in principle to be 100% right using a relative truth, provided you carefully consider the relations involved. Relative truth simply implies that a proposition's truth value is modulated with respect to some variable, whereas an absolute truth is constant with respect to all variables.

I agree. Where do you think that leaves something like the incompleteness theorems. They are true for all sets of variables. Does that make them absolute truths?

 

[Zero]

Originally posted by Canute
Zero

Yes but if 99% of a proof will do the job then why not 98%?

I agree that usually we have to make do. But surely usefulness is nothing to do with proof, or even with what is true.

Right, but I don't need to know what is "true", I need to know how to get from point A to point B, and hopefully sometime before the clock runs out. "Truth" that isn't practical is a useless notion, because it doesn't get you anywhere. Further, how do you know it is 100% true? While you go figure out how you go about confirming the truth about something, I'm going to go live a little, ok?

 

[Canute]

Fair enough. You are clearly content in the world of appearances.

 

[Zero]

Originally posted by Canute
Fair enough. You are clearly content in the world of appearances.

And you'll have to show that there is anything more to reality than that, you dig?

 

[hypnagogue]

Originally posted by Zero
And you'll have to show that there is anything more to reality than that, you dig?

You concede as much yourself when you say you get by on "99%" truth.

 

[Zero]

Originally posted by hypnagogue
You concede as much yourself when you say you get by on "99%" truth.

Do I? It was just a random number I threw in there, you know...what I mean to say is that whenever I know enough to get from A to B, I feel like that is enough knowledge. Is there more knowledge out there? Quite possibly, but if it isn't going to do me any practical good, I don't sweat it much.

For every question that we have an answer to, there are hundreds that we either haven't answered, can't answer as far as we know right now, or the answer doesn't satisfy someone.

Gravity seems to be a favorite "whipping boy" for my sort of position. There are lots of theories of gravitation. Do we need to know which one is the "true" one, in order to make accurate predictions as to what effect gravity is going to have in 99% of situations we are going to encounter?

 

[Canute]

It's your choice. But Hypno's point holds.

If you feel that usefuleness is enough then that's fine, I suspect that many people agree. However at first glance you seem to be deciding what knowledge is useful and what is not before having the knowledge, which is quite a trick.

 

[Zero]

Originally posted by Canute
It's your choice. But Hypno's point holds.

If you feel that usefuleness is enough then that's fine, I suspect that many people agree. However at first glance you seem to be deciding what knowledge is useful and what is not before having the knowledge, which is quite a trick.

Trial and error, plus a little instinct, chum...it works great for woodpeckers, it works great for me.

The whole "search for truth" thing seems a little bit of navel-gazing to me. If a thing works, that's about all the proof we can hope for.

 

[Les Sleeth]

Originally posted by Zero
Trial and error, plus a little instinct, chum...it works great for woodpeckers, it works great for me.

The whole "search for truth" thing seems a little bit of navel-gazing to me. If a thing works, that's about all the proof we can hope for.

It's so seldom we agree I thought I should make note of it.
Of course, I don't totally agree, but 99% is close enough.

I love the pragmatic concept. Almost more than any other single idea it has guided me in understanding reality/truth. However, I'd have to say that the most guiding factor has been what feels good. That might sound superficial, but by following what feels good (over the long haul, I don't mean mere immediate gratification) I've been led into some pretty nice realms of conscousness.

The question I have for you is, how do you decide the extent of what is practical? One can limit the definition to everyday matters of life, but one might also say it is practical to be content, more conscious, enlightened . . . If one can demonstrate the practicality of such achievements, would you still say seeking them is "navel-gazing"?

 

[Njorl]

"99% proof" is good enough for 99% of my life. The other 1% is dedicated to navel gazing. But then again, I have a damned atractive navel.

Njorl

 

[hypnagogue]

Originally posted by Canute
I agree. Where do you think that leaves something like the incompleteness theorems. They are true for all sets of variables. Does that make them absolute truths?

I don't know. Do they generalize to all systems of logic?

 

[hypnagogue]

Originally posted by Njorl
"99% proof" is good enough for 99% of my life. The other 1% is dedicated to navel gazing. But then again, I have a damned atractive navel.

Well said. What's wrong with navel gazing anyway? Practical things are only worthwhile insofar as they enable us to ultimately pursue things we deem worthy of pursuing in their own right (eg love, entertainment, etc). Don't see why 'navel gazing' should not be included in that list.

 

[Canute]

Originally posted by hypnagogue
I don't know. Do they generalize to all systems of logic?

As far as I know they generalise to all systems of proof in all possible universes. (The only proviso being the definition of 'proof').

I lke to think that this is what Lao-Tsu meant when he wrote 'true words seem to paradoxical', but that could be a misreading.

 

[Zero]

Originally posted by LW Sleeth
It's so seldom we agree I thought I should make note of it.
Of course, I don't totally agree, but 99% is close enough.

I love the pragmatic concept. Almost more than any other single idea it has guided me in understanding reality/truth. However, I'd have to say that the most guiding factor has been what feels good. That might sound superficial, but by following what feels good (over the long haul, I don't mean mere immediate gratification) I've been led into some pretty nice realms of conscousness.

The question I have for you is, how do you decide the extent of what is practical? One can limit the definition to everyday matters of life, but one might also say it is practical to be content, more conscious, enlightened . . . If one can demonstrate the practicality of such achievements, would you still say seeking them is "navel-gazing"?

Hey, a certain amount of "non-practical" behavior actually ispractical...you have to let off steam, have hopes and dreams, whatever. I'm just saying that you can't let a search for "absolute truth" get in the way of using the "relative truth" that you've already got.

 

[Canute]

I suppose it all depends what you call 'practical'.

 

[hypnagogue]

Originally posted by Canute
As far as I know they generalise to all systems of proof in all possible universes. (The only proviso being the definition of 'proof').

If this were true I suppose they would be an absolute truth. However, I have my doubts, since the proofs themselves have been built from our familiar system of logic and so they would seem to depend on that logic rather than transcend it. That is, if logic really worked differently from how we conceive of it, perhaps it would then be impossible in principle to construct such proofs.

 

[Les Sleeth]

Originally posted by Canute
I suppose it all depends what you call 'practical'.

I know that to a lot of people "practical" refers only to material conditions. I think of it as anything which helps me do what I want to do. Under that broad umbrella I include anthing which can help further my happiness and contentment, since I want them in my life.

But I think happiness and contentment are practical to material concerns too. Think about how well people do their jobs, interact with a mate, raise children, contribute to the world, etc. when they are miserable versus when they feel good. In fact, a great many of the problems of the world can be traced to discontent, miserable people. The rest of the problems can probably be attributed to ignorance and selfishness, both of which might be helped by the active development of consciousness. Now, there are a great many people involved in inner practices specifically to develop their consciousness, so might we not include effective inner practices on the list of what's practical too?

 

[Zero]

Well, once we start down that road, we need to decide which path is more valid, "happiness" or mental well being?

 

[hypnagogue]

Define 'mental well being.' If someone can be happy and at the same time not 'mentally well' in perpetuity (read: the mental illness does not critically hinder their ability to remain happy, eg via the threat of mental breakdowns or an inability to support themselves) I'm not sure the mental un-wellness is really a problem.

Would a society of people that we would classify as mentally ill but nonetheless was peaceful and happy and could sustain itself not be preferable to the society we live in? Are there even any grounds on which we could really justify claiming that such a society is mentally ill?

 

[Zero]

Originally posted by hypnagogue
Define 'mental well being.' If someone can be happy and at the same time not 'mentally well' in perpetuity (read: the mental illness does not critically hinder their ability to remain happy, eg via the threat of mental breakdowns or an inability to support themselves) I'm not sure the mental un-wellness is really a problem.

Would a society of people that we would classify as mentally ill but nonetheless was peaceful and happy and could sustain itself not be preferable to the society we live in? Are there even any grounds on which we could really justify claiming that such a society is mentally ill?

"Mental health" is, in many ways, defined by your ability to accept and deal with reality on its own terms, which means that part of mental illness is not being able to cope with reality. That sort of precudes your whole "well, if it doesn't cause any problems" approach.

On the other hand, the happiest person on Earth is a junkie with a needle in her arm, so happiness alone isn't always a great idea.

 

[Canute]

Originally posted by hypnagogue
If this were true I suppose they would be an absolute truth. However, I have my doubts, since the proofs themselves have been built from our familiar system of logic and so they would seem to depend on that logic rather than transcend it. That is, if logic really worked differently from how we conceive of it, perhaps it would then be impossible in principle to construct such proofs.

I agree that there's something very paradoxical about the incompletenmess theorems. They seem to prove that they cannot be proved. But there is a get out clause.

In a very real sense Goedel did not prove anything. The theorems work because for some self-contradictory sentences the system cannot decide what is true but we (the meta-system) can decide. This shows that knowledge and truth extend further than proof.

However the fact that we can decide Goedel-sentences cannot actually be proved since it is never provable in the system within which those sentences appear. One is always forced to retreat to the meta-system and this leads to an infinite regression of near-proofs.

This means that the incompleteness theorems are not really provable, but just demonstrable, which is a different thing. Because of this we can know that they are true without falling foul of them.

I only just thought of this so may be wrong. Any mathematicians around?