Sunday, May 10, 2009

95 Gödel

Meno: And how will you enquire, Socrates, into that which you do not know? What will you put forth as the subject of enquiry? And if you find what you want, how will you ever know that this is the thing which you did not know?

Socrates: I know, Meno, what you mean; but just see what a tiresome dispute you are introducing. You argue that man cannot enquire either about that which he knows, or about that which he does not know; for if he knows, he has no need to enquire; and if not, he cannot; for he does not know the very subject about which he is to enquire.

More than 2000 years ago some Greeks debated about the question whether new knowledge is possible and if so where eventualy does it come from. And by interrogating the uneducated slave of Meno, he shows that the boy seems to know answers, which werent taught to him.

This brings Socrates to the conclusion that all these answers already must have been in the mind of the boy and that only by good questioning he seems to recall this knowledge. In other words all knowledge is already present in our minds. We only have to dig it up.

We call this Platonism, as Plato was the writer of this dialogue.

Those who have attended my class from the beginning may remember, that I would make our philosphical journey with a special eye for epistemological matters.

With only 5 philosophers to go we are in the center of the epistemological question: what do we know? Or to put it in a wider historical perspective referring to Kant's philosophy in one single formula: He wished to insist on the authority of science and yet preserve the authority of morals.

For many centuries since that discussion between Meno and Socrates the debate was about the source of these recollections: revelation, God, innate ideas, universalia, you name it.

In the 16th century there came cracks in the philosophical walls caused by the rise of physical sciences and Kant saw this: there is an increase of insights, new knowledge about the universe, natural processes and so on; laws of nature.

Does this mean that man will be submerged by this scientific knowledge, become cause and effect in it, an atom among atoms or is he more than just that: has he still to decide about what is right and what is wrong?

Is man just an empty vessel which fills himself with sensory experiences and generates knowledge from that input, as Locke and Hume said? And where is the moral question in this context?

The development of science in all fields could not be stopped and shaped our world and we already have seen a number of answers to the epistemological questions involved.

On the one hand we have the epistemological battle regarding sensory experience and how it leads to certified new knowledge: verification, falsification?

And Popper adds the idea, that hypotheses are generated by moments of creative imagination, which we have. Where do they come from, those ideas? And it is the Logic of Scientific Discovery that has to control and guide the process of the growth of knowledge.

In this context we also saw, beginning with the Vienna Circle, a drive to make the language of science as formal as possible as if it were pure logic and mathematics only, because in logic and mathematics you can PROOF things irrefutably.

That is to say, that is what philosophers of science believed in the 30s of the 20th century and then there is that one man, Gödel, who even seems to smash that last stand of absolute certainty.

In 1931 the Czech logician and mathematician publishes a paper which had historic consequences for formal languages and mathematics. The math involved here is way over our head, but I'll try to give you an impression of what it is about.

In any formal system adequate for number theory there exists an undecidable formula -- that is, a formula that is not provable and whose negation is not provable. That of course is a logical horrorstory: a statement S of which you can't proof whether S or not-S is true, but in a way yet you need that statement for your formal system.

A second theorem of incompleteness says that the consistency of a formal system adequate for number theory can not be proven within the system.

When you look at the whole body of human knowledge, Gödel showed, that the old ideal of one great deductive system could not be maintained. There always shall be that incompleteness, so to speak.

However, all sciences other than mathematics are so remote from a complete formalization that this conclusion remains of little consequence outside mathematics.

The bearing of Gödel's theorems on epistemological problems remains uncertain, but it made me think. Logic and mathematics is a product of our mind and Gödel showed that it isnt, as was maintained for centuries, perfect: you can not proof the consistency of a system with the system itself.

And here I saw an analogy, an issue I have brought up several times: we use our mind as the tool to analyze and understand the mind. It is as in Gödel's theorem. We try to proof something - the mind - within the same system - the mind. In other words, like the snake, who thought he had found a delicious meal, we are biting constantly in our own tail.

That fascinates me and is the general conclusion of my long journey together with you. It was a terrific journey and with the help of the last five philosophers I think I can show you my personal tentative findings, which will set the mark for my philosophical future.

The Discussion

[13:22] Herman Bergson: So much on Gödel.....(and me:-)
[13:23] Herman Bergson: If you have any questions or remarks..feel free
[13:23] Gemma Cleanslate: It wil be wonderful to have some conclusions i think
[13:23] itsme Frederix: I think its a relief, Godels incompleteness theoreme
[13:24] Herman Bergson: In a way it is completes the incompleteness we all have observed in epistemological matters :-)
[13:24] itsme Frederix: it also states something about absolute metaphysical issues
[13:24] Zen Arado: that reminds me of zen meditation - you step back from thoughts and just become aware of them. But it's still the mind looking at the mind i guess
[13:25] arabella Ella: Herman you presented us with some links here in such a fascinating way thank you
[13:25] herman Bergson smiles
[13:25] Herman Bergson: thnx Arabella...and yes is still the mind...even in meditation
[13:25] arabella Ella: it is all quite a revelation for me ... plato ... hume ... kant ... popper and now Godel
[13:26] Zen Arado: what about the unconscious
[13:26] Herman Bergson: I followed the same route Arabella after 30 years
[13:26] Herman Bergson: redoing my academic years here
[13:26] arabella Ella: fantastic
[13:26] itsme Frederix: you should have studied math earlier Herman
[13:26] Herman Bergson: Oh yes...Itsme..I am so wel aware of that
[13:27] Herman Bergson: I only began to understand the meaning of math when I studied philosophy
[13:27] arabella Ella: an analogy with what you just said Herman ... the eye ... we know our eyes exist but the eye can never see itself except in a mirror ... but never directly ... similar to what you said about the mind
[13:27] itsme Frederix: but still its only a statement in an incomplete system, so maybe we find a way out ...
[13:27] Samuel Okelly: so...., rationalism or empiricism? I am still undecided ;-)
[13:28] Herman Bergson: Yes arabella....that will fascinate me the coming 5 philosophers
[13:28] itsme Frederix: egoism might do it Sam
[13:28] Samuel Okelly: is that an observation or a deduction itsme?
[13:28] Cailleach Shan: Try hitting yourself Sam... see if you really exist or not!!
[13:28] Herman Bergson: and there I am back philosphically where I was when I was graduating
[13:28] itsme Frederix: a reduction to soliphism Sam (I did not mean it ugly or personal)
[13:29] Samuel Okelly: lol oh i know itsme :) "i refute it thus!"
[13:29] Herman Bergson: Yes Samuel....that seems to be our only choice...but still I am not certain
[13:29] itsme Frederix: Herman even you can not be certain (Godel)
[13:30] Aya Beaumont: What are you refuting?
[13:30] Herman Bergson: Hey Aya :-)
[13:30] Aya Beaumont: Ello =)
[13:30] Zen Arado: there was radio programme about Godel a couple of weeks ago but you might not be able to listen outside the UK l
[13:31] Gemma Cleanslate: ty Zen
[13:31] Herman Bergson: Philosophically Gödel fortunately isnt such a big is all logoic and maths
[13:32] Herman Bergson: I really have trouble understand what he is all telling us
[13:32] Herman Bergson: But I think I gave you the basic idea today
[13:32] itsme Frederix: Herman still he tells us to be not to sure or profound about our own system/thinking
[13:32] arabella Ella: yes you certainly did herman
[13:32] Aya Beaumont: How about "no system can ever cover everything you hope it would"? =)
[13:33] Herman Bergson: Right Itsme...and that is so amazing and yet from my perspective almost logical
[13:33] Zen Arado: is it a good idea to look?
[13:33] arabella Ella: it is also a bit like language i think ... we try to resolve problems of language by using language ... thus remaining with the system itself ... but what is language? what is meaning? how can we proove anything about a system from within the system itself?
[13:33] itsme Frederix: would be good, if more found that logical and behave themselves like that
[13:33] Zen Arado: Stephen hawking is searching for a theory of everything I think
[13:33] Cailleach Shan: That's the essence of philosophy isn't it Herman... to keep questioning.
[13:34] Herman Bergson: Oh Zen...that is interesting to check out...especially in the light of what I have said today
[13:34] Aya Beaumont: Stephen Hawking is most likely going to find one... one that applies under certain circumstances... =)
[13:35] itsme Frederix: Zen I guess SH will leave out a lot as not belonging to everything
[13:35] Herman Bergson: It is what arabella seems that we are a collection of systems that all suffer of incompleteness
[13:35] Herman Bergson: It yet is interesting Itsme..
[13:35] Zen Arado: its in human nature to always wonder and enquire isn't it?
[13:36] Alarice Beaumont: i would agree on this
[13:36] Herman Bergson: A final objective of (some) science has always been to create one overall science...the absolute deductive system
[13:36] itsme Frederix: wonder & enquire - or knowing & controll (to stay alive)
[13:36] Herman Bergson: to show that everything is related to everything
[13:37] Aya Beaumont: I think it's a question of detail as well...
[13:37] arabella Ella: if i may suggest a set of videos on Youtube linked to quantum physics and these last few lectures, there are about 15 short 10 min videos ... use the keywords ... what the bleep do we know ... the videos raise some fascinating questions concerning philosophy and science
[13:37] Aya Beaumont: As long as you don't require the predictions of the system to be all that precise, you CAN have the perfect system.
[13:37] Zen Arado: ty Arabella
[13:37] Gemma Cleanslate: ah good
[13:37] itsme Frederix: so speculative and narrowed (in a way)
[13:37] Aya Beaumont: But as soon as you want detail, it won't work anymore.
[13:38] Rough Jewell: but why does everything has to relate to everything else... is it due to the cause and effect... the butterfly wings idea? maybe things are seperate and there will never be a theory of everything.. because everything is not one
[13:38] Herman Bergson: That sounds like sophism Aya.....
[13:38] arabella Ella: and on youtube i also found a 4 min video on the particle accelerator at CERN ... keywords ... LHC Rap
[13:38] Aya Beaumont: Perhaps, herman.
[13:38] Herman Bergson: if you dont want to be too precise , you have the PERFECT system....^_^
[13:38] Aya Beaumont: But it's true.
[13:38] Samuel Okelly: isnt that the danger with empricism as the scientific method cannot explain such ideas as mathematics and logic as it presupposes them?
[13:38] arabella Ella: Rough ... have a look at the videos i mentioned and you will see why and how everything relates to everything else
[13:38] Herman Bergson: I wonder what a perfect woman is in your opinion..^_^
[13:38] Alarice Beaumont: but a perfect system would be boring... nothing left to explore
[13:39] itsme Frederix: sounds like Heisenberg again
[13:39] Aya Beaumont: Systems are not only constructs of thought... they are also used, every moment of every day.
[13:39] arabella Ella: Herman ... not just a perfect woman ... a perfect human being perhaps
[13:39] Aya Beaumont: And in that USE, we have to choose how much use we have of the system, and how many exceptions there are.
[13:39] Herman Bergson: matter of perspective Arabella :-)
[13:39] Zen Arado: you have to define system
[13:39] arabella Ella: LOL
[13:40] Rough Jewell: it's still not proven aya... proximity comes into it a lot... in physics to every action there is an equal and opposite reaction but only if we apply force to colliding objects
[13:40] arabella Ella: Rough ... the perspective of quantum physics proves that everything is interelated
[13:40] Rough Jewell: the universe is so large that proximity could just not be there... more like a ripple effect when u throw a stone.. the further you go out.. the less one feels it
[13:40] Aya Beaumont: In measurements, the terms specificity and sensitivity are more established.
[13:40] Herman Bergson: Do I understand you correctly Aya, in that you are bringing in pragmatism here?
[13:40] arabella Ella: in ways we would not imagine possible
[13:41] Aya Beaumont: And when you choose the cutoff value for a positive result, we decide what sensitivity and what specificity we want.
[13:41] Herman Bergson: I am still not sure what this Quantum Physics means
[13:41] arabella Ella: bút Aya is that not merely the human perspective?
[13:41] Aya Beaumont: I can't help but feel there is a relationship here.
[13:42] Aya Beaumont: human perspective? Of course.
[13:42] arabella Ella: Herman ... if you watch the videos they make quantum physics much clearer
[13:42] Gemma Cleanslate: I hope so
[13:42] arabella Ella: Aya ... the human perspective may tend to distort what it perceives
[13:42] Qwark Allen: :-)
[13:43] Herman Bergson: brings back an idea of the old greeks, Democritus, but one I had myself too...that everything that is , is just a big soup of matter
[13:43] Gemma Cleanslate: but arabella it is the only one we have
[13:43] arabella Ella: exactly herman
[13:43] Rough Jewell: Herman... quantum physics is the science that looks at energy.. forces..waves.. etc etc
[13:43] Cailleach Shan: That's it Herman.
[13:43] itsme Frederix: Still I think it is strange that in one way we use quantum details to explain everything (or want to use it), and on th eother hand just use a system as a black box, describing its purpuse/goal and forget the how it does it. Such an abstraction is a great benefit in life
[13:43] AristotleVon Doobie: the question that remains is whose distortion is the truth
[13:43] Rodney Handrick: I think Mick fell asleep
[13:44] arabella Ella: yes gemma ... but some scientific experiments give different results ... with human observers and without human observers
[13:44] Ze Novikov: lol
[13:44] Gemma Cleanslate: ah i saw that phrase at burning life the soup
[13:44] Gemma Cleanslate: we are alll part of the big soup
[13:44] Herman Bergson: But all this doesnt make us escape from our brain/mind
[13:44] Herman Bergson: it still is all in our mind only
[13:45] Herman Bergson: created by our mind only
[13:45] Cailleach Shan: Just for entertainment!!
[13:45] Rough Jewell: mick is afk.. dont worry guys
[13:45] itsme Frederix: created, you mentioned Socrates ... digging it up ..
[13:45] Laila Schuman: in an oblique way, this is related to existentalism
[13:45] Aya Beaumont: How to explain what I mean...
[13:45] Herman Bergson: yes..Itsme..such questions still remain
[13:46] Herman Bergson: There is a link to solipsism...
[13:46] itsme Frederix: I do not experience math as to invent it, it is just discovering what there already is
[13:46] Herman Bergson: and in my existentialist moments I say to mysef: I am the prisoner of my own skin
[13:46] Laila Schuman: or a drop in the soup
[13:47] herman Bergson smiles
[13:47] arabella Ella: i am a prisoner of my perceptions
[13:47] Herman Bergson: Yes Laila
[13:47] Aya Beaumont: Assume that we live in a world as we tend to perceive it, rather constant and predictable. We have a brain that registers signals from said world, and we create an image of the world, a system of predictions.
[13:47] Zen Arado: this is realism as opposed to anti realist view
[13:47] Herman Bergson: ok Aya
[13:47] Cailleach Shan: If you create yourself as a prisoner... that's what you will be.
[13:47] Rough Jewell: aren't we all ara... and others want us to bind us with their own perceptions of us ! :-)
[13:48] Aya Beaumont: That system, also, will run into trouble, for the simple reason that we are not able to deal with the mass of information registered.
[13:48] itsme Frederix: Rough that your perception
[13:48] Aya Beaumont: So we simplify. And normally we think nothing of it.
[13:48] Rough Jewell: maybe itsme... maybe....
[13:48] Herman Bergson: But that is a supposition Aya..
[13:48] Aya Beaumont: But once the time comes to detail HOW THE WORLD WORKS, those simplifications will hurt us.
[13:48] Cailleach Shan: Aya... maybe that's why so many philosophers went crazy.
[13:49] Herman Bergson: How can you know that you simplify when you dont know the complexity?
[13:49] Herman Bergson: We are back to Meno here
[13:49] Aya Beaumont: And it's still an open question whether we CAN find and remove those simplifications.
[13:49] arabella Ella: and Aya your citing simplification is another assumption
[13:49] itsme Frederix: Aya what could you do with the details, not even fix a flat tire
[13:49] Zen Arado: yes our sensory apparatus is very limited
[13:49] Aya Beaumont chuckles.
[13:50] Samuel Okelly: isnt that the danger with empiricism herman (that it presupposes so much)?
[13:50] Aya Beaumont: Without the details (at one level), you couldn't MAKE said tire, itsme
[13:50] Gemma Cleanslate: itsme always brings it down to a practical leval
[13:50] Herman Bergson: Yes may have a point there....but rationaism is good at that too
[13:50] Aya Beaumont: And yet, by learning the details, people have actually made tires.
[13:51] itsme Frederix: Gemma well - sometimes I wonder - what does it tell me, how can I deal with it what shoul I do, what can I hope
[13:51] Herman Bergson: Oh..that is what I only refered to in my lecture Itsme....the moral aspect of being
[13:51] Samuel Okelly: indeed however there i perceive a humility that the comes with rationlism and an arrogance with empiricism
[13:52] Herman Bergson: That is a rather unphilosophical statement Samule
[13:52] Herman Bergson: Humility and arrogance are our inventions
[13:52] Samuel Okelly: well one is concrete and the other is not and considering absolutes is very philosphical i would have thought
[13:53] Herman Bergson: How Saddly you just showed up, Saddly
[13:53] itsme Frederix: Herman the same brain invents phil.
[13:53] Saddly Offcourse: =)
[13:53] Aya Beaumont: Rationalism is saying "there are all sorts of stuff going on and we can't find out about them but let's assume they are true" while empiricism is "leave me alone while I catalogue the colours of these swans, eventually my research will be useful and then you'll be sorry!!!"
[13:53] Gemma Cleanslate: ah nice explanation
[13:53] Ze Novikov: smiles
[13:53] herman Bergson smiles
[13:54] Herman Bergson: wonder whom you have spoken to Aya..:-)
[13:54] Rough Jewell: cool aye!
[13:54] Aya Beaumont looks innocent. =)
[13:54] Ze Novikov: lol
[13:54] itsme Frederix: Popper tells you to add a hypothesis & test - both lack that AYA
[13:54] Herman Bergson: It begins to sound as if rationalism or empirism is a kind of political stand...:-)
[13:54] Saddly Offcourse: Aya makes it sound like..assuming and testing are comparable.
[13:55] Aya Beaumont: As I said in another forum... the catch is the idea of knowledge.
[13:55] Herman Bergson: Well...I hope we'll discuss these issues when we will deal with ourtr last 5 philosphers
[13:55] Aya Beaumont: If by knowledge, you mean something you can be CERTAIN is true, it's a truly useless concept.
[13:56] itsme Frederix: Herman you told us to do also a list of female phils. is Aya on that list?
[13:56] Aya Beaumont: In the use of information and research, we always work with uncertainties.
[13:56] Herman Bergson: Itsme, Aya is not yet history for us
[13:56] Cailleach Shan: What are you giving us next Herman.
[13:56] Aya Beaumont: =)
[13:56] Alarice Beaumont: :-)
[13:57] itsme Frederix: Well maybe she is in a historical moment yet
[13:57] Ze Novikov: lol
[13:57] Herman Bergson: My plan is to give a series of lectures un 25 female philosophers, maybe some more
[13:57] Saddly Offcourse: Aya, your definition for "certain" is perfectionistic, and makes it useless.
[13:57] Cailleach Shan: How excellent.... some balance for the Feminine Divine!!
[13:57] Alarice Beaumont: that sounds very good Herman :-)
[13:57] Aya Beaumont: Yeah, I know! Isn't it beautiful, Saddly? =)
[13:58] Alarice Beaumont: wonder what kind of women we are going to meet
[13:58] arabella Ella: but who is our next philosopher for the moment herman please?
[13:58] Herman Bergson: Yes...I really like the idea and already started my research on the list
[13:58] Saddly Offcourse: lol beauty is uselessness?
[13:58] Herman Bergson: Oh..Our next one is a cutie: Alan Turing
[13:58] Ze Novikov: ummm
[13:58] arabella Ella: oh yea i like turing ... he was brilliant too
[13:58] itsme Frederix: Great again, but very abstract again
[13:58] Herman Bergson: Oh yes....
[13:58] arabella Ella: poor Turing
[13:59] Gemma Cleanslate: oh
[13:59] Herman Bergson: I think I'll say some about Gödel,and Hilbert in relation to Turing too
[13:59] itsme Frederix: He proved his system - did a better job than Godel
[13:59] Samuel Okelly: have to leave early but thanks again herman! tc every1 :)
[13:59] arabella Ella: bye Sam
[13:59] Cailleach Shan: cu
[13:59] Ze Novikov: bye sam
[13:59] Rough Jewell: bye
[13:59] Aya Beaumont: Godel proved his system, that's the annoying part. =)
[13:59] Saddly Offcourse: bye Sam
[13:59] Gemma Cleanslate: lol
[13:59] Ze Novikov: lol
[13:59] Zen Arado: bye Sam
[13:59] itsme Frederix: Aya you "proved" your system
[14:00] Saddly Offcourse: Goedel proves that IF you talk about entirely arbitrary rules sets, he's right.
[14:00] Herman Bergson: Stop public flattering, Itsme..:-)
[14:00] itsme Frederix: Sure Herman, you did a great job again
[14:00] Ze Novikov: yes tyvm!1
[14:00] herman Bergson grins
[14:01] Saddly Offcourse: these talks are always on teusdays at this time?
[14:01] Herman Bergson: I think you for this brilliant debate
[14:01] Aya Beaumont: Thanks, herman
[14:01] Herman Bergson: Sunday, Tuesday and Thursday, Saddly :-)
[14:01] itsme Frederix: think, we were there Herman
[14:01] Gemma Cleanslate: and thursday
[14:01] Gemma Cleanslate: yes
[14:01] Saddly Offcourse: and the time?>
[14:01] itsme Frederix: and sunday
[14:01] Alarice Beaumont: thank you, herman :-)
[14:01] arabella Ella: Saddly ... this time always ... on Tues, Thurs and Sun
[14:01] Gemma Cleanslate: lol
[14:01] Herman Bergson: always 1 PM PDT
[14:01] Cailleach Shan: When does Daylight Saving happen in SL?
[14:01] Gemma Cleanslate: is sometimes a problem
[14:02] Saddly Offcourse: thank you
[14:02] Gemma Cleanslate: with the usa
[14:02] arabella Ella: good point Cail
[14:02] Gemma Cleanslate: november 2 i think
[14:02] Aya Beaumont: Oh, and itsme, I never proved anything. I merely provided working definitions of empiricism and rationalism. =)
[14:02] arabella Ella: when does daylight savings change in the USA?
[14:02] Gemma Cleanslate: le me check
[14:02] arabella Ella: ok ty
[14:02] Herman Bergson: Oh...we'll havea chang ein time too, I think
[14:02] Herman Bergson: end of october...
[14:02] Gemma Cleanslate: yes sunday nov 2
[14:03] arabella Ella: in europe it is the last sunday in october
[14:03] Gemma Cleanslate: for the usa
[14:03] Gemma Cleanslate: yes
[14:03] itsme Frederix: Thx Aya, providing sounded good enough I guess
[14:03] arabella Ella: so in the USA it is one week later
[14:03] Gemma Cleanslate: last fall we had a few problems
Posted by herman_bergson on 2008-10-15 07:31:40

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