In the 30s of the twentieth century there was an unbelievable development in mathematics. Really breath taking. Not that I understand much of it, but I think I understand the philosophical undercurrent.
Why all that mathematics in those days? I have a hunge. From my highshcool period I remember the physics classes. They tried to make you understand all kinds of formulas regarding volumes, electric currents, waves, movements, chemical processes.
And always there was that mathemetics: law of Ohm, Ampere, resistance, pressure and whatever. A waste on me in those days, but now I see that in the beginning of the 19th century we discovered how well natue could be described and predicted my all kinds of mathematical calculations.
And maybe we must see alll that frantic mathematical research and theory development from that perspective. The world was mathematical .....so study mathematics and physis can go on with its research!
Really, when you look at the amount of publications and at the brilliant minds that produced it all, you really wonder, what is happening here? And in particular, what is the philosophical importance of it all?
It is of great philosophical importance. My only problem is: how to tell you....^_^ .... in a way that we dont need to be an Einstein and yet understand what it is al about. I guess it will work, if I do it my way.
The German David Hilbert, one of those super brilliant minds, was working on the axiomatization of mathematical issues. Let's first investigate the meaning of axiomatization.
The axiomatic method is the method of studying a subject by beginning with a list of undefined terms and a list of axioms and then deriving the truths of the subject from those axioms by the methods of formal logic.
For example, I have the undefined terms, pino, pano and puno and I have the axioms (i) pino is pano and (ii) puno is infinite. Then I could logicaly deduce by using the axioms and the rules of logic, that pino is not infinite.
It wouldnt surprise me when all mathematicians now are rolling outloud laughing on the ground,, but I hope you get the main philosophical question here: it is beautiful that you can deduce all these statements from your axioms, but where did you get these axioms?
Here again we are at the heart of our epistemological quest. I could quote William James: "In my opinion are all laws of nature the product of our psychological need to feel comfortable with nature." So all concepts that transcend sensory experience are of my own making for that purpose.
Can you understand that when my axioms are the result of my interaction with nature and from my axioms I can deduce EVERY statement and proof its truth, that I have the perfect and absolute knowledge of nature and thence absolute control over it?
However, I get into serious trouble when it is possible that I can deduce two statements from my axions, which are both true individually but can not be true together at the same time: we have a contradiction in our system! So my axioms must be incomplete.
There must be something wrong with my axioms or in other words sensory experience doesnt lead to absolute knowledge. Somewhere in the process something goes wrong. That was what Gödel demonstrated and that was what made Hilbert cry (in a manner of speaking:-).
What next? Sensory experience isnt sufficient. Then where do all these terrific mathematical ideas come from? Gödel was convinced that the human mind was capable of "inventing" truths --- and axioms are regarded as unproven true statements --- which can not be proven by any formal or mechanical or sensory procedure.
If you are still with me, here you hear the echo of Popper's view that hypotheses are the product of human creativity and imagination for instance. If you add a metaphysical touch you could think of the slave of Meno and how he 'recalled' the truths. Gödel was a convinced platonist.
This all leads to a sensational conclusion. The only way to achieve a growth of knowledge depends on what creatively pops up in our mind ...so to speak ..out of the blue or to speak with Plato ....it depends on what we are able to recall.
The conclusion : artificial intelligence isnt possible, if it is understood as equivalent with our intelligence as humans. Keep in mind that within this intelligence you also have to think of our moral sense and ethics.
Then there is Alan Turing. He was one of the first to point at a weakness in Gödel's argumantation. It may be true that a machine which uses a formal language has its limitations.But it is without question assumed that the human mind is not subjected by such limitations.
But in the light of I have said I begin to wonder how interesting Turing is at the end. First of all we come in the moor of definitions of 'consciousness', 'mind', 'intelligence'.
And second, the only thing that Turing wanted to proof is, that when you have a conversation using only MSN and you do not discover that the answers and questions come from a machine, you must admit that the machine is equal to man in respect to intelligence and that a machine can think
We'll take a break and you all do the Turing test. Go to : http://www.cyberpsych.org/eliza/ and tak to Eliza. You have 5 minutes to discover that there is a lovely girl at the other keyboard.
Turing was a brilliant mathematician, but given the present level of the debate on the philosophy of mind, I think his Turing-test is a bit outdated,as well as its philosophical importance.
Turing worked for British intelligence. He was a code breaker in World War II. He died in 1954 and was found with an apple poisened with cyanide. They said it was suicide, but others say he was murdered because he knew too much.
There is a story that the logo of Apple Computers, an apple with one bite missing, is a secret hommage to Alan Turing. According to his biographer, Andrew Hodges, is this not the case. A pitty...such a nice story.
For your information, "ELIZA - A computer program for the study of natural language communication between man and machine"(1966), was an article written by Joseph Weizenbaum, who was a MIT professor. http://i5.nyu.edu/~mm64/x52.9265/january1966.html