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46569.  Wed Jan 18, 2006 12:56 pm Reply with quote

From Digraphs to actual graphs perhaps?

As seems to be happening a lot recently I don't really think I'm all that well qualified to talk about this subject from a point of authority. I've just about heard of Cartesian co-ordinates, a technique so useful that a special sort of paper was printed to facilitate its use! If no-one else pitches in I'll give it a bash but I'm not in advance vouching for the quality of my ramblings in this regard I just think the old codger deserves a mention.

46571.  Wed Jan 18, 2006 1:00 pm Reply with quote

Give it a whirl, it is usually easier to understand when a non-expert explains something anyway.

We can pull your ego to bits later.

46573.  Wed Jan 18, 2006 1:06 pm Reply with quote


46602.  Wed Jan 18, 2006 4:21 pm Reply with quote

I love graph paper, especially the more exotic species; log/lin, log/log, probability, exponential. And I've got a slide-rule, and I know how to use it. But I'm rubbish at maths, never got beyond elementary calculus.

Quaintly Ignorant
46632.  Wed Jan 18, 2006 6:47 pm Reply with quote

His most famous phrase: "cogito ergo sum" was never actually uttered or written by him, it is a translation from his 'Discourse on Method' in which he wrote in french "Je pense, donc je suis". He also wasn't the first to ponder this concept, Augustine of Hippo had pondered it and predicted many of the more modern refutations of Descartes'.

Descartes' most important work 'Meditations on First Philosophy' is often refered to as 'cogito' even the the famous thought 'I think therefore I am' does not occur therein. In his second meditation he goes as far as 'I am, I exist', he isn't saying existence is necessary but that because he is aware he must necessarily exist. It is called the instantation principle, if something has a property it must exist. An apple cannot be red and also not exist, that is absurd. "I am thinking" is assumed. Thinking is then a property of a thing. Therefore, a thinking thing must exist, and this Descartes says is himself. I am thinking therefore I exist.

46639.  Wed Jan 18, 2006 7:34 pm Reply with quote

Did Descartes momentarily stop existing when he wasn't thinking?

Quaintly Ignorant
46640.  Wed Jan 18, 2006 7:35 pm Reply with quote

I don't think therefore I'm probably not.

46647.  Thu Jan 19, 2006 12:24 am Reply with quote

Quaintly, the quote from Med is

I have convinced myself that there is absolutely nothing in the world, no sky, no earth, no minds, no bodies. Does it now follow that I too do not exist? No: if I convinced myself of something then I certainly existed. But there is a deceiver of supreme power and cunning who is deliberately and constantly deceiving me. In that case I too undoubtedly exist, if he is deceiving me; and let him deceive me as much as he can, he will never bring it about that I am nothing so long as I think that I am something. So after considering everything very thoroughly, I must finally conclude that this proposition, I am, I exist, is necessarily true whenever it is put forward by me or conceived in my mind. (Med. 2, AT 7:25)


I'm sure with a bit of further digging it could provide a very good GI question

46659.  Thu Jan 19, 2006 5:31 am Reply with quote

The great flaw being, of course, that a human mind is capable of distinguishing between 'something' and 'nothing'. After all, we can conjour 'somethings' out of 'nothings' at the drop of a hat. Jealousy, offence, paranoia, optical illusions, WMDs...

Quaint Idiot
46708.  Thu Jan 19, 2006 12:27 pm Reply with quote

Yes, but we (or at least I) must still exist in order to do the conjouring.

46713.  Thu Jan 19, 2006 1:19 pm Reply with quote

Oops - sorry, I meant 'incapable'. It was never clear to me that an 'I' needs to actually exist for anything, simply because the kind of thing that 'I' is is so poorly defined, and thus the whole concept of 'exist' is a bit vague too.

We constantly convince ourselves that we are an 'I' without ever really understanding what that is. Saying it's the thing that does the convincing or the thinking isn't really an answer or a definition - it's just circular, which means it's just as likely to be nonsense as it is true.

46734.  Thu Jan 19, 2006 4:15 pm Reply with quote

My main encounters with Descartes were in AS level Philosophy. Sadly I only got a mid level C on that paper so I can barly describe myself as an expert on his meditations and such. The discussion I had about the quantum computer being capable of simulating an entire universe was QI and slightly relevant here. That went slightly beyond the "I must exist in order to be decieved" argument in that in the quantum computer scenario, the fact that every calculation in the universe could be made (thus simulating in some form the existence of every particle in a person's body and therefore capable of simulating thought) creates the possibility that even our own thoughts are fabricated. Effectively the result is that "I do not need to exist in order to be deceived", at least not in a sense of existence that we can distinguish between "I" and the "deceptions". In this hypothetical situation of a simulated universe, whether "I" exist or not depends upon the definition of existence. Does the fact that the simulation exists mean that "I" exist?

BTW I am sure there will be some hole in my logic here but this is my first attemot at this idea really (someone has probably already come up with it anyway).

46736.  Thu Jan 19, 2006 5:10 pm Reply with quote

Descartes is sat at a cafe enjoying the view, a waiter approaches and asks if he would like more coffee. He replies 'I think not', and dissapears in a puff of logic.

i know its old, but so far thats all i can come up with on the subject

Quaintly Ignorant
46743.  Thu Jan 19, 2006 7:07 pm Reply with quote

The simulation problem is an interesting one. Descartes said that we had primary Objects and Secondary Objects:

Secondary Objects of Sense
hardness, heat, light, odour, colour, taste, sound

Primary Objects of Mathematics
quantity, shape, time, magnitude

Once Descartes recognizes the indubitable truth that he exists, he then attempts to further his knowledge by discovering the type of thing he is. Trying to understand what he is, Descartes recalls Aristotle's definition of a human as a rational animal. This is unsatisfactory since this requires investigating into the notions of 'rational' and 'animal.' Continuing his quest for identity, he recalls a more general view he previously had of his identity, which is that he is composed of both body and soul. He can't refer to himself as a thing that has a body, though, since this involves sensory perception. According to classical philosophers such as Plato and Aristotle, the key attributes of the soul involve eating, movement, and sensation. He can't claim to have these attributes of the soul since this involves a body, knowledge of which, in turn, is based on the senses. Descartes continues examining other theories of human existence and attributes about himself that he can imagine. Descartes concludes that the attribute of thinking is the only quality that he can justifiably claim at this point. But he is quick to point out that thinking is the only attribute about which he is sure - not that thinking is the only attribute that he has. I am, then, at least a thing that thinks.

The quantum simulation is too, at least a thing that thinks and so has existence.
[S]ince I sometimes believe that others go astray in cases where they think they have the most perfect knowledge, may I not similarly go wrong every time I add two and three or count the sides of a square, or in some even simpler matter, if that is imaginable? (II, 14)

During his life, Descartes's fame rose to such an extent that (despite the theological controversies centering on him) many Catholics believed he would be a candidate for sainthood. As his body was transported from Sweden back to France, anxious relic collectors along the path removed pieces of his body. By the time his body reached France, it was considerably reduced in size.


46747.  Fri Jan 20, 2006 3:45 am Reply with quote

It's actually a misconception to say "I think therefor I am".
Descartes obviously meant: "I doubt therefor I am"
(As doubt is an action you can allways have. You can doubt that you're doubting, but you'd be doubting none the less.)

So, a quantum computer wouldn't exist, untill it could doubt wether or not it existed.

Then Descartes tries to mathematicly prove that there is more then only this doubting. (Else we'd have a cogito fermé). His proof however is faulty in many aspects. (For instance he proves the goodness of God by invoking causality, and says that causality exists due to the goodness of God) (Well, that the causality we perceive is correct)

At any rate, his starting point remains valid, I doubt, therefor I exist.
@ some of the previous posters: It's a common misconception to see the "I" as we see it now. The "I" that exist is simply the cogito, the doubting subject. The body is part of the outside world, which existance Descartes will try to prove later.


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