Greetz,
1. For
Mentat:
I don't see any proof against this statement...
No. Read it again, please. It's a "supposed" (we've this word in comon) proof against any statement of the form "I [beep] therefore I exist." You needn't go there again, it's here:
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Every statement of the sort "I [beep] therefore I am" is erroneous when viewed with linear logic (I mean, no self-contradiction and/or loops allowed). Here's my proof:
Consider having said "I [beep]", you have to choose one of the two following statements:
P([beep]) : There need be an "I" to "[beep]."
P'([beep]) : There needn't be an "I" to "[beep]."
Since the above statements are contrary, only one of them may be yours (for we're using Aristotelian logic where a statement can be either true or false and nothing else and there's no escape from having chosen one of them).
If you choose 1, you've clearly pre-assumed that there need be an "I" to "[beep]" and you haven't done much in mentioning the consequence that "therefore I am." This is a self-referential statement giving no more information than what was known before.
If you choose 2, you've made another mistake. How could you say it isn't necessary to be an "I" to "[beep]" and then conclude that "therefore I (necessarily) am?" This is paradoxical for the statement is made up of two parts which are contradictory.
(This proof may be wrong. If so, please show my mistake(s))
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Hint: I asked one of forum members to please take a look at this. She/he suggested it wasn't of much creditability and I agree with her/him. However, as long as "you" haven't shown its absurdity you have to take it.
... This requires that there be something for you to convince, and thus you cannot convince me that I don't exist...
I'm not convincing you that you don't exist, I repeat for 102th time. I'm showing how meaningless it may be to take any statement (even this well-shaped one) for granted.
You say it "requires" that so and so, where does this "requirement" come from? You think there's a "requirement", you think a specific entity must be prior to another one, how did you come to think so? I've learned that you, like Descartes, are insisting that "I think therefore I am" is a firm ground. If everything is going to built upon this statement, the statement itself must be "proven" independently. No assumptions, no beliefs, no pre-suppositions are allowed.
Hint: the above paragraph suffers internal inconsistency, see if you can find the point of weakness.
Say what? The proposition that something can think necessitates the existence of the "something" that is thinking.
No, it's an assertion. An assertion that you can't prove wrong, because you'd be attempting to prove it wrong to someone (even if just yourself), and that someone would have to exist, in order for you to prove something to them.
There are no "necessities" at this level. See, Descartes had gone a long way when he came to "I think therefore I am." He'd put away his religious and scientific suppositions along with the common sense. This is the purifying of the mind. He purified his mind to see beyond what he was usually supposed to see.
He, however, slipped once, only once. He saw it necessary for the thinker to exist prior to thinking. He shouldn't have made this mistake but he was feeling the pain of groundlessness and that explains well why he made it. He was a great mathematician, he was a great thinker, he needed a firm ground to put all this upon. The efforts of his life, like the efforts of all human beings, would be lost if this firm ground wasn't found.
Unfortunately, you know, our deepest feelings have noway into the magnificent palace of logic. It's made of cold dull grey marble.
If he'd continued purifying his mind (perhaps he did but didn't find it suiting his favor) he would have seen that all "necessities", even the most basic ones, are assumptions unless that firm ground is found.
This level, this brink, this verge at which we're standing is the terminus. No assumptions, no suppositions, no beliefs, no obligations, no preferences, no prejudices, no discrimination, no significance, absolutely none is permitted.
Eventually, only few things are left: uncertainty, self-reference and paradox. These remain for they're as basic as the most basic.
Uncertainty is the principle of doubting everything, even uncertainty.
Paradox is the principle of the collocation of the opposites.
Self-reference is the principle by which everything may claim its status quo for its pointing at itself.
And these three penetrate both our feelings and our logic, they're the junction point.
These three are perhaps the facets of one entity. Since they're all self-sufficient perhaps the inner core facets of which they are may not be revealed. If one's going to assume something, "I think therefore I am" is too big an assumption compared to these three.
Proving one's existence is not an event happening everyday, it's the final quest to see if there's anything we can hold on to (Whitney Houston sang: "Oh! What I can hold on to?" Did she mean that?

).
What does "je pons donc je suis" mean?
It's "I think therefore I am", "Cogito ergo sum", "je pons donc je suis." I thought Descartes' word would seem better in his native language.
There is a book, "Zen and the Art of Motorcycle Maintenance" by Robert M. Pirsig. I've a translation of it into my native language. It's from the 1976 print published by Corgi Books. The book is available now and, simply put, is great. I suggest you read it. It may show you many things I'm unable to show.
2. For
Another God:
It is a pragmatic necessary truth.
If I am able to say that I exist, or that I am thinking, then of course I exist.
Being is a pragmatically superior supposition but it's nothing more than a supposition.
Being there or not being there won't affect our thoughts/lives. We live as we live. It's the way it is. We do it as we do it.
Nothing is prior to existence. If you say "If I'm able to [beep] then of course I exist" then you have to prove you're "able to [beep]." This is noway easier than proving you exist.