>>>>>First, Descartes must prove that he himself exists, and he
>>>>>does so through his famous statement, "I think therefore I
>>>>>am", as it is a clear and distinct statement that is self
>>>>>evident, no proof beyond the act of saying it is required.
>>>>
>>>>Well, that's a question of epistemology, not a tenet of
>>>>logic.
>>>>
>>>>>The reasoning behind this statement is as follows; if I am
>>>>>able to percieve my own existence from within, I must
>>>>>therefore exist.
>>>>
>>>>And that's not reasoning, it's just repetition.
>>>>
>>>
>>>Hmm, I disagree with you. Please explain how it is
>>>repetition and not reasoning.
>>
>>I disagree right back. Read the two statements again. You
>>didn't really state anything new, you just took the original
>>statement and stretched it out. You inserted more words,
>>the words don't serve a purpose, except to satiate those
>>people who judge the value of a statement by the number of
>>words. Some words are more valuable than others. (and I
>>admit this in full knowledge of the fact that I've been
>>known to write some very long posts)
>
>I wasn't attempting to state anything new. Hmm, I find your
>analysis of what I wrote very strange, as I don't see how I
>could have given that impression.

Hmm. Okay. You and I seem to have different standards for "explanation." You merely meant to state your interpretation of his statement, whereas I thought you were trying to justify it. I propose a truce on this part of the argument. I think we were just misunderstanding each other.



>>>Also, if you do not like the wax block experiment, you could
>>>just think of numbers, and counting from 1, to infinity.
>>>Correct? Are you stating that even that is finite?
>>
>>Haha! No, I'm not stating that the set of positive integers
>>is finite. But note that Descartes did not cite the
>>positive integers as his example. He used wax for a reason.
>> It's easy to argue that wax "exists," that is, that it is
>>an artifact of the larger universe, and not of our
>>imaginations; that it retains its reality regardless of
>>whether people are considering its existence. The same is
>>not true of the positive integers. Despite their name, the
>>real numbers are an invention of the mathematician's mind.
>>This might be hard to accept, since the real numbers are so
>>familiar. But consider other number systems: the complex
>>numbers, the quaternions, the octonions, the supernumbers.
>>We have invented all sorts of number systems over the
>>centuries. You want a number system, I'll give you one
>>right now. The "integers mod 2." This consists of the set
>>{0,1}, and the arithmetic DEFINED by:
>>
>>0+0=0
>>0+1=1
>>1+0=1
>>1+1=0 (notice that one)
>>
>>0*0=0
>>0*1=0
>>1*0=0
>>1*1=1
>>
>>This number system is just as valid, philosophically, as the
>>real number field. In fact, in recent decades, it has
>>become exceedingly important, for an obvious reason. You
>>will note, also, that it does not involve an infinite number
>>of elements. There are only two.
>
>I see your point. I am curious, why is:
>">1+1=0 (notice that one) " philosophically valid?

Because it is logically self-consistent. You can do all the mathematics you want with that *definition* of the addition operation (people do it all the time in signal processing), and you will never end up with a contradiction. That is, no amount of math built on the above arithmetic will ever lead to a result like "1=0."



>>>You are making sense. You mentioned "physical phenomena", I
>>>am not speaking about physical phenomena, I am speaking
>>>about God.
>>
>>Oh, okay. What the hell is that?
>>
>>>Is God physical?
>>
>>You tell me. I don't even know what you're talking about.
>
>If God exists? is it a physical phenomena? how do you define
>physical?

Tricky question, so I'll just toss it back. How do you define God?

I mean, to define physics is really to define science. All other "branches" of science are really just applied physics. Biology, chemistry, astronomy; not math, by the way, that's a branch of pure logic and is therefore removed from any relationship with inferred experience.

So I think experience is one of the defining factors. Science is the study of those experiences which we do not believe we are merely imagining. We define "not merely imagining" by assuming we can interact honestly with a community. Community consensus then separates imagination from fact.

You might now point out that world consensus holds that God indeed exists, and ask me if that forces me to admit His existence as fact. However the consensus is not nearly universal among those people who think deeply about the problem, and such essentially universal acceptance is, I believe, necessary to promote an idea to scientific fact.

Also, and more importantly, the people who claim God exists generally do so not by citing specific experiences, but rather by citing "faith." They are faithful despite a lack of experience. I am not trying to criticize this stand, merely pointing out that it removes the "God consensus" from the jurisdiction of science.

Now there are also a few people who do cite "experience" with God. However, such experiences are not testable. That is, nobody has yet designed an experiment by which one can conjure up God at will. The existence of repeatable experiments is another defining requirement of science. That's what enforces the honesty in the scientific community.


Now, I'm happy to admit that the assumption or repeatable testability may be too restrictive in removing experiences from the "imagined" category. There could very well be experiences which are not imagined yet are also not repeatably testable. The assumed completeness of testable reality shows a certain degree of unjustified hubris on the part of some scientists.

I do not believe that everything which is not imagined is repeatably testable. I simply assume that all those things which are not repeatably testable are either imagined or are unnecessary. I see no practical reason to assume God exists, rather I actually see a long history of such beliefs being used to drum up support for despicable political acts.


>Okay, I want to ask you a question. How do you feel about
>Mathematics as a divine language?

I cringe at the idea.

>In a philosophical
>statement, Saukrates asks a slave boy, to draw a triangle,
>and the boy was able to, without knowing the formula for it
>as he did not have an education.

Well, I could have drawn a triangle before I had an education as well. The word is so broad that anything with three sides (or three angles) would satisfy the request. If a child is asked to draw a euclidean isosceles triangle, he would fail if he has not studied geometry.

>Or, pythagoream theory in
>showflakes. What do you see mathematics as?

Mathematics is a work of art. It was built by an enormous number of artists, but they have all worked together to force it to conform to a consistent (if complex) set of fundamental principles. It is that collection of principles which forms the soul of mathematics. Those principles are so popular that we are tempted to use them to model experience, as we have done, with some success, in science, but I don't believe the principles come from anywhere other than us.

>And, is it
>logical to say that math itself is infinite, as it is
>possible to do anything with it? Not in the sense that it
>has a finite number in it's calcuation, but the calculation
>itself?

Well, yes, but again only in the same sense that a work of art is infinite. There is no limit, in principle, to the insights I can gain from studying a Rothko canvas. But for this I thank Rothko, not God.