Okay so I have done some philosophical thinking, but I hadn't realised something pretty important about it. I'll kick things off by discussing that little theorem that Tarwyn posted. She said "If n is a prime number greater than 3, then n^2 -1 is divisible by 24" and my response was, Yes this is absolutely true because it is a corollory of a more general theorem, namely, if n is an integer, n odd and not divisible by 3, then n^2 -1 is divisible by 24.
You might ask, why is this true ?...
the first step is to factor the number 24 into it's prime components thus 24 = 2x2x2x3,
next we look at the factorization n^2 - 1 = (n-1)(n+1),
by assumption that n is odd we know that (n-1),(n+1) are consecutive even numbers ... now we pose a simple theroem... if a,b are consecutive even numbers then either
a is divisible by 4 or b is divisible by 4. For we know that b = a + 2 , if we suppose that a is not divisible by 4 then we have a = 2q where q is odd, hence
b = 2q + 2 = 2(q+1), but since q was odd, q + 1 is even and hence q+1 is divisibly by 2 so that 2(q+1) is divisible by 4. If on the contrary we were to suppose that b is not divisibly by 4, then we have b = 2q where q is odd and a = b - 2 = 2q - 2 = 2(q-1) and the same argument about (q-1) being even shows that a is divisibly by 4.
Hence we know that one of the factors,(n-1),(n-2) is divisibly by 4 and that, for certain, the other is divisibly by 2, since it is even,
hence,
we know that n^2 -1 is divisible by 8 = 2x2x2, for any odd number n.
Step two ...
since n is not divisibly by 3, we have, by division with remainder, n = 3q + b where b is a posative integer less than 3... thus either b = 1 or b = 2
in either case we have n^2 = (3q+b)^2 = (3q)^2 + 6qb + b^2 , if b = 1 then b^2 = 1 and hence n^2 -1 = 3( 3q^2 + 2qb) which is divisibly by 3,
if b = 2 then b^2 = 4 = 3 + 1 and so n^2 -1 = 3(3q^2 + 2bq + 1 ) which is also divisibly by three, hence, we have proved

If n is any number not divisible by 3, then n^2 -1 is divisibly by 3.. and thus we have

if n is an odd number not divisibly by three, then n^2 -1 is divisible by 8 and n^2 -1 is divisible by 3 and since 8,3 have no common factors, n^2 - 1 is divisible by
8x3 = 24... Q.E.D. .. can you believe I thought of all that on my own ? Anyway, that is number theory......
The point is certainty, of that theorem I am certain, I have true knowledge about .. well..... about what ?... about numbers, which, do not exist..... I have no true knowledge about myself, the world, life, death... anything really.... I have gained certainty about imaginary entities..... hu...hum... One night not long ago Adam and I were talking with Sami over coffee at Sharie's restaurant. We were talking about Sami's beliefe that we are all actually a single conciousness creating our own reality in a single dream... Of course, there is no way to shoot this down, no rational argument against it, in short, there is no base to any philosophy of human nature/origin/destiny or any philosophy of good or god or morals or other...... Hence the inability to shoot down Sami, or anyone else for that matter... when we left Adam said to me "when you talk philosophy you leave with a strange feeling, a feeling as though you have accomplished nothing." I said, "of course, that is the feeling of the incomprehinsibility of reality, of the fact that, no matter what you may try, you can never prove any philosophical standpoint, and yet, what you believe about the word "ought" is the most powerful thing you can ever call your own...".. The thing about philosophy is, do not search there for answers, I promise that there are none which are "satisfying" in the sense of the provability of the previouse theorem, which, I am certain of...The only thing I have found is an unending collection of answers, but, different answers which are all equally based and hence equally justifyable. All I have learned is what questions I can, and most likely, need to ask in my life. I learned to find doubt in everything, to question everything, and to torture any answer until it revealed the obscurity of it's roots. So that is the case with me lately. I can be certain of what I imagine, I can learn about the abstract and imaginary, or I can be lost in questions about life, realising, I will always doubt and that I can never truly know anything............ Reality somehow escapes understanding, trancends the minds ability to grasp, to comprehend... The feeling of the inexplicable nature of the world is an intense, often desparate, feeling of being almost lost in existence with no answers, no idea why one ought to move about or think or dream or wonder......etc .........