1 + 1 is 2
this nuch is true


did you like my little poem?

1 + 1 = 2 is an identity, which means it's true. it is actually the definition of the number 2

1 is defined as the identity under multiplication,

0 is defined as the identity under multiplication.

addition and multiplication are operators, I can't remember their definitions , I think they are defined in terms of each other, and in terms of an ordered field (the real numbers are an ordered field)

thereby any mathematical statement is true if there exists an ordered field, and as the real numbers are an ordered field then all mathematical statements are true by the very nature of their existance.

this means that a proven mathematical statement cannot be false as in order to be false it has to be, and if it is then it is true.

so that's a proof of all mathematical statements from a grand total of 0 assumptions. therefore we have some truth in the world.

however, maths is entirely self contained, and whereas pure maths is true applied maths (where we apply these things to the real world) is not as true. (I didn't say it was'nt true, I said it wasn't definatly true)

as for the 1+1=1 proof it assumes the statement a^2+b^2=ab-b^2 => 1+1 = 0 (a = b =1)

so you proved that if 1+1 = 0 then 1+1 = 1 (and no you can't use that to prove 0 = 1)

meg
Tell me, what is the difference between 2 and 3? In order for something to belong into 2, does it have to work out mathematicaly? i.e 1 + 1 = 2?
a = b means that a is the same number as b (a number is an element of the ordered field "the real numbers") there are no 2 distinct elements a and b of an ordered field such that a = b, if a = b then a and b are simply different names for the same number. for any 2 distinct numbers a and b either a>b or a<b. (usually is we simply refer to 2 numbers a and b we are not ruling out the possibility that a = b)

kedmanology.

me and kedman had a natter on ICQ last night and I think that it can be shown that you cannot classify statements into a finite number of catagories distinguishing between them by how true they are. (ie for a theory like kedman's to be true you would need an infinite number of catagories)

The proof involves the Russell Paradox which I don't fully understand but from the little I do know about it I think it can be applied to show an infinite number of catagories would be needed. (the proof involves the Idea that for any finite number of catagories we must put the statement "every statement must belong to one of these catagories" into a catagory, for some reason this means that the statement cannot be proven to be true so must go either into the catagory false or a catagory that says it's true but cannot be proven,(call this catagory A) which goes on to show that the statement "Some statements must go into the catagory A" cannot be proven but it must be true since we have a statement in catagory A so there is a contradiction and the original statement must be fale.


If anyone has a good understanding of Russell then if they want to have a look at this argument I would be greatfull.

Realistic Graphics.

Be glad it wasn't me who marked your essay on the lack of truth.

, "Cognito ergo sum." - Rene Descartes. Of course, he was also a raving alcholic.
If an alcoholic told you you were about to be his by a bus would you not believe him even if you could se it coming?

Descartes proved the existance of everything that is observed from the single assumption that the observer existed. it involves the concept of a reality, a reality doesn't have to be real, a dream is a reality, the world in a book or a film is a reality, he defines something as existing if it is in the same reality as the observer. Truth is truth with respect to the reality you are in.

Your Idea that there is a reality that is real and that truth implies truth in that reality is to exlude yourself from this reality by denying its truth and existance, however you as an observer exist in this reality and that is the one we're discussing.so you might as well take your head out of the sand and accept the existance of objects in this reality.

As Werner Heisenberg observed, one can not be an objective observer of events in which one is directly involved. The very attempt of observation is changing the outcome of the events.
a paradox in itself, if he observed this then that means he affected how true it was, surely it was just as true before he thought of it as afterwards.

Heisenberg in fact did nothing of the sort, he proved some quirky properties of the position of particles. The uncertainty principal is the most misinterpreted piece of physics ever, it is a statistical law that applies to small particles and small particles only.

[qoute]If someone is brought up to believe that red is actually green, are you going to have any success trying to prove to them that it is actually red? [/quote] so what?

if I ask you what 1+1 is you'd say 2 (actually you'd say 1 but you'd be wrond) if I went back in time somehow and asked a roman he'd say 11 because that's his name for 2, the statement 1+1=2 and 1+1=11 are equivilent, it's just different names for 2. Likewise if I asked a frenchman what colour something was he'd say rouge, it doesn't matterwhat names we use for things, a statement is still the same statement whatever language it's in. If you're confused man says something is green when it's actually red it's still true in his language.