Blackrook #fundie

Blackrook #fundie atheistforums.org

You can't assume based on lack of evidence that something is true, that it is untrue.

For example, it has never been proven that 1 = 1.

Mathematicians start with that as an assumption because without it, all other mathematics is impossible.

But it has never been proven that 1 = 1.

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old comment by dionysus

For example, it has never been proven that 1 = 1.

You don't have to. That's called an identity. Something is what it is and isn't what it isn't. Saying that 1=1 just means that we aren't changing the definition of the number '1' whenever we feel like it and that it's definition is consistent.

Mathematicians start with that as an assumption because without it, all other mathematics is impossible.

All of logic and reasoning starts with the axiom that something is what it is and isn't what it isn't. a=a is the basis of all knowledge and given that we can use our five senses to confirm that something is what it is, it's not an unreasonable axiom to make. Yes, I'm aware of illusions and hallucinations, but generally the identity of something is still verifiable. And guess what? It doesn't matter. If I see a hologram of a rock and call it a rock, it's me that is in error. That a convincing illusion of a rock exists does not mean that rocks are not rocks. It means that the illusion is strong enough to make someone use the wrong label. However, the axiom of a=a or 1=1 only guarantees that something is what it is and not that it is what it appears to be. Besides, we can run other tests to make sure that something really is a rock.

old comment by Dr. Razark

"You can't assume based on lack of evidence that something is true, that it is untrue."

True. Absence of evidence is not evidence of absence.

However, if my neighbor says "I have a dog.", I can either accept that statement, or not. Let's say I decide to investigate this statement. I examine my neighbor's yard. I find no dog droppings. I have never seen a dog in my neighbor's yard, and I have never heard barking from his house. I speak with my other neighbors, and they say that they have never seen or heard a dog there. I examine my neighbor's house. I find no dog food. I find no food bowl and no water dish. I find no dog toys. I find no leash. I find no dog hair. I find nothing that is in any way related to a dog in an extensive search of my neighbor's house.

Is it still reasonable to accept that my neighbor owns a dog?

Absence of evidence is not evidence of absence. Overwhelming absence of evidence where one expects to find large amounts of evidence is pretty damning evidence, though.

old comment by Sgt

Oddly enough, in a way we /have/ proven 1=1 by virtue of defining 1. Allow me to explain.

Let function A(x,y,z) return 'true' when 'x+y=z'. We define '0' as all values x for which A(x,y,y) is true. I.e. '0' is all numbers which when added to a second number does not change that second number.

Now let function B(x,y,z) return 'true' when 'x*y=z'. We define '1' as all values x for which B(x,y,y) is true EXCEPT where 'y' is '0' (as defined above). In other words, 1 is any number which, when multiplied by a second number, does not change that second number (except where the second number is '0').

And since B(x,y,z) (multiplication) can be derived from A(x,y,z) (addition) by process of recursion, the real unproven statement can then be said to be 'a+b=c'.

old comment by checkmate

Mathematicians start with that as an assumption

Right: "Axiom of Equality. ... For each variable x, the formula x = x is universally valid."

They're called axioms: "An axiom is a premise or starting point of reasoning. As classically conceived, an axiom is a premise so evident as to be accepted as true without controversy."

http://en.wikipedia.org/wiki/Axiom

Axioms aren't proven and can't be proven, simply because that proof would rely on the truth of the axiom itself being true, that again being circular logic.

Therefore, no, 1=1 hasn't been proven, simply because proving it would rely on the truth of the axiom being used to prove itself as true.

However, this means nothing at all. 1=1, i.e. x=x is "so evident as to be accepted as true without controversy."

God isn't an axiom, simply because God isn't "so evident as to be accepted as true without controversy." Axioms only work for the absolute basics. They can't be used to generalize for higher level subjects. E.g. one can't say "existence /= non-existence, therefore God and not Big Bang." It doesn't work that way.

old comment by Anon

Actually, it has been proven that 1 = 1. As others have noted, the equality relation is the axiom. 1 = 1 follows from it. The axioms of arithmetic go like this (Peano's formulation, to be technical):

- 0 exists and is a natural number.
- For every natural number x, x = x.
- For all natural numbers x and y, if x = y then y = x.
-For all natural numbers x, y, and z, if x = y and y = z, then x = z.
-For all a and b, if a is a natural number and a = b, then b is a natural number.
-For every natural number n, there is a successor S(n) such that S(n) is a natural number.
-For every natural number n, S(n) != 0 (that is, there is no natural number smaller than zero)
-For all natural numbers m and n, if S(m) = S(n) then m = n.
-If K is a set of natural numbers that contains 0 and if for every n in K, S(n) is also in K, then K contains all natural numbers.

From these axioms, 1 = 1 follows because we have defined 1 = S(0). 1 + 1 = 2 is derived by defining addition as recursive application of the S() operator.

Blackrook #fundie atheistforums.org

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