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Quote# 89844


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.

Blackrook, Atheist Forums 30 Comments [10/1/2012 3:04:05 AM]
Fundie Index: 45
Submitted By: Stimbo
WTF?! || meh
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If I hold one apple, there is 1 apple in my hand. I can see it, feel it, count it, and it remains constant.

You'd have had better luck with 0, which is under philisophical debate by some mathematicians who probably have too much time under their hands.

Or negative integers that represent theoretical values and debts, though they are still quantifiable.

10/1/2012 4:00:43 AM

Freethinker

For starters:
http://en.wikipedia.org/wiki/Mathematical_fallacy

If you can't grasp what's standing above, go back to school.

10/1/2012 4:01:17 AM

Reynardine

Does this mean anything?

10/1/2012 4:19:14 AM

UHM

With the difference that mathematics is a defined system of rules.

"You can't assume based on lack of evidence that something is true, that it is untrue."
So tell me, is there any evidence that the world around you really exists? What if your brain is victim of fraud giving it signals that just make you believe it is true? You can't refute that? With your train of thought, you have to accept this as reality know. Congratulations, you're a brain in a jar.

10/1/2012 4:24:54 AM

gravematter

So proof doesn't exist? I can understand why a religious moron might want to believe that. Unfortunately, something specific does equal something specific, as much as you might wish that were not the case. 1 is 1, a cat is a cat, a moron is a moron. Because, do you see, we humans have defined 1, a cat, and a moron, and so, anything that meets that specific definition, is that thing.

10/1/2012 4:28:36 AM

Leighton Buzzard

I see Blackrook has been in Room 101 ...

10/1/2012 4:44:32 AM

Doubting Thomas

I believe that it has been proven. It's not hard to do.

I love how fundies keep twisting logic so badly that now they can't even admit that basic tenants of logic, that is, 1=1, is actually real.

10/1/2012 5:28:12 AM

Mister Spak

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

So the Flying Spaghetti Monster really exists?

10/1/2012 5:46:58 AM

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.

10/1/2012 6:21:03 AM

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.

10/1/2012 6:41:23 AM

Jeff Weskamp

"What is the Axiom of Identity, Alex?"

10/1/2012 6:53:10 AM

Anon-e-moose

"But it has never been proven that 1 = 1"

Just as 2+2=5. Doubleplusgoodthink, Blackrook. See you at the next Two Minutes Hate.

10/1/2012 7:03:05 AM

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'.

10/1/2012 7:52:26 AM

SpukiKitty

I award you with the "SUPERSPORT AWARD"!

10/1/2012 8:14:00 AM



1 is a label applied to a fixed quantity of anything. One apple, one pear, one truck, one gallon of milk. They are identical only in the aspect of not being more or less than one thing.

(1/7) * 7 = 7/7 = 1 there ya go .


10/1/2012 8:51:31 AM

Filin De Blanc

Deep, man.

10/1/2012 8:52:35 AM

plesner

Bertrand Russell did indeed prove that 1+1=2 in his "Principia Mathematica *56".

10/1/2012 9:59:17 AM

farpadokly

This is very true, but if you follow this to its logical conclusion, you end up undermining ALL of thought and language, and you end up not being able to say anything at all.
So you have to have some sort of logical and conceptual framework in order to have ideas or use language at all, and some sort of mathematical framework to do scientific work. The alternative is sheer nihilism.

10/1/2012 12:56:40 PM

Old Viking

But it has never been proven that 1 = 1.

Wrong. Next, please.

10/1/2012 1:44:01 PM

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.

10/1/2012 2:08:28 PM

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.

10/1/2012 2:49:42 PM

Ebon

Wha...?

10/1/2012 3:46:53 PM



*speechless*

10/2/2012 8:00:14 PM

anothga

"It has never been proven that 1 = 1."

Anyone read 50 Shades of Stupid?

10/3/2012 6:22:28 AM

JGC

You can however conclude that if there's a complete lack of evidence something is true it's foolish to believe that it is true.

10/5/2012 8:23:51 AM
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