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Divide by zero

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abyaly:

--- Quote from: ashton15 ---
--- Quote from: abyaly ---Assigning meaning to a word is not the same thing as ascribing a property to an object.
--- End quote ---

What's the diffrence?

--- End quote ---
The first is saying something about a word. Specifying what object or concept you're going to use that word to refer to.
Eg: "The word gold refers to the element with atomic number 79"

The second is saying something about the object or concept the word is referring to.
Eg: "Gold is yellow"

The reason you can define a word to be whatever you want is that a definition says -nothing- about the object the word is referring to. It doesn't even guarantee such a thing exists. A definition is a statement about the person who is making it. If I define the word "splaz" to mean "gold", this doesn't say anything about gold. All it means is when I say the word "splaz", I'm talking about gold.

So if you define the word "Earth" to mean the same thing as the word "orange", this doesn't mean that the thing I think of as the Earth is the same thing as an orange. It means that when I see you use the word "Earth", I should think of it as if you had said the word "orange" instead.


--- Quote from: bacillus ---There's a proof by somebody whose name eludes me at this moment that states that if mathematics is without contradictions, then it is contradictory itself. Don't ask me how it works, but I thought this would be the best time to bring it up.
--- End quote ---
You are probably thinking of Gödel's incompleteness theorem, which says no consistent set of axioms can prove its own consistency.

Houshalter:
I was trying to think of a way to define number in strict logical terms that could be used by a computer. Its not as easy as it sounds. You might say that a number is or represents a single value, but how do you define a value? Maybe you can take a short cut and define a number as a set of binary digits, but thats not an actual number. It just represents a number, and were back to the same problem.

bacillus:

--- Quote from: abyaly ---You are probably thinking of Gödel's incompleteness theorem, which says no consistent set of axioms can prove its own consistency.
--- End quote ---

That's the one!

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