3 ms·

It's not. It's a fact derived a priori from the definition of addition and the axioms of the field of real numbers. There's nothing special about the claim that

by mik1998 4y ago

It's not. It's a fact derived a priori from the definition of addition and the axioms of the field of real numbers. There's nothing special about the claim that 1 + 1 = 2. You can also define addition such that 1 + 1 = 0 or anything else.

yazaddaruvala 4y ago
“a priori from the definition of addition” is effectively saying “a social construct” And I hate to break it to you but all “axioms” are social constructs that we use to create hopefully useful models.
- mik1998 4y ago
  No, this is not true at all. It is a certain _mathematical_ construction. It has nothing to do with society. Given the specific definition of addition in the field of real numbers, the statement 1 + 1 = 2 is true in any society. > but all “axioms” are social constructs Again, they are mathematical constructs. Axioms don't have anything to do with society. I can construct any axiom I want, and derive true statements from it. Perhaps the only "social" thing here is what axioms we generally deem interesting enough to investigate - this does not change the facts derived from them. > that we use to create hopefully useful models. I think you underestimate pure mathematics :)
  - yazaddaruvala 4y ago
    I’ll try one last time: > definition of addition What do you think any definition is other than the creation of a socially shared construct? > I can construct any axiom I want, and derive true statements from it. Let’s test this. Axiomatically I am always right! As such, I derive that it is illogical, dare I say irrational, of you to disagree with me. A truer statement has never even been written! Facts! Hmm… turns out you disagree that it’s a true statement. Why? I had an axiom! You don’t agree with my axiom? If that’s allowed, I guess I’ll have to convince you (and society) of my axiom!
    - mik1998 4y ago
      > What do you think any definition is other than the creation of a socially shared construct? A definition is simply a definition. It doesn't have to be social or shared. I can define addition in any manner, and in fact there are many other definitions of addition. > Let’s test this. Axiomatically I am always right! As such, I derive that it is illogical, dare I say irrational, of you to disagree with me. A truer statement has never even been written! Facts! You have a very interesting misunderstanding here. A fact is true only relative to an axiom. So yes, relative to such an axiom you are right, similarly how relative to the axioms of the field of real numbers the statement 1 + 1 = 2 is true. You can construct any axiom and derive facts from it. I can construct axioms such that 1 + 1 = 0. That doesn't make the statement 1 + 1 = 2 in the real numbers any less false!
- deleted 4y ago
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yazaddaruvala 4y ago

“a priori from the definition of addition” is effectively saying “a social construct” And I hate to break it to you but all “axioms” are social constructs that we use to create hopefully useful models.

mik1998 4y ago
No, this is not true at all. It is a certain _mathematical_ construction. It has nothing to do with society. Given the specific definition of addition in the field of real numbers, the statement 1 + 1 = 2 is true in any society. > but all “axioms” are social constructs Again, they are mathematical constructs. Axioms don't have anything to do with society. I can construct any axiom I want, and derive true statements from it. Perhaps the only "social" thing here is what axioms we generally deem interesting enough to investigate - this does not change the facts derived from them. > that we use to create hopefully useful models. I think you underestimate pure mathematics :)
- yazaddaruvala 4y ago
  I’ll try one last time: > definition of addition What do you think any definition is other than the creation of a socially shared construct? > I can construct any axiom I want, and derive true statements from it. Let’s test this. Axiomatically I am always right! As such, I derive that it is illogical, dare I say irrational, of you to disagree with me. A truer statement has never even been written! Facts! Hmm… turns out you disagree that it’s a true statement. Why? I had an axiom! You don’t agree with my axiom? If that’s allowed, I guess I’ll have to convince you (and society) of my axiom!
  - mik1998 4y ago
    > What do you think any definition is other than the creation of a socially shared construct? A definition is simply a definition. It doesn't have to be social or shared. I can define addition in any manner, and in fact there are many other definitions of addition. > Let’s test this. Axiomatically I am always right! As such, I derive that it is illogical, dare I say irrational, of you to disagree with me. A truer statement has never even been written! Facts! You have a very interesting misunderstanding here. A fact is true only relative to an axiom. So yes, relative to such an axiom you are right, similarly how relative to the axioms of the field of real numbers the statement 1 + 1 = 2 is true. You can construct any axiom and derive facts from it. I can construct axioms such that 1 + 1 = 0. That doesn't make the statement 1 + 1 = 2 in the real numbers any less false!
deleted 4y ago
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