🎓 Dr. Freemo :jpf: 🇳🇱 on Nostr: npub1ktvle…4fv3a > I feel like you're unnecessarily equating labels with their ...
npub1ktvleg4d765hrvqh7sx3fm6z5lxwgl8ef58fvt530nlcz2jea4hqg4fv3a (npub1ktv…fv3a)
> I feel like you're unnecessarily equating labels with their underlying concepts here.
> The concept of two is still two whether we write it as "2" in base-10 or as "10" in base-2.
No this is exactly what i said at the offset, there are two ways to discuss this, both very different but both agree with what I'm saying here.
What i just expressed was the "by mathemical definition" where I showed "1+1=2" is **not** a universal truth, it is only true when defined to be true, and not in any sense in reality.
> Likewise, the concept of integer addition is distinct from the addition symbol "+" which is also used to denote many similar-yet-distinct concepts (such as the ones you describe). While those may be referred to as "addition", they aren't the concept of integer addition that I'm specifically referring to.
So lets use the other half of the coin, since that is what you are asserting here you mean. Not by definition but due toi the real world concepts they represent.
> These are, as you initially described them, effectively "definitions" that prove themselves circularly, but a tiny subset of such definitions describe concepts that would seem to be universally constant, that are independently and repeatably verifiable regardless of perspective. If we don't call those "facts", what do we call them?
So even in the real world, not by definition, the real world concept that "1+1=2" is not a universal fact in reality either.
I mean sure, if I have one duck, and add to that one apple, I now have two things... but again that is only because we define what a duck is, and where one thing ends and another starts, its still all by linguistic definition, and ONLY works for some things even if we accept their definittions...
Here are all the counter examples where "1+1 does not equal 0":
One electron added to one positron results in 0 physical things. So in this scenario "1+1=0"
one blob of water added to another blob of water results in a single blob of water, therefore "1+1=1"
If you put two humans who are attractive to eachother in a room and wait 9 months you get an extra human. Therefore in some cases "1+1=3"
> I feel like you're unnecessarily equating labels with their underlying concepts here.
> The concept of two is still two whether we write it as "2" in base-10 or as "10" in base-2.
No this is exactly what i said at the offset, there are two ways to discuss this, both very different but both agree with what I'm saying here.
What i just expressed was the "by mathemical definition" where I showed "1+1=2" is **not** a universal truth, it is only true when defined to be true, and not in any sense in reality.
> Likewise, the concept of integer addition is distinct from the addition symbol "+" which is also used to denote many similar-yet-distinct concepts (such as the ones you describe). While those may be referred to as "addition", they aren't the concept of integer addition that I'm specifically referring to.
So lets use the other half of the coin, since that is what you are asserting here you mean. Not by definition but due toi the real world concepts they represent.
> These are, as you initially described them, effectively "definitions" that prove themselves circularly, but a tiny subset of such definitions describe concepts that would seem to be universally constant, that are independently and repeatably verifiable regardless of perspective. If we don't call those "facts", what do we call them?
So even in the real world, not by definition, the real world concept that "1+1=2" is not a universal fact in reality either.
I mean sure, if I have one duck, and add to that one apple, I now have two things... but again that is only because we define what a duck is, and where one thing ends and another starts, its still all by linguistic definition, and ONLY works for some things even if we accept their definittions...
Here are all the counter examples where "1+1 does not equal 0":
One electron added to one positron results in 0 physical things. So in this scenario "1+1=0"
one blob of water added to another blob of water results in a single blob of water, therefore "1+1=1"
If you put two humans who are attractive to eachother in a room and wait 9 months you get an extra human. Therefore in some cases "1+1=3"