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I think this is a really good comment. Are you implying that the concept of integer is a consequence of the abstraction of an apple, an abstraction which is ent

I think this is a really good comment. Are you implying that the concept of integer is a consequence of the abstraction of an apple, an abstraction which is entirely human? I really like this point of view.

teucris 6y ago
That’s exactly what I’m saying. I’m glad you like it!
- smokel 6y ago
  I have been entertaining this idea for years. First time I hear someone else voice it. Do you have an idea what the philosophical term for this idea is? It seems related to connectionism. One might assume that abstraction and pattern matching in the brain are required to determine that two "things" are the same. It is perhaps a small step to go from comparing things to comparing integers. Unfortunately, this line of reasoning quickly goes awry, because one cannot assume even the existence of things to describe brains or pattern matching.
  - lmm 6y ago
    > Unfortunately, this line of reasoning quickly goes awry, because one cannot assume even the existence of things to describe brains or pattern matching. You might be interested in the univalent foundations approach, where the idea is that mathematics is fundamentally the study of equivalences between constructions, and equivalences themselves are first-class objects that are just as easy to talk about as any other mathematical object.
  - myWindoonn 6y ago
    The abstraction from counting to the natural numbers is called "decategorification", in category theory. The abstraction of sameness is called "equivalence" or "isomorphism".
  - teucris 6y ago
    I don’t. I’ll do some research. The origin of this concept comes from discussions I had on identity, specifically the ability to separate the “self” from the rest of the universe, or to isolate some quantity of stuff and claim it’s an apple. Ultimately the universe has no concept of such boundaries. [update] the study of this concept seems to be semiotics, which examines the creation and use of symbols. I don’t know what branch of semiotics examines the creation of the concepts of unity and succession.

teucris 6y ago

That’s exactly what I’m saying. I’m glad you like it!

smokel 6y ago
I have been entertaining this idea for years. First time I hear someone else voice it. Do you have an idea what the philosophical term for this idea is? It seems related to connectionism. One might assume that abstraction and pattern matching in the brain are required to determine that two "things" are the same. It is perhaps a small step to go from comparing things to comparing integers. Unfortunately, this line of reasoning quickly goes awry, because one cannot assume even the existence of things to describe brains or pattern matching.
- lmm 6y ago
  > Unfortunately, this line of reasoning quickly goes awry, because one cannot assume even the existence of things to describe brains or pattern matching. You might be interested in the univalent foundations approach, where the idea is that mathematics is fundamentally the study of equivalences between constructions, and equivalences themselves are first-class objects that are just as easy to talk about as any other mathematical object.
- myWindoonn 6y ago
  The abstraction from counting to the natural numbers is called "decategorification", in category theory. The abstraction of sameness is called "equivalence" or "isomorphism".
- teucris 6y ago
  I don’t. I’ll do some research. The origin of this concept comes from discussions I had on identity, specifically the ability to separate the “self” from the rest of the universe, or to isolate some quantity of stuff and claim it’s an apple. Ultimately the universe has no concept of such boundaries. [update] the study of this concept seems to be semiotics, which examines the creation and use of symbols. I don’t know what branch of semiotics examines the creation of the concepts of unity and succession.