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> It understands the axioms because they've been literally built into its tiny brain. No they have not. Do you know what an axiom is? Do you know how a calcula

by anyfoo 4y ago

> It understands the axioms because they've been literally built into its tiny brain. No they have not. Do you know what an axiom is? Do you know how a calculator is implemented? It’s not about metaphysics, it’s about the difference in the experience of a lifetime compared to a car on a road. „Training data“, if you like.

jstanley 4y ago
I don't think it's a question of knowing what an axiom is or how a calculator is implemented. I think it's a question of disagreeing on what "understanding" means. What does it mean to understand something? Obviously (to me and I presume to you) a calculator doesn't understand anything! It doesn't have the capacity for understanding. Obviously (according to, I presume, feoren and Dennett) "understanding" means something very different, and a calculator is perfectly capable of "understanding" arithmetic.
- hamburglar 4y ago
  There is no math in a calculator. It’s a pile of logic gates assembled in a way to appear to perform mathematical operations. An ALU has no “understanding” of arithmetic, it’s just a canned, finite set of inputs and outputs. Not an axiom to be found.
  - jstanley 4y ago
    I expect the argument would go like: The pile of logic gates is an encoding of the axioms. The fact that it evaluates mathematical expressions correctly is both necessary and sufficient to show that it understands arithmetic. Therefore the calculator knows the axioms and understands arithmetic.
    - hamburglar 4y ago
      Except it doesn’t implement the axioms of math, it implements a crude facsimile of them for a certain subset of numbers, because what it’s really doing is a non-mathematical physical process.
  - Gordonjcp 4y ago
    > It’s a pile of logic gates assembled in a way to appear to perform mathematical operations In what way is Boolean logic not maths?
    - hamburglar 4y ago
      If you want to argue that an ALU is performing “boolean logic” just because it’s made of logic gates, be my guest, but in my opinion that’s a bit like saying a bucket is “doing math” because if you put 5 rocks in and add 7 rocks, it’s smart enough to contain 12 rocks when you’re done.

by anyfoo 4y ago

jstanley 4y ago

I don't think it's a question of knowing what an axiom is or how a calculator is implemented. I think it's a question of disagreeing on what "understanding" means. What does it mean to understand something? Obviously (to me and I presume to you) a calculator doesn't understand anything! It doesn't have the capacity for understanding. Obviously (according to, I presume, feoren and Dennett) "understanding" means something very different, and a calculator is perfectly capable of "understanding" arithmetic.

hamburglar 4y ago
There is no math in a calculator. It’s a pile of logic gates assembled in a way to appear to perform mathematical operations. An ALU has no “understanding” of arithmetic, it’s just a canned, finite set of inputs and outputs. Not an axiom to be found.
- jstanley 4y ago
  I expect the argument would go like: The pile of logic gates is an encoding of the axioms. The fact that it evaluates mathematical expressions correctly is both necessary and sufficient to show that it understands arithmetic. Therefore the calculator knows the axioms and understands arithmetic.
  - hamburglar 4y ago
    Except it doesn’t implement the axioms of math, it implements a crude facsimile of them for a certain subset of numbers, because what it’s really doing is a non-mathematical physical process.
- Gordonjcp 4y ago
  > It’s a pile of logic gates assembled in a way to appear to perform mathematical operations In what way is Boolean logic not maths?
  - hamburglar 4y ago
    If you want to argue that an ALU is performing “boolean logic” just because it’s made of logic gates, be my guest, but in my opinion that’s a bit like saying a bucket is “doing math” because if you put 5 rocks in and add 7 rocks, it’s smart enough to contain 12 rocks when you’re done.