The Meaning of the Number System ("quantity" is incorrect)

[Iwannaplato]

Is this a category mistake?

I'm trying to find out.

[Agent Smith]

Is this a category mistake?

I'm trying to find out.

Assumptions made by the OP, what can they be?

[Iwannaplato]

Assumptions made by the OP, what can they be?

In responding to his responses I ended up getting this response....
viewtopic.php?p=624980#p624980
So, it's not directly in the OP stuff.

[Agent Smith]

Assumptions made by the OP, what can they be?

In responding to his responses I ended up getting this response....
viewtopic.php?p=624980#p624980
So, it's not directly in the OP stuff.

So, humanity is headed to jahanam? This has something to do with alleged voices in our heads. Math then, because it's incorrect, proves it! I shouldn't be laughing, but it's so crazy, the idea, right?

One can't escape causality, you know; I mean only old folks can.

[roydop]

Assumptions made by the OP, what can they be?

In responding to his responses I ended up getting this response....
viewtopic.php?p=624980#p624980
So, it's not directly in the OP stuff.

So, humanity is headed to jahanam? This has something to do with alleged voices in our heads. Math then, because it's incorrect, proves it! I shouldn't be laughing, but it's so crazy, the idea, right?

One can't escape causality, you know; I mean only old folks can.

I think it would be hilarious for you to show me how it is that 1+1=2.

What also is funny is you trying to stop that voice in your head from talking. You can't, can you? Why not? Why don't you have any control over your own mind?

Funny, right?

[Skepdick]

I think it would be hilarious for you to show me how it is that 1+1=2.

Would you accept a proof written in the Agda proof assistant?

Here is the relevant snippet in the free course on Programming Language Foundations.

Operations on naturals are recursive functions - it should be plenty hilarious.

[Iwannaplato]

In responding to his responses I ended up getting this response....
viewtopic.php?p=624980#p624980
So, it's not directly in the OP stuff.

So, humanity is headed to jahanam? This has something to do with alleged voices in our heads. Math then, because it's incorrect, proves it! I shouldn't be laughing, but it's so crazy, the idea, right?

One can't escape causality, you know; I mean only old folks can.

I think it would be hilarious for you to show me how it is that 1+1=2.

What also is funny is you trying to stop that voice in your head from talking. You can't, can you? Why not? Why don't you have any control over your own mind?

Funny, right?

I continue to think it is confused to refer to 'that voice' as if there is one voice. Further there are people who can control the voices in their minds. Or really have integrated the positive ones (those that are intrapsychic) and distanced themselves from the toxic ones. And then, there are voices that come from without, and some of these are just peachy. As long as they aren't babbling away.

1+1=2 is conventional. And useful. There are many things we cannot demonstrate to others that are useful.

You can not 'show' us that you have eliminated the voices in your head. You can just claim it's true. Just because you can't demostrate that, doesnt' mean you're lying.

[Iwannaplato]

So, humanity is headed to jahanam? This has something to do with alleged voices in our heads.

I think there is some truth to this, but he doesn't or can't discriminate between voices in his head. He's shut them all out or claims he has.

Math then, because it's incorrect, proves it! I shouldn't be laughing, but it's so crazy, the idea, right?

Hey, it's interesting, at least. He's more creative than some people out there. Creativity can be a two-edged sword of course.

[alan1000]

Jesus read this thread, and Jesus wept.

Prove to me how 1+1=2 is correct. You are assuming it to be correct and putting the emphasis on me to disprove it. But I have not been convinced that 1+1=2 makes any intuitive sense whatsoever. What does it even mean?

So please do explain to me how 1+1=2, and what truth it is relating to.

1 + 1 = 1 + S(0) = S(0 + 1) = S(1) = 2

[for the pedants, S(0) + S(0) = S(S(0)) = 2, by definition]

I suppose you also need someone to define the number 1 for you. Do you understand what a "natural" or "inductive" number is? Have you ever heard of the Peano/Dedekind axioms? Have you ever considered reading a textbook on mathematics, or googling the question before you post it?

[Skepdick]

Jesus read this thread, and Jesus wept.

Prove to me how 1+1=2 is correct. You are assuming it to be correct and putting the emphasis on me to disprove it. But I have not been convinced that 1+1=2 makes any intuitive sense whatsoever. What does it even mean?

So please do explain to me how 1+1=2, and what truth it is relating to.

1 + 1 = 1 + S(0) = S(0 + 1) = S(1) = 2

[for the pedants, S(0) + S(0) = S(S(0)) = 2, by definition]

I suppose you also need someone to define the number 1 for you. Do you understand what a "natural" or "inductive" number is? Have you ever heard of the Peano/Dedekind axioms? Have you ever considered reading a textbook on mathematics, or googling the question before you post it?

No, I need you to give me intensional definitions for "+", "=" in some sufficiently strong type-system.

For the sake of consistency I would very much like it if you used prefix notation everywhere.

[for the pedants, S(0) + S(0) = S(S(0)) = 2, by definition]

Here, let me help you...

Here's the Haskell type signatures.

Code: Select all

s :: Int -> Int
s x = undefined

add :: Int -> Int -> Int
add x y = undefined

equal :: Int -> Int -> Bool
equal x y = undefined

Define the functions such that S(0) + S(0) = S(S(0)) is true.

e.g such that the following expression

Code: Select all

equal (add (s 0) (s 0)) s(s(0))

evaluates to True