Numbers Grounded in Counting 0s, Thus Number/Math Has No Foundations.

What is the basis for reason? And mathematics?

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Skepdick
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Re: Numbers Grounded in Counting 0s, Thus Number/Math Has No Foundations.

Post by Skepdick » Fri Nov 29, 2019 3:35 am

wtf wrote:
Fri Nov 29, 2019 2:52 am
The distinction is completely arbitrary and is implemented by the writers of the interpreter. It's not God-given or fundamental in any way.
Obviously it's arbitrary! ALL Formal Systems are arbitrary! How could it be any other way?

Only the Turing Machine is fundamental and it's a blank slate until you teach it how to recognise a formal language. It has no comprehension of a 'number', 'integer' or 'string' until you teach it how to interpret and manipulate the otherwise-meaningless symbols.

This is where you completely miss the point. The arbitrary choice that is available to a Formalist is not available to a Mathematician because in the Mathematical Universe Alphabets, Symbols, Characters, Strings, Words and Sentences don't exist.

The Formalist Universe is richer!
wtf wrote:
Fri Nov 29, 2019 2:52 am
You have a very narrow perspective. I'll let you have the last word.
My field is a superset of yours and I am the one with a "narrow perspective"? Heh!

Skepdick
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Re: Numbers Grounded in Counting 0s, Thus Number/Math Has No Foundations.

Post by Skepdick » Fri Nov 29, 2019 9:57 am

Eodnhoj7 wrote:
Thu Nov 28, 2019 7:31 pm
You are quantifying zero, whether as an individual or string, zero is equated to a number
I am not quantifying it - I am objectifying it.

I am stripping the symbol 0 of all its meaning and value and I am treating it as a concrete ontological object.

It's a perfectly valid thing to do if you were to answer the question "How many digits are there in your preferred number system?"

Skepdick
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Re: Numbers Grounded in Counting 0s, Thus Number/Math Has No Foundations.

Post by Skepdick » Fri Nov 29, 2019 12:34 pm

wtf wrote:
Fri Nov 29, 2019 12:53 am
In the Mython interpreter, the Boolean expression

Code: Select all

0000 == 4 
evaluates to True
How can somebody who claims to understand Homotopy Type Theory be so ignorant of Type Systems?!?

I am going to do this in C++ so that you can convince yourself this has nothing to do with Python or Interpreted languages.
I can do it in Haskell too if you are going to fuss about "pure functions".

This is about polymorphism and the meaning of the "==" operator when applied to incompatible types. Comparing a String to an Integer is a meaningless notion unless you implement an Identity Type that does it.
In intensional type theory under the propositions as types paradigm, an identity type (or equality type) is the incarnation of equality. That is, for any type A and any terms x,y:A, the type IdA(x,y) is “the type of proofs that x=y” or “the type of reasons why x=y”.
In this particular case you want a function which takes (String, Integer) as inputs and returns a Boolean. This is called a Type signature.

https://repl.it/repls/BiodegradablePleasedBit

Code: Select all

#include <iostream>
using namespace std;

bool identity(string a, int b) {
  /* magic sauce required here by the Genius-Mathematician */
  return 0;
};

int main() {
  string a = "0000";
  int b = 4;
  cout << identity(a, b) << endl;
  return 0;
}
This is the practical implication of the Curry-Howard isomorphism. 0000 == 4 => True is a proposition. You need to prove that proposition by writing the implementation of the bool identity(string a, int b) function above.

So go right ahead and prove it.

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Eodnhoj7
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Re: Numbers Grounded in Counting 0s, Thus Number/Math Has No Foundations.

Post by Eodnhoj7 » Fri Nov 29, 2019 5:48 pm

Skepdick wrote:
Fri Nov 29, 2019 9:57 am
Eodnhoj7 wrote:
Thu Nov 28, 2019 7:31 pm
You are quantifying zero, whether as an individual or string, zero is equated to a number
I am not quantifying it - I am objectifying it.

I am stripping the symbol 0 of all its meaning and value and I am treating it as a concrete ontological object.
And all concrete ontological objects ate countable. Regardless 0 can be zero or whatever,..."0" is just a symbol.

It's a perfectly valid thing to do if you were to answer the question "How many digits are there in your preferred number system?"

Skepdick
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Re: Numbers Grounded in Counting 0s, Thus Number/Math Has No Foundations.

Post by Skepdick » Sat Nov 30, 2019 8:49 am

Eodnhoj7 wrote:
Fri Nov 29, 2019 5:48 pm
"0" is just a symbol.
Duh! All forms of language are "just symbols". Until interpreted by something or somebody they have no inherent meaning.

That is exactly the symbol-grounding problem.

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Eodnhoj7
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Re: Numbers Grounded in Counting 0s, Thus Number/Math Has No Foundations.

Post by Eodnhoj7 » Sat Nov 30, 2019 8:46 pm

Skepdick wrote:
Sat Nov 30, 2019 8:49 am
Eodnhoj7 wrote:
Fri Nov 29, 2019 5:48 pm
"0" is just a symbol.
Duh! All forms of language are "just symbols". Until interpreted by something or somebody they have no inherent meaning.

That is exactly the symbol-grounding problem.
Yet this interpretation is grounded in an empty assumption, where the act of assuming as fundamentally void inverts the symbol from one state into another.

Even with the nature of assumption itself a "point 0" is inherent.
Last edited by Eodnhoj7 on Sun Dec 01, 2019 11:34 am, edited 1 time in total.

wtf
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Re: Numbers Grounded in Counting 0s, Thus Number/Math Has No Foundations.

Post by wtf » Sun Dec 01, 2019 8:40 am

Skepdick wrote:
Sat Nov 30, 2019 8:49 am
Duh! All forms of language are "just symbols". Until interpreted by something or somebody they have no inherent meaning.
At the risk of once again feeling like a fool for thinking there is rational dialog to be had with you: Isn't this point exactly what I'm trying to explain to you?

Skepdick
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Re: Numbers Grounded in Counting 0s, Thus Number/Math Has No Foundations.

Post by Skepdick » Sun Dec 01, 2019 9:59 am

wtf wrote:
Sun Dec 01, 2019 8:40 am
At the risk of once again feeling like a fool for thinking there is rational dialog to be had with you: Isn't this point exactly what I'm trying to explain to you?
You shouldn't feel like a fool, but you should feel like a condescending idiot. There is absolutely no need for you to explain my own position to me. I have been arguing Anti-foundationalism all along.

Many Mathematicians suffer from the same superiority complex as you: https://xkcd.com/435/
Skepdick wrote:
Fri Nov 29, 2019 3:35 am
Obviously it's arbitrary! ALL Formal Systems are arbitrary! How could it be any other way?

Only the Turing Machine is fundamental and it's a blank slate until you teach it how to recognise a formal language. It has no comprehension of a 'number', 'integer' or 'string' until you teach it how to interpret and manipulate the otherwise-meaningless symbols.
Turing Machines are Language RECOGNIZERS (emphasis on this word because its etymology is the word cognition) - they interpret languages. Exactly like humans do!

Which is why I have been pointing out that Programming Language Theory (and broadly - computer science) is a viable (if incomplete) theory of mind.

Skepdick
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Re: Numbers Grounded in Counting 0s, Thus Number/Math Has No Foundations.

Post by Skepdick » Tue Dec 03, 2019 10:22 am

Eodnhoj7 wrote:
Sat Nov 30, 2019 8:46 pm
Yet this interpretation is grounded in an empty assumption.
You call it assumption - I call it choice.
Eodnhoj7 wrote:
Sat Nov 30, 2019 8:46 pm
where the act of assuming as fundamentally void inverts the symbol from one state into another.
Then make another choice - choose that the symbol doesn't invert from one state into another.

You are literally describing how equivocation works - using one symbol to mean multiple things.

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Eodnhoj7
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Re: Numbers Grounded in Counting 0s, Thus Number/Math Has No Foundations.

Post by Eodnhoj7 » Tue Dec 03, 2019 2:03 pm

Skepdick wrote:
Tue Dec 03, 2019 10:22 am
Eodnhoj7 wrote:
Sat Nov 30, 2019 8:46 pm
Yet this interpretation is grounded in an empty assumption.
You call it assumption - I call it choice.

Both are a point of inversion.
Eodnhoj7 wrote:
Sat Nov 30, 2019 8:46 pm
where the act of assuming as fundamentally void inverts the symbol from one state into another.
Then make another choice - choose that the symbol doesn't invert from one state into another.

That is recursion of assumptions. When I assume one thing it inverts from one state into another state, when I reassume this new state and/or the one state inverting into a new state a new assumption occurs.



You are literally describing how equivocation works - using one symbol to mean multiple things.

Tautology as well:

1 leads to 2. Two is not equal to 1 in the context of 2=2, it is however equal to one as both 1 set and composed of "one".

All phenomenon as having simultaneous positive/thetical and negative/antithetical meanings always by default are subject to equivocation and non equivocation.

Everything equivocates as an extension of the original source and simulataneously non-equivocable due to them being a progressive variation of the source as an adaptation to chaos.

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