The metaphysical presuppositions of formal logic • Hacker News Board

Re: The metaphysical presuppositions of formal logic

#111

Post by the_af » Mon, Jul 19, 2021, 8:17 PM UTC

ukj wrote: post #98

dragonwriter wrote: post #57

Earlier quoted context omitted.

> The function I am talking about doesn't take any arguments. All impure functions have an implicit dependency on (some subset of) the state of the universe when they execute; in mathematics and logic something with this kind of dependency is typically noted by parameterizing it by time when the actual precise nature of the dependency is outside of the scope of the immediate analysis (because a dependency on the stat…

Well, it seems our disagreeme is obvious. You only want to talk about pure functions. I want to talk about ALL functions. So lets define the function "pure" such that pure(f) -> True when f is a pure function pure(g) -> False when g is an impure function What would you say is the truth-value of pure(pure) ? https://en.wikipedia.org/wiki/Impredicativity

dragonwriter wrote:

> "All impure functions have an implicit dependency on (some subset of) the state of the universe when they execute"

You wrote:

> "You only want to talk about pure functions. I want to talk about ALL functions."

Find the error.

Re: The metaphysical presuppositions of formal logic

#112

Post by ukj » Mon, Jul 19, 2021, 9:06 PM UTC

the_af wrote: post #111

ukj wrote: post #98

Earlier quoted context omitted.

Well, it seems our disagreeme is obvious. You only want to talk about pure functions. I want to talk about ALL functions. So lets define the function "pure" such that pure(f) -> True when f is a pure function pure(g) -> False when g is an impure function What would you say is the truth-value of pure(pure) ? https://en.wikipedia.org/wiki/Impredicativity

dragonwriter wrote: > "All impure functions have an implicit dependency on (some subset of) the state of the universe when they execute" You wrote: > "You only want to talk about pure functions. I want to talk about ALL functions." Find the error.

>Find the error.

Still waiting for you to implement equal() as a "pure" function.

We can discuss what you mean by "error" once we have a referent (that's not just in your head) to talk about.

Re: The metaphysical presuppositions of formal logic

#113

Post by ukj » Mon, Jul 19, 2021, 10:10 PM UTC

the_af wrote: post #111

ukj wrote: post #98

Earlier quoted context omitted.

Well, it seems our disagreeme is obvious. You only want to talk about pure functions. I want to talk about ALL functions. So lets define the function "pure" such that pure(f) -> True when f is a pure function pure(g) -> False when g is an impure function What would you say is the truth-value of pure(pure) ? https://en.wikipedia.org/wiki/Impredicativity

dragonwriter wrote: > "All impure functions have an implicit dependency on (some subset of) the state of the universe when they execute" You wrote: > "You only want to talk about pure functions. I want to talk about ALL functions." Find the error.

You know what... let me take your red herring away from you. Forget the Time.now function. Here's a !=a as a "pure" function.

   In [1]: class A:
   ...:     def __eq__(self, other):
   ...:         return False
   ...:
   In [2]: a = A()
   In [3]: assert a != a
   In [4]: assert a == a
   AssertionError

Will you now permit me to speak freely about A != A without you moralising about my reasoning?

Will you now recognise my right to free speech and free thought, or must I fall in line?

Re: The metaphysical presuppositions of formal logic

#114

Post by ukj » Tue, Jul 20, 2021, 11:01 AM UTC

dragonwriter wrote: post #57

ukj wrote: post #48

Earlier quoted context omitted.

You are talking about a different function. The function I am talking about doesn't take any arguments. [1] pry(main)> Time.now(1) ArgumentError: wrong number of arguments (given 1, expected 0)

> The function I am talking about doesn't take any arguments. All impure functions have an implicit dependency on (some subset of) the state of the universe when they execute; in mathematics and logic something with this kind of dependency is typically noted by parameterizing it by time when the actual precise nature of the dependency is outside of the scope of the immediate analysis (because a dependency on the stat…

By the way... your conception of a pure function is incoherent.

Parameters ARE inputs. Results ARE outputs. Renaming them to something else is just obscuring the fact that you are still talking about a function with side-effects.

So using Python as my model of computation this is a pure function, but it does nothing:

   def f(): pass

This is NOT a pure function. It has outputs.

   def g(): return True

This is NOT a pure function. It mandates input.

   def h(x): pass

This is NOT a pure function - it mandates input and produces output:

   def j(x): return x

This is a pure function. It calculates the answer to 2+2, but doesn't tell you what it is.

   def k(): 2+2

If pure functions take no input and produce no output, what is there left to analyse? What is Logic and Mathematics talking ABOUT?