Fun with logic, Peano and Constructivism!

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Eodnhoj7
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Re: Fun with logic, Peano and Constructivism!

Post by Eodnhoj7 »

nothing wrote: Sun Mar 08, 2020 11:31 pm
Scott Mayers wrote: Sat Mar 07, 2020 11:03 pm I'm atheist. Given a reality where 'god' cannot be scientificaly rationalized, whatever we are made up of, if by 'laws', these have no foundation for being "obeyed" even by nature without some underlying LOGIC of abstract factors that lack any SPECIAL case, like our particular Universe that has laws. As such, reality HAS TO BE 'mathematical' (ie logical) with the only 'constants' possible as "absolutely nothing" or "absolutely everything" as elemental inputs.
Excellent post - made me happy reading.

To approach this idea in another way:
Image
wherein {alpha+/-omega} serve as a universally bestowed, locally employed null binary
which can be assumed by any (meta-)physical binary relationship:
conjugation, reciprocation, denial (ie. thesis/antithesis) etc.

If we say all-knowing is a valid state (ie. as often attributed to 'god') then
...to know {all thus not} to believe...
indefinitely approaches such an all-knowing state,
revealing that {knowledge and belief} are antithetical, thus:
all knowledge negates all belief-based ignorance(s) ad infinitum.
If Satan had a phallus, he'd have named it 'BELIEF'
would that all "believers" be incessant suckers.
-nothing
That one will sting the "believers".
No it won't.
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bahman
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Re: Fun with logic, Peano and Constructivism!

Post by bahman »

RCSaunders wrote: Fri Mar 06, 2020 2:27 am
Skepdick wrote: Wed Feb 12, 2020 6:39 pm If the Mathematical universe was truly immutable, no information could ever leave it under observation. No Mathematician could ever learn anything about Mathematics.
(...continued...)
There is no such thing as a, "mathematical universe." "Mathematics is a human invention for dealing with those aspects of existence which can be counted and measured. Outside human minds, mathematics does not exist at all.
I would say is mathematics is a human construct which part can be real and another part cannot.
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RCSaunders
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Re: Fun with logic, Peano and Constructivism!

Post by RCSaunders »

bahman wrote: Fri Mar 27, 2020 8:35 pm I would say is mathematics is a human construct which part can be real and another part cannot.
Oh, well, that's helpful. What does it mean? Mathematics is certainly a human invention, like language, logic, and geometry, and only exists epistemologically, but it really does exist, but it does no exist ontologically.
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bahman
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Re: Fun with logic, Peano and Constructivism!

Post by bahman »

RCSaunders wrote: Sat Mar 28, 2020 1:08 am
bahman wrote: Fri Mar 27, 2020 8:35 pm I would say is mathematics is a human construct which part can be real and another part cannot.
Oh, well, that's helpful. What does it mean? Mathematics is certainly a human invention, like language, logic, and geometry, and only exists epistemologically, but it really does exist, but it does no exist ontologically.
I mean, only some mathematical frameworks Apply to reality. The rest are not coherent.
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RCSaunders
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Re: Fun with logic, Peano and Constructivism!

Post by RCSaunders »

bahman wrote: Sat Mar 28, 2020 7:56 pm I mean, only some mathematical frameworks Apply to reality. The rest are not coherent.
Mathematics only pertains to those aspects of the ontological that can be counted or measured. Whether all of mathematics can be used for those purposes cannot be known. There are certainly aspects of physical existence that at one time nobody could have guessed could be understood in terms of logarithms, simultaneous linear equations, the calculus, or transcendental numbers, but they can.
Skepdick
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Re: Fun with logic, Peano and Constructivism!

Post by Skepdick »

RCSaunders wrote: Sat Mar 28, 2020 1:08 am Oh, well, that's helpful. What does it mean? Mathematics is certainly a human invention, like language, logic, and geometry, and only exists epistemologically, but it really does exist, but it does no exist ontologically.
To claim that language/maths/logic/geometry doesn't exist ontologically is to also claim that the contents of your brain don't exist ontologically.

Oops?
RCSaunders wrote: Sun Mar 29, 2020 1:03 am There are certainly aspects of physical existence that at one time nobody could have guessed could be understood in terms of logarithms, simultaneous linear equations, the calculus, or transcendental numbers, but they can.
All of those things you mention are computational concepts.

Thought is computation.
Computation is entanglement.

https://www.quantamagazine.org/landmark ... -20200304/

Ontological dualism is deeply flawed.
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RCSaunders
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Re: Fun with logic, Peano and Constructivism!

Post by RCSaunders »

Skepdick wrote: Sun Mar 29, 2020 10:35 am
RCSaunders wrote: Sat Mar 28, 2020 1:08 am Oh, well, that's helpful. What does it mean? Mathematics is certainly a human invention, like language, logic, and geometry, and only exists epistemologically, but it really does exist, but it does no exist ontologically.
To claim that language/maths/logic/geometry doesn't exist ontologically is to also claim that the contents of your brain don't exist ontologically.
Well, the contents of your dead brain can easily be examined, and all that will be found that is onotological will be water, various assorted proteins, colesterol, and fats. No language, math, logic, geometry, will be found there, nor will there be any consciousness found there, because they are all products of the perfectly natural but non-physical attribute, life. When life is gone, all the intellectual product of your brain is gone, and so are you.
Skepdick wrote: Sun Mar 29, 2020 10:35 am
RCSaunders wrote: Sun Mar 29, 2020 1:03 am There are certainly aspects of physical existence that at one time nobody could have guessed could be understood in terms of logarithms, simultaneous linear equations, the calculus, or transcendental numbers, but they can.
All of those things you mention are computational concepts.

Thought is computation.
Ah, the great equivocation of our age. Just as:
Hot dogs are better than nothing.
Nothing is better than steak.
Therefore, hot dogs are better than steak.
is absurd, so is:
Mathematical thinking is computation.
Computation is what computers do.
Therefore, mathematical thinking is what computers do.
Just as the word, "nothing," is used with two different meanings in the first argument, the word, "computation," is used with two different meanings in the second argument. Human "computation," is the conscious process of using concepts of counting and measurement to discover relationships of magnitude in the physical world, and requires that whatever is being counted or measured is consciously recognized or identified. Computer "computation," is nothing more than physical states with no meaning whatsoever. The product of no computer process means anything at all unless a human consciousness interprets it.
Skepdick wrote: Sun Mar 29, 2020 10:35 am Ontological dualism is deeply flawed.
Oh, I agree. Life, consciousness, and the conscious human mind are ontological, just not physical, but perfectly, "natural." To deny something based solely on the notion that physical properties are the only properties possible to existence is as superstitious as any religion.
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bahman
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Re: Fun with logic, Peano and Constructivism!

Post by bahman »

RCSaunders wrote: Sun Mar 29, 2020 1:03 am
bahman wrote: Sat Mar 28, 2020 7:56 pm I mean, only some mathematical frameworks Apply to reality. The rest are not coherent.
Mathematics only pertains to those aspects of the ontological that can be counted or measured. Whether all of mathematics can be used for those purposes cannot be known. There are certainly aspects of physical existence that at one time nobody could have guessed could be understood in terms of logarithms, simultaneous linear equations, the calculus, or transcendental numbers, but they can.
Yes, there are aspect of reality that cannot be described in term of mathematics. Because there is mind.
Skepdick
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Re: Fun with logic, Peano and Constructivism!

Post by Skepdick »

bahman wrote: Sun Mar 29, 2020 7:12 pm Yes, there are aspect of reality that cannot be described in term of mathematics. Because there is mind.
The mind is a a Turing machine. Obviously - it's incomplete.
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bahman
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Re: Fun with logic, Peano and Constructivism!

Post by bahman »

Skepdick wrote: Sun Mar 29, 2020 7:24 pm
bahman wrote: Sun Mar 29, 2020 7:12 pm Yes, there are aspect of reality that cannot be described in term of mathematics. Because there is mind.
The mind is a a Turing machine.
Yes, but only when it comes to intellect. There are other aspects of mind, such as ability to experience, decide and cause.
Skepdick wrote: Sun Mar 29, 2020 7:24 pm Obviously - it's incomplete.
The content of mind is incomplete, unless you know everything.
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Re: Fun with logic, Peano and Constructivism!

Post by Skepdick »

bahman wrote: Sun Mar 29, 2020 7:31 pm Yes, but only when it comes to intellect. There are other aspects of mind, such as ability to experience, decide and cause.
Any software in any modern programming language has those abilities.

"Experiencing" is just reading data from the senses - Input.
"Choose" is the very name of the non-deterministic operator
"Causing" is the same as producing output.
bahman wrote: Sun Mar 29, 2020 7:31 pm The content of mind is incomplete, unless you know everything.
Well. It's kinda the same thing. Having a Turing machine is not the same thing as having an algorithm to run on it.
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bahman
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Re: Fun with logic, Peano and Constructivism!

Post by bahman »

Skepdick wrote: Sun Mar 29, 2020 7:33 pm
bahman wrote: Sun Mar 29, 2020 7:31 pm Yes, but only when it comes to intellect. There are other aspects of mind, such as ability to experience, decide and cause.
Any software in any modern programming language has those abilities.

"Experiencing" is just reading data from the senses - Input.
"Choose" is the very name of the non-deterministic operator
"Causing" is the same as producing output.
bahman wrote: Sun Mar 29, 2020 7:31 pm The content of mind is incomplete, unless you know everything.
Well. It's kinda the same thing. Having a Turing machine is not the same thing as having an algorithm to run on it.
You cannot possibly write an algorithm which can possibly freely decide.
Skepdick
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Re: Fun with logic, Peano and Constructivism!

Post by Skepdick »

bahman wrote: Sun Mar 29, 2020 7:44 pm You cannot possibly write an algorithm which can possibly freely decide.
That is literally what non-deterministic algorithms do.

https://en.wikipedia.org/wiki/Nondeterm ... _algorithm
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bahman
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Re: Fun with logic, Peano and Constructivism!

Post by bahman »

Skepdick wrote: Sun Mar 29, 2020 8:44 pm
bahman wrote: Sun Mar 29, 2020 7:44 pm You cannot possibly write an algorithm which can possibly freely decide.
That is literally what non-deterministic algorithms do.

https://en.wikipedia.org/wiki/Nondeterm ... _algorithm
Free decision is different. You need to get ride of all constraints yet be able to decide.
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Re: Fun with logic, Peano and Constructivism!

Post by Skepdick »

bahman wrote: Sun Mar 29, 2020 10:46 pm Free decision is different. You need to get ride of all constraints yet be able to decide.
Different how? Even humans are constrained in their decision-making.

In fact - unconstrained decision-making is impossible. Even you can't enumerate a set of infinite options, let alone choose from such a set.
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