Conceptual Truth can be understood as math

What is the basis for reason? And mathematics?

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Skepdick
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Re: Truth can be understood as math

Post by Skepdick » Tue Aug 13, 2019 8:14 am

PeteOlcott wrote:
Tue Aug 13, 2019 1:13 am
I don't know about model depended realism.
When I talked about a model of physical reality I was talking about the
phenomenological things (interpreted sensory stimulus) associated with
words such these: "I just saw a bright red car drive by".
The thing about phenomenology... its central concept for understanding experience is intentionality

Intentionality, in phenomenology, the characteristic of consciousness whereby it is conscious of something—i.e., its directedness toward an object.

I am sure you saw more than just the car drive by. I am sure you saw the sky. I am sure you saw people. I am sure you saw trees. Other cars even.

But your intentionality was directed at that particular object - the bright red car.
You also chose to communicate that to me. Not the trees, not the sky, not the people, but the car.

And so it begs the question: Why? What was the intentionality behind observing and communicating that particular sub-set of your experiences?

Perhaps it's just a difference in the way our minds work. When I look out the window I don't have words associated with every single things I see.
There are many objects I see for which I have no English words. In fact - the labels don't form in my mind until I actually want to describe/express/communicate what I am seeing.

e.g Pure phenomenological experience is unhindered by language.

PeteOlcott
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Re: Truth can be understood as math

Post by PeteOlcott » Tue Aug 13, 2019 3:53 pm

Skepdick wrote:
Tue Aug 13, 2019 7:49 am
PeteOlcott wrote:
Mon Aug 12, 2019 10:15 pm
I have no idea what a self-hosting compiler would be. I already wrote a parser for it.
The parser translates expressions into their equivalent XML parse tree.
A parser/interpreter for MTT written in MTT.

A language that can interpret itself.
PeteOlcott wrote:
Mon Aug 12, 2019 10:21 pm
That is metaphysics and thus not logic and math.
PeteOlcott wrote:
Mon Aug 12, 2019 10:19 pm
We only look outside the system when we are looking at physically manifest things in the world.
This is also connected - because all dualisms are connected. Yes - there are two ways to reason about every system.
Logic and meta-logic.
Mathematics and meta-mathematics.
Inside and outside view.
Grammar and semantics.
Structure and behaviour.

In computer science this is the data plane vs control plane distinction. And the way you erase the line in the sand between the two is with the concepts of

Metaprogramming and homoiconicity.

A language is homoiconic if a program written in it can be manipulated as data using the language, and thus the program's internal representation can be inferred just by reading the program itself.

But back to the first bit. A language is homoiconic if it can compile/interpret itself.
I have it simplified down to this now:
I want to make the formal system itself as simple as possible.
The entire system that can represent every concept known to
humanity is comprised of a set of Boolean functions that take
Unicode finite string arguments. Although types are required
they are (as everything else) simply implemented as relations
between finite strings.


Which is a simplification of this:
https://en.wikipedia.org/wiki/History_o ... B6del_1944
Gödel 1944

By the theory of simple types I mean the doctrine which says that the objects of thought (or, in another interpretation, the symbolic expressions) are divided into types, namely: individuals, properties of individuals, relations between individuals, properties of such relations...

I transformed the above into objects of thought are stipulated relations between objects of thought. Properties of individuals, relations between individuals, properties of such relations are all a kind of relation.

PeteOlcott
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Re: Truth can be understood as math

Post by PeteOlcott » Tue Aug 13, 2019 3:57 pm

Skepdick wrote:
Tue Aug 13, 2019 8:14 am
PeteOlcott wrote:
Tue Aug 13, 2019 1:13 am
I don't know about model depended realism.
When I talked about a model of physical reality I was talking about the
phenomenological things (interpreted sensory stimulus) associated with
words such these: "I just saw a bright red car drive by".
The thing about phenomenology... its central concept for understanding experience is intentionality

Intentionality, in phenomenology, the characteristic of consciousness whereby it is conscious of something—i.e., its directedness toward an object.

I am sure you saw more than just the car drive by. I am sure you saw the sky. I am sure you saw people. I am sure you saw trees. Other cars even.

But your intentionality was directed at that particular object - the bright red car.
You also chose to communicate that to me. Not the trees, not the sky, not the people, but the car.

And so it begs the question: Why? What was the intentionality behind observing and communicating that particular sub-set of your experiences?

Perhaps it's just a difference in the way our minds work. When I look out the window I don't have words associated with every single things I see.
There are many objects I see for which I have no English words. In fact - the labels don't form in my mind until I actually want to describe/express/communicate what I am seeing.

e.g Pure phenomenological experience is unhindered by language.
Yes but that side steps my point that Tarski is wrong about undefinability and and Gödel is wrong about incompleteness.
Since I only need the analytical side of the analytic versus synthetic distinction to show this I usually make sure
to exclude the synthetic side as off-topic.

Skepdick
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Joined: Fri Jun 14, 2019 11:16 am

Re: Truth can be understood as math

Post by Skepdick » Tue Aug 13, 2019 7:58 pm

PeteOlcott wrote:
Tue Aug 13, 2019 3:53 pm
I want to make the formal system itself as simple as possible.
What is your metric for simplicity?
PeteOlcott wrote:
Tue Aug 13, 2019 3:53 pm
The entire system that can represent every concept known to
humanity is comprised of a set of Boolean functions that take
Unicode finite string arguments.
How do you capture the concept of recursion/self-reference as a finite string?

Skepdick
Posts: 831
Joined: Fri Jun 14, 2019 11:16 am

Re: Truth can be understood as math

Post by Skepdick » Tue Aug 13, 2019 8:02 pm

PeteOlcott wrote:
Tue Aug 13, 2019 3:57 pm
Yes but that side steps my point that Tarski is wrong about undefinability and and Gödel is wrong about incompleteness.
Since I only need the analytical side of the analytic versus synthetic distinction to show this I usually make sure
to exclude the synthetic side as off-topic.
We went down that rabbit hole. Godel and Tarski aren't wrong, because they are talking about systems of knowledge built atop of arithmetic.

Any system you build is build on top of arithmetic. Trivially demonstrable when I ask you about the cardinality of your knowledge-base.

wtf
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Re: Truth can be understood as math

Post by wtf » Tue Aug 13, 2019 9:03 pm

Skepdick wrote:
Tue Aug 13, 2019 8:02 pm
Any system you build is build on top of arithmetic. Trivially demonstrable when I ask you about the cardinality of your knowledge-base.
When I asked him about that he said I was insulting his mother. Go figure.

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vegetariantaxidermy
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Re: Truth can be understood as math

Post by vegetariantaxidermy » Tue Aug 13, 2019 9:11 pm

It's mathS!!!!

And don't say 'well it's 'math' in 'American' '. No, it isn't. Properly educated Americans say 'maths'. And 'towards'. They know how to use English.
It's the ignorant, arrogant uneducated majority over there that takes great pride in butchering the 'snobby Limey language' that they seem to think they don't speak. It's only yanks who take great pride in being as stupid and uneducated as possible.

PeteOlcott
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Joined: Mon Jul 25, 2016 6:55 pm

Re: Truth can be understood as math

Post by PeteOlcott » Tue Aug 13, 2019 9:45 pm

Skepdick wrote:
Tue Aug 13, 2019 7:58 pm
PeteOlcott wrote:
Tue Aug 13, 2019 3:53 pm
I want to make the formal system itself as simple as possible.
What is your metric for simplicity?
PeteOlcott wrote:
Tue Aug 13, 2019 3:53 pm
The entire system that can represent every concept known to
humanity is comprised of a set of Boolean functions that take
Unicode finite string arguments.
How do you capture the concept of recursion/self-reference as a finite string?
BNF defines recursion as relations between finite strings.
Self-reference is generally erroneous: "This sentence in not true"

PeteOlcott
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Joined: Mon Jul 25, 2016 6:55 pm

Re: Truth can be understood as math

Post by PeteOlcott » Tue Aug 13, 2019 9:51 pm

Skepdick wrote:
Tue Aug 13, 2019 8:02 pm
PeteOlcott wrote:
Tue Aug 13, 2019 3:57 pm
Yes but that side steps my point that Tarski is wrong about undefinability and and Gödel is wrong about incompleteness.
Since I only need the analytical side of the analytic versus synthetic distinction to show this I usually make sure
to exclude the synthetic side as off-topic.
We went down that rabbit hole. Godel and Tarski aren't wrong, because they are talking about systems of knowledge built atop of arithmetic.

Any system you build is build on top of arithmetic. Trivially demonstrable when I ask you about the cardinality of your knowledge-base.
Tarski and Gödel are both wrong yet the convoluted mess of the incompleteness Theorem hides this.

It is always necessarily the case that any relation expressible between two finite string expressions
of a language are necessarily provable in this same language.

"This sentence cannot be be proven" is provably unprovable if you ignore
the self-contradiction, otherwise it is simply erroneous because of the
self-contradiction.

Skepdick
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Joined: Fri Jun 14, 2019 11:16 am

Re: Truth can be understood as math

Post by Skepdick » Tue Aug 13, 2019 10:05 pm

PeteOlcott wrote:
Tue Aug 13, 2019 9:45 pm
BNF defines recursion as relations between finite strings.
I have no idea what that means.
PeteOlcott wrote:
Tue Aug 13, 2019 9:45 pm
Self-reference is generally erroneous: "This sentence in not true"
Self-reference is not erroneous. Any textbook implementation of N-th Fibonacci is recursive.
At the other end of the spectrum (but still in the realm of halting/decidable functions) are the Ackermann functions.

Either way - I can't tell what you are bringing to the table that is not equivalent to total functional programming.
PeteOlcott wrote:
Tue Aug 13, 2019 9:51 pm
It is always necessarily the case that any relation expressible between two finite string expressions
of a language are necessarily provable in this same language.
Surely you are aware that Type-checking is still undecidable in System-F (and higher order lambda calculus)?

PeteOlcott
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Re: Truth can be understood as math

Post by PeteOlcott » Tue Aug 13, 2019 10:31 pm

Skepdick wrote:
Tue Aug 13, 2019 10:05 pm
PeteOlcott wrote:
Tue Aug 13, 2019 9:45 pm
BNF defines recursion as relations between finite strings.
I have no idea what that means.
https://en.wikipedia.org/wiki/Backus%E2%80%93Naur_form

Skepdick
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Re: Truth can be understood as math

Post by Skepdick » Tue Aug 13, 2019 10:35 pm

Right... BNF is for context-free grammars. e.g Type 2 in the Chomsky hierarchy.

Back to expressive power then.

Are you aware that English is AT LEAST a Type 1 grammar? Which means that if you are trying to formalize all human knowledge in a Type 2 grammar then there will necessarily be things that you can say in English that cannot be expressed in BNF notation.

Recursion mandates a Type 0 grammar.
Last edited by Skepdick on Tue Aug 13, 2019 10:36 pm, edited 1 time in total.

PeteOlcott
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Re: Truth can be understood as math

Post by PeteOlcott » Tue Aug 13, 2019 10:36 pm

Skepdick wrote:
Tue Aug 13, 2019 10:05 pm
PeteOlcott wrote:
Tue Aug 13, 2019 9:45 pm
Self-reference is generally erroneous: "This sentence in not true"
Self-reference is not erroneous. Any textbook implementation of N-th Fibonacci is recursive.
At the other end of the spectrum (but still in the realm of halting/decidable functions) are the Ackermann functions.

Either way - I can't tell what you are bringing to the table that is not equivalent to total functional programming.
I am bringing a sufficient simplification of the notion of formal system
such that Incompleteness can be shown to be a misconception and True(x)
can always be defined:

The entire system that can represent every concept known to
humanity is comprised of a set of Boolean functions that take
Unicode finite string arguments. Although types are required
they are (as everything else) simply implemented as relations
between finite strings.

Skepdick
Posts: 831
Joined: Fri Jun 14, 2019 11:16 am

Re: Truth can be understood as math

Post by Skepdick » Tue Aug 13, 2019 10:37 pm

PeteOlcott wrote:
Tue Aug 13, 2019 10:36 pm
I am bringing a sufficient simplification of the notion of formal system
such that Incompleteness can be shown to be a misconception and True(x)
can always be defined:
But you are paying for it in expressive power!

You are making a trade-off.

PeteOlcott
Posts: 659
Joined: Mon Jul 25, 2016 6:55 pm

Re: Truth can be understood as math

Post by PeteOlcott » Tue Aug 13, 2019 10:39 pm

Skepdick wrote:
Tue Aug 13, 2019 10:35 pm
Right... BNF is for context-free grammars. e.g Type 2 in the Chomsky hierarchy.

Back to expressive power then.

Are you aware that English is AT LEAST a Type 1 grammar? Which means that if you are trying to formalize all human knowledge in a Type 2 grammar then there will necessarily be things that you can say in English that cannot be expressed in BNF notation.
I made this point:
Skepdick wrote:
Tue Aug 13, 2019 10:05 pm
PeteOlcott wrote:
Tue Aug 13, 2019 9:45 pm
BNF defines recursion as relations between finite strings.
I have no idea what that means.
Everything else is beside that point

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