Conceptual Truth can be understood as math

What is the basis for reason? And mathematics?

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PeteOlcott
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Conceptual Truth can be understood as math

Post by PeteOlcott » Mon Aug 12, 2019 6:36 pm

https://plato.stanford.edu/entries/analytic-synthetic/
If we make the analytic versus synthetic distinction this way:

An analytic sentence is any sentence that can be verified as
completely true entirely on the basis of the meaning of its words.


The meaning of the words of every analytic sentence is defined entirely using other words, recursively until every nuance of the meaning of every word has been exhaustively defined in terms of other words.

It turns out that the body of conceptual knowledge already works this way. The only way that we can know that a conceptual expression of language is true is by the full compositional meaning of its words (including its discourse context).

The actual meaning of words comes from the defined stipulated relations that words have to each other. True(x) is merely satisfying one or more of these stipulated relations.

The entire body of conceptual knowledge can be formalized as tuples of finite strings where the first finite string is the named relation to the remaining finite string arguments:
Tuple(">", "5", "3")
Tuple("type", "cat", "animal")
Tuple("type", "animal", "organism") // Now a rule-of-inference has been defined
Tuple("type", "gasoline", "fuel")
Tuple("purchase", "buyer", "seller", "item", "price")

Tuple("→", "p", "q", 0)
Tuple("∧", "p", "q", 0)
X = "It is raining outside"
Y = "I go outside"
Z = "I will get wet"
E = "X ∧ Y → Z"

X
Y
X ∧ Y → Z
------------
∴ Z

Evaluate(E, True(X), True(Y))
∴ "I will get wet"

Copyright 2019 Pete Olcott
Last edited by PeteOlcott on Fri Aug 16, 2019 6:01 pm, edited 15 times in total.


PeteOlcott
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Re: Truth can be understood as math

Post by PeteOlcott » Mon Aug 12, 2019 7:53 pm

I already showed that this is included.

Skepdick
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Re: Truth can be understood as math

Post by Skepdick » Mon Aug 12, 2019 7:57 pm

PeteOlcott wrote:
Mon Aug 12, 2019 7:53 pm
I already showed that this is included.
I am showing that this is what your idea boils down to.

But you are mistaken as to the WHY.

It's not truth that can be understood as math, it's that understanding/reasoning/thinking is computation. The Universal in UTM gives it away.

I have no idea what Truth is...

PeteOlcott
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Re: Truth can be understood as math

Post by PeteOlcott » Mon Aug 12, 2019 8:15 pm

Skepdick wrote:
Mon Aug 12, 2019 7:57 pm
PeteOlcott wrote:
Mon Aug 12, 2019 7:53 pm
I already showed that this is included.
I am showing that this is what your idea boils down to.

But you are mistaken as to the WHY.

It's not truth that can be understood as math, it's that understanding/reasoning/thinking is computation. The Universal in UTM gives it away.

I have no idea what Truth is...
That stipulated relations between finite strings involves type theory is the reason why I invented minimal type theory.
https://www.researchgate.net/publicatio ... y_YACC_BNF

Stipulated relations between expressions of language boil down to type theory simply because IT IS WHAT IT IS.

Truth can be understood as math and math can be understood as computer science.

Truth is simply the satisfaction of stipulated relations between expressions of language that correspond to reality.
Conceptual truth is simply a set of stipulated relations between expressions of language defining the meaning of terms.
Empirical truth is a set of stipulated relations between expressions of language that map to a model of reality.

Skepdick
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Re: Truth can be understood as math

Post by Skepdick » Mon Aug 12, 2019 9:48 pm

PeteOlcott wrote:
Mon Aug 12, 2019 8:15 pm
That stipulated relations between finite strings involves type theory is the reason why I invented minimal type theory.
https://www.researchgate.net/publicatio ... y_YACC_BNF
Can you write a self-hosting compiler for it?

If yes - it's Turing-complete. It's just another programming language.
If no - It's not Turing-complete, so - who cares?
PeteOlcott wrote:
Mon Aug 12, 2019 8:15 pm
Stipulated relations between expressions of language boil down to type theory simply because IT IS WHAT IT IS.
Well, that's the structuralist perspective anyway.

Structuralism is a theory in the philosophy of mathematics that holds that mathematical theories describe structures of mathematical objects. Mathematical objects are exhaustively defined by their place in such structures. Consequently, structuralism maintains that mathematical objects do not possess any intrinsic properties but are defined by their external relations in a system.
PeteOlcott wrote:
Mon Aug 12, 2019 8:15 pm
Truth can be understood as math and math can be understood as computer science.
Sure. Physics too. Everything can be understood as computer science in a computational universe.

The Principle of Computational Equivalence.
And it's the same conclusion as computational trinitarianism.
And it's the same conclusion as the CTD thesis

And if you care about pop-cultures science marketing. The Universe is a computer simulation!
PeteOlcott wrote:
Mon Aug 12, 2019 8:15 pm
Truth is simply the satisfaction of stipulated relations between expressions of language that correspond to reality.
Conceptual truth is simply a set of stipulated relations between expressions of language defining the meaning of terms.
Empirical truth is a set of stipulated relations between expressions of language that map to a model of reality.
1. Model theory
2. Model-dependent realism.

When you amalgamate the Platonists, Nominalists, Structuralists (and all other ists) into a single, coherent framework - you end up with System Theory. Which is the holistic/synthetic extension of computer science.

PeteOlcott
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Re: Truth can be understood as math

Post by PeteOlcott » Mon Aug 12, 2019 10:15 pm

Skepdick wrote:
Mon Aug 12, 2019 9:48 pm
PeteOlcott wrote:
Mon Aug 12, 2019 8:15 pm
That stipulated relations between finite strings involves type theory is the reason why I invented minimal type theory.
https://www.researchgate.net/publicatio ... y_YACC_BNF
Can you write a self-hosting compiler for it?

If yes - it's Turing-complete. It's just another programming language.
If no - It's not Turing-complete, so - who cares?
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.

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

Re: Truth can be understood as math

Post by PeteOlcott » Mon Aug 12, 2019 10:19 pm

Skepdick wrote:
Mon Aug 12, 2019 9:48 pm
PeteOlcott wrote:
Mon Aug 12, 2019 8:15 pm
Stipulated relations between expressions of language boil down to type theory simply because IT IS WHAT IT IS.
Well, that's the structuralist perspective anyway.

Structuralism is a theory in the philosophy of mathematics that holds that mathematical theories describe structures of mathematical objects. Mathematical objects are exhaustively defined by their place in such structures. Consequently, structuralism maintains that mathematical objects do not possess any intrinsic properties but are defined by their external relations in a system.

The only thing that I would change (when we are saying within the boundary of pure concepts) is that intrinsic properties are defined by their relations to other objects within the system.

We only look outside the system when we are looking at physically manifest things in the world.

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

Re: Truth can be understood as math

Post by PeteOlcott » Mon Aug 12, 2019 10:21 pm

Skepdick wrote:
Mon Aug 12, 2019 9:48 pm
PeteOlcott wrote:
Mon Aug 12, 2019 8:15 pm
Truth can be understood as math and math can be understood as computer science.
Sure. Physics too. Everything can be understood as computer science in a computational universe.

The Principle of Computational Equivalence.
And it's the same conclusion as computational trinitarianism.
And it's the same conclusion as the CTD thesis

And if you care about pop-cultures science marketing. The Universe is a computer simulation!

The universe is a simulation, yet, that is off-topic for this post. That is metaphysics and thus not logic and math.

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

Re: Truth can be understood as math

Post by PeteOlcott » Mon Aug 12, 2019 10:22 pm

Skepdick wrote:
Mon Aug 12, 2019 9:48 pm
PeteOlcott wrote:
Mon Aug 12, 2019 8:15 pm
Truth is simply the satisfaction of stipulated relations between expressions of language that correspond to reality.
Conceptual truth is simply a set of stipulated relations between expressions of language defining the meaning of terms.
Empirical truth is a set of stipulated relations between expressions of language that map to a model of reality.
1. Model theory
2. Model-dependent realism.

When you amalgamate the Platonists, Nominalists, Structuralists (and all other ists) into a single, coherent framework - you end up with System Theory. Which is the holistic/synthetic extension of computer science.
OK cool. That makes sense to me.

PeteOlcott
Posts: 730
Joined: Mon Jul 25, 2016 6:55 pm

Re: Truth can be understood as math

Post by PeteOlcott » Tue Aug 13, 2019 1:13 am

PeteOlcott wrote:
Mon Aug 12, 2019 10:22 pm
Skepdick wrote:
Mon Aug 12, 2019 9:48 pm
PeteOlcott wrote:
Mon Aug 12, 2019 8:15 pm
Truth is simply the satisfaction of stipulated relations between expressions of language that correspond to reality.
Conceptual truth is simply a set of stipulated relations between expressions of language defining the meaning of terms.
Empirical truth is a set of stipulated relations between expressions of language that map to a model of reality.
1. Model theory
2. Model-dependent realism.

When you amalgamate the Platonists, Nominalists, Structuralists (and all other ists) into a single, coherent framework - you end up with System Theory. Which is the holistic/synthetic extension of computer science.
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".

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HexHammer
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Location: Denmark

Re: Truth can be understood as math

Post by HexHammer » Tue Aug 13, 2019 2:09 am

PeteOlcott wrote:
Mon Aug 12, 2019 6:36 pm
Truth can be understood as math
Pure nonsense and babble! Then we could just make computers do the lawsuits and sentence.

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Eodnhoj7
Posts: 4940
Joined: Mon Mar 13, 2017 3:18 am

Re: Truth can be understood as math

Post by Eodnhoj7 » Tue Aug 13, 2019 2:19 am

Skepdick wrote:
Mon Aug 12, 2019 9:48 pm
PeteOlcott wrote:
Mon Aug 12, 2019 8:15 pm
That stipulated relations between finite strings involves type theory is the reason why I invented minimal type theory.
https://www.researchgate.net/publicatio ... y_YACC_BNF
Can you write a self-hosting compiler for it?

If yes - it's Turing-complete. It's just another programming language.
If no - It's not Turing-complete, so - who cares?
PeteOlcott wrote:
Mon Aug 12, 2019 8:15 pm
Stipulated relations between expressions of language boil down to type theory simply because IT IS WHAT IT IS.
Well, that's the structuralist perspective anyway.

Structuralism is a theory in the philosophy of mathematics that holds that mathematical theories describe structures of mathematical objects. Mathematical objects are exhaustively defined by their place in such structures. Consequently, structuralism maintains that mathematical objects do not possess any intrinsic properties but are defined by their external relations in a system.
PeteOlcott wrote:
Mon Aug 12, 2019 8:15 pm
Truth can be understood as math and math can be understood as computer science.
Sure. Physics too. Everything can be understood as computer science in a computational universe.

The Principle of Computational Equivalence.
And it's the same conclusion as computational trinitarianism.
And it's the same conclusion as the CTD thesis

And if you care about pop-cultures science marketing. The Universe is a computer simulation!
PeteOlcott wrote:
Mon Aug 12, 2019 8:15 pm
Truth is simply the satisfaction of stipulated relations between expressions of language that correspond to reality.
Conceptual truth is simply a set of stipulated relations between expressions of language defining the meaning of terms.
Empirical truth is a set of stipulated relations between expressions of language that map to a model of reality.
1. Model theory
2. Model-dependent realism.

When you amalgamate the Platonists, Nominalists, Structuralists (and all other ists) into a single, coherent framework - you end up with System Theory. Which is the holistic/synthetic extension of computer science.
You are repeating similar patterns to timeseeker, logic, and univalence.

Skepdick
Posts: 1621
Joined: Fri Jun 14, 2019 11:16 am

Re: Truth can be understood as math

Post by Skepdick » 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.
Last edited by Skepdick on Tue Aug 13, 2019 8:02 am, edited 3 times in total.

Skepdick
Posts: 1621
Joined: Fri Jun 14, 2019 11:16 am

Re: Truth can be understood as math

Post by Skepdick » Tue Aug 13, 2019 7:50 am

Eodnhoj7 wrote:
Tue Aug 13, 2019 2:19 am
You are repeating similar patterns to timeseeker, logic, and univalence.
Imagine that!

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