Conceptual Truth can be understood as math

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 Joined: Mon Jul 25, 2016 6:55 pm
Conceptual Truth can be understood as math
https://plato.stanford.edu/entries/analyticsynthetic/
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 ruleofinference 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
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 ruleofinference 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.

 Posts: 806
 Joined: Mon Jul 25, 2016 6:55 pm
Re: Truth can be understood as math
I already showed that this is included.
Re: Truth can be understood as math
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...

 Posts: 806
 Joined: Mon Jul 25, 2016 6:55 pm
Re: Truth can be understood as math
That stipulated relations between finite strings involves type theory is the reason why I invented minimal type theory.Skepdick wrote: ↑Mon Aug 12, 2019 7:57 pmI 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...
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.
Re: Truth can be understood as math
Can you write a selfhosting compiler for it?PeteOlcott wrote: ↑Mon Aug 12, 2019 8:15 pmThat 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
If yes  it's Turingcomplete. It's just another programming language.
If no  It's not Turingcomplete, so  who cares?
Well, that's the structuralist perspective anyway.PeteOlcott wrote: ↑Mon Aug 12, 2019 8:15 pmStipulated relations between expressions of language boil down to type theory simply because IT IS WHAT IT IS.
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.
Sure. Physics too. Everything can be understood as computer science in a computational universe.PeteOlcott wrote: ↑Mon Aug 12, 2019 8:15 pmTruth can be understood as math and math can be understood as computer science.
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 popcultures science marketing. The Universe is a computer simulation!
1. Model theoryPeteOlcott wrote: ↑Mon Aug 12, 2019 8:15 pmTruth 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.
2. Modeldependent 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.

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 Joined: Mon Jul 25, 2016 6:55 pm
Re: Truth can be understood as math
I have no idea what a selfhosting compiler would be. I already wrote a parser for it.Skepdick wrote: ↑Mon Aug 12, 2019 9:48 pmCan you write a selfhosting compiler for it?PeteOlcott wrote: ↑Mon Aug 12, 2019 8:15 pmThat 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
If yes  it's Turingcomplete. It's just another programming language.
If no  It's not Turingcomplete, so  who cares?
The parser translates expressions into their equivalent XML parse tree.

 Posts: 806
 Joined: Mon Jul 25, 2016 6:55 pm
Re: Truth can be understood as math
Skepdick wrote: ↑Mon Aug 12, 2019 9:48 pmWell, that's the structuralist perspective anyway.PeteOlcott wrote: ↑Mon Aug 12, 2019 8:15 pmStipulated relations between expressions of language boil down to type theory simply because IT IS WHAT IT IS.
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.

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Re: Truth can be understood as math
Skepdick wrote: ↑Mon Aug 12, 2019 9:48 pmSure. Physics too. Everything can be understood as computer science in a computational universe.PeteOlcott wrote: ↑Mon Aug 12, 2019 8:15 pmTruth can be understood as math and math can be understood as computer science.
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 popcultures science marketing. The Universe is a computer simulation!
The universe is a simulation, yet, that is offtopic for this post. That is metaphysics and thus not logic and math.

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Re: Truth can be understood as math
OK cool. That makes sense to me.Skepdick wrote: ↑Mon Aug 12, 2019 9:48 pm1. Model theoryPeteOlcott wrote: ↑Mon Aug 12, 2019 8:15 pmTruth 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.
2. Modeldependent 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.

 Posts: 806
 Joined: Mon Jul 25, 2016 6:55 pm
Re: Truth can be understood as math
PeteOlcott wrote: ↑Mon Aug 12, 2019 10:22 pmI don't know about model depended realism.Skepdick wrote: ↑Mon Aug 12, 2019 9:48 pm1. Model theoryPeteOlcott wrote: ↑Mon Aug 12, 2019 8:15 pmTruth 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.
2. Modeldependent 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.
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".
Re: Truth can be understood as math
Pure nonsense and babble! Then we could just make computers do the lawsuits and sentence.
Re: Truth can be understood as math
You are repeating similar patterns to timeseeker, logic, and univalence.Skepdick wrote: ↑Mon Aug 12, 2019 9:48 pmCan you write a selfhosting compiler for it?PeteOlcott wrote: ↑Mon Aug 12, 2019 8:15 pmThat 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
If yes  it's Turingcomplete. It's just another programming language.
If no  It's not Turingcomplete, so  who cares?
Well, that's the structuralist perspective anyway.PeteOlcott wrote: ↑Mon Aug 12, 2019 8:15 pmStipulated relations between expressions of language boil down to type theory simply because IT IS WHAT IT IS.
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.
Sure. Physics too. Everything can be understood as computer science in a computational universe.PeteOlcott wrote: ↑Mon Aug 12, 2019 8:15 pmTruth can be understood as math and math can be understood as computer science.
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 popcultures science marketing. The Universe is a computer simulation!
1. Model theoryPeteOlcott wrote: ↑Mon Aug 12, 2019 8:15 pmTruth 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.
2. Modeldependent 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.
Re: Truth can be understood as math
A parser/interpreter for MTT written in MTT.PeteOlcott wrote: ↑Mon Aug 12, 2019 10:15 pmI have no idea what a selfhosting compiler would be. I already wrote a parser for it.
The parser translates expressions into their equivalent XML parse tree.
A language that can interpret itself.
This is also connected  because all dualisms are connected. Yes  there are two ways to reason about every system.PeteOlcott wrote: ↑Mon Aug 12, 2019 10:19 pmWe only look outside the system when we are looking at physically manifest things in the world.
Logic and metalogic.
Mathematics and metamathematics.
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.
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