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Eliminating decision problem undecidability
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olcott
Mar 12, 2021, 4:00:00 PM3/12/21
to
When we hypothesize that the body of analytical knowledge is entirely
comprised of the following two types of expressions of language:
(1) Elementary Theorems that are defined to be true in a way similar to
Curry: “an elementary theorem is an elementary statement which is
true...” (Curry:1977:45)
(2) Derived Consequences that result from applying truth preserving
operations to Elementary Theorems and/or Derived Consequences.
Curry, Haskell 1977. Foundations of Mathematical Logic. New York: Dover
Publications. http://www.liarparadox.org/Haskell_Curry_45.pdf
then undecidable decision problems cease to exist. Every input that
previously proved undecidability is now simply construed as untrue.
The above can also be applied to natural language semantics. That dogs
are a type of animal can be construed as an [Elementary Theorem] of
natural language.
[Derived Consequences] of natural language are the result of applying
sound deductive inference to Elementary Theorems and/or Derived
Consequences of natural language.
--
Copyright 2021 Pete Olcott
"Great spirits have always encountered violent opposition from mediocre
minds." Einstein
comprised of the following two types of expressions of language:
(1) Elementary Theorems that are defined to be true in a way similar to
Curry: “an elementary theorem is an elementary statement which is
true...” (Curry:1977:45)
(2) Derived Consequences that result from applying truth preserving
operations to Elementary Theorems and/or Derived Consequences.
Curry, Haskell 1977. Foundations of Mathematical Logic. New York: Dover
Publications. http://www.liarparadox.org/Haskell_Curry_45.pdf
then undecidable decision problems cease to exist. Every input that
previously proved undecidability is now simply construed as untrue.
The above can also be applied to natural language semantics. That dogs
are a type of animal can be construed as an [Elementary Theorem] of
natural language.
[Derived Consequences] of natural language are the result of applying
sound deductive inference to Elementary Theorems and/or Derived
Consequences of natural language.
--
Copyright 2021 Pete Olcott
"Great spirits have always encountered violent opposition from mediocre
minds." Einstein
olcott
Mar 12, 2021, 4:58:48 PM3/12/21
to
On 3/12/2021 2:59 PM, olcott wrote:
> When we hypothesize that the body of analytical knowledge is entirely
> comprised of the following two types of expressions of language:
>
> (1) Elementary Theorems that are defined to be true in a way similar to
> Curry: “an elementary theorem is an elementary statement which is
> true...” (Curry:1977:45)
>
> (2) Derived Consequences that result from applying truth preserving
> operations to Elementary Theorems and/or Derived Consequences.
>
> Curry, Haskell 1977. Foundations of Mathematical Logic. New York: Dover
> Publications. http://www.liarparadox.org/Haskell_Curry_45.pdf
>
> then undecidable decision problems cease to exist. Every input that
> previously proved undecidability is now simply construed as untrue.
>
> The above can also be applied to natural language semantics. That dogs
> are a type of animal can be construed as an [Elementary Theorem] of
> natural language.
>
> [Derived Consequences] of natural language are the result of applying
> sound deductive inference to Elementary Theorems and/or Derived
> Consequences of natural language.
>
When any expression of language and its negation are untrue within the
> When we hypothesize that the body of analytical knowledge is entirely
> comprised of the following two types of expressions of language:
>
> (1) Elementary Theorems that are defined to be true in a way similar to
> Curry: “an elementary theorem is an elementary statement which is
> true...” (Curry:1977:45)
>
> (2) Derived Consequences that result from applying truth preserving
> operations to Elementary Theorems and/or Derived Consequences.
>
> Curry, Haskell 1977. Foundations of Mathematical Logic. New York: Dover
> Publications. http://www.liarparadox.org/Haskell_Curry_45.pdf
>
> then undecidable decision problems cease to exist. Every input that
> previously proved undecidability is now simply construed as untrue.
>
> The above can also be applied to natural language semantics. That dogs
> are a type of animal can be construed as an [Elementary Theorem] of
> natural language.
>
> [Derived Consequences] of natural language are the result of applying
> sound deductive inference to Elementary Theorems and/or Derived
> Consequences of natural language.
>
above system, then this expression of language is not a truth bearer.
Richard Fateman
Mar 15, 2021, 5:24:40 PM3/15/21
to
Since there are undecidable problems in computer algebra system having to do with zero-equivalence,
for example, see
https://en.wikipedia.org/wiki/Richardson%27s_theorem
your conclusion is false.
From this one can conclude that at least one of your premises is false, and/or your method of
deduction is flawed.
RJF
for example, see
https://en.wikipedia.org/wiki/Richardson%27s_theorem
your conclusion is false.
From this one can conclude that at least one of your premises is false, and/or your method of
deduction is flawed.
RJF
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