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Absolute Logical Truth Has No Foundations But Random Occurence
Posted: Fri Jan 24, 2025 7:02 am
by Eodnhoj7
If a tautology is absolute within the context of certain logical systems, and these absolute truths very with the logical system applied, does this necessitate these absolute truths are purely relative to specific logical structures where the logical structure applied is strictly a choice thus making absolute truth simultaneously relative and paradoxical, further leading to the conclusion that absolute logical truth is a byproduct of randomness and has no real foundations other than occurence?
Re: Absolute Logical Truth Has No Foundations But Random Occurence
Posted: Fri Feb 14, 2025 3:12 pm
by alan1000
I'm sure you are right.
Re: Absolute Logical Truth Has No Foundations But Random Occurence
Posted: Sat Feb 15, 2025 2:05 am
by Impenitent
could be wrong
randomly
-Imp
Re: Absolute Logical Truth Has No Foundations But Random Occurence
Posted: Sat Feb 15, 2025 2:36 am
by Noax
Eodnhoj7 wrote: ↑Fri Jan 24, 2025 7:02 am... is absolute within the context of ...
Conditionally absolute. I guess if you start with a contradiction, contradiction follows.
You also pulled a bait & switch, starting with 'absolute within a context' and switching to
these absolute truths
You never posited an absolute truth. You posited one confined to a context (said contradiction)
Re: Absolute Logical Truth Has No Foundations But Random Occurence
Posted: Sat Feb 15, 2025 4:03 am
by Eodnhoj7
Noax wrote: ↑Sat Feb 15, 2025 2:36 am
Eodnhoj7 wrote: ↑Fri Jan 24, 2025 7:02 am... is absolute within the context of ...
Conditionally absolute. I guess if you start with a contradiction, contradiction follows.
You also pulled a bait & switch, starting with 'absolute within a context' and switching to
these absolute truths
You never posited an absolute truth. You posited one confined to a context (said contradiction)
No, quote the whole sentence...not three words...I posited absolute truth purely exists within context and "these absolute truths" is in reference to what exists as purely within context as the previous sentence states.
Absolute truth is purely contextual as it is dependent upon a framework of interpretation and this framework is neither fixed as a set universal standard by which to interpret reality nor determined by any law as to what framework is chosen.
The framework by which absolute truth exists is a context.
What is absolute in one framework is not absolute in another, thus making absolute truth relative and a paradox ensues.
Re: Absolute Logical Truth Has No Foundations But Random Occurence
Posted: Sat Mar 08, 2025 7:42 pm
by roydop
Re: Absolute Logical Truth Has No Foundations But Random Occurence
Posted: Wed Mar 19, 2025 3:23 am
by tsda
Eodnhoj7 wrote: ↑Fri Jan 24, 2025 7:02 am
If a tautology is absolute within the context of certain logical systems, and these absolute truths very with the logical system applied, does this necessitate these absolute truths are purely relative to specific logical structures where the logical structure applied is strictly a choice thus making absolute truth simultaneously relative and paradoxical, further leading to the conclusion that absolute logical truth is a byproduct of randomness and has no real foundations other than occurence?
A tautology is a statement that is true in all models of a given logical system. For example, in classical logic, "A or not A" (the law of excluded middle) is always true.
However, different logical systems (e.g., classical, intuitionistic, paraconsistent logics) may define "absolute" truths differently. What is a tautology in one system might not hold in another.
Re: Absolute Logical Truth Has No Foundations But Random Occurence
Posted: Fri Mar 21, 2025 12:59 am
by Impenitent
do untied shoelaces make a loose tautology?
-Imp
Re: Absolute Logical Truth Has No Foundations But Random Occurence
Posted: Fri Mar 21, 2025 5:18 am
by godelian
Eodnhoj7 wrote: ↑Fri Jan 24, 2025 7:02 am
If a tautology is absolute within the context of certain logical systems, and these absolute truths very with the logical system applied, does this necessitate these absolute truths are purely relative to specific logical structures where the logical structure applied is strictly a choice
Yes, in model theory, truth is an interpretation that makes a particular chosen logic sentence true:
https://plato.stanford.edu/entries/model-theory/
1. Basic notions of model theory
Sometimes we write or speak a sentence S that expresses nothing either true or false, because some crucial information is missing about what the words mean. If we go on to add this information, so that S comes to express a true or false statement, we are said to interpret S, and the added information is called an interpretation of S. If the interpretation I happens to make S state something true, we say that I is a model of S, or that I satisfies S, in symbols ‘I ⊨ S’. Another way of saying that I is a model of S is to say that S is true in I, and so we have the notion of model-theoretic truth, which is truth in a particular interpretation.
Without choice of logic sentence, there is nothing to interpret, and therefore there is no truth possible. Hence, absolute truth does not exist. It is always relative to a context.
Eodnhoj7 wrote: ↑Fri Jan 24, 2025 7:02 am
thus making absolute truth simultaneously relative and paradoxical
There is no absolute truth. Truth always requires a choice first, which will be the context of the truth.
Eodnhoj7 wrote: ↑Fri Jan 24, 2025 7:02 am
further leading to the conclusion that absolute logical truth is a byproduct of randomness and has no real foundations other than occurence?
In absence of a context, there is no truth possible, not even a random one.
Re: Absolute Logical Truth Has No Foundations But Random Occurence
Posted: Tue Apr 01, 2025 8:39 am
by Eodnhoj7
tsda wrote: ↑Wed Mar 19, 2025 3:23 am
Eodnhoj7 wrote: ↑Fri Jan 24, 2025 7:02 am
If a tautology is absolute within the context of certain logical systems, and these absolute truths very with the logical system applied, does this necessitate these absolute truths are purely relative to specific logical structures where the logical structure applied is strictly a choice thus making absolute truth simultaneously relative and paradoxical, further leading to the conclusion that absolute logical truth is a byproduct of randomness and has no real foundations other than occurence?
A tautology is a statement that is true in all models of a given logical system. For example, in classical logic, "A or not A" (the law of excluded middle) is always true.
However, different logical systems (e.g., classical, intuitionistic, paraconsistent logics) may define "absolute" truths differently. What is a tautology in one system might not hold in another.
Thus absolute truth is relative to a framework and as such makes absolute truth relativistic and a paradox ensues. Now if all absolute truth is relativistic to structure then this relativistic nature of truth is absolute as framework is the constant quality that exists across all truths...and another paradox ensues.
Re: Absolute Logical Truth Has No Foundations But Random Occurence
Posted: Tue Apr 01, 2025 8:45 am
by Eodnhoj7
godelian wrote: ↑Fri Mar 21, 2025 5:18 am
Eodnhoj7 wrote: ↑Fri Jan 24, 2025 7:02 am
If a tautology is absolute within the context of certain logical systems, and these absolute truths very with the logical system applied, does this necessitate these absolute truths are purely relative to specific logical structures where the logical structure applied is strictly a choice
Yes, in model theory, truth is an interpretation that makes a particular chosen logic sentence true:
https://plato.stanford.edu/entries/model-theory/
1. Basic notions of model theory
Sometimes we write or speak a sentence S that expresses nothing either true or false, because some crucial information is missing about what the words mean. If we go on to add this information, so that S comes to express a true or false statement, we are said to interpret S, and the added information is called an interpretation of S. If the interpretation I happens to make S state something true, we say that I is a model of S, or that I satisfies S, in symbols ‘I ⊨ S’. Another way of saying that I is a model of S is to say that S is true in I, and so we have the notion of model-theoretic truth, which is truth in a particular interpretation.
Without choice of logic sentence, there is nothing to interpret, and therefore there is no truth possible. Hence, absolute truth does not exist. It is always relative to a context.
Eodnhoj7 wrote: ↑Fri Jan 24, 2025 7:02 am
thus making absolute truth simultaneously relative and paradoxical
There is no absolute truth. Truth always requires a choice first, which will be the context of the truth.
Eodnhoj7 wrote: ↑Fri Jan 24, 2025 7:02 am
further leading to the conclusion that absolute logical truth is a byproduct of randomness and has no real foundations other than occurence?
In absence of a context, there is no truth possible, not even a random one.
If all truth is relative to context, thus true in some contexts and false in others, and "all truth is relative to context" is a context than by default it defeats itself as sometimes "all truth is relative to context" is true and other times it is false.
If "there is no absolute truth" is not an absolute truth than sometimes it is false. If "there is no absolute truth" is an absolute truth than an contradiction occurs...and anything goes.
Re: Absolute Logical Truth Has No Foundations But Random Occurence
Posted: Tue Apr 01, 2025 11:54 am
by godelian
Eodnhoj7 wrote: ↑Tue Apr 01, 2025 8:45 am
"there is no absolute truth" is not an absolute truth
Sounds true.
ChatGPT: In model theory, is truth possible without a theory?
In model theory, truth is always defined relative to a structure (or model) and a formal language. This means that truth in the model-theoretic sense is not an absolute notion but rather something that depends on the existence of a theory or, at minimum, a structure interpreting the relevant statements.
If by "truth" you mean "semantic truth" (i.e., whether a statement holds in a given model), then truth is only meaningful in the context of a structure that provides interpretations for symbols. Without a structure, statements are just syntactic objects with no assigned meaning.
If by "truth" you mean something more abstract, such as an objective or metaphysical truth independent of formal systems, then model theory does not directly address this kind of truth. It only provides a framework for discussing truth within a mathematical system.
Would you like to discuss this in a more philosophical or technical sense?
You are saying the following within a particular context:
"there is no absolute truth" is not an absolute truth.
Say that you are saying this within the context of first-order logic (FOL), then it means:
"there is no absolute truth in FOL" is not an absolute, i .e. context -free truth.
From within FOL, we don't know how things work in other logics. So, it is indeed not an absolute, i.e. context-free truth.
Re: Absolute Logical Truth Has No Foundations But Random Occurence
Posted: Tue Apr 01, 2025 5:38 pm
by Eodnhoj7
godelian wrote: ↑Tue Apr 01, 2025 11:54 am
Eodnhoj7 wrote: ↑Tue Apr 01, 2025 8:45 am
"there is no absolute truth" is not an absolute truth
Sounds true.
ChatGPT: In model theory, is truth possible without a theory?
In model theory, truth is always defined relative to a structure (or model) and a formal language. This means that truth in the model-theoretic sense is not an absolute notion but rather something that depends on the existence of a theory or, at minimum, a structure interpreting the relevant statements.
If by "truth" you mean "semantic truth" (i.e., whether a statement holds in a given model), then truth is only meaningful in the context of a structure that provides interpretations for symbols. Without a structure, statements are just syntactic objects with no assigned meaning.
If by "truth" you mean something more abstract, such as an objective or metaphysical truth independent of formal systems, then model theory does not directly address this kind of truth. It only provides a framework for discussing truth within a mathematical system.
Would you like to discuss this in a more philosophical or technical sense?
You are saying the following within a particular context:
"there is no absolute truth" is not an absolute truth.
Say that you are saying this within the context of first-order logic (FOL), then it means:
"there is no absolute truth in FOL" is not an absolute, i .e. context -free truth.
From within FOL, we don't know how things work in other logics. So, it is indeed not an absolute, i.e. context-free truth.
The necessity of context observes a thing is true only within a given context and false under another. If I say "there is no absolute truth" this necessitates it as true in one context and false under another.
"There is no absolute truth" is false under its own context.
Dually if all there is is context than all is one under context and then there is no context to define context as context is not distinct from itself to provide further context. If all contexts are completely different, completely different, than there can be only one context as there is nothing to share between things to say context is universal.
Re: Absolute Logical Truth Has No Foundations But Random Occurence
Posted: Tue Apr 01, 2025 6:15 pm
by godelian
Eodnhoj7 wrote: ↑Tue Apr 01, 2025 5:38 pm
"There is no absolute truth" is false under its own context.
What is this context?
Re: Absolute Logical Truth Has No Foundations But Random Occurence
Posted: Tue Apr 01, 2025 6:42 pm
by godelian
Eodnhoj7 wrote: ↑Tue Apr 01, 2025 5:38 pm
If
all contexts are completely different
Expressed in the context of first-order logic, the following sentence s would be true in every context M:
∃s∀M (M⊨s)
So, the sentence s would be an absolute truth.
However, it is not possible to quantify in first-order logic over every context M. The term "
all contexts" (∀M) is therefore not supported.
This is a problem similar to the problem of trying to deal with "the set of all sets" in ZFC set theory. Such set would be in violation of the axiom of foundation and the axiom of separation.
You would need a context in which the notion of "all contexts" is definable. Such context may not exist.