On 12/11/23 11:54 PM, olcott wrote:
On 12/11/2023 10:07 PM, Ross Finlayson wrote:
On Monday, December 11, 2023 at 4:59:55 PM UTC-8, Richard Damon wrote:
On 12/11/23 11:43 AM, olcott wrote:
On 12/11/2023 5:37 AM, Mikko wrote:
On 2023-12-10 15:09:28 +0000, olcott said:
On 12/10/2023 4:10 AM, Mikko wrote:
On 2023-12-09 15:27:08 +0000, olcott said:
On 12/9/2023 3:53 AM, Mikko wrote:
On 2023-12-08 17:10:15 +0000, olcott said:
On 12/8/2023 1:52 AM, Mikko wrote:
On 2023-12-05 19:26:20 +0000, olcott said:
The way that is works for the entire body of analytic
knowledge:
True(x) ≡ (⊢ x)
False(x) ≡ (⊢ ¬x)
Note that those don't define the semantical thruth, which is the >>>>>>>>>>> usual meaning of "true".
∀L ∈ Formal_System ∀x ∈ Language(L)
True(L,x) ≡ (T ⊢ x)
False(L,x) ≡ (T ⊢ ¬x)
Yes they do:
(1) The notions of True and False are inherently semantic.
The usual notions. The expression (T ⊢ x) does not involve any >>>>>>>>> semantics of T, so True as defined above is not a semantic notion. >>>>>>>>>
(2) I am saying that dividing semantics from syntax thus enabling >>>>>>>>>> logic to diverge from the model of the syllogism is a huge
mistake.
A syllogism is a formal inference that does not depend on
semantics.
https://en.wikipedia.org/wiki/Syllogism#Basic_structure
It always depends on defined sets providing its semantics as
Categorical propositions
https://en.wikipedia.org/wiki/Categorical_proposition
Not for purposes that do not need any semantics.
Mikko
*Yes for all purposes. I am changing logic into correct reasoning* >>>>>>
The only way that we can tell the the principle of explosion
is nonsense is by plugging semantics into it and then see
that this semantics is not semantically carried though.
That does not show that the principle of explosion is nonsense.
Ross Finlayson said that the principle of explosion cannot exist in
relevance logic, thus making my point.
Ye, *IF* you accept the logical limitations of "Relevence Logic", you
can avoid the problems of the Principle of Explosion. But then you need
to accept that you logic system is "weaker" as there will be statements
that can not be proven in it (or even stated) then in "Classical" logic. >>>>
The principle of explosion "proves" nonsense when semantics are
required.
(a) Cat are dogs
(b) Cats are not dogs
(c) Therefore the Moon is made from green cheese
But
The cow jumped over the Moon and The cow did not jump over the Moon >>>>>> therefore the Moon is made from green cheese.
Have you ever met the cow that both jumped over the Moon and did not >>>>> jump over the Moon?
It has always been the case that contradictions only proof falsehood.
The principle of explosion violates
https://en.wikipedia.org/wiki/Law_of_noncontradiction
No, Contradictions prove that something is incorrect. If you get to a
Contradicition in your logic, you KNOW that something prior was
incorreect (or your logical system is just inherently broken)
The correct way to process the principle of explosion is:
(A ∧ ¬A) ⊢ False
That does not process the principle of explosion.
That is what a contradiction actually semantically entails.
People that only learn these things by rote never notice
errors that are discerned by the coherent philosophical foundation.
Nope.
Your never ever learned attitude means you just naturally speak
incorrect statements, which when you repeat them after being told
otherwise, make you into a habitual patholgocial liar.
You can't refute climate change because your native tongue is lies an
illogic, so of course you don't know how to show that.
One way to interprete the situation where False is proven is that
instead of the usual two truth values (False and True) there is only >>>>> one that has two names, i.e., False is the same as True.
Nonsense gibberish. Bivalent formal systems inherently have a set of
immutable properties. This is not merely a game, unless we formalize
True(L,x) defeating Tarski dangerous lies will cause climate change
to destroy all life on Earth by the time we hit +8C as early as 2100.
https://phys.org/news/2023-12-million-year-history-carbon-dioxide-comfort.html?fbclid=IwAR3paozWIzEXvRp0swQVLRO8cbjXADWmSNZw8r5w41ULyYElSxNLqccDxXU
So, you don't understand that "Bivalent" isn't the only type of Logic?
or Formal System?
What does Tarski have to do with disproving Lies?
Tarski says that there are SOME statements which we can not determine
their Truth Value, he does NOTHING to limit the ability to show that
some things are just false.
That you think it does, just shows how little you understand about what
you pontificate on.
Then every
True sentence is False and every False sentence is True. If there
are no other truth values then every sentence is both True and False. >>>>> Not very useful but coherent.
Mikko
Everything Zen? Yes, I think so.
Actually a bunch of times here I've also written little extensions to
classical logic
that just leave out material implication and ex falso quodlibet.
It's not like you need it for free will or speculation of any sort,
absurd or not,
you can have your own private language of things, though it results not
equi-interpretability as far as there's interpretability.
Mostly this was recently when it was for "D.C.'s linear editor of
syllogistic
constructs, what D.C. says", where long ago I put down material
implication
as flawed, that a model from the universe of models is different than
a bit-set
of state-flags.
Or, you know, "chucks" and "jigs", bits and their states.
You perfectly agree with my assessment of the two key issues of
classical logic. When we encode the entire body of human knowledge using Higher Order Logic such that the meaning of the terms is fully
integrated into this logic using a knowledge ontology then it seems that
we have a logic much more powerful than classical logic that excludes
the above two issues.
When we hypothesize that all human knowledge is formalized syntactically
then provable does entail true. To simplify the idea of a knowledge
ontology we can call this a tree of knowledge arranged as an inheritance hierarchy of sound deductions. We don't have to build this tree we
merely imagine that it exists as the architecture of the notion of
True(L,x).
Nope. One point, by restricting the domain of your logic, you need to
eliminate much of the "knowledge" you had, as it was based on logic that
you have now prohibited.
Remember, every statement shown to be true in a Formal System is based
on the properties of that Formal System, including the rules of logic
that it used.
The "Logic" isn't more powerful, as it can, by definition, do less
things. Perhaps you can claim that the meaning of being Known is "More Powerful", as what is known has passed a stronger test, but if that
comes at the cost of having to unknow a lot of what is known, is that
what you want?
Note, your statement:
When we hypothesize that all human knowledge is formalized syntactically
then provable does entail true.
Just isn't true, as formalizing knowledge, even all of it, doesn't, in
itself, change the definition of "True".
It is a well accepted given that we don't, and can't, know everything
that is actually true, because Truth is independent of Knowledge even if Knowledge is made dependent on Truth.
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