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On 6/3/2024 2:19 AM, Mikko wrote:No. To assume something does not make it true and does not make usOn 2024-06-02 13:01:15 +0000, olcott said:(1) We know that "Not all lemons are yellow", as it has been assumed to be true.
On 6/2/2024 2:29 AM, Mikko wrote:Those laws don't prevent from assuming p. Those laws don't preventOn 2024-06-01 15:41:46 +0000, olcott said:*Three laws of logic apply to all propositions*
On 6/1/2024 2:32 AM, Mikko wrote:The inconsistencies are not inconsistencies of logic. No logic canOn 2024-05-31 15:47:31 +0000, olcott said:The ONLY THING that can ever be correctly derived from a contradiction
On 5/31/2024 2:17 AM, Mikko wrote:Principle of exposion is empirically true. It is not a problem ofOn 2024-05-30 13:43:11 +0000, olcott said:*You removed the relevant context that the principle of explosion*
On 5/30/2024 1:52 AM, Mikko wrote:No, that has not been shown. Classical logic shows that no sentenceOn 2024-05-29 13:31:31 +0000, olcott said:What has now been shown is that L is true if, and only if, it is
On 5/29/2024 3:25 AM, Mikko wrote:It does not expose any flaw in classical logic. Flaws in yourOn 2024-05-28 14:59:30 +0000, olcott said:It correctly determines that there is a cycle in the directed graph
On 5/28/2024 1:59 AM, Mikko wrote:Prolog does not reject LP = not(true(LP)). It can accept it asOn 2024-05-27 14:34:14 +0000, olcott said:That Prolog construes any expression having the same structure as the
?- LP = not(true(LP)).The words "not" and "true" of Prolog are meaningful in some contexts
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
In other words Prolog has detected a cycle in the directed graph of the
evaluation sequence of the structure of the Liar Paradox. Experts seem
to think that Prolog is taking "not" and "true" as meaningless and is
only evaluating the structure of the expression.
but not above. The word "true" is meaningful only when it has no arguments.
Liar Paradox as having a cycle in the directed graph of its evaluation
sequence already completely proves my point. In other words Prolog
is saying that there is something wrong with the expression and it must
be rejected.
You could tryYes exactly. If I knew that Prolog did this then I would not have
?- LP = not(true(LP), true(LP).
or
?- LP = not(true(LP), not(true(LP)).
The predicate unify_with_occurs_check checks whether the resulting
sructure is acyclic because that is its purpose. Whether a simple
created Minimal Type Theory that does this same thing. That I did
create MTT that does do this same thing makes my understanding much
deeper.
syntactically valid. Thaat unify_with_occurs_check(LP, not(true(LP))
fails does not mean anything except when it is used, and then it
does not reject but simplu evaluates to false, just like 1 = 2
is false but not erroneous.
of the evaluation sequence of the expression, which is like an
infinite loop in a program.
You can understand this or fail to understand this, disagreement is
incorrect. If you have any disagreement then please back up your
claims with proof.
It is relevant to sci.logic in that it exposes fundamental flawsNot necessarily. What happes depends on the implementation and on whatunification like LP = not(true(LP)) does same is implementationISO Prolog implementations have the built-in predicate
dependent as Prolog rules permit but do not require that. In a
typical implementation a simple unification does not check for
cycles.
unify_with_occurs_check/2 for sound unification
https://en.wikipedia.org/wiki/Occurs_check#Sound_unification
Alternatively such expressions crash or remain stuck in infinite loops.
you do with such structures. You already saw that your
?- LP = not(true(LP)).
does not crash and does not remain stuck in infinite loop.
If you want to talk nore about Prolog do it in comp.lang.prolog.Anyway, none of this is relevant to the topic of this thread or
topics of sci.logic.
with classical logic.
understanding of calssical logics are already sufficiently known.
false. Since L must be one or the other, it is both.
is true if and only if it is false. If you assumoe otherwise then
your assumption is false.
*of classical logic is shown to be the source of the issue*
classical logic. You have not shown that any paraconsistent system,
where principle of exposion does not apply, is any better.
is FALSE. People taking classical logic as infallible by simply ignoring
its inconsistencies are inherently incorrect.
prevent you from assuming an inconsistency but then it is your
inconsistency.
People taking classical logic as infallible do so because no situation
where it is wrong has been observed.
¬(p ∧ ¬p) Law of non-contradiction
(p ∨ ¬p) Law of excluded middle
p = p Law of identity
from assuming ¬p. Assuming both is assuming something false.
(2) We know that "All lemons are yellow", as it has been assumed to be true.
(3) Therefore, the two-part statement "All lemons are yellow or unicorns exist" must also be true, since the first part of the statement ("All lemons are yellow") has already been assumed, and the use of "or" means that if even one part of the statement is true, the statement as a whole must be true as well.No, it need not be true as a mere assumption does change the color of lemons.
There is nothing about the color of lemons that has anything to doPeople who have studied semantics and logic have found that more
with the existence of unicorns, thus the root cause of the huge mistake
of classical logic is to allow semantics to be divorced from logic.
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