— Impossible Worlds (Stanford Encyclopaedia, my bolding) — Banno

That was a very apt cite.

I said it is not recognized in philosophy. Or Philosophy, for the proper name. The words "logically impossible" is never formally accepted as epistemic terms.

However, you might be thinking of "logical possibility" which the likes of Chalmers are prone to use. But we can't state the opposite: logically impossible. It's nonsense.

Contradictions are not the same as logically impossible.

Here's an excerpt from a book which I did not purchase:

I don't know what your point is. But "logical impossibility" is a term used by philosophers and logicians, with a clear meaning.

I said it is not recognized in philosophy. Or Philosophy, for the proper name. The words "logically impossible" is never formally accepted as epistemic terms. — L'éléphant

Impossible worlds is the exact same concept as logically impossible.
[logically impossible] is contrast wth [physically impossible] and
covers every expression of language that is proved to be impossible
entirely on the basis of the meaning of its words.

There are zero possible worlds where someone can correctly draw a
a square circle.

Here's an excerpt from a book which I did not purchase: — L'éléphant

Logical possibilities are all the statements that cannot be proven false entirely on the basis of the meaning of their words. Here is a very strange logical possibility.

Although this is attributed to Bertrand Russell, I remember creating this myself in 1993 and then reading that Bert came up with the same thing. Bert's version lacks the key detail that this creation event must have been instantaneous otherwise subconsious memory would have a record of it.

https://neurochatter.com/continuity-of-self-was-the-world-put-into-place-five-minutes-ago/#:~:text=The%20%E2%80%9Cfive%20minute%20hypothesis%E2%80%9D%20by,into%20existence%20five%20minutes%20ago.

Please refer to modal logic. Don't focus on the symbols, rather focus on the explanation provided by the writer for why using the terminology "logically impossible" in propositions is misguided.

The concept of contingent content
Every proposition satisfies both the Law of the Excluded Middle and the Law of Noncontradiction. The first says that every proposition is either true or false, that there is no 'middle' or third truth-value. The second law says that no proposition is both true and false. Together these two laws say that the properties of truth and falsehood are mutually exclusive and jointly exhaustive of the entire class of propositions.

Corresponding to each of these two laws just cited we can state two analogues for modal status. In the first place we can say that every proposition is either contingent or noncontingent. And in the second, we can say that no proposition is both contingent and noncontingent. The two properties, contingency and noncontingency, are mutually exclusive and jointly exhaustive of the class of propositions.

Between contingency and noncontingency there is no 'middle' or third category. Contingency and noncontingency, like truth and falsehood, do not come in degrees. No proposition is 'half contingent' or 'three-quarters noncontingent5 or any other fractional measure, just as no proposition is half or three-quarters true (or false). No contingent proposition is more contingent or less contingent than any other contingent proposition; and no noncontingent proposition is more noncontingent or less noncontingent than any other noncontingent proposition.

None of this means, however, that we cannot talk cogently of one proposition being closer to being necessarily true than another. To explicate this latter concept we shall introduce the concept of the contingent content of a proposition. And to do this we begin by noticing a curious fact about necessary truths.

You present a quote that doesn't support your claim, and without references. :meh:

Here's the Ngram.

Because the Liar Paradox is self-contradictory it cannot be included in formal systems
that require all expressions to be either satisfiable or their negation satisfiable.

...14 Every epistemological antinomy can likewise be used for a similar undecidability proof...
(Gödel 1931:43-44)

Antinomy
...term often used in logic and epistemology, when describing a paradox or unresolvable contradiction. https://www.newworldencyclopedia.org/entry/Antinomy

Thus when we plug the formalized {epistemological antinomy} of the Liar Paradox into
a similar undecidability proof, we find that this semantically unsound expression "proves"
that the formal system that contains it is incomplete.

The Liar is a bit more involved than just that. There are a wide range of formalisations.

Gödel does not use the liar. The sentence of interest is not "This sentence is not true" but "This sentence cannot be proved".

But we've covered this, earlier.

↪PL Olcott The Liar is a bit more involved than just that. There are a wide range of formalisations. — Banno

I created Minimal Type Theory that spits out the directed graph of its own WFF.

This is the only system that I know of where the Liar Paradox can be formalized correctly,
every other system cheats and knowingly formalizes self-reference incorrectly.
https://www.researchgate.net/publication/331859461_Minimal_Type_Theory_YACC_BNF

LP := ~True(LP)

Gödel does not use the liar. The sentence of interest is not "This sentence is not true" but "This sentence cannot be proved". — Banno

G := (F ⊬ G)

Prolog rejects both of the above expressions as semantically unsound.
It detects that same cycle in their directed graph that I call pathological
self reference.

WFF = well formed formula.

I am not talking about squaring a circle I am talking about drawing a circle that <is> a square thus not a circle. It must be in the same two dimensional plane.

"all points on a two dimensional surface that are equidistant from the center" and these exact same points form four straight sides of equal length in the same two dimensional plane. — PL Olcott

When you started off in your OP, you wanted to make a statement that is necessarily false. Which is fine. But now I think this whole thread is just nonsense.
Do the properties of a circle hold necessarily? And do the properties of a square hold necessarily? Then it goes without saying that the circle and square have asymmetrical relations. It is necessarily false that a circle can be drawn as a square.

Thus when we plug the formalized {epistemological antinomy} of the Liar Paradox into
a similar undecidability proof, we find that this semantically unsound expression "proves"
that the formal system that contains it is incomplete. — PL Olcott

Thank god that "incompleteness" is not accepted as one of the logical status of a statement.

Thank god that "incompleteness" is not accepted as one of the logical status of a statement. — L'éléphant

Incompleteness <is> accepted when any WFF cannot be either proved or refuted within a formal system EVEN IF it cannot be proved or refuted in this formal system because it <is> self-contradictory in this formal system. That seems to be its huge error.

Incompleteness <is> accepted when any WFF cannot be either proved or refuted within a formal system EVEN IF it cannot be proved or refuted in this formal system because it <is> self-contradictory in this formal system. That seems to be its huge error. — PL Olcott

If that happens, we don't judge it as incomplete -- we judge it as contingently false in this system, but not in all possible worlds. A proposition is non-contingent only if, necessarily, it cannot be the case (that is, in all possible worlds, it is false).

Self-contradictory statements are not truth bearers.

If that happens, we don't judge it as incomplete -- we judge it as contingently false in this system, but not in all possible worlds. A proposition is non-contingent only if, necessarily, it cannot be the case (that is, in all possible worlds, it is false). — L'éléphant

That is factually incorrect. As soon as any WFF of any formal system is determined to neither be provable nor refutable in that formal system then that formal system <is> determined to be incomplete.

Gödel himself said that this does include self-contradictory expressions.

...14 Every epistemological antinomy can likewise be used for a similar undecidability proof...
(Gödel 1931:43-44)

Antinomy
...term often used in logic and epistemology, when describing a paradox or unresolvable contradiction. https://www.newworldencyclopedia.org/entry/Antinomy

That is factually incorrect. As soon as any WFF of any formal system is determined to neither be provable nor refutable in that formal system then that formal system <is> determined to be incomplete. — PL Olcott

You're applying something like Gödel's theorem to something like modal logic. No wonder we can't understand each other. Logic uses a lot of propositions that aren't theorems. The "logical status" of a statement does not need a "complete theorem" in order to be .. a logical conclusion.

In effect, we aren't claiming a "complete theorem" when we say that, to say "It is raining and it is not raining at the same time" is a contradictory statement. We also aren't claiming a complete theorem, or even an incomplete theorem when we say that "if Paul is older than Tom, then Paul must have been born earlier than Tom".

Think. Do you really need a theorem to say that a square can't be drawn like a circle? No. While it is true that the definition of the square and the definition of the circle are both theorems themselves, when we make a determination that a circle cannot be drawn like a square, our own statement is not, or does not require a formulation of a theorem itself. We make a decision based on the existing theorems.

You're applying something like Gödel's theorem to something like modal logic. No wonder we can't understand each other. Logic uses a lot of propositions that aren't theorems. The "logical status" of a statement does not need a "complete theorem" in order to be .. a logical conclusion. — L'éléphant

Mathematical Incompleteness determines that a formal system <is> incomplete when-so-ever
WFF x of the language L of a formal system F can neither be proved nor refuted in F.
Tarski even uses the actual Liar Paradox as the key basis of his whole Undefinability Theorem:
(3) x ∉ Provable if and only if x ∈ True. https://liarparadox.org/Tarski_275_276.pdf

Here is the Liar Paradox as a WFF of Minimal Type Theory LP := ~True(LP)
The ":=" operator is like macro substitution and provides the means for an expression to directly refer to its actual self.

Prolog rejects the same expression when encoded in Prolog:
?- LP = not(true(LP)).
LP = not(true(LP)).

?- unify_with_occurs_check(LP, not(true(LP))).
false.

Yet mathematical incompleteness still blames the formal system and not the semantically unsound expression.

For people trying to feel smart about arguing that you can square a circle — Vaskane

I have never been talking about that. I am talking about making single geometric object that <is> entirely a square (and thus not a circle) and simultaneously <is> entirely a circle (thus not a square) in the same two-dimensional plane. I wanted to define a task that even God could not do.

I wanted to define a task that even God could not do. — PL Olcott

But your thread is called: 'Requiring the logically impossible is always an invalid requirement'.

According to this premise, why should we demand from 'God' to make a single geometric object that is entirely a square and, simultaneously, is entirely a circle on the same two-dimensional plane then?

Maybe you were suggesting that a deity could do the logically impossible, because 'God' tends to be beyond human understanding. But again, we are in a paradox, because we are accepting that it is invalid to require logically impossible tasks...

Your threads are always very knotty!

According to this premise, why should we demand from 'God' to make a single geometric object that is entirely a square and, simultaneously, is entirely a circle on the same two-dimensional plane then? — javi2541997

That is not what I meant. I want to define a task that is logically impossible. Most people don't know what logically impossible means.

I want to define a task that is logically impossible. — PL Olcott

Ah, I see.

Most people don't know what logically impossible means. — PL Olcott

Myself included, I am not going to lie to you. What you explain and write in your threads is very interesting, but I admit that I don't usually understand what it really means.

Myself included, I am not going to lie to you. What you explain and write in your threads is very interesting, but I admit that I don't usually understand what it really means. — javi2541997

Logically impossible is the maximum of all impossibilities.

Things that the creator of the universe cannot do are logically impossible things. God could make
a real live two-dimensional Bugs Bunny, this only require rewriting the laws of nature. God
cannot make a square circle, because it is contradictory, it must have (mutually exclusive)
properties that it cannot have.

​Everything in your argument is fine, until you put God's touch on everything. I think there is not a possibility for a square circle because it is logically contradictory, simple. And this contradiction comes from the way we see and understand the reality we live in. I think the 'creator' has nothing to do with these principles. If we ever had to put on God's shoulder the responsibility of being logical, some principles of theology would vanish. For example: Omnipresence. Does 'God is able to see everything and to act anywhere he chooses' sounds logical to you?

My original example of an impossible task was to bake a perfect angel food cake using only house bricks for ingredients. Someone pointed out the rearranging the molecules of the bricks could make this possible. He suggested that I use the term logically impossible. Then people here complained that they never heard of this and had no idea what it means. The key example that I knew was the existence of a thing that required simultaneous mutually exclusive properties.

I think I understand you better now. I did brief research on the internet and I found this: https://www.jstor.org/stable/2105946 and this one too: https://philosophy.stackexchange.com/questions/2970/can-something-be-actually-possible-yet-logically-impossible

Well, logically impossible means something that is self-contradictory. I understand clearly your example of the 'square circle'. This is logically impossible because the concepts of reality contradict each other. So, we can assume that a 'square circle' is both actually impossible and logically impossible.

Nonetheless, to bake a cake using only house bricks is something which is logically impossible but actually possible. Because depending on the concepts of my - or your - reality, that cake can eventually be cooked using only house bricks. Maybe it is an impossible task for you, but not for me. Agree?

Nonetheless, to bake a cake using only house bricks is something which is logically impossible but actually possible. Because depending on the concepts of my - or your - reality, that cake can eventually be cooked using only house bricks. Maybe it is an impossible task for you, but not for me. Agree? — javi2541997

If one can rearrange the molecules of a house brick to become an angel food cake then it is not logically impossible to make an angel food cake from house bricks.

There is nothing that anyone can do to make an object that has four equal length sides and simultaneously has zero equal length sides.

There is nothing that anyone can do to make an object that has four equal length sides and simultaneously has zero equal length sides. — PL Olcott

Yes, because there is simply nothing that a round square could be. I think this is the main point after all.

Yes, because there is simply nothing that a round square could be. I think this is the main point after all. — javi2541997

No the actual main point is that the halting problem proofs are incorrect because they require a computer program to provide a correct answer to a self-contradictory question that has no correct answer because it is a self-contradictory question.

When we correct the halting problem so that it is no longer asking a self-contradictory question we get a different answer.

Termination Analyzer H is Not Fooled by Pathological Input D
https://www.researchgate.net/publication/369971402_Termination_Analyzer_H_is_Not_Fooled_by_Pathological_Input_D