If I can imagine it, it's logically possible?

[Logik]

sqc.jpg

Nice picture, but irrelevant.
And, notice that there is a projection of a circle which is indeed a square (and vice versa).
So?
EB

Not sure what your criteria for relevancy are here?

x^2 + y^2 = 4 (equation for a circle with diameter 4)
z = 4 ( height of a cylinder equal to its diameter )

And so this can be simplified as:

x^2 + y^2 = z

Any values of (x,y,z) which satisfy the equation above are points in 3D space which exist inside a cylinder described by the equation and portrayed in the picture.

To sum up:
1. I can imagine it
2. I can draw it.
3. I can write a mathematical expression which express it.
4. I can say it in English.
5. I can realise it (make a physical object as per imagination, diagram, Mathematics and English)

If you claim this is "irrelevant" then please explain why. Perhaps you expect me to turn water into wine again?

[Speakpigeon]

If I can imagine it, it's logically possible?

What do you mean, "logically possible"? Logic is a formal tool to show that if something is true, then something else is also true, given some circumstances and restrictions.

Something is logically possible if it does not contradict whatever you already know, or possibly, something you assume to be true.
Tell me if that's OK.

Logic has nothing to do with reality, although it can be applied to things i the real world

It certainly has something to do with what we can accept as being true.

logic deals with propositions, with conclusions.
How can you imagine, for instance,
"All men are mortals.
Socrates is a man.
Therefore Socrates is mortal."

Sure, and that's because the idea that Socrates is mortal is a logical possibility given that you accept that Socrates was a man and that all men are mortal.
That's being said, this is the wrong kind of example. What about this one:

My subjective experience is a mental process in my brain;
What I do voluntarily is essentially determined by mental processes in my brain;
Therefore, what I do voluntarily may be essentially determined by my subjective experience.

All especially for you. What do you think?

Are you sure you did not want to write, "If I can imagine it, is it physically / empirically / metaphysically possible?"

Certainly not. It's rather obvious that we can imagine things that turn out to be false or non-existent. There's just one reality. Things are what they are and we may be mistaken in our beliefs. So, what is logically possible may not be physically real.
EB

[Speakpigeon]

Why must I always waste time on self explanatory things.............
It's a really bad question only showing your lack of rationale, the question has no meaning and only a skitzo would ask such blatant nonsense!

LOL
EB

[Speakpigeon]

Nice picture, but irrelevant. And, notice that there is a projection of a circle which is indeed a square (and vice versa). So?

Circles are per definition two-dimensional.

You wouldn't be able to prove that because it's false.

You can't invoke or imagine a three-dimensional circle.

I didn't say I could.

Not allowed.

???
I'll do it if I bloody want to. What will anyone do about that?!
EB

[Speakpigeon]

[Well, no surprise here, it's possibly the most famous case of assumed logical impossibility...
And this shows an infinite past with a beginning is logically possible even though that doesn't help with the ordinary notion of an infinite past without a beginning.

A square circle is not a logical impossibility. It is an impossibility due to the definitions of the circle and of the square, respectively. One is a circle, the other, one of the infinite amount of forms that are not a circle. Or, one is a square, the other, one of the infinite amount of forms of what are not squares.

What does this has to do with anything I said?!
EB

[Speakpigeon]

Not sure what your criteria for relevancy are here? x^2 + y^2 = 4 (equation for a circle with diameter 4) z = 4 ( height of a cylinder equal to its diameter) And so this can be simplified as: x^2 + y^2 = z Any values of (x,y,z) which satisfy the equation above are points in 3D space which exist inside a cylinder described by the equation and portrayed in the picture. To sum up: 1. I can imagine it 2. I can draw it. 3. I can write a mathematical expression which express it. 4. I can say it in English. 5. I can realise it (make a physical object as per imagination, diagram, Mathematics and English)
If you claim this is "irrelevant" then please explain why. Perhaps you expect me to turn water into wine again?

Circle
a. A plane curve everywhere equidistant from a given fixed point, the center.

Square
1. A polygon having four equal sides and four equal angles.

Polygon
A closed plane figure bounded by three or more line segments.

EB

[Logik]

Circle
a. A plane curve everywhere equidistant from a given fixed point, the center.

Square
1. A polygon having four equal sides and four equal angles.

Polygon
A closed plane figure bounded by three or more line segments.

EB

Why are you artificially constraining your imagination to an Euclidian space when you exist in a multi-dimensional universe?
Why are you appealing to dictionaries to speak on your behalf? The dictionary can't read your mind and tell us what you have imagined.
The dictionary is a point of departure - not an authority on meaning.

That which YOU have imagined is for you to express using whatever language you have at your disposal as a medium of communication.

Pencil drawings. Mathematics. English. Photos. Memes. Whatever - express your idea so that others can understand it.

I didn't need a dictionary to explain to you what I mean by "square circle". I explained it to you with pictures and followed it up with high school Mathematics.

Since Mathematics is logic you are no closer to telling me why my geometric and algebraic expression of the N-dimensional concept is "not logically possible".

It's just a cylinder whose height is equal to its diameter. I have labeled that object a "square circle" for my own, communicative convenience.

"But that's not a square circle!", objected the Sophist.
"OK, but it is what I imagined and it is the concept I am trying to communicate to you, so if it's not a 'square circle' then what would you like to call? How about a 'squirkle' ? ", asked Logik.

If you can imagine it AND communicate it AND realize it. It's possible.

[commonsense]

What do you mean, "logically possible"? Logic is a formal tool to show that if something is true, then something else is also true, given some circumstances and restrictions.

Something is logically possible if it does not contradict whatever you already know, or possibly, something you assume to be true.

For me, something is logical(ly possible) if it does not contradict a priori knowledge, the rules of logic or the thing itself. If anyone objects to this refinement of Speakpigeon’s and -1-‘s statement, please say so and give your reasons.

[Logik]

the rules of logic

Logic doesn't have rules. It is 100% constructive and constructed.

[-1-]

the rules of logic

Logic doesn't have rules. It is 100% constructive and constructed.

The rules of logic are the operators that drive operations performed. If you say "P or Q" it is a rule that either P or Q, or both, if true, then the result is true. That is one rule of logic.

It is constructive and constructed. But that alone says nothing about the presence of rules.

The driving of a car on a city street is an action that is constructed and constructive. But there are rules how to drive a car.

You are just your own old self, Logik: contrarian even to the detriment of being right.

[-1-]

Circle
a. A plane curve everywhere equidistant from a given fixed point, the center.

Square
1. A polygon having four equal sides and four equal angles.

Polygon
A closed plane figure bounded by three or more line segments.

EB

Why are you artificially constraining your imagination to an Euclidian space when you exist in a multi-dimensional universe?
Why are you appealing to dictionaries to speak on your behalf? The dictionary can't read your mind and tell us what you have imagined.

Honey... these are not empty definitions. A two-dimensional figure is two-dimensional, in a three-dimensional space, in a four-dimensional space, and up. Living in a multi-dimensional universe has no effect on the definition of a circle.

The definitions stand. They are stringent, and if you want to define "circle" in some other way, then you have to give it a name that delineates it from the geometric form defined as "circle".

Again, being contrarian is useless if you bang your head against a brick wall. You just keep at it, and then you go into a Narcissistic rage.

[commonsense]

Picasso can. Escher can.

Could you evidence that? From what I remember, they don't.

For Picasso, let me say:

1. Every human face has 1 nose. (a priori knowledge)
2. Picasso can imagine a human face with 2 noses. (q.v. Wikipedia)
3. If Picasso can imagine a human face with 2 noses, then every human face has 1 nose. (logical contradiction with a priori knowledge)

To me, this says that Picasso can imagine something that isn’t logically possible.

For Escher, the argument is similar. Search Escher on Google images or in Wikipedia to view some evidence.

However, you seem to remember these differently than I do. If so, please explain.

I can imagine illogical shapes; my favorite is a fork that has 3 tines and has 4 tines.

Any way you could prove you can?

I am weary and I have neither the software nor the graphics skills to prove that I can do this. The fork with the incongruous number of tines is an optical illusion that was the first time I imagined something that is logically impossible. You may be able to find this among Escher’s drawings as well.

I can envision examples of Magic Art.

I'm not sure what is Magic Art and in the event how that would provide a ready counter-example...
EB

https://en.wikipedia.org/wiki/Magic_Eye

[commonsense]

the rules of logic

Logic doesn't have rules. It is 100% constructive and constructed.

The rules of logic are the operators that drive operations performed. If you say "P or Q" it is a rule that either P or Q, or both, if true, then the result is true. That is one rule of logic.

It is constructive and constructed. But that alone says nothing about the presence of rules.

The driving of a car on a city street is an action that is constructed and constructive. But there are rules how to drive a car.

You are just your own old self, Logik: contrarian even to the detriment of being right.

Sorry. I meant to say “laws” of which I know only 3.

[Speakpigeon]

What do you mean, "logically possible"? Logic is a formal tool to show that if something is true, then something else is also true, given some circumstances and restrictions.

Something is logically possible if it does not contradict whatever you already know, or possibly, something you assume to be true.

For me, something is logical(ly possible) if it does not contradict a priori knowledge,

I believe a priori knowledge reduces to our logical intuition, which personally I take to be a perception and therefore a species of a posteriori knowledge.
Still, could you elaborate on your suggestion of the role of a priori knowledge in this context. Perhaps with an example?

the rules of logic

Logic, sure, absolutely.
But what are the rules of logic?
I think people are not going to wait for some self-professed expert to tell them what are the rules of logic.
Still, perhaps you can convince me that certain rules I don't know are better than my logical intuition?

or the thing itself.

???
How would you know about the thing itself if not as an instance of what you know.
And if you don't know, how could you possibly decide something isn't a logical possibility?
Aren't you confusing logical possibility and physical possibility?
Could you explain? For example with the case of an actual infinite.

If anyone objects to this refinement of Speakpigeon’s and -1-‘s statement, please say so and give your reasons.

I'm not sure it's a refinement. Rather a different conception?
EB

[Speakpigeon]

Picasso can. Escher can.

Could you evidence that? From what I remember, they don't.

For Picasso, let me say:
1. Every human face has 1 nose. (a priori knowledge)
2. Picasso can imagine a human face with 2 noses. (q.v. Wikipedia)
3. If Picasso can imagine a human face with 2 noses, then every human face has 1 nose. (logical contradiction with a priori knowledge)
To me, this says that Picasso can imagine something that isn’t logically possible.

But this is not imagining a man with two noses. This is imagining something that vaguely suggests a man with two noses.

For Escher, the argument is similar. Search Escher on Google images or in Wikipedia to view some evidence.
However, you seem to remember these differently than I do. If so, please explain.

Take Relativity, 1953. Three stairs in different orientations. It's a logical possibility if you think of it in the abstract, not as something in our universe in a natural field of gravity. Either way, no contradiction.

I can imagine illogical shapes; my favorite is a fork that has 3 tines and has 4 tines.

Any way you could prove you can?

I am weary and I have neither the software nor the graphics skills to prove that I can do this. The fork with the incongruous number of tines is an optical illusion that was the first time I imagined something that is logically impossible. You may be able to find this among Escher’s drawings as well.

But it's not something you imagine as logically possible. It's something designed to trick your perception. I think it works like paradoxes of self-reference. You have to look at it carefully before dismissing it as not saying anything about reality.

I can envision examples of Magic Art.

I'm not sure what is Magic Art and in the event how that would provide a ready counter-example...

https://en.wikipedia.org/wiki/Magic_Eye

OK, that's interesting. I had forgotten about this thing. Still, I'm not clear how that relates to the OP...
EB