In this page (http://home.sandiego.edu/~baber/logic/logicalpossibility.html) it said that "If something can be imagined, even though it may be physically impossible, it is logically possible" But can we imagine also logically impossible things? Illogical things? And if we can't do that, why?
The answer really lies in the simplicity of the division between "logical" and "not logical." Its too simplified to capture the full nuances of our imagination.
"If something can be imagined, even though it may be physically impossible, it is logically possible"
If I may borrow from a non-Western culture, consider the concept of the Dao(道). It is a fascinating concept which is almost certainly outside of the realm of logical possibility because, as Laozi put it, "The Tao that can be told is not the eternal Tao". Surely one would need to be able to enumerate it (via speech or writing) in order to determine if it is logical or not. And yet, it is. It is the is-ing, if I may try to turn "is" into a present transitive verb. It is perfectly physically possible, for it is. So it would be an example from another culture of an idea which can be imagined, is physically possible, but I would argue is logically impossible in the sense that it defies logic.
First I thought of my own dreams being logically impossible as well as physically so. Then I wondered about all that Alice found down the rabbit hole.
Now I'm wondering - Is there such a thing as logical possibility and impossibility?
When I dream of going into house X and inside it becomes house Y, surely it is a matter of true versus false rather than possibility.
You probably can't imagine the illogical, in a certain sense of the word.
Wittgenstein describes nonsense as not a sense which is empty but rather the absence of sense at all. (Of course in this stage of his thought he also said that a great number of apparently meaningful statements are actually nonsense. Presumably we do not want to follow him that far down the road.) For a certain sense of illogical, of course a totally illogical thought is nonsensical.
This is Plato's sense of logic (see Theatetus 155a): logic as the law of thought. In other words we cannot but think with logic, because logic is constitutive of thought. (Of course there is a lot of debate about which, if any, logical principles belong to the law of thought.) So "thinking" without logic (in this sense) is not thinking at all. It is just putting words together without any meaning.
A classic example: picture a circular square. Obviously circular squares are illogical, internally contradictory. Are you picturing it? You can't do it, can you? (If you can, I'd be very interested in hearing what a round square looks like.) You can say the words "circular square" but as soon as you try to spell out what that means the idea falls through your fingers like sand. Language has given us the false appearance of possibility.
Language can give the false appearance of impossibility as well. Say I am both inside and outside. But inside and outside are opposites; each one can be defined as the negation of the other. And yet if I stand in a doorway I am both inside and outside. Here the problem is not a violation of any law of thought, just an improper application of that law. Of course a single point cannot be both inside and outside, but I am composed of infinitely many such points. Some of me is inside and some of me is outside.
Of course there are a number of formal systems, all of which capture our idea of thought to some degree. So if you choose the wrong logical system, or describe things in that system strangely enough, you can easily imagine states of affairs in violation of the system. Or you can formulate sentences in the system, and even prove them, without being able to imagine them. But there certainly are unimaginable things, and perhaps this is because they are violations of the law of thought.