If we agrre with the definition: "If something can be imagined, then it is logically possible", then, by contraposition: "If it is not logically possible, then it can not be imagined".

And if we can't do that, why? @MauroALLEGRANZA

Difficult to answer... maybe our "mental hardware" has some limitations; thus, the "logic" of our brain is the product of the specifications that rule it.

We should probably distinguish the psychological / neuroscientific why from a more philosophical why. Answers to the first might be (very crudely) ‘Our brains aren’t made for imagining that’ or ‘Mankind never learned to use that sort of concept’. E.g., ‘Why is it so hard to imagine an infinity of numbers’ might receive that type of answer. On the philosophical side, we might instead talk about the nature of thought or thought content. E.g., we might say that you can’t imagine that a isn't a, because there’s nothing there to imagine, no state of affairs for your mind to conceive of.

PS: There’s quite a bit of literature on the question of whether conceivability entails metaphysical possibility. The situation may well be different for logical and metaphysical modalities, but perhaps that can serve as a starting point. Chalmers talks a lot about this, and Tim Williamson also has some stuff on imagination and possibility.

This just seems like someone who hasn't defined his terms. With standard non-colloquial definitions of logic, the Collatz conjecture is either logically impossible or its negation is, but I can imagine both scenarios easily. At least one of those is imagining the logically impossible.

But that doesn't really help, since Baber never described his term except by saying that the logically possible is the set of things you can imagine. Which I can't say is invalid, but it seems silly at the least. We already have much better words for that, like "conceivable".

@MarkOxford are these two possibilities for explaining this (the neuroscientific and the philosophical one) the same? I mean, do they say the same but the first one from a scientific perspective and the other from a philosophical perspective?

I don’t think so. The one is going to cite facts about our brain/psyche, and those facts are presumably contingent. They’ll explain why we in particular (and relevantly similar creatures) can’t imagine such-and-such. The other is going to deal in concepts that are much less specific to our neural/psychological makeup. It’s not even clear they are going to be co-extensional.

@MarkOxford But when we try to explain why can't we imagine "x" thing, can we use both explanations? I mean, obviously they aren't saying literally the same, but could we say that the nature of thought/thought content (philosophical perspective) or from a scientific perspective, our brain structure prevents us from imaging "x" things

We can listen to both explanations, but it’s not clear they are explanations of the same thing. I think this goes back to what @Veedrac was saying. Both the philosopher and the neuroscientist may say: ‘it is impossible to imagine x’, but it’s not obvious that they're talking about the same concept when they say imagine (or when they say (im-)possible.) That doesn’t mean that one answer is better than the other, but it highlights that we must keep track of what we are trying to do: learn something about the human brain, or learn something about metaphysics / epistemology?

@MarkOxford and if it was right that the nature of thought or thought content prevents us from imaging something, could it also be explained by the scientific perspective? If we say that we can't imagine the illogical or what can't exist or can't be imagined because of the proper nature of thought, could we also say that this limitations of the nature of thought are due to the brain structure?

Suppose you can only imagine what’s logically possible, so that you can’t imagine p and not-p both being true. Then the main reason you can’t imagine this has nothing to do with your brain structure: the reason is that p and not-p are inconsistent. In turn, suppose you can imagine some logical impossibilities. (Maybe Frege could imagine Basic Law V.) Then if we’re using imagine in a philosophically interesting sense, the explanation for why you can imagine this will probably cite facts beyond your brain structure - like propositions being presented under different guises.

@MarkOxford but it is our brain what allow us to imagine, so if I can't imagine logical impossibilities, I can't imagine them because they are not consistent: so my brain, and its "design", cannot organise the information from the neurons to make an illogical non consistent thought. The laws of thought, nature of thought and our capacity to imagine or reason depend on the brain, which is the structure that allows them to exist, isn't it?

There are two reasons why you can’t run faster than the speed of light: the laws of physics, and the physiological laws about your legs, muscles, etc. that explain why you can only propel yourself forward so-and-so fast. Now, it’s just not helpful to reduce one reason to the other: we can learn something interesting from the physicist, and something else interesting from the physiologist. Similarly, maybe your brain’s design strops you from imagining the impossible; but that’s not the point. The point is, there may be constraints on imaginability other than and external to the brain.

@MarkOxford And if a good-enough brain was built somehow, and these philosophical limitations were overtaken, what impact would it have in philosophy of thought? Would it have to reinvent itself?

The philosophical limitations can’t be overtaken. It’s not somehow a flaw in our philosophy that p and not-p can’t both be true: it’s a fact that holds of logical necessity, and there’s just no sense in which one can ‘overtake’ logical necessity. Building a better brain won’t help, no more than working out at the gym could help you ‘overtake’ the fact that nothing travels faster than the speed of light.

@MarkOxford And I suppose that these limitations also apply to knowledge. I mean, we couldn't know or reason about an illogical idea or thing because of these limitations isn't it?

You can’t know any falsehoods – including plain old falsehoods like ‘Trump lost to Clinton’. That’s because of what knowledge is. As for reasoning about logical falsehoods, it depends on what you mean by ‘reasoning about’: we can disprove them in a formal system. So, if that counts as reasoning about them, we can reason about logical falsehoods. By contrast, if reasoning about x involves imagining x, you can’t reason about what you can’t imagine.

@MarkOxford what do you exactly mean with "You can’t know any falsehoods"?

I mean that if S knows that p, then p is true. To see this, suppose I say: ‘Jill is not pregnant, but she is pregnant’. Then unless there’s some pun involved, I’m contradicting myself. Now consider: ‘Jill is not pregnant, but Tim believes that she’s pregnant’. I can say this without contradicting myself, as Tim can believe something false. Finally, consider: ‘Jill is not pregnant, but Tim knows that she’s pregnant’. Most people feel that this is just as self-contradictory as the first statement. If so, this means that Tim can't know that Jill is pregnant unless she really is pregnant.

But we can know falsehoods in the sense that they are not true isn't it? I mean if I know that Jill is not pregnant and i say "I certainly know that she's not pregnant" that would be true and that would be knowledge isn't it?

And returning to what we were saying at first: Suppose we could only imagine what is only logically possible. But somehow something or someone show us an illogical situation. Then we could imagine it now because we have seen it. Then, would philosophical laws related to the thought and thought's nature change?

@MarkOxford

Yes, if Jill is not pregnant, you can know that she is not pregnant. Yet then you’re still knowing a truth: after all, it is true that Jill is not pregnant. As for the second issue, if you think that the logical impossible can’t be imagined, you’ll be hard-pressed to accept also that the logical impossible can’t be depicted/shown. Again, the idea would be that there’s nothing there to depict/show.

So it could not be depicted because that someone or something would not know how to represent it? @MarkOxford

Because they couldn't imagine it, they wouldn't know how to do it?

Essentially, yes. Let’s try a concrete example: Since Joseph Ratzinger is in fact the same man as Benedict XVI, most philosophers would agree that Joseph Ratzinger is necessarily the same man as Benedict XVI. Now let’s try to imagine/describe/depict a scenario in which Ratzinger and Benedict are different people. Well, we can imagine a scenario in which Ratzinger is never elected pope, and some other cardinal else ends up adopting the name ‘Benedict XVI’.

Now have we imagined a scenario in which Ratzinger isn’t Benedict? No: really, we’ve just imagined a different version of the first scenario, where someone (something) other than Ratzinger ends up with the name ‘Benedict XVI’. The only difference is that in the second scenario, we falsely believed for a while that Ratzinger is Benedict. Apart from that, in the said scenario Ratzinger is still identical to all and only those people to whom he is in fact identical.

Finally, let’s suppose we draw a picture with two people in it, both of whom look like Ratzinger/Benedict. Say one of them is wearing a white, papal cassock, while the other is wearing a black-and-scarlet one. Perhaps they also both have a name tag in the drawing, one saying ‘Joseph Ratzinger’, the other saying ‘Benedict XVI’. Have we depicted a scenario in which Ratzinger isn’t Benedict? Well, we have a picture where it looks like they are distinct, but what is this a picture of?