Self contradictory things that can't really exist: can they be fully conceived of?

Question

It seems like we can conceive of self contradictory things that can exist. e.g. the proposition expressed by "this sentence is false" is self contradictory but I don't seem to have any trouble understanding the sentence. e.g. Lazerowitz says that there it is straight-forwardly true that self contradictory propositions "exist" if we mean "declarative sentence".

However, what about self contradictory things that's parts can't really exist? I would say we may be able to vaguely imagine them, but not fully grasp and conceive of them or their meaning.

Am I right?

---

Supposing inconceivability amounts to lack of knowledge, it would make sense to me to say that things that are self contradictory to us must exist empirically to be conceived of, to be known, rationally or empirically.

Maybe that's why triangles without 180 degrees of angles were, like round squares, thought inconceivable: because mathematicians couldn't see how it might apply to the world.

[Hilbert] was also partly inspired by work on non-Euclidean geometry, which at the the time was still completely controversial since it didn't seem physical. Now we know that it is physical

But that is complete guess work.

---

The example I am thinking of, why I ask, are Ron Silliman's poetic "effects", as they appear in his 1970s book The New Sentence. You can find the following claims:

1. a device changes the whole
2. there is really no such thing as a whole
3. effects are aggregated devices
4. effects can be self contradictory

I believe it follows that any "effect" (so defined) may be more than our conception of them, may be working outside of our conscious processes and conceptions, if the question in the title is answered with a "no".

Answer 1

It seems like we can conceive of self contradictory things that can exist. e.g. the proposition expressed by "this sentence is false" is self contradictory but I don't seem to have any trouble understanding the sentence. e.g. Lazerowitz says that there it is straight-forwardly true that self contradictory propositions "exist" if we mean "declarative sentence".

Strictly speaking, there are no self-contradictory sentences. Sentences don't speak themselves. We do.

So, in effect, sentences are definitely not examples of existing self-contradictory things.

However, anyone willing to assert a "self-contradictory" sentence would indeed contradict themselves, and thus, become an example of, literally, a self-contradictory thing. I'm sure most people can speak the sentence "It rains and it doesn't rain".

However, speaking a sentence is not conceiving the idea expressed by that sentence. So, can we conceive a situation where it is both raining and not raining?

Conceiving is the most abstract form of thought. The most concrete is imagining, usually relying on the visualisation of the situation. Then, I don't think anybody could imagine in this sense a situation where it would be both raining and not raining. I certainly can't visualise such a situation.

But, there is no difficulty in conceiving the same situation.

To conceive the situation where it is both raining and not raining, we only need to be able to conceive a situation where it is raining and to be able to conceive a situation where it is not raining. If we can do each, then we can conceive of the conjunction of the two. The logical conjunction. And so we're done.

Conceiving is largely a logical operation. As such, it can do pretty much all which is ordinarily discussed in the context of formal logic.

However, your question may be taken to be about the possibility of "self-contradictory" propositions. Assuming that propositions exist outside of the human mind--and this is a seriously metaphysical assumption to make--self-contradictory propositions would be examples of existing self-contradictory things.

And in this case, not only are there existing self-contradictory propositions, but there is one such for every ordinary proposition. Assume one proposition p. Then, the proposition p and not p is a self-contradictory proposition.

Thus, there would be, if propositions exist at all, an infinity of existing self-contradictory propositions. All false, obviously.

And things we can't even imagine.