Extra-logical reality:
According to your view, as I understand it, the analytic position tries to ground all of reality in logic, that is, in language. According to this approach there is no place for dualism; that is, there is no content to our claims about reality.
The synthetic position, by contrast, holds that there is an ontology separate from the verbal (logical) description itself. There is an extra-logical reality.

Isn’t that your position?

You did not understand my position. An analytic thinker is someone who thinks that the logical is the whole picture. That is, he accepts only the conclusions of valid logical arguments (and not analogies or inductions and the like). He holds that anything beyond logic (such as values, for example, or metaphysics) is worthless and subjective. The synthetic thinker also accepts softer arguments, and not only logical deductions. But he too of course does not accept what is beyond logic in the sense of accepting contradictions, because there is no such thing. That is just nonsense.

So it seems to me that I did understand after all..

I did not claim, nor do I think, that the synthetic approach, insofar as it itself is expressed in language and words (and after all it too conducts a philosophical discussion…), has the privilege of accepting contradictions. It has no such privilege.
And still, subject to logical lawfulness, you can describe a world in which the entities themselves do not answer to logic (to the law of non-contradiction).
Examples of such entities: space, time, God, soul, values, etc. The description of these entities can (and should) be coherent, that is, free of contradictions. Nevertheless, such a description carries content and is not tautological.

A rational (synthetic) view is committed to as sharp a dualism as possible, and it claims that logic alone will not be able to provide it for us (see the early Wittgenstein and your criticism of him). A “leap of faith” is required, for otherwise you have not effectively distinguished yourself from someone who advocates the analytic view.

I did not understand a word. A description free of contradictions—so in what sense is it outside logic? And what does it mean that “nevertheless such a description carries content and is not tautological”? What connection is there between being free of contradictions and being empty of content? What is that “leap of faith”?

Sorry for butting in, but do you mean that “space, time, God, the soul, values, etc.” are entities that do not answer to the law of non-contradiction?! Are you sure?

Citizen, I assume your question is addressed to Doron. I do not understand the expression “entities that do not answer to the law of non-contradiction.”

Dear Michi and Citizen,
Do you think that someone who holds a synthetic position can claim that logic (the law of non-contradiction) applies to objects that are separate from the human being, that is, separate from the logic he uses in order to speak about those objects?
To my mind such a claim is meaningless. I think the law of non-contradiction holds only with respect to concepts, not with respect to the objects those concepts represent. Those objects, at least in the eyes of someone who holds a synthetic position, are separate from their concepts.

Of course, those who hold an analytic position will seize on this claim of mine like someone finding great spoils, and will say that my very claim above is made in human language and therefore is itself “logical” as well (that is, on their view there is no real object, only an “object,” and therefore the law of non-contradiction does indeed apply to it).
For those who hold such a position, logic really is the whole picture (example: Parmenides—”what exists exists, and what does not exist does not exist”).

Although such a position is certainly tempting, in the final analysis it is not rational. In my view, only a position that accepts that there is something basically “strange” in the world itself (that is, in reality as separate from us, not in our language and logic) can be truly synthetic (and rational).
That is why I called it a “leap of faith.”

Note that I am not claiming that one can depart from logic within ordinary human language or thought. All I am claiming is that logic is not the whole picture (we have, for example, intellectual intuitions).

As for Gödel’s theorems… well, apparently we will not get to that after all… I will only say that many people greater and better than I am (including apparently Gödel himself) thought they were excellent evidence for the Platonism that Gödel held. I think they were right.
On that point I had some rather weak intuition, according to which proving Platonism by means of Gödel’s theorems ought to take us one step further (for the sake of consistency) and lead to theology.
That was the question I asked at the beginning of my remarks, peace be upon it.