It wasn't intended as an insult and I apologise if it comes across as such. It's easy to say things on the internet that we wouldn't say in person.

It did come from a place of annoyance, after your middlebrow dismissal of Penrose' argument as "stupid".

And you do it again, you apologise while insulting me. When challenged you refuse to defend the points you brought up, so that you can pretend to be right rather than be proved wrong. Incompleteness theorem is where the idea came from, but you don’t want to discuss that, you just want to drop the name, condescend to people and run away.

Here are the substantive things you've said so far (i.e. the bits that aren't calling things "stupid" and taking umbridge at imagined slights):

1. You think that instead of actually perceiving mathematical truth we use heuristics and "just guess that it's true". This, as I've already said, is a valid viewpoint. You disagree with one of Penrose' assumptions. I don't think you're right but there is certainly no hard proof available that you're not. It's something that (for now, at least) it's possible to agree to disagree on, which is why, as I said, this is a philosophical debate more than a mathematical one.

2. You strongly imply that Penrose simply didn't think of this objection. This is categorically false. He discusses it at great length in both books. (I mentioned such shallow dismissals, assuming some obvious oversight on his part, in my original comment.)

3 (In your latest reply). You think that Godel's incompleteness theorem is "where the idea came from". This is obviously true. Penrose' argument is absolutely based on Godel's theorem.

4. You think that somehow I don't agree with point 3. I have no idea where you got that idea from.

That, as far as I can see, is it. There isn't any substantive point made that I haven't already responded to in my previous replies, and I think it's now rather too late to add any and expect any sort of response.

As for communication style, you seem to think that writing in a formal tone, which I find necessary when I want to convey information clearly, is condescending and insulting, whereas dismissing things you disagree with as "stupid" on the flimsiest possible basis (and inferring dishonest motives on the part of the person you're discussing all this with) is, presumably, fine. This is another point on which we will have to agree to disagree.