[ordu]

> This resolved the most basic liar paradox, but not every diagonal attack, since not all functions on [0, 1] have fixed points. To make this work in general, we can for example allow only continuous functions on [0, 1] (which always have a fixed point by Brouwer’s fixed-point theorem). But that restriction comes at the cost of expressivity: "This sentence has truth score less than 0.5" is not a continuous function of the truth score of the sentence.

Ok, I get it. Either expressiveness or completeness, but the question arises: did mathematicians explore systems with limits on expressiveness? In a field of computer programming there is Rust with limited expressiveness that doesn't solve all the problems, but still makes things much simpler. How about a mathematics with limited expressiveness and some unsafe blocks here and there?

[layer8]

Of course this has been explored: https://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_... The bar is rather low, however (like Robinson arithmetic). Basically, you’d have to forgo integer arithmetics with multiplication.