Comment by moi2388
Why not? Bigger is a measure of size and ought to be easy enough to formalise.
Apply a transformation to B which increases its area and leaves the proportion of its sides equal.
Why would this statement not be formalisable?
Why not? Bigger is a measure of size and ought to be easy enough to formalise.
Apply a transformation to B which increases its area and leaves the proportion of its sides equal.
Why would this statement not be formalisable?
Ah, gotcha. I agree it would be difficult. I’m still not convinced it would be impossible though.
LLMs could even formalise what you want in the context, even now.
Or do you mean that you can’t formalise every statement when given incomplete information about the context of the statement, since then we have a single word pointing to multiple different contexts?
Oh yes, it's not impossible, I'm just saying we don't know how to do it yet. LLMs themselves are probably our best attempt so far.
Yeah you could make it one pixel bigger but if someone asked you that, is that what they actually want?
I'm not saying that the statement "I want this button to be bigger" can't be formalized. I'm saying that there is no formal process you can follow to get from this problem to a formal problem that is equivalent. There isn't even a formal process you can use to check if a formal definition is equivalent to this problem.
Consider that if someone asked you solve this problem for them with just this statement, either of the following could be a sketch of a more formal statement of what they actually want:
1. In a given web page, the css class used for a particular <button> element should be changed to make the button's height larger by 10%, without changing any other <button> element on the page, or any other dimension.
2. For a particular piece of garment that you are given, the top most button must be replaced with a different button that appears to have the same color and finish to a human eye, and that has the same 3D shape up to human observational precision, but that has a radius large enough to not slip through the opposing hole under certain forces that are commonly encountered, but not so large that it doesn't fit in the hole when pushed with certain forces that are comfortable for humans.
I think you would agree that (a) someone who intended you to solve either of these problems might reasonably describe them with the statement I suggested, and (b), that it would be very hard to devise a formal mathematical process to go from that statement to exactly one of these statements.