> In what sense, I ask you, does a number with no possible definition actually exist? There is a difference between "describe" and "define". You are talking ab

> In what sense, I ask you, does a number with no possible definition actually exist? There is a difference between "describe" and "define". You are talking about what are mathematically called "indescribable numbers". They still have a definition, because we have sets that include them. > Nobody wants to consider these odd questions. But if somewhere in the middle of a proof you ask what it all means, you may find that classical mathematics doesn't necessarily make that much sense.Nobody wants to consider these odd questions. But if somewhere in the middle of a proof you ask what it all means, you may find that classical mathematics doesn't necessarily make that much sense. I don't think that describes the situation very well. It's just that they're not bothered by not being able to touch things. Most mathematicians have no problem working with things that they can't touch, it certainly doesn't have to inhibit their understanding of it. It isn't like mathematicians are uncomfortable with the question "but what does it mean if I can't touch it?", they simply reply with "why would I care about such a question?" (Of course, some people do care, but they are in the minority. The point is that the separation of opinion is mainly about whether the question makes sense to ask to begin with.)