Compared to mathematics and its logic, ordinary language is often portrayed as a poor way to describe the world because of its tendency to mix up meanings.
But isn’t it strange that the idea on which most mathematics is based - “the set” - appears vague. And there can be no vague meanings - so mathematics cannot provide any description of the world at all, by right.
The mathematical “set”, unlike the ordinary language term “set”, is a vanishing, insignificant proposal. It could mean either a whole, like a herd, it could mean a sum of parts, like cows in a herd. It could also be, or not be, a group, or a list. In mathematics, no-one asks or cares it seems. All we have is the empty, pontiffical mathematical sign “set”, creating paradoxes by being, and not being, both one thing and another thing, and, at the end of the day, not any of them.
I can answer that. Totals - or “all”, cannot be expressed within their domain, as I have indicated. So, if the set is in that domain then a set cannot be expressed outside it, as you have done.
What I have done is take a particular set of words to make a particular point about sets. Then I asked others to imagine additional sets of words that have not been taken to make additional points about sets.
The words are meant to define and defend other words. Therefore, the rationality of the set follows from the internal logic of the assumptions I make regarding the meaning of the words I use.
It is analagous perhaps to the assumptions helptheherd makes about God.
Because you haven’t? What exactly do you find difficult? This is a discussion board, please discuss.
You seem to have trouble with a herd being a different thing to a group of cows which in turn seems a different thing to a list of the cows. This is a category error. Ryle wrote a lot about it, it was one of the things Wittgenstein appreciated - a philosopher not getting confused about the language used. They’re different ways of referring to the same thing.
I have ten cows. If we call it a set, that says nothing. The ten cows could be single cows scattered across continents, or they could be cows in the same field charging about and knocking down fences without looking where they are going.
JJ - a set is an abstraction. It’s not “real”. I see in your posts an overall theme that abstractions are somehow inferior to things as we find them. A set is merely an abstraction - either it has a use or it doesn’t. But sets have no epistemic existence - if you never want to count the cows that you own, you do not need sets, or any arithmetic at all. But if you look into the the matter, the “questioning of assumptions” has already been done.
John,
Among the best refutations of the idea of sets as providing some “real” standard for discussions of the human sense of realty is Hofstadter’s “I Am A Strange Loop.”