The fact that someone can add one to some number in no way implies some notion of infinity. If anything, adding one to some number just produces a finite sum, not an infinite sum, hence my mention of Aristotle's actual vs potential infinity. Potential infinity is an idea that can never be realized as actual infinity.So if numbers are an aspect if counting, and one cant count to infinity, then finitism.
— frank
That's a bit too fast, but in being wrong, might be the gist of what is going on. It's worth talking to a child about infinity to see the change in thinking as they realise that for any number they construct, someone can make a bigger one; they say "a squillion billion", you say "a squillion billion plus one". Then the confusion when they begin to realise that "infinity plus one" is still infinity. The game changes before them. — Banno
hence my mention of Aristotle's actual vs potential infinity. Potential infinity is an idea that can never be realized as actual infinity. — Harry Hindu
Right, so in your example, you'd be just making noises with your mouth.Now, if you could offer some examples of "language use" where words and numbers are not used to inform or communicate, and does not equate to just making scribbles and noises, then I would be interested in talking about those cases.
— Harry Hindu
When I'm at home alone, playing a game and losing, I often shout out "for fuck's sake". I'm not informing or communicating with anyone. It's an expression of frustration, much like laughing is an expression of happiness and crying is an expression of sadness. I wouldn't say that any of these expressions point to or are about anything (in the sense of reference). They may indicate something, but that's not quite the same thing – talking fast indicates that I'm in a hurry, but that doesn't mean that my words refer to the fact that I'm in a hurry. — Michael
Only that our thoughts are finite. We don't know if the universe is.That's finitism I believe. — frank
The page you referenced quite explicitly sets out the difference between average velocity and instantaneous velocity. — Banno
So the rule is that for every number, one can add one. The rule only generates one new number. One has to see the rule in a different way in order to understand infinity: imagine a number bigger than any number the rule could generate... — Banno
Do you see how this notion of infinity is inconsistent with constructivism? — Metaphysician Undercover
If "1" refers to an idea, then it is an idea shared. Else your idea of 1 would not be the same as mine.
So what sort of thing is that? — Banno
My thought was that "1" might refer to "1". A circularity. Not that "1" might refer to 1. — ZzzoneiroCosm
The prevailing view among mathematicians is that it's an abstract object. You can call it whatever you want. — frank
I don't see how '1' could refer to '1' ; it is the referrer. not the referent, according to any logic that makes sense to me. I don't see a problem with '1' referring to 1; the apparent problem arises because we want to reify 1, and be able to say just what it is. I think it's just a conceptual illusion of substance. — Janus
Clearer to say "1" refers (not to 1 but) to the concept of the singular or of the first.
At any rate, I don't find all of this very useful or interesting. It's obvious enough that "1" refers to something. — ZzzoneiroCosm
"That 1" refers to that 1.
Neither of these make much sense to me. — ZzzoneiroCosm
How about "'that one' refers to that one"? Would saying "'one' refers to one" be different than saying "'1' refers to 1"? — Janus
The fact that someone can add one to some number in no way implies some notion of infinity. — Harry Hindu
Notice the word "average" there? — Metaphysician Undercover
The bigger number referred to is not something which the human mind could ever apprehend — Metaphysician Undercover
But that's not right; mathematicians, even those in primary school, do apprehend infinity in their considerations. There are whole books about it.
Further it is clear that infinity of one sort or another is easily constructed from a few simple considerations.
And i think that is an end to this discussion. — Banno
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