But otherwise yes, "1" obviously doesn't refer to anything at all. — StreetlightX
StreetlightX" refers to StreetlightX, whereas "1" refers to "1". — ZzzoneiroCosm
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
Anther way to approach it that the rule "For every number, you can add one. to make a bigger number" is not generating all the numbers, but only the integers. We can find infinity by calculating 1 divided by 3, as a decimal; or by asking what number times itself makes 2. — Banno
SO we learn how to count, and then we learn how to do other things with counting. — Banno
We can count anything we would ever need to count using the first rule, so what's the point of the second? — Metaphysician Undercover
Re Wittgenstein's finitism, for me it always just fell out from his view that mathematics is nothing over and above a human activity, and since we are finite, nothing we can construct is going to be infinite. — jkg20
Well, with a bit of work it allows us to find an instantaneous velocity... among other things. — Banno
Smoke and mirrors. — Metaphysician Undercover
There is no velocity at an instant. — Metaphysician Undercover
I am driven to correct you on this: "1" refers to 1. — Janus
"1" represents an idea of quantity. Does it follow that "1" refers to an idea of quantity? I would sy the answer to that depends on what you mean by "refer". — Janus
You keep saying that, as if it were an argument. — Banno
↪bongo fury So you want to argue that — Banno
If the rule allows to construct a finite extension, then we can get extensions from it, too.
— Pneumenon
This is the bit that I've been unable to find clearly articulated.
— Banno
Just to be clear, are you both dropping (or taking as read) an "infinite"? — bongo fury
↪bongo fury There are infinities. — Banno
For my own part, I'm thinking that the extension/intension juxtaposition in this context is ill-defined and confusing... or it might be just me. Anyway, hence the OP; that "1" does not have an extension; or rather that talk of extension/intension is misplaced in mathematics. — Banno
So... you are asking what I think Pneumenon meant that Wittgenstein meant at — Banno
I can see why you would want to change the topic. — Banno
Instantaneous Velocity
The quantity that tells us how fast an object is moving anywhere along its path is the instantaneous velocity, usually called simply velocity. It is the average velocity between two points on the path in the limit that the time (and therefore the displacement) between the two points approaches zero.
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
Instantaneous velocity is an average, — Metaphysician Undercover
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