To understand a word is just to be able to make use of it. — Banno
SO the argument would be that he understands the concept, but is unable to use the word. — Banno
On one hand, I know that the professional mathematicians do not define sets in a way which assumes they must be finite collections. On the other hand, I was running into a wall where the insistence was that the very meaning of "collection" entails finitude. — MindForged
Can you help me, by describing what a collection would actually be, if we allow that collections may be infinite. — Metaphysician Undercover
The shared understanding you talk about is exactly our capacity to make use of words. But of course you can't maintain that and still insist that there is a seperate, mystical thing which is the meaning of a word. — Banno
If he could not signal, there would be no reason to conclude that he understood "sixty". — Banno
Let's just collect all the odd numbers and ignore him. — Banno
An arbitrary quantity of elements referred to as a whole and which gain membership in said whole by means of sharing a common property we pick out or by being subject to the same stipulated rule. — MindForged
That would be a never ending task, — Metaphysician Undercover
I dunno, maybe I've missed something but this move of essentializing (it's a real word, fight me) the meaning of some word doesn't seem to really move the debate along at all unless all parties involved already agree on the same meaning. — MindForged
Meanings are too slippery, too inherently viewpoint-dependent, to be concretely defined. So words are just ways to limit the scope of possible understandings to the point where they can be usefully shared.
To use words properly, you need to be willing to do two things. Accept they do intend to narrow the scope for interpretation to some habitual conceptual essence. And then also show tolerance or charity for the vagueness that must always remain. — apokrisis
What sort of thing could a meaning be? — Banno
Did I include anything that shouldn't be there? No! — Banno
That's fine, but if there's an infinite amount of such an element, I don't see how this qualifies as " "quantity". Don't you know that "quantity" is defined as a measurable property of something, or the number of something" Infinite is neither a measurable property nor is it a number, so you really haven't given me a definition which allows for infinity. — Metaphysician Undercover
Really, I wish you would give more thought to what you say MindForged. How could "infinite" signify a quantity? Any such so-called "quantity" would clearly be indefinite and therefore not a quantity at all.
"How could it?" How could it not? It's not indefinite, the members of the "set of natural numbers" never increases or decreases, it is exactly what it is and has always been. — MindForged
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