Okay, but "separate" implies something that is obviously incompatible with true continuity, which is why I could not give an immediate and simple answer to your initial question. — aletheist
The nominalist must reject the reality of any true continuum, — aletheist
First, the stuff above this comment--your first two paragraphs--is about mathematical thinking and/or the conventions of mathematical thinking ... What does that have to do with anything that's not itself mathematical thinking? — Terrapin Station
Also, if a "multitude" refers to an infinity(?) of potential numbers in between two "actual numbers," how the heck would we "exceed" that? That seems incoherent to me. — Terrapin Station
Nominalism isn't about discrete versus continuous ... — Terrapin Station
I'd need to be convinced that it's not just nonsense. — Terrapin Station
It is about individual versus general, or particular versus universal - right? Discrete versus continuous is another expression of the same contrast. — aletheist
I thought that your view was that each instant of time - each discrete change - introduces a new particular. — aletheist
Imagine that everything is continuous. Well, under nominalism, then, all particulars are continuous. — Terrapin Station
The only thing that makes a difference for universalism versus nominalism is whether we're saying that there are properties that somehow obtain where they can be identically instantiated, multiple times, in numerically distinct instances. — Terrapin Station
In other words, re green, whether we're saying that green can be identically instantiated multiple times. — Terrapin Station
Each change or motion results in the "thing" in question being different/non-identical to what it was. — Terrapin Station
This frankly suggests to me that you can't understand what you read. I don't know how else to explain it.This is not what Wikipedia actually says - not in what you quoted, and not anywhere else in the same article. — aletheist
This is incoherent to me. Particulars cannot be continuous; anything that is truly continuous can only be general. In Peirce's words, "Generality, then, is logically the same as continuity." — aletheist
I am saying that the green in one chair is not identical to the green in the other one, no matter how closely the two colors may resemble each other. — aletheist
I am suggesting that this requires a discrete step, since each change or motion constitutes the actualization of a new individual. — aletheist
So even a particular form is "all essence".
...
So all form is tolerant of accidents to some degree. And particularity arises from generality by narrowing the definition of the accidental - making it also more particular. Or crisper. — apokrisis
Yet it contradicts dialectical reasoning to not accept that there must be the unintelligible for there to be the intelligible. It can make no sense to claim the one except in the grounding presence of its other. So as soon as you commit to crisp intelligibility, you are committed to its dichotomous other - vague unintelligibility - as a necessity. — apokrisis
But you need vagueness to make its inverse an intelligible possibility. The difficulty is then to represent this in some fundamental metaphysical framework. — apokrisis
This frankly suggests to me that you can't understand what you read. I don't know how else to explain it. — Terrapin Station
A particular is what exhibits a(n instantiation of a) property. It has nothing to do with anything being continuous or discrete. — Terrapin Station
Would you say that there can't be change or motion if time and/or space aren't discrete? — Terrapin Station
It does if a property is itself a real continuum — aletheist
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