For instance, the number “2” exists outside spacetime. — Art48
... and including this cat person — Bartricks
By the way, and roughly speaking, I think implication in logic is something that happens within statements (if then), whereas entailment happens within arguments, that is, between sets of statements and a conclusion. — Jamal
So, tell me,when someone says 'imply' do you think they mean 'entail'? — Bartricks
imply : strongly suggest the truth or existence of (something not expressly stated):
"the salesmen who uses jargon to imply his superior knowledge" · "the report implies that two million jobs might be lost"
woo-woo : dubiously or outlandishly mystical, supernatural, or unscientific
A metaphysical infinity has absolutely no limits or boundaries. Due to this, it cannot be discerned as a unit: it is immeasurable in all senses and respects and hence, when ontically addressed (rather than addressed in terms of being a concept) it is nonquantifiable. As a thought experiment, try to imagine two ontically occurring metaphysical infinities side by side; since neither holds any delimitations (be these spatial, temporal, or any other) how would you either empirically or rationally discern one from the other so as to establish that there are two metaphysical infinities? In wordplay games, we can of course state, “two metaphysical infinities side by side” but the statement is nonsensical. More concretely, ontic nothingness, i.e. indefinite nonoccurrence - were it to occur (but see the paradox in this very affirmation: the occurrence of nonoccurrence, else the being (is-ness) of nonbeing) - is one possible to conceive example of metaphysical infinity. Can one have 1, 2, 3, etc., ontic nothingnesses in any conceivable relation to each other? (My answer will be “no” for the reasons just provided regarding metaphysical infinity. However, if you believe this possible, please explain on what empirical or rational grounds.) — javra
... and that of “non-metaphysical" (aka, countable, mathematical) infinity (such as can be found in a geometric line of infinite length), — javra
Seeing how I’m having a hard time in even getting people to understand the problem, my only current conclusion regarding this problem is that it’s so dense that I needn’t concern myself with it when specifying metaphysical possibilities of determinacy. — javra
...with the supposition that any of this makes sense. — Banno
determinacy/indeterminacy and finitude/infinitude are defined by the ontic presence or absence of limits/boundaries — javra
its width and shape is subject to fully set limits or boundaries, thereby endowing the geometric line with a definite uncurved length. — javra
Yet the infinite length of a geometric line is definite, — javra
Mapping : any prescribed way of assigning to each object in one set a particular object in another (or the same) set. Mapping applies to any set: a collection of objects, such as all whole numbers, all the points on a line, or all those inside a circle. For example, “multiply by two” defines a mapping of the set of all whole numbers onto the set of even numbers. A rotation is a map of a plane or of all of space into itself. In mathematics, the words mapping, map, and transformation tend to be used interchangeably.
If there was a spot on the reflective surface, a point on the plane, which reflected back on itself, "itself" being a point on the reflective surface, would reflect it again. back on itself, and again and again. — Metaphysician Undercover
The analogy really does not work Real Gone Cat. A reflection is light rebounding back off a reflective surface, which you represent as a plane. If there was a spot on the reflective surface, a point on the plane, which reflected back on itself, "itself" being a point on the reflective surface, would reflect it again. back on itself, and again and again. This would create an endless back and forth between the spot and itself. This is like having two mirrors in front of each other, accept that your proposal builds this right into the single plane, or reflective surface..
If such spots existed on the surface, each spot would effectively annihilate the capacity of the mirror to properly reflect at that point because the reflection would get absorbed into the infinite back and forth with itself. So if the rules of mathematics allow that zero "maps to itself" in this way, this would effectively annihilate the integrity of the concept "zero", as such a reflective surface (separation) between positive and negative, just like a spot on the mirror reflecting back and forth on itself would absorb the light and not reflect outward, ruining the integrity of the mirror as a reflective surface. — Metaphysician Undercover
If we allow that "zero" implies both positive and negative (in a self reflecting way) in common applications, instead of neither (as we actually do), this would destroy the integrity of "zero" — Metaphysician Undercover
By the way, 0 is neither positive nor negative, so let's drop that nonsense now. — Real Gone Cat
Okay. But isn't that just to say either there's no math that defines a value for it or that you're unfamiliar with math that does.
To just say, nope, is like saying negative numbers don't have square roots, or, for that matter, that 2 doesn't. — Srap Tasmaner
Why not use a pair of these? . They are commonly used in math. You could come up with the first being infinitesimals just to the right of zero, etc.
There are your "opposites" of zero. — jgill
You're the one who seems to be insisting that the rules you've mentioned have no use even within the realm of math itself. — frank