Everything that exists does so in some definite quantity. Existence is that property of conceptual referents such that they necessarily exist in some definite quantity.
I'm confused by this mix of referring to things that exist and referring to existence as a property of conceptual referents. Are you saying that conceptual referents are the things that exist in finite and definite quantity? Or are you saying something else?
definite quantity
I see that you are claiming that existing things are bounded in some quantifiable way, but you do not seem to account for the inherent uncertainty of determining quantities.
The identification of a definite quantity requires a quantifier. Some uncertainty comes from the implementation of this quantifier; if it is incorrect then the identified quantity would be wrong. You could handle this by verifying the implementation of the quantifier, but that only pushes the uncertainty into the context of verification. To use the quantifier you must choose to halt the regression of verification and accept the remaining uncertainty.
Additional uncertainty comes from the choice of the quantifier. The quantifier used is one choice from a large and possibly infinite set of possible quantifiers. Not all of these quantifiers would provide the same answer--or even provide a "reasonable" answer, for example by replying with "hat" instead of a number like "2".
For example: I scoop up a handful of gravel from a beach. I want to count the stones in my hand. But my hand contains all kinds of stuff; rocks and dirt from the size of dust to a couple inches across, bits of wood, shell, and other organic debris. Out of this mess which bits of the stuff are stones? It depends on how I quantify stones; is it by volume, apparent area, mass, composition, color, texture... there are many possible measurements, and combination of measurements. I choose one way of counting stones and get a quantity of 5, but it could have been 1 or 1000 or "blue hat" if I had made other choices.
Given this uncertainty, how can I know that only a "definite quantity" of stones exist in my hand?
[Crossposted; Based on Can infinite quantities exist? A philosophical approach (downvoted)
The topic is the concept of existence, not why there's something rather than nothing—not the fact of existence—but the bare concept brings its own austere delights. Philosophical problems arise from our conflicting intuitions, but “existence” is a primitive element of thought because our intuitions of it are so robust and reliable. Of course, we disagree about whether certain particulars (such as Moses) have existed and even about whether some general kinds (such as the real numbers) exist, but disputes don’t concern the concept of existence itself. If Moses’s existence poses any conceptual problem, it concerns what counts as being him, not what counts as existence. Adult readers never seriously maintain that fictitious characters exist; they disagree about whether a given character is fictitious; even the question of the existential status of numbers is a question about numbers rather than about existence. As will be seen, sometimes philosophers wrongly construe these disputes as being about existence.
When essay 19.0 asked “Can infinite quantities exist?” existence’s meaning wasn't in play—infinity’s was. Existence is well-suited for the role as a primitive concept in philosophy because it is so unproblematic, but it’s unproblematic nature can be thought of as a kind of problem, in that we want to know why this concept is uniquely unproblematic. We would at least like to be able to say something more about it than merely that it’s primitive, but in philosophy, we acquire knowledge by solving problems and existence fails to provide any but the unhelpful problem of its being unproblematic. The problem of infinity provides, in the end, some purchase on the concept of existence, which concept I assumed in dealing with infinity.
In one argument against actual infinity, I proposed as conceptually possible that separate things might be distinguishable only concerning their being separate things. Then, if we assume that infinite sets can exist, the implication is the contradiction that an infinite set and its successor—when still another point pops into existence—are the same set because you can’t distinguish them. (In technical terms, the only information that could distinguish the set and its successor, given that their members are brutely distinguishable, is their cardinality, which is the same—countably infinite—for each set.)
What’s interesting here is the role of existence, which imposes an additional constraint on concepts besides the internal consistency imposed by the mathematics of sets. Whereas we are unable to distinguish existing points, we are able—in a manner of speaking—to distinguish points that exist from those that don’t exist. While no proper subsets are possible for existing brutely distinguishable points, the distinction within the abstract set of points between “those” that exist and “those” that don’t exist allows us to extend the successor set by moving the boundary, resulting in contradiction.
If finitude is a condition for existence, we’ve learned something new about the concept of existence. Its meaning is imbued with finitude, with definite quantity. Everything that exists does so in some definite quantity. Existence is that property of conceptual referents such that they necessarily exist in some definite quantity.
Existence is primitive because almost everyone knows the term and can apply it to the extent they understand what they’re applying it to. The alternative to primitive existence is primitive sensation, as when Descartes derived his existence from his “thinking.” But sensationalism is incoherent; “experiences” inherently lacking in properties (“ineffable”) are conceived as having properties (“qualia”). So, the heirs of extreme logical empiricism, from Rudolf Carnap to David Lewis, have challenged existence’s primitiveness. Carnap defined existence by the place of concepts in a fruitful theory. Lewis applies this positivist maxim to find that all possible worlds exist. Lewis isn’t impelled by an independent theory of logical existence, such as a Platonic theory that posits actually realized idealizations. Rather, the usefulness of possible worlds in logic requires their acceptance, according to Lewis, because that’s all that we mean by “exists.” Lewis is driven by this theory of existence to require infinitely many existing possible worlds, which disqualifies it on other grounds. But the grounds aren’t separate. When you don’t apply the constraints of existence because you deny their intuitive force, you lose just that constraint imposing finitude. The incoherence of sensationalism and of actual infinities argues for a metaphysics upholding the primacy of common-sense existence.