Q:

What is existence and what kinds of it can be distinguished?

Existence, for instance of a human being, need not be restricted to the material body. Also the influence exerted on the environment can be considered a part of their existence. A discussion with Conifold has made me think that there are at least three kinds of existence:
(a) Material things like particles, substances, bodies, liquids, gases, creatures with or without labels or names stored in memories but exerting some physical influence on their environment. As an example the gravitational force of a body, the electromegnetic fileld of a particle, a picture of a human or a letter written by him/her belongs to his/her existence. 
(b) Ideas with representations like "electron" or "number three". Every electron and every triple are representations of these notions and belong to the existence of these notions. But also a picture or a symbol standing for them belong to their existence.
(c) Ideas with only representations like unicorns. There are no material representations of unicorns but plenty of pictures. But there are also bones which (for instance by Leibniz) had been attributed to unicorns. And there are organic molecules which would belong to unicorns if they were bred.
My question: Are there philosophers who have thought along these lines already? In particular have the influence exerted on the environment and the representation been considered part of existence? And if so, could the blurred border between (b) and (c) be cleared? 

A:

The problem of hierarchy of being dates back to Plato, who introduced "becoming" to reconcile the sensible world with Parmenides's prohibition on change in being. In Aristotle, who recognizes forms and matter as aspects of being this leads to the problem of universals, prominent in the medieval scholastics, if they are not Platonic entities what is their mode of being? I will not go over the general problem of universals since the subject is vast and well-covered by encyclopedias. The closest positions to the OP description I can think of are Peirce's theory of entia rationis ("creations of mind", as he also calls them), and Meinong's theory of non-existent objects. Peirce directly studied scholastic doctors involved with the problem of universals, especially Duns Scotus, and so did Meinong's teacher, Brentano, who introduced intentionality and intentional inexistence into modern discourse (Husserl was also a student of Brentano's).
According to Peirce, entia rationis are initially introduced by nominalizing predicates into subjects, "the new individual spoken of is ens rationis; that is, its being consists in some other fact". So we pass from "x is red" to "x has redness", this is called nominalization or hypostatic abstraction, and the new "object" fully supervenes on whatever underlies the pre-nominalized facts ("representations", "manifestations", etc.). It is the latter, which determine its mode of being. Frege had a similar notion of abstraction based on his context principle, but he did not develop it into a hierarchy of being for abstracta. Peirce uses entia rationis to even partly rehabilitate Molière's famous satire of a scholastic "explanation" that opium puts people to sleep because it has dormitive virtue, "for it does say there is some peculiarity in the opium to which sleep must be due". While it is ridiculous as a final explanation, it is exactly the kind of operational that-which definition that sets off a scientific inquiry. At their inception, temperature (that which thermometer measures), weight, voltage, etc., were such hypostatic that-whiches. I'll quote from Peirce's Theory of Signs by Short:

"These same examples teach us to be cautious about denying reality to an ens rationis. For all of the quantities mentioned – voltage, temperature, and so on – are consequential: all explain a range of effects. And each exists or obtains at a particular place and time (however vaguely these may be defined). Thus they have a physical reality, even if that reality
  ‘consists’ in the reality of certain other facts. Some entia rationis have only the being of a mathematical abstraction;
  others have physical reality; and some entities introduced by hypostatic abstraction are not entia rationis at all, for example, the alkaloid that is opium’s dormitive virtue..."
"If the inference is from true premisses and apodeictic, the introduced entity is an ens rationis, and it will have the same mode of being as those entities represented in the premisses: ideal in the case of pure mathematics, real in the case of empirical science. If the inference is not apodeictic but is abductive, then the entity introduced may fail to be real at all (even though the premisses be true), but, if it is real, it will be as real as the effects in terms of which it is introduced, whether it is an ens rationis or not".

In other words, the process of introducing entia rationis converts indefinite descriptions into objects on which they supervene, the description then may or may not have a further supervenience base in reality, and different kinds of bases are possible. In particular, numbers supervene not only on natural occurrences (sticks, grains of sand, etc.), but also on facts of our use of them as tools in counting, measuring, etc., i.e. on artifacts. This brings about the distinction between "physical" and "mathematical" numbers. The former can be empirically repudiated if certain class of real objects fails to conform to arithmetic, but not the latter. As our tools numbers are as "indestructible" as our cultural memory. So Ptolemy's epicyclics converted into a piece of pure geometry is still alive today, and so is Euclidean geometry, their revision as physical theories notwithstanding (Resnik calls such conversion "Euclidean rescue").
What about unicorns? They are also a that-which, that which is like a live horse with a horn. Does this make them akin to numbers in their artifactual role? Indeed it does. The distinction, if any, is to be found in our use of them as tools, on which their being supervenes. Unicorns are loose, poetic tools, their being is accordingly ephemeral, numbers, on the other hand, supervene on facts of a highly regimented practice, now supported by symbolic formalisms of decimals, Peano arithmetic, etc. Hence, facts about them have a much firmer hold on reality, although the difference is of degree and not of kind. And of course numbers do also have physical base of supervenience from which they were abstracted, while unicorns, so far as we know, do not.
Meinong goes even futher than Peirce in diluting being, he allows even inconsistent objects (e.g. round squares) to "subsist", if not to "exist", see SEP's Nonexistent Objects.

