An attempt is made in the present essay to accommodate various senses of the notion of existence and ofthat of non-existence within the framework of logic. With this aim in view a system of Lesniewski's Ontology, referred to as System S, is outlined. Equipped with appropriate definitions and illustrated with a selection of theses it offers a logical theory of existence and non-existence. The usefulness of the theory is then tested by interpreting in its terms some of the principal notions and assertions of Meinong's ontology. A few brief comments on the notion of 'possible object' and on 'semantics' of fiction conclude the essay.

Four questions are raised about the semantics of Quantified Modal Logic (QML). Does QML admit possible objects, i.e. possibilia? Is it plausible to admit them? Can sense be made of such objects? Is QML committed to the existence of possibilia?The conclusions are that QML, generalized as in Kripke, would seem to accommodate possibilia, but they are rejected on philosophical and semantical grounds. Things must be encounterable, directly nameable and a part of the actual order before they may plausibly enter into the identity relation. QML is not committed to possibiha in that the range of variables may be restricted to actual objects.Support of the conclusions requires some discussion of substitution puzzles; also, the semantical distinction between proper names which are directly referring, and descriptions even where the latter are "rigid designators".Views of W.V. Quine, B. Russell, K. Donnellan, D. Kaplan as well as S. Kripke are invoked or evaluated in conjunction with these issues.

Brentano's famous thesis of the Intentionality of the Mental was already formulated by Thomas Reid who used it in his campaign against the Locke-Berkeley-Hume Theory of Ideas. Apphed to the case of conceiving the thesis says that to conceive is to conceive something. This principle stands in apparent conflict with the common-sensical view, defended by Reid, that we can conceive what does not exist. Both principles, it is argued, are plausible and should be retained. The problem is how to resolve the apparent contradiction. Reid's way out of the dilemma is clarified by contrasting it with less satisfactory solutions.

The view that a possible world is an existing abstract object implies that all nonexistent possible individuals have a principle of individuation in terms of existing objects, properties, and relations. However, some individuals of this kind are totally out of this world both in the subjective sense that nobody in this world can pick them out, and in the ontological sense that they would neither be created by assembling or arranging existing bits of matter nor otherwise be generated by existing items. The only acceptable principle of individuation for such nonexistent possibles is that they are individuated by their unexemplified haecceities.

The question ''Was 'existence' ever a predicate?" in a way already suggests its own answer, that this is really the wrong question to ask, because 'existence' has always been a predicate. Even those, such as Kant, who supposedly opposed this view, in fact held it. They merely denied that 'existence' is a "normal" first-order predicate. Not only Kant, but also Bolzano, Frege and Russell claimed that it is a second-order predicate. There is substantive disagreement between Kant and Bolzano on the one hand and Frege and Russell on the other over two issues: the former claim that this second-order predicate apphes to no concept analytically and that it can be properly ascribed to a singular concept, whereas the latter deny both of these claims.

Meinong justifies the need of his Gegenstandstheorie by presenting it as a generalization of (existing) metaphysics, in that the former deals with both existent and non-existent objects, whereas the latter used to deal with existent objects only. But this justification is disingenuous, since the notion of a non-existent object is virtually a contradiction in terms for the traditional paradigm. What Meinong is really proposing is a conceptual revolution of a Kantian variety, and we need to get clearer about the full import of this revolution. This is what the present paper attempts to do.

Nothing can be said about a nonexistent object, but something can be said about the act of (unsuccessfully) attempting to refer to one or, as in fiction, of pretending to refer to one. Unsuccessful reference, whether by expressions or by speakers, can be explained straightforwardly within the context of the theory of speech acts and communication. As for fiction, there is nothing special semantically, as to either meaning or reference, about its language. And fictional discourse is just a distinctive use of ordinary language: pretended communication and within it, pretended reference. However, discourse about fiction is not pretense but is normal communication, a kind of indirect discourse. To describe the world of a fiction is to state what the fiction says (or implies); and what seems to be reference to a fictional character is really attributing (usually implicitly) a feigned reference by the author.

Kant asserts that we cannot represent to ourselves the non-existence of space. In his discussion of the Ontological Argument he maintains that there is nothing whose non-existence is inconceivable. He thus seems to contradict himself. If the non-existence of space is unthinkable, so is the non-existence of a part of space — a place. Indicating a particular place, we might say "There are no objects there", but it would be nonsense to say "There doesn't exist". We can say, as Aristotle saw, "There is a place where there was water and where there is now air"; but to do so is to bind an adverbial variable with a quantifier, not to attach "exists" to the name of a place. To assert of a place, or of space, that it exists or that it does not exist would be nonsense, and the unthinkable in that sense is not something whose negation is, as Kant thought, a necessary truth.

How are we to understand the intentionality of mental acts which lack existing objects? Two alternatives present themselves: the Meinongian, which would involve the postulation of special nonexistent objects; and the adverbial, which would appeal instead to special qualities of the acts themselves. The present paper, which draws on the hitherto neglected aesthetic writings of the Meinong school, is concerned with certain psychological and aesthetic implications of the adverbial approach. The 'substitution theory' of the title consists in the view that our experience of works of art can best be conceived in terms of special sorts of'modified' psychic phenomena which may be said to substitute or stand proxy for our normal emotional experiences. The job of the work of art, on this view, is precisely to bring about such proxy emotions within the psychic subject. This idea is shown to have imphcations for the treatment of aesthetic pleasure, as also for our understanding of the nature of artistic traditions and of the value of works of art.

Russell brought three arguments forward against Meinong's theory of objects. None of them depend upon a misinterpretation of the theory as is often claimed. In particular, only one is based upon a clash between Meinong's theory and Russell's theory of descriptions, and that did not involve Russell's attributing to Meinong his own ontological assumption. The other two arguments were attempts to find internal inconsistencies in Meinong's theory. But neither was sufficient to refute the theory, though they do require some revisions, viz. a trade-off between freedom of assumption and unhmited characterization. Meinong himself worked out the essentials of the required revisions.

This essay examines the role of non-existent objects in "epistemological ontology" — the study of the entities that make thinking possible. An earlier revision of Meinong's Theory of Objects is reviewed, Meinong's notions of Quasisein and Außersein are discussed, and a theory of Meinongian objects as "combinatorially possible" entities is presented.

The proposed synthesis is set within general object-theory. The underlying idea of the synthesis is that the alternative worlds semantics — arrived at in pursuit of a universal semantics (a general semantics for all languages, including relevant ones) and, connectedly, as part of a comprehensive object-theory — be applied also in fundamental physics, most importantly to the matter of the origin, history, and physical features of the cosmos, but as well, again connectedly, elsewhere, in particular in the interpretation of quantum theory. The universal semantics is a many worlds — a many nonexistent worlds — theory. The point of applying such an interpretation in cosmology also is explained by way of examples, concerning the understanding of the contingency of existence and the improbability of present arrangements. A resolution of the basic question, 'Why does anything at all exist?' is sketched, leading to the further question why the fundamental constants of physics have the particular surprisingly sensitive values they appear to have. Chauvinistic answers through anthropic principles are critically rejected, in favour of resolution by way of world selection.

Following Bolzano, I suggest that there are two types of entity: those that are states of other things and those that are not. The second type includes, not only substances, in the traditional sense, but also such abstract objects as numbers, attributes and propositions. It is argued that the theory of states, when combined with an intentional account of negative attributes, will yield a theory of negative entities and of events.

The God of the Biblical and patristic tradition, though perhaps incomplete, possesses properties including those that involve genidentity or C-connections with us. Thus God's existence is at least possible. Using a modified version of Parson's elaboration of Meinong's theory of objects, we find that God exists if we do. But we also find that much else exists if we do; rather too much for confident belief.

Anti-Meinongian philosophers, such as Russell, do not explain what they mean by existence when they deny that there are nonexistent objects — they just sense robustly. I argue that any plausible explanation of what they mean tends to undermine their view and to support the Meinongian view. But why are they so strongly convinced that they are right? I argue that the reason is to be found in the special character of the concept of existence, which has been insufficiently examined by anti-Meinongian as well as by Meinongian philosophers.

This essay argues for the importance of developing theories of nonexistent objects. The grounds are utility and smoothness of logical theory. In the latter case a parallel with the theory of negative and imaginary numbers is exploited. The essay concludes with a counterexample to a general argument against the enterprise of developing theories of nonexistent objects, and outlining the foremost problem an adequate theory of nonexistent objects must solve.

In a recent book, K. Lambert argues that philosophers should adopt Mally's Principle of Independence (the principle that an object can have properties even though it lacks being of any kind) by abandoning a constraint on true predications, namely, that all of the singular terms in a true predication denote objects which have being. The constraint may be abandoned either by supposing there is a true predication in which one of the terms denotes a beingless object (Meinong) or by supposing there is a true predication in which one of the terms denotes nothing at all (free logic). However, Lambert's conclusions can be undermined by showing that the data he produces in support of his position can be explained by either of two recent theories of abstract and nonexistent objects, both of which are couched in languages which conform to the traditional constraint.

Parmenides didn't mention reference as such, but if he had he would have undoubtedly agreed with the philosophers who nowadays hold what is called "the axiom of existence": that one can only refer to what exists. The sources of possible support for this view are examined and rejected. Primary support for the axiom is given by two sorts of argument; one concerning quantification, the other summarizing a standard Parmenidean puzzle. Weaknesses in both are exposed. Finally, the relations between the axiom and connected claims about predication and truth are probed, and an attempt is made to determine the limits of the mutual support these claims give one another.