Edward Zalta

In this paper, the author develops a theory of concepts and shows that it captures many of the ideas about concepts that Leibniz expressed in his work. Concepts are first analyzed in terms of a precise background theory of abstract objects, and once concept summation and concept containment are defined, the axioms and theorems of Leibniz's calculus of concepts (in his logical papers) are derived. This analysis of concepts is then seamlessly connected with Leibniz's modal metaphysics of complete individual concepts. The fundamental theorem of Leibniz's modal metaphysics of concepts is proved, namely, whenever an object x has F contingently, then (i) the individual concept of x contains the concept F and (ii) there is a (counterpart) complete individual concept y which doesn't contain the concept F and which `appears' at some other possible world. Finally, the author shows how the concept containment theory of truth can be made precise and made consistent with a modern conception of truth

In this paper, the authors show that there is a reading of St. Anselm's ontological argument in Proslogium II that is logically valid (the premises entail the conclusion). This reading takes Anselm's use of the definite description "that than which nothing greater can be conceived" seriously. Consider a first-order language and logic in which definite descriptions are genuine terms, and in which the quantified sentence "there is an x such that..." does not imply "x exists". Then, using an ordinary logic of descriptions and a connected greater-than relation, God's existence logically follows from the claims: (a) there is a conceivable thing than which nothing greater is conceivable, and (b) if <em>x</em> doesn't exist, something greater than x can be conceived. To deny the conclusion, one must deny one of the premises. However, the argument involves no modal inferences and, interestingly, Descartes' ontological argument can be derived from it.

The foregoing set of theorems forms an effective foundation for the theory of situations and worlds. All twenty-five theorems seem to be basic, reasonable principles that structure the domains of properties, relations, states of affairs, situations, and worlds in true and philosophically interesting ways. They resolve 15 of the 19 choice points defined in Barwise (1989) (see Notes 22, 27, 31, 32, 35, 36, 39, 43, and 45). Moreover, important axioms and principles stipulated by situation theorists are derived (see Notes 33, 37, and 38). This is convincing evidence that the foregoing constitutes a theory of situations. Note that worlds are just a special kind of situation, and that the basic theorems of world theory, which were derived in previous work, can still be derived in this situation-theoretic setting. So there seems to be no fundamental incompatibility between situations and worlds — they may peacably coexist in the foundations of metaphysics. The theory may therefore reconcile two research programs that appeared to be heading off in different directions. And we must remind the reader that the general metaphysical principles underlying our theory were not designed with the application to situation theory in mind. This suggests that the general theory and the underlying distinction have explanatory power, for they seem to relate and systematize apparently unrelated phenomena

In its approach to fiction and fictional discourse, pretense theory focuses on the behaviors that we engage in once we pretend that something is true. These may include pretending to name, pretending to refer, pretending to admire, and various other kinds of make-believe. Ordinary discourse about fictions is analyzed as a kind of institutionalized manner of speaking. Pretense, make-believe, and manners of speaking are all accepted as complex patterns of behavior that prove to be systematic in various ways. In this paper, I attempt to show: (1) that this systematicity is captured in the basic distinctions and representations that are central to the formal theory of abstract objects, and (2) that this formal theory need not be interpreted platonistically, but may instead have an interpretation on which the `objects' of the theory are things that pretense theorists already accept, namely, complex patterns of linguistic behavior. The surprising conclusion, then, is that a certain Wittgensteinian approach to meaning (e.g., the meaning of a term like `Holmes' is constituted by its pattern of use) bears an interesting relationship to a formal metaphysical theory and the semantic analyses of discourse constructed in terms of that theory---the former offers a naturalized interpretation of the latter, yet the latter makes the former more precise.

In this paper, I respond to D. Jacquette's paper, "Mally's Heresy and the Logic of Meinong's Object Theory" (History and Philosophy of Logic, 10 (1989): 1-14), in which it is claimed that Ernst Mally's distinction between two modes of predication, as it is employed in the theory of abstract objects, is reducible to, and analyzable in terms of, a single mode of predication plus the distinction between nuclear and extranuclear properties. The argument against Jacquette's claims consists of counterexamples to his reductions and analyses. Reasons are offered for thinking that no such reduction/analysis of the kind Jacquette proposes could be successful.

This book tackles the issues that arise in connection with intensional logic -- a formal system for representing and explaining the apparent failures of certain important principles of inference such as the substitution of identicals and existential generalization -- and intentional states --mental states such as beliefs, hopes, and desires that are directed towards the world. The theory offers a unified explanation of the various kinds of inferential failures associated with intensional logic but also unifies the study of intensional contexts and intentional states by grounding the explanation of both phenomena in a single theory. When an axiomatized realm of abstract entities is added to the metaphysical structure of the world, we can use them to identify and individuate the contents of directed mental states. The special abstract entities can be viewed as the objectified contents of mental files, and they play a crucial role in the analysis of truth conditions of the sentences involved in inferential failures.

These lecture notes were composed while teaching a class at Stanford and studying the work of Brian Chellas (Modal Logic: An Introduction, Cambridge: Cambridge University Press, 1980), Robert Goldblatt (Logics of Time and Computation, Stanford: CSLI, 1987), George Hughes and Max Cresswell (An Introduction to Modal Logic, London: Methuen, 1968; A Companion to Modal Logic, London: Methuen, 1984), and E. J. Lemmon (An Introduction to Modal Logic, Oxford: Blackwell, 1977). The Chellas text influenced me the most, though the order of presentation is inspired more by Goldblatt.2 My goal was to write a text for dedicated undergraduates with no previous experience in modal logic. The text had to meet the following desiderata: (1) the level of difficulty should depend on how much the student tries to prove on his or her own—it should be an easy text for those who look up all the proofs in the appendix, yet more difficult for those who try to prove everything themselves; (2) philosophers (i.e., colleagues) with a basic training in logic should be able to work through the text on their own; (3) graduate students should find it useful in preparing for a graduate course in modal logic; (4) the text should prepare people for reading advanced texts in modal logic, such as Goldblatt, Chellas, Hughes and Cresswell, and van Benthem, and in particular, it should help the student to see what motivated the choices in these texts; (5) it should link the two conceptions of logic, namely, the conception of a logic as an axiom system (in which the set of theorems is constructed from the bottom up through proof sequences) and the conception of a logic as a set containing initial ‘axioms’ and closed under ‘rules of inference’ (in which the set of theorems is constructed from the top down, by carving out the logic from the set of all formulas as the smallest set closed under the rules); finally, (6) the pace for the presentation of the completeness theorems should be moderate—the text should be intermediate between Goldblatt and Chellas in this regard (in Goldblatt, the completeness proofs come too quickly for the undergraduate, whereas in Chellas, too many unrelated....

The authors investigated the ontological argument computationally. The premises and conclusion of the argument are represented in the syntax understood by the automated reasoning engine PROVER9. Using the logic of definite descriptions, the authors developed a valid representation of the argument that required three non-logical premises. PROVER9, however, discovered a simpler valid argument for God's existence from a single non-logical premise. Reducing the argument to one non-logical premise brings the investigation of the soundness of the argument into better focus. Also, the simpler representation of the argument brings out clearly how the ontological argument constitutes an early example of a ?diagonal argument? and, moreover, one used to establish a positive conclusion rather than a paradox

In this paper, the authors discuss Frege's theory of "logical objects" and the recent attempts to rehabilitate it. We show that the 'eta' relation George Boolos deployed on Frege's behalf is similar, if not identical, to the encoding mode of predication that underlies the theory of abstract objects. Whereas Boolos accepted unrestricted Comprehension for Properties and used the 'eta' relation to assert the existence of logical objects under certain highly restricted conditions, the theory of abstract objects uses unrestricted Comprehension for Logical Objects and banishes encoding formulas from Comprehension for Properties. The relative mathematical and philosophical strengths of the two theories are discussed. Along the way, new results in the theory of abstract objects are described, involving: the theory of extensions, the theory of directions and shapes, and the theory of truth values.

The author engages a question raised about theories of nonexistent objects. The question concerns the way names of fictional characters, when analyzed as names which denote nonexistent objects, acquire their denotations. Since nonexistent objects cannot causally interact with existent objects, it is thought that we cannot appeal to a `dubbing' or a `baptism'. The question is, therefore, what is the starting point of the chain? The answer is that storytellings are to be thought of as extended baptisms, and the details of this response receive attention in the paper. Once the storytelling is complete, and the characters have been baptized, a priori metaphysical principles linking the storytelling with the realm of nonexistent objects provide the referential, non-causal connection between the names used in the storytelling and the objects denoted by such names. [This is the original English version of an article that first appeared in German translation, translated into German by Arnold Günther and published in the Zeitschrift für Semiotik 9/1-2 (1987): 85-95. The version that appears here is, for the most part, unaltered.].