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. (shrink)

Though Frege was interested primarily in reducing mathematics to logic, he succeeded in reducing an important part of logic to mathematics by defining relations in terms of functions. By contrast, Whitehead & Russell reduced an important part of mathematics to logic by defining functions in terms of relations (using the definite description operator). We argue that there is a reason to prefer Whitehead & Russell's reduction of functions to relations over Frege's reduction of relations to functions. There is an interesting (...) system having a logic that can be properly characterized in relational but not in functional type theory. This shows that relational type theory is more general than functional type theory. The simplification offered by Church in his functional type theory is an over-simplification: one can't assimilate predication to functional application.<br>. (shrink)

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. (shrink)

Formulations of Anselm’s ontological argument have been the subject of a number of recent studies. We examine these studies in light of Anselm’s text and (a) respond to criticisms that have surfaced in reaction to our earlier representations of the argument, (b) identify and defend a more refined representation of Anselm’s argument on the basis of new research, and (c) compare our representation of the argument, which analyzes that than which none greater can be conceived as a definite description, to (...) a representation that analyzes it as an arbitrary name. (shrink)

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. (shrink)

To explain the phenomena in the world of our experience, to answer the question “why?” rather than only the question “what?”, is one of the foremost objectives of all rational inquiry; and especially, scientific research in its various branches strives to go beyond a mere description of its subject matter by providing an explanation of the phenomena it investigates. While there is rather general agreement about this chief objective of science, there exists considerable difference of opinion as to the function (...) and the essential characteristics of scientific explanation. In the present essay, an attempt will be made to shed some light on these issues by means of an elementary survey of the basic pattern of scientific explanation and a subsequent more rigorous analysis of the concept of law and of the logical structure of explanatory arguments. (shrink)

The authors evaluate the soundness of the ontological argument they developed in their 1991 paper. They focus on Anselm’s first premise, which asserts that there is a conceivable thing than which nothing greater can be conceived. After casting doubt on the argument Anselm uses in support of this premise, the authors show that there is a formal reading on which it is true. Such a reading can be used in a sound reconstruction of the argument. After this reconstruction is developed (...) in precise detail, the authors show that the conclusion, a reading of the claim “God exists”, does not quite achieve the end Anselm desired. (shrink)

We wish to give a precise formulation of the intuitive concept: The degree to which the known facts support a given hypothesis.

Our computational metaphysics group describes its use of automated reasoning tools to study Leibniz’s theory of concepts. We start with a reconstruction of Leibniz’s theory within the theory of abstract objects (henceforth ‘object theory’). Leibniz’s theory of concepts, under this reconstruction, has a non-modal algebra of concepts, a concept-containment theory of truth, and a modal metaphysics of complete individual concepts. We show how the object-theoretic reconstruction of these components of Leibniz’s theory can be represented for investigation by means of automated (...) theorem provers and finite model builders. The fundamental theorem of Leibniz’s theory is derived using these tools. (shrink)

The authors evaluate the soundness of the ontological argument they developed in their 1991 paper. They focus on Anselm’s first premise, which asserts that there is a conceivable thing than which nothing greater can be conceived. After casting doubt on the argument Anselm uses in support of this premise, the authors show that there is a formal reading on which it is true. Such a reading can be used in a sound reconstruction of the argument. After this reconstruction is developed (...) in precise detail, the authors show that the conclusion, a reading of the claim “God exists”, does not quite achieve the end Anselm desired. (shrink)

1. The problem. The concept of confirmation of an hypothesis by empirical evidence is of fundamental importance in the methodology of empirical science. For, first of all, a sentence cannot even be considered as expressing an empirical hypothesis at all unless it is theoretically capable of confirmation or disconfirmation, i.e. unless the kind of evidence can be characterized whose occurrence would confirm, or disconfirm, the sentence in question. And secondly, the acceptance or rejection of a sentence which does represent an (...) empirical hypothesis is determined, in scientific procedure, by the degree to which it is confirmed by relevant evidence. (shrink)

"A wild and exuberant romp through the terrain of the monstrous . . . Oppenheimer's lucid explanations are the perfect antidotes to the sordid scenes he recreates." -American Book Review "A masterly and original study of one of the most frightening topics with which human beings have to struggle." -Literary Review "What is compelling, different and page-turning about this impressive book is that the author analyses evil through the medium of films and literature . . . Cinema buffs will find (...) it a fascinating read." -Evening Standard The notion of evil- does it exist? what forms does it take? -has always fascinated humankind. The evil underlying such atrocities as the Holocaust, Communist China's Tibetan abattoir, and the murderous ethnic cleansing undertaken by the Serbs and Croats seems beyond explanations or analysis. In this powerfully original work, Oppenheimer analyzes the phenomenon of evil in a mental behavior that emerges in particular conditions. Oppenheimer argues that evil contains specific, predictable ingredients. By understanding its nature, we can diagnose its specific manifestations in mass murder, genocide, and serial killings. Utilizing a variety of cinematic and literary genres in developing its evidence, the book considers such familiar films as The Silence of the Lambs and Brazil , and draws upon such literary works as Richard III, Oedipus the King and the Picture of Dorian Gray. Evil and the Demonic takes a bold first step, providing a framework in which to place the horrors of human existence. (shrink)

The topic of fictional objects is a familiar one, the topic of fictional properties less so. But it deserves its own place in the philosophy of fiction, if only because fictional properties have such a prominent role to play in science fiction and fantasy. What, then, are fictional properties and how does their apparent unreality relate to the unreality of fictional objects? The present paper explores these questions in the light of familiar debates about the nature of fictional objects.

ABSTRACT The target article uses the metaphysics of properties to make its meta-ethical claims. This comment discusses two general points in the metaphysics of properties. The first point has to do with the conditions for property identity. Philosophers who accept the existence of properties have proposed a variety of criteria for their identity. The standard Broome applies is medium coarse. Other standards for property identity could be evaluated for their appropriateness for addressing questions in the metaphysics of ethics. Use of (...) a formalized theory of properties might help in such an evaluation. The second point has to do with Broome’s suggestion of a distinction between a property and a reified property. A suggestion will be offered for a range of ways such a distinction could be filled out using the resources of a formalized theory of properties and objects. Objects will be proposed that could serve as Broome’s reified properties. (shrink)

Carrier in a recent paper urges for consideration an argument for skepticism which is based on premises one of which in turn is to be defended by yet another principle (the "Janus Principle" of the text). We feel that the latter principle and the way Carrier wants to use it to defend his skeptical argument will find adherents, but we show that this argument rests on an interesting equivocation quite beyond repair even if we accept the "Janus Principle".

La théorie traditionnelle des concepts étant classificatoire, ne comprend qu’une partie des formes de notre pensée. Comme complément nécessaire, l’auteur met en relief l’importance d’une catégorie de concepts qu’il propose de dénommer « concepts ordinateurs », parce qu’ils déterminent un certain ordre des objets de leur domaine d’application. Leur structure logique est élucidée par la théorie logistique des relations. L’auteur compare les avantages et les désavantages des deux formes de pensée et explique les raisons pour lesquelles une tendance à favoriser (...) les concepts ordinateurs correspond au progrès de notre connaissance. (shrink)

In 1948 Hempel and Oppenheim proposed an explicatum for the concept of systematic power 1, pp. 164–167. Since that time some shortcomings have been found in this first attempt. It is the purpose of this paper to show that one can keep the basic approach of the ‘48 paper, and overcome the known disadvantages by means of changes in the details of the definition. In this improvement certain tools will be used that were not available in 1948.

Like a number of other authors, Miller uses the term “emergent” interchangeably with “unpredictable” and employs it as a property term, i.e., in contexts of the form “Event E is emergent.” As we showed in our article, however, predictability and unpredictability as well as emergence are relations; they can be predicated of an event only relatively to some body of information. Thus, a lunar eclipse is predictable by means of information including data on the locations and speeds, at some particular (...) time, of the celestial bodies involved, and the laws of celestial mechanics plus certain principles of optics; it is unpredictable on the basis of, say, alone. Consequently, the phrase “Event E is unpredictable” is incomplete, and hence meaningless, in much the same sense as the expression “Straight line l is parallel.” Similar observations apply to the term “emergent,” which is frequently used to characterize events which, in a sense examined in detail in our article, are not explainable by a micro-structure theory. (shrink)