Ontological dependence is a relation—or, more accurately, a family of relations—between entities or beings. For there are various ways in which one being may be said to depend upon one or more other beings, in a sense of “depend” that is distinctly metaphysical in character and that may be contrasted, thus, with various causal senses of this word. More specifically, a being may be said to depend, in such a sense, upon one or more other beings for its existence or (...) for its identity. Some varieties of ontological dependence may be analyzed in modal terms—that is, in terms of distinctly metaphysical notions of possibility and necessity—while others seem to demand an analysis in terms of the notion of essence. The latter varieties of ontological dependence may accordingly be called species of essential dependence. Notions of ontological dependence are frequently called upon by metaphysicians in their proposed analyses of other metaphysically important notions, such as the notion of substance. (shrink)

In this paper, we discuss formal reconstructions of Anselm’s ontological argument. We first present a number of requirements that any successful reconstruction should meet. We then offer a detailed preparatory study of the basic concepts involved in Anselm’s argument. Next, we present our own reconstructions—one in modal logic and one in classical logic—and compare them with each other and with existing reconstructions from the reviewed literature. Finally, we try to show why and how one can gain a better understanding of (...) Anselm’s argument by using modern formal logic. In particular, we try to explain why formal reconstructions of the argument, despite its apparent simplicity, tend to become quite involved. (shrink)

Traditional logical reconstruction of arguments aims at assessing the validity of ordinary language arguments. It involves several tasks: extracting argumentations from texts, breaking up complex argumentations into individual arguments, framing arguments in standard form, as well as formalizing arguments and showing their validity with the help of a logical formalism. These tasks are guided by a multitude of partly antagonistic goals, they interact in various feedback loops, and they are intertwined with the development of theories of valid inference and adequate (...) formalization. This paper explores how the method of reflective equilibrium can be used for modelling the complexity of such reconstructions and for justifying the various steps involved. The proposed approach is illustrated and tested in a detailed reconstruction of the beginning of Anselm’s De casu diaboli. (shrink)

We present an embedding of quantified multimodal logics into simple type theory and prove its soundness and completeness. A correspondence between QKπ models for quantified multimodal logics and Henkin models is established and exploited. Our embedding supports the application of off-the-shelf higher-order theorem provers for reasoning within and about quantified multimodal logics. Moreover, it provides a starting point for further logic embeddings and their combinations in simple type theory.

Davidson attacks the intelligibility of conceptual relativism, i.e. of truth relative to a conceptual scheme. He defines the notion of a conceptual scheme as something ordering, organizing, and rendering intelligible empirical content, and calls the position that employs both notions scheme-content dualism. He argues that such dualism is untenable since: not only can we not parcel out empirical content sentence per sentence but also the notion of uninterpreted content to which several schemes are relative, and the related notion of a (...) theory ”fitting the evidence’, can be shown to lack intelligibility too. Davidson argues further that belief in incommensurable schemes or non-intertranslatable languages is possible only on violating a correct understanding of interpretability : if we succeed in interpreting someone else then we have shown there is no need to speak of two conceptual schemes, while if we fail ”there is no ground for speaking of two.’. (shrink)

The term ‘meaning holism’ has been used for a number of more or less closely interrelated ideas. According to one common view, meaning holism is the thesis that what a linguistic expression means depends on its relations to many or all other expressions within the same totality. Sometimes these relations are called ‘conceptual’ or ‘inferential’. A related idea is that what an expression means depends, mutually, on the meaning of the other expressions in the totality, or alternatively on some semantic (...) property of this totality itself. The totality in question may be the language to which the expressions belong, or a theory formulation in that language. (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)

Peter Pagin Is the principle of semantic compositionality compatible with the principle of semantic holism? The question is of interest, since both principles have a lot that speaks for them, and since they do seem to be in conflict. The view that natural languages have compositional structure is almost unavoidable, since linguistic communication by means of new combinations of words would be virtually incomprehensible otherwise. And holism too seems generally plausible, since the meaning of an expression is directly connected with (...) the way that expression interacts with other. (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)

Kurt Gödel’s version of the ontological argument was shown by J. Howard Sobel to be defective, but some plausible modifications in the argument result in a version which is immune to Sobel’s objection. A definition is suggested which permits the proof of some of Godel’s axioms.

We describe a KB Gödelian ontological system, and some other weak systems, in a fully formal way using theory of types and natural deduction, and present a completeness proof in its main and specific parts. We technically and philosophically analyze and comment on the systems (mainly with respect to the relativism of values) and include a sketch of some connected aspects of Gödel's relation to Kant.

Different religious traditions offer apparently very different pictures of the world. How are we to make sense of this radical diversity of religious belief? In this book, Professor Godlove argues that religions are alternative conceptual frameworks, the categories of which organise experience in diverse ways. He traces the history of this idea from Kant to Durkheim, and then proceeds to discuss two constraints on the diversity of all human judgment and belief: first that human experience is made possible by shared, (...) a priori rules, and second, that as language-users we must presuppose that we hold the vast bulk of our beliefs in common. Given these unavoidable constraints, it is clear how religions may offer encompassing symbolic systems that often diverge dramatically from one another. 'An original and brilliant critique of Durkheim and Kant from within the framework of Davidson's semantic theory. This book is required reading for anyone interested in the academic study of religion, and the problems of relativism and the diversity of belief.' -- Hans H. Penner, Dartmouth CollegeDifferent religious traditions offer apparently very different pictures of the world. How are we to make sense of this radical diversity of religious belief? In this book, Professor Godlove argues that religions are alternative conceptual frameworks, the categories of which organise experience in diverse ways. He traces the history of this idea from Kant to Durkheim, and then proceeds to discuss two constraints on the diversity of all human judgment and belief: first that human experience is made possible by shared, a priori rules, and second, that as language-users we must presuppose that we hold the vast bulk of our beliefs in common. Given these unavoidable constraints, it is clear how religions may offer encompassing symbolic systems that often diverge dramatically from one another. 'An original and brilliant critique of Durkheim and Kant from within the framework of Davidson's semantic theory. This book is required reading for anyone interested in the academic study of religion, and the problems of relativism and the diversity of belief.' -- Hans H. Penner, Dartmouth College. (shrink)