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)
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)
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)
De argumenti ontologici forma logicaTractatione proposita auctores manifestant, „Argumentum Ontologicum“ St. Anselmi in 2° capitulo eius Proslogii inscriptum ut validum exponi posse (i. e. consequentiam bonam servando). Hac in interpretatione vis et notio descriptionis illae „id quo maius cogitari nequit“, qua Anselmus usus est, rite agnoscitur. Datis enim lingua formali „primi ordinis“, ut aiunt, et systemati deductivo logicae huiusmodi, in quo descriptiones definitae genuini sunt termini et ubi a sententia „datur x quod…“ signo quantitatis praefixa ad sententiam „x exsistit“ consequentia (...) non valet, et adhibendo adhuc regulas ordinarias logicae descriptionumrelationemque comparationis, quae „continua“ dicitur, exsistentia Dei sequitur duabus ex praemissis: Una quidem, „datur cogitabile aliquid, quo maius cogitari nequit“; et altera, „x non exsistente, aliquid eo maius cogitari potest“. Conclusio praedicta non potest negari, nisi una quoque harum praemissarum saltem negatur. Argumentum hoc vero nulla deductione modali utitur; et, quod notabile est, ratio ontologica Cartesii ex eo derivari potest.On the Logic of the Ontological ArgumentIn 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 x does not 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)
This article brings together the Sartrean concept of bad faith and Edward Upward's novel, Journey to the Border , first published in 1938. The aim is to provide an overtly political reading that challenges the surreal obscurity of Upward's psychological narrative, while at the same time showing the continuing relevance of Sartre's understanding of the psychological tensions and existential dilemmas of the modern condition. Upward's novel has been the focus of much critical debate as to the meaning of the (...) story - the descent of the main character towards madness in the context of the 1930s threat of fascism and war - as well as the generic characterisation of the text in terms of satire, fable, fantasy or political parable. The article argues in contrast a more unequivocally ideological reading of the series of existential choices, both personal and political, of the main character as a struggle for individual freedom and authenticity through a radical commitment to socialism and responsibility for the Other. (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)
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".
Introduction: "Know yourself" -- The revelation of God's wisdom -- Credo ut intellegam -- Intellego ut credam -- The relationship between faith and reason -- The interventions of the Magisterium in philosophical matters -- The interaction between philosophy and theology -- Current requirements and tasks -- Conclusion.
Auster contributed an extract from Moon Palace to the collection “Edward Hopper and the American Imagination,” and it is clear that Hopper’s images of alienated individuals have had a profound resonance for him. This paper employs two main ideas to compare them. First, a pivotal moment in American literature: the hotel room drama watched by Coverdale in Hawthorne’s Blithedale Romance. Secondly, Aby Warburg’s concept of the “pathos formula” in art, which bypasses the problematic issue of influence, choosing instead to (...) posit sets of inherited cultural memories. It therefore allows discussion of the re-emergence of Hawthorne’s puritan tropes of paranoid specularity and transcendence in the work of Hopper and Auster. (shrink)