James E. Taylor As the title of this book makes clear, the essays contained in it are unified by their focus on models of God and alternative ultimate realities. But what is ultimate reality, what does 'God' mean, and what would count as a model ...

In his recent trilogy, J. L. Schellenberg presents a new religious option: to have beliefless faith in a general object of religious concern that he thinks is referenced at the core of most sectarian religions UUU’. After explaining what UUU is more fully, I argue that the claim that UUU exists should not be, as Schellenberg says, the only focus for philosophy of religion. Still, I argue that such a claim is a good basis for a new form of religion, (...) especially if it is modified in a couple of ways. (shrink)

I introduce a distinction between global and local versions of atheism and theism, where global ones are about all notions of God and local ones are about specific notions. Current expressions of atheism are ambiguous between the two. I argue that global atheism is difficult to enunciate and even more difficult to defend, so much so that global atheism is not yet justified. Until it is, atheists should be local atheists.

Classic perfect being theologians take ‘being perfect’ to be conceptually necessary and sufficient for being God. I argue that this claim is false because being perfect is not conceptually necessary for being God. I rest my case on a simple thought experiment inspired by an alternative I developed to perfect being theology that I call “functional theology.” My findings, if correct, are a boon for theists since if it should turn out that there is no perfect being, there could still (...) be a God. (shrink)

Gödel interpreted Heyting arithmetic HA in a “logic-free” fragment T 0 of his theory T of primitive recursive functionals of finite types by his famous Dialectica-translation D . This works because the logic of HA is extremely simple. If the logic of the interpreted system is different—in particular more complicated—, it forces us to look for different and more complicated functional translations. We discuss the arising logical problems for arithmetical and set theoretical systems from HA to CZF . We want (...) to test the thesis: While the functionals take care of the proof theoretic strength of the interpreted system, it is the functional translation that has to cope with the logical complexities of the system. (shrink)

This book is a debate about the existence of God in the form of a worldview comparison, meaning that it sets two worldviews—comprehensive pictures of what there.

This book gives a detailed treatment of functional interpretations of arithmetic, analysis, and set theory. The subject goes back to Gödel's Dialectica interpretation of Heyting arithmetic which replaces nested quantification by higher type operations and thus reduces the consistency problem for arithmetic to the problem of computability of primitive recursive functionals of finite types. Regular functional interpretations, i.e. Dialectica and Diller-Nahm interpretation as well as Kreisel's modified realization, together with their Troelstra-style hybrids, are applied to constructive as well as classical (...) systems of arithmetic, analysis, and set theory. They yield relative consistency and conservativity results and closure under relevant rules of the theories in question as well as axiomatic characterizations of the functional translations. Prerequisites are: familiarity with classical and intuitionistic predicate logic, basics of computability theory, Gödel's incompleteness theorems. (shrink)

Gödel's dialectica interpretation of Heyting arithmetic HA may be seen as expressing a lack of confidence in our understanding of unbounded quantification. Instead of formally proving an implication with an existential consequent or with a universal antecedent, the dialectica interpretation asks, under suitable conditions, for explicit 'interpreting' instances that make the implication valid. For proofs in constructive set theory CZF-, it may not always be possible to find just one such instance, but it must suffice to explicitly name a set (...) consisting of such interpreting instances. The aim of eliminating unbounded quantification in favor of appropriate constructive functionals will still be obtained, as our ∧-interpretation theorem for constructive set theory in all finite types CZFω- shows. By changing to a hybrid interpretation ∧q, we show closure of CZFω- under rules that – in stronger forms – have already been studied in the context of Heyting arithmetic. In a similar spirit, we briefly survey modified realizability of CZFω- and its hybrids. Central results of this paper have been proved by Burr 2000a and Schulte 2006, however, for different translations. We use a simplified interpretation that goes back to Diller and Nahm 1974. A novel element is a lemma on absorption of bounds which is essential for the smooth operation of our translation. (shrink)

I offer a solution to an old puzzle about how God can be both just and merciful at the same time—a feat which seems required of God, but at the same time seems impossible since showing mercy involves being more lenient than justice demands. Inspired by two of Jesus’ parables and work by Feinberg, Johnson and Smart, I suggest that following a “principle of merciful justice”—that persons ought to receive what they deserve or better—delivers mercy and justice simultaneously, certainly in (...) cases of distributions of goods, and even in cases of distribution of harms as well, if we can accept some qualifications. (shrink)

Bishop’s main claims are: (I) that James’ criteria on the admissibility of faith leaps need the addition of two moral criteria to be complete; (II) that a Kantian, at least, could not admissibly leap toward God, classically understood, and (III) that a Kantian, and anyone else, could admissibly leap toward God, understood his way. Here I will affirm (I) with a qualification; deny (II); affirm (III); and close with some reservations about Bishop’s novel model of God. This paper was delivered (...) at the APA Pacific 2007 Mini-Conference on Models of God. (shrink)