This volume announces a new era in the philosophy of God. Many of its contributions work to create stronger links between the philosophy of God, on the one hand, and mathematics or metamathematics, on the other hand. It is about not only the possibilities of applying mathematics or metamathematics to questions about God, but also the reverse question: Does the philosophy of God have anything to offer mathematics or metamathematics? The remaining contributions tackle stereotypes in the philosophy of religion. The (...) volume includes 35 contributions. It is divided into nine parts: 1. Who Created the Concept of God; 2. Omniscience, Omnipotence, Timelessness and Spacelessness of God; 3. God and Perfect Goodness, Perfect Beauty, Perfect Freedom; 4. God, Fundamentality and Creation of All Else; 5. Simplicity and Ineffability of God; 6. God, Necessity and Abstract Objects; 7. God, Infinity, and Pascal's Wager; 8. God and (Meta-)Mathematics; and 9. God and Mind. (shrink)

استدلال کانتوری گریم از جمله براهینی است که در مباحث فلسفی اخیر ناسازگاری مفهوم علم مطلق را مورد هدف قرار داده است. گریم با استناد به اصل ریاضی کانتور و بر مبنای تعریف پذیرفته‌شدۀ علم مطلق، یعنی علم به تمامی گزاره­های صادق، وجود عالم مطلق را به دلیل عدم امکان وجود متعلق علم او، یعنی «مجموعه گزاره­های صادق»، انکار می­نماید. در این زمینه پاسخ­های متعددی در دفاع از علم مطلق الهی از سوی متفکران مسیحی معاصر ارائه شده که یکی از (...) مهم­ترین آنها خودمتناقض دانستن این استدلال است که پلانتینگا آن را مطرح کرده است. سنت فلسفه اسلامی از جهت تبیین ماهیت علم مطلق با سنت الهیات مسیحی تفاوت مبنایی دارد. اما با توجه به ظرفیت حکمت متعالیه صدرایی، با استناد به مباحثی چون تعریف و ماهیت مجموع و همچنین شرایط تسلسل محال، می‌توان علاوه بر ابطال فرض استدلال گریم مبنی بر وجود حقایق بیشتری از مجموعه تمام حقایق، امکان علم عالم مطلق به سلسله نامتناهی از مجموعه حقایق را اثبات نمود. (shrink)

O presente volume se trata de uma coletânea de artigos que reúne alguns dos trabalhos propostos para o evento “III International Colloquium of Analytic Epistemology and VII Conference of Social Epistemology”, realizado entre os dias 27 e 30 de Novembro de 2018, na Universidade Federal de Santa Maria. O “III International Colloquium of Analytic Epistemology and VII Conference of Social Epistemology” é um dos principais eventos de Epistemologia analítica da América Latina e reúne especialistas do Brasil e do exterior para (...) promover debates de alto nível sobre temas que fazem parte da agenda contemporânea no que se refere ao debate analítico contemporâneo acerca da Epistemologia. (shrink)

G. Priest's anti-consistency argument (Priest 1979, 1984, 1987) and J. R. Lucas's anti-mechanist argument (Lucas 1961, 1968, 1970, 1984) both appeal to Gödel incompleteness. By way of refuting them, this paper defends the thesis of quartet compatibility, viz., that the logic of the mind can simultaneously be Gödel incomplete, consistent, mechanical, and recursion complete (capable of all means of recursion). A representational approach is pursued, which owes its origin to works by, among others, J. Myhill (1964), P. Benacerraf (1967), J. (...) Webb (1980, 1983) and M. Arbib (1987). It is shown that the fallacy shared by the two arguments under discussion lies in misidentifying two systems, the one for which the Gödel sentence is constructable and to be proved, and the other in which the Gödel sentence in question is indeed provable. It follows that the logic of the mind can surpass its own Gödelian limitation not by being inconsistent or non-mechanistic, but by being capable of representing stronger systems in itself; and so can a proper machine. The concepts of representational provability, representational maximality, formal system capacity, etc., are discussed. (shrink)

I argue that ‘Moore’s paradox for God’. I do not believe this proposition shows that nobody can be both omniscient and rational in all her beliefs. I then anticipate and rebut three objections to my argument.

There are various argumentative strategies for advancing the claim that God does not exist. One such strategy is this. First, one notes that God is meant to have a certain divine attribute (such as omniscience). One then argues that having the relevant attribute is impossible. One concludes that God doesn't exist. For instance, Dennis Whitcomb's recent paper, ‘Grounding and omniscience’, proceeds in exactly this way. As Whitcomb says, ‘I'm going to argue that omniscience is impossible and that therefore there is (...) no God.’ This is not, I hope to show, a very promising way to start a paper. If having a given property is impossible, the greatest possible being need not have that property. Accordingly, the argumentative strategy in question is doomed to failure. The upshot of this article is a quite general one concerning how arguments against the existence of God in fact must proceed. (shrink)

A god is a cosmic designer-creator. Atheism says the number of gods is 0. But it is hard to defeat the minimal thesis that some possible universe is actualized by some possible god. Monotheists say the number of gods is 1. Yet no degree of perfection can be coherently assigned to any unique god. Lewis says the number of gods is at least the second beth number. Yet polytheists cannot defend an arbitrary plural number of gods. An alternative is that, (...) for every ordinal, there is a god whose perfection is proportional to it. The n -th god actualizes the best universe(s) in the n -th level of an axiological hierarchy of possible universes. Despite its unorthodoxy, ordinal polytheism has many metaphysically attractive features and merits more serious study. (shrink)

Ordinal polytheism is motivated by the cosmological and design arguments. It is also motivated by Leibnizian–Lewisian modal realism. Just as there are many universes, so there are many gods. Gods are necessary concrete grounds of universes. The god-universe relation is one-to-one. Ordinal polytheism argues for a hierarchy of ranks of ever more perfect gods, one rank for every ordinal number. Since there are no maximally perfect gods, ordinal polytheism avoids many of the familiar problems of monotheism. It links theology with (...) counterpart theory, mathematics and computer science. And it entails that the system of universes has an attractive axiological structure. (shrink)

The multiverse theodicy says that because God can without cost create an infinite number of universes, the standards of acceptability that a conceivable universe must meet to be worthy of divine creation are significantly laxer than is typically supposed in discussions of the problem of evil. While the prospect of a theistic multiverse arguably helps the theist to explain suffering, I argue that it also poses a serious skeptical worry. Given the alleged laxity of the standards that a universe must (...) meet to be worthy of inclusion in a theistic multiverse, there is reason to think that God would be justified in creating a great many deceptive universes that, while good overall, are inhabited by creatures who are radically mistaken in their beliefs. And these deceptive universes would arguably be no less abundant than the nondeceptive universes. After developing this skeptical challenge, I assess some possible theistic responses. One of the more promising responses I consider argues that in order to secure the great good of true friendship between God and creatures, God has reason to exclude deceptive universes from the multiverse even when those universes have great intrinsic value. (shrink)

Philosophers of today are easy to stupefy. Try suggesting that some situations, such as enjoying a chess problem, really are in themselves better than others such as being burned alive: in themselves better in the sense that situations of the first sort would be preferable to those of the second if they existed all alone, so that one did not need to take consequences into account, and really better much as Africa is really bigger than Iceland, so that talk of (...) real betterness is not just a genuine, wholehearted act of prescribing, or an expression of personal taste like the remark that mustard really is nasty. You will stupefy many a philosopher. (shrink)

Although recent evidence is somewhat ambiguous, if not confusing, Patrick Grim still seems to believe that his Cantorian argument against omniscienceis sound. According to this argument, it follows by Cantor’s power set theorem that there can be no set of all truths. Hence, assuming that omniscience presupposes precisely such a set, there can be no omniscient being. Reconsidering this argument, however, guided in particular by Alvin Plantinga’s critique thereof, I find it far from convincing. Not only does it have an (...) enormously untoward side effect, but it is self-referentially incoherent as well. (shrink)

Patrick Grim advances arguments meant to show that the doctrine of divine omniscience—the classical doctrine according to which God knows all truths—is false. In particular, we here have in mind to focus on two such arguments: the set theoretic argument and the semantic argument. These arguments due to Grim run parallel to, respectively, familiar paradoxes in set theory and naive truth theory. It is beyond the purview of this article to adjudicate whether or not these are successful arguments against the (...) classical doctrine of omniscience. What we are here interested in is a way in which these arguments can be generalized. In particular, we show how generalizations of those arguments can target, explicitly, alternatives to the classical doctrine of omniscience, including what we here call 'restricted omniscience' and 'open future open theism'. As a corollary, considerations of Grim-style arguments do not support these alternatives to the classical doctrine of omniscience over the classical doctrine. We conclude that what is paradoxical is not the classical doctrine of omniscience just as such; rather, what is paradoxical is a core commitment shared by the classical doctrine and its more modest alternatives, namely, the thesis that God is a perfectly logical reasoner. (shrink)

God, by definition, is all-powerful, all-good, all-wise, and all-knowing. Therein lies a problem for the theist, of course, for every one of these attributes has been the subject of fierce debate. In this paper I want to return to the debate by introducing a new problem for the idea that anyone could have the kind of perfect knowledge God is supposed to have. What distinguishes my problem from others is that the sort of knowledge it focuses on is self-knowledge, hence (...) knowledge of a particularly intimate kind. My claim is that God cannot have infallible knowledge of at least some of his own perfections, in particular his being all-wise or ideally rational. Such ignorance is not only inconsistent with the usual conception of God's omniscience, given that whatever knowledge God possesses is traditionally thought to be be a priori and infallible, but, more importantly, is inconsistent with the fundamental idea that God at least knows infallibly or incorrigibly that he has what it takes to be God: qualities such as omnibenevolence, omnipotence, and supreme wisdom. In short, my claim is that God must have a deep “blindspot” about his own nature, something which is inconsistent with a traditional picture of that nature. (shrink)

The negative zombie argument concludes that physicalism is false from the premises that p ∧¬q is ideally negatively conceivable and that what is ideally negatively conceivable is possible, where p is the conjunction of the fundamental physical truths and laws and q is a phenomenal truth (Chalmers 2002; 2010). A sentence φ is ideally negatively conceivable iff φ is not ruled out a priori on ideal rational reflection. In this paper, I argue that the negative zombie argument is neither a (...) priori nor conclusive. First, I argue that the premises of the argument are true only if there exists an adequate finite ideal reasoner R that believes ◊(p ∧ ¬q) on the basis of not believing p→q on a priori basis. Roughly, a finite reasoner is a reasoner with cognitive limitations (e.g. finite memory). I argue that R is finite only if R reasons nonmonotonically and only approach ideal reflection at the limit of a reasoning sequence. This would render the argument nonconclusive. Finally, I argue that, for some q, R does not believe ◊(p ∧ ¬q) on the basis of not believing p→q on a priori basis (e.g. for q =‘something is conscious’). This would render the choice of an adequate q dependent on empirical information (and the argument a posteriori). I conclude that the negative zombie argument (and, maybe, all zombie arguments) is neither a priori nor conclusive. (shrink)

The divine attributes of omniscience and omnipotence have faced objections to their very consistency. Such objections rely on reasoning parallel to semantic paradoxes such as the Liar or to set-theoretic paradoxes like Russell's paradox. With the advent of paraconsistent logics, dialetheism—the view that some contradictions are true—became a major player in the search for a solution to such paradoxes. This paper explores whether dialetheism, armed with the tools of paraconsistent logics, has the resources to respond to the objections levelled against (...) the divine attributes. (shrink)

As a result of his studies in metalogicEssler became convincedthat an absolute fixed totality of alltruths and a final metalanguage doesnot exist. Taking this result into account,it is shown that the usualabsolute concept of omniscience isuntenable. From this it can be concludedthat definitions of knowledge whichappeal to such a concept of omnisciencelead to serious problems.

The most widespread models of rational reasoners (the model based on modal epistemic logic and the model based on probability theory) exhibit the problem of logical omniscience. The most common strategy for avoiding this problem is to interpret the models as describing the explicit beliefs of an ideal reasoner, but only the implicit beliefs of a real reasoner. I argue that this strategy faces serious normative issues. In this paper, I present the more fundamental problem of logical omnipotence, which highlights (...) the normative content of the problem of logical omniscience. I introduce two developments of the notion of implicit belief (accessible and stable belief ) and use them in two versions of the most common strategy applied to the problem of logical omnipotence. (shrink)

The notion of an ideal reasoner has several uses in epistemology. Often, ideal reasoners are used as a parameter of (maximum) rationality for finite reasoners (e.g. humans). However, the notion of an ideal reasoner is normally construed in such a high degree of idealization (e.g. infinite/unbounded memory) that this use is unadvised. In this dissertation, I investigate the conditions under which an ideal reasoner may be used as a parameter of rationality for finite reasoners. In addition, I present and justify (...) the research program of computational epistemology, which investigates the parameter of maximum rationality for finite reasoners using computer simulations. (shrink)