I argue that Graham Oppy’s attempt to redefend his charge that all modal theistic arguments “must be question-begging” is unsuccessful. Oppy’s attempt to show that theism and modal concretism are compatible is not only tangential for his purposes, it is marred by a misunderstanding of theism, and vulnerable to a counterexample that actually demonstrates incompatibility. Moreover, the notion of begging the question employed by Oppy against the theist is seen to be far too permissive.

This article aims to draw on the ‘Qur'anic Rationalism’ of Taqī al-Dīn Ibn Taymiyya (1263–1328) in elucidating an Islamic epistemology of theistic natural signs, in the lens of contemporary philosophy of religion. In articulating what Ibn Taymiyya coins ‘God's method of proof through signs (istidlāluhu taʿālā bi'l-āyāt)’, it seeks aid in particular from the work of C. Stephen Evans and other contemporary philosophers of religion, in an attempt to understand the relevance and force of this alternative to natural (...) theology within the Islamic tradition. In doing so, it aims to respond to existing criticisms of Ibn Taymiyya's perspective in the literature, and to consider the implications of a Taymiyyan reading of theistic natural signs, on the epistemic function of Qur'anic āyāt as theistic evidence. (shrink)

This chapter discusses Kant's 1763 "possibility proof" for the existence of God. I first provide a reconstruction of the proof in its two stages, and then revisit my earlier argument according to which the being the proof delivers threatens to be a Spinozistic-panentheistic God—a being whose properties include the entire spatio-temporal universe—rather than the traditional, ontologically distinct God of biblical monotheism. I go on to evaluate some recent alternative readings that have sought to avoid this result by (...) arguing that the relevant facts about real modality can be ultimately grounded in God’s powers or thoughts – or that Kant just leaves the grounding relations mysterious. I argue that the textual and philosophical costs of each of these alternative readings are formidable. The chapter concludes with a discussion of the fate of the proof in the critical period. Some commentators think that it disappears altogether, or that it is downgraded such that it produces a mere regulative idea of God as the most real being. I suggest that the proof survives but that the mode of assent it licenses towards its conclusion changes from knowledge to a certain kind of Belief (Glaube). (shrink)

Kant's speculative theistic proof rests on a distinction between “logical” and “real” modality that he developed very early in the pre-critical period. The only way to explain facts about real possibility, according to Kant, is to appeal to the properties of a unique, necessary, and “most real” being. Here I reconstruct the proof in its historical context, focusing on the role played by the theory of modality both in motivating the argument (in the pre-critical period) and, ultimately, (...) in undoing it as a source of knowledge of God's existence (in the critical period). Along the way I examine Kant's version of the now-popular “actualist” thesis that facts about what is possible must be explained by facts about what is actual. I conclude by discussing why the critical Kant claims both that there are rational grounds for accepting the conclusion of his theistic proof, and that such acceptance can not count as knowledge. This is important, I argue, because the same considerations ultimately motivate his prohibition on knowledge of things-in-themselves generally. -/- . (shrink)

After reviewing Kant’s well-known criticisms of the traditional proofs of God’s existence and his preferred moral argument, this paper presents a detailedanalysis of a densely-packed theistic argument in Religion within the Bounds of Bare Reason. Humanity’s ultimate moral destiny can be fulfilled only through organized religion, for only by participating in a religious community (or “church”) can we overcome the evil in human nature. Yet we cannot conceive how such a community can even be founded without presupposing God’s existence. (...) Viewing God as the internal moral lawgiver, empowering a community of believers, is Kant’s ultimate rationale for theistic belief. (shrink)

In the following paragraphs, I will describe ten strategies through which we can show the weaknesses of every form of theism based on the "One God", while postulating that the Trinity is a good solution. This approach follows up on Swinburne’s claims about the existence of a priori and a posteriori proofs for the existence of the Trinity (his proofs are part of the sixth strategy). Clearly, these strategies are not “new”: they have been advocated by many thinkers in the (...) past and in the present. I merely revived them, and brought them together in a kind of cumulative reasoning: the strength of them arises when these strategies are considered together, showing that the Trinity is a reasonable hypothesis even though it is contradictory. The proposed strategies lead to the conclusion that there must exist in God something similar to what we call ‘real relations’ and ‘multiplicity’; and in order for God to be relational, there must exist in Him some “distincts” that relate to one another. This is postulated by philosophical reasoning, not just by Revelation, and regardless of the choice to support a process metaphysics. As Trinitarian theology contains the mystery of eternal generation, the strategies do account for the fact that in philosophy we contemplate the mystery of eternal self-distinction and of all the other ‘self-actions’ of the One. The eternal generation remains mysterious, but it is the idea that best helps us describe how God is (One and Triune) and how he creates the world. God must be Triune in every theistic system. The One God is, as One, also Triune. The Unity-Trinity of the Principle is the only apophatic point that we can reach from many quarters. Once autonomous paths of reason have established that God is a Person and Persons, One-Multiple, Creator (communicated), Free, Relational and Infinite possibility, it therefore emerges that our most reliable hypothesis is that of the Trinitarian God. (shrink)

This article serves to explore the historical development of the ontological argument from Anselm to Present. Initially, the main goal is to introduce the lay reader to one of the most perplexing arguments for the theistic conception of God. Logically, this is an a priori argument, similar to one of a mathematical proof. Oddly, the argument has sort of fallen out of place in contemporary philosophy, apart from a reboot from Alvin Plantinga. The goal is to illustrate that (...) the initial argument as stated by Anselm seems to be an unsolved problem in philosophical inquiry. (shrink)

It can be easy to assume that since the “theist in the street” is unaware of any of the traditional arguments for theism, he or she is not in position to offer independent rational support for believing that God exists. I argue that that is false if we accept with William Alston that “manifestation beliefs” can enjoy rational support on the basis of suitable religious experiences. I make my case by defending the viability of a Moorean-style proof for theism—a (...) proof for the existence of God that parallels in structure G. E. Moore’s famous proof for the existence of the external world. I argue that this shows that even if the theist in the street has nothing to offer for helping to convince the religious sceptic, this needn’t entail that she cannot offer independent rational support in defense of her theistic belief. (shrink)

Faith has many aspects. One of them is whether absolute logical proof for God’s existence is a prerequisite for the proper establishment and individual acceptance of a religious system. The treatment of this question, examined here in the Jewish context of Rabbi Prof. Eliezer Berkovits, has been strongly influenced in the modern era by the radical foundationalism and radical skepticism of Descartes, who rooted in the Western mind the notion that religion and religious issues are “all or nothing” questions. (...) Cartesianism, which surprisingly became the basis of modern secularism, was criticized by the classical American pragmatists. Peirce, James and Dewey all rejected the attempt to achieve infallible absolute knowledge, as well as the presumptuousness of establishing such a knowledge by means of casting Cartesian hyperbolic doubt. They advocated an alternative approach which was more holistic and humane. This paper lays out Descartes’s approach and the pragmatists’ critique. Despite the place that pragmatic considerations hold in Jewish tradition, some thinkers reject the relevance of these ideas. Yet Berkovits’s thought suggest a different path. He rejected Descartes’ radical skepticism and his radical foundationalism, in favor of a moderate foundationalism, which allows for a belief in God alongside constructive doubts. Similar to Peirce’s conception of the fixation of belief, Berkovits views local doubts (distinct from the hyperbolic doubt) as necessary for thought. Berkovits’s understanding of the biblical human-divine encounter, following Rosenzweig, Buber, and Heschel, is conceptualized here as “encounter theology”. Berkovits criticizes the propositionalist attempts to prove God’s existence logically, as well as the presumptuousness of basing religious belief on the teleological world-order. However, Berkovits’s conception of the ‘caring God’ is not provable, and thus defined as a pragmatic ‘postulate’. The article concludes by considering Berkovits’s “encounter theology”. In contrast to the approach described by Haym Soloveitchik, of halakhic stringency and lack of subjective experience of God’s face, Berkovits’s approach is dialogic through and through. (shrink)

The study pursues, in a historical as well as in a systematic-analytical way, the reading of Descartes' philosophy as a project of a fundamental critique of theology and transcendence. Besides the exclusion of everything 'theological' from the field of rational discourse and its relegation to the field of fideism, this also involves the reinterpretation of the concept of 'God' as Descartes uses it, in a sense that is to be purified of transcendental, but especially of theistic implications.

In Sections 1–7, I provide a detailed description of some of the advantages of theistic modal realism. The aim is to show specifically how theistic modal realism solves many of the intractable problems of philosophical theology. A detailed description of all of the advantages would require a much longer treatment. The aim is to give a good sense of the theoretical benefits that theistic modal realism affords traditional theists. I offer some concluding remarks in Section 8.

The main aim in the forthcoming discussion is to contrast theistic modal realism and theistic actualist realism. Actualist realism is the dominant view among theists and presents the most serious challenge to theistic modal realism. I discuss various prominent forms of theistic actualist realism. I offer reasons for rejecting the view of metaphysical reality that actualist realism affords. I discuss theistic modal realism and show that the traditional conception of God is perfectly consistent with the (...) metaphysics of genuine modal realism. Indeed theistic modal realism is more suited to traditional theism than is any version of actualist realism. (shrink)

Smith argues that, unlike other forms of evidence, naked statistical evidence fails to satisfy normic support. This is his solution to the puzzles of statistical evidence in legal proof. This paper focuses on Smith’s claim that DNA evidence in cold-hit cases does not satisfy normic support. I argue that if this claim is correct, virtually no other form of evidence used at trial can satisfy normic support. This is troublesome. I discuss a few ways in which Smith can respond.

In this paper, I propose that applying the methods of data science to “the problem of whether mathematical explanations occur within mathematics itself” (Mancosu 2018) might be a fruitful way to shed new light on the problem. By carefully selecting indicator words for explanation and justification, and then systematically searching for these indicators in databases of scholarly works in mathematics, we can get an idea of how mathematicians use these terms in mathematical practice and with what frequency. The results of (...) this empirical study suggest that mathematical explanations do occur in research articles published in mathematics journals, as indicated by the occurrence of explanation indicators. When compared with the use of justification indicators, however, the data suggest that justifications occur much more frequently than explanations in scholarly mathematical practice. The results also suggest that justificatory proofs occur much more frequently than explanatory proofs, thus suggesting that proof may be playing a larger justificatory role than an explanatory role in scholarly mathematical practice. (shrink)

Predication is an indisputable part of our linguistic behavior. By contrast, the metaphysics of predication has been a matter of dispute ever since antiquity. According to Plato—or at least Platonism, the view that goes by Plato’s name in contemporary philosophy—the truths expressed by predications such as “Socrates is wise” are true because there is a subject of predication (e.g., Socrates), there is an abstract property or universal (e.g., wisdom), and the subject exemplifies the property.1 This view is supposed to be (...) general, applying to all predications, whether the subject of predication is a person, a planet, or a property.2 Despite the controversy surrounding the metaphysics of predication, many theistic philosophers—including the majority of contemporary analytic theists—regard Platonism as extremely attractive. At the same time, however, such philosophers are also commonly attracted to a form of traditional theism that has at its core the thesis that God is an absolutely independent.. (shrink)

Evolutionary debunking arguments, whether defended by Street (2006), Joyce (2006), or others against moral realism, or by Plantinga (1993, 2011) and others against atheism, seek to determine the implications of the still-dominant worldview of naturalism. Examining them is thus a critical component of any defense of a theistic philosophy of nature. Recently, several authors have explored the connection between evolutionary debunking arguments against moral realism (hence: EDAs) and Plantinga’s evolutionary argument against naturalistic atheism (hence: EAAN). Typically, responses in this (...) vein have been critical of EDAs, arguing that they are in some way self-undermining. Different critics have argued that, in the course of defending the EAAN, the theist loses her best response to the probabilistic argument from evil for atheism. Here, I provide the first systematic comparison of all three arguments—EDAs, the EAAN, and the problem of evil—and suggest that the first charge succeeds while the second fails. (shrink)

The traditional view of evidence in mathematics is that evidence is just proof and proof is just derivation. There are good reasons for thinking that this view should be rejected: it misrepresents both historical and current mathematical practice. Nonetheless, evidence, proof, and derivation are closely intertwined. This paper seeks to tease these concepts apart. It emphasizes the role of argumentation as a context shared by evidence, proofs, and derivations. The utility of argumentation theory, in general, and argumentation (...) schemes, in particular, as a methodology for the study of mathematical practice is thereby demonstrated. Argumentation schemes represent an almost untapped resource for mathematics education. Notably, they provide a consistent treatment of rigorous and non-rigorous argumentation, thereby working to exhibit the continuity of reasoning in mathematics with reasoning in other areas. Moreover, since argumentation schemes are a comparatively mature methodology, there is a substantial body of existing work to draw upon, including some increasingly sophisticated software tools. Such tools have significant potential for the analysis and evaluation of mathematical argumentation. The first four sections of the paper address the relationships of evidence to proof, proof to derivation, argument to proof, and argument to evidence, respectively. The final section directly addresses some of the educational implications of an argumentation scheme account of mathematical reasoning. (shrink)

The problem of religious disagreement between epistemic peers is a potential threat to the epistemic justification of one’s theistic belief. In this paper, I develop a response to this problem which draws on the central epistemological thesis of skeptical theism concerning our inability to make proper judgements about God’s reasons for permitting evil. I suggest that this thesis may extend over to our judgements about God’s reasons for self-revealing, and that when it does so, it can enable theists to (...) remain steadfast amid disagreement with epistemic peers who hold a contrary theistic belief (i.e., atheistic belief). For if we’re unable to make proper judgements about God’s reasons for self-revealing, then for all we know, God has some reason for not revealing Himself to our apparent epistemic peer. Thus, their epistemic credentials needn’t provide reason to reduce one’s confidence to such a degree as to no longer uphold one’s theistic belief. (shrink)

The proof theory of many-valued systems has not been investigated to an extent comparable to the work done on axiomatizatbility of many-valued logics. Proof theory requires appropriate formalisms, such as sequent calculus, natural deduction, and tableaux for classical (and intuitionistic) logic. One particular method for systematically obtaining calculi for all finite-valued logics was invented independently by several researchers, with slight variations in design and presentation. The main aim of this report is to develop the proof theory of (...) finite-valued first order logics in a general way, and to present some of the more important results in this area. In Systems covered are the resolution calculus, sequent calculus, tableaux, and natural deduction. This report is actually a template, from which all results can be specialized to particular logics. (shrink)

The impossibility results in judgement aggregation show a clash between fair aggregation procedures and rational collective outcomes. In this paper, we are interested in analysing the notion of rational outcome by proposing a proof-theoretical understanding of collective rationality. In particular, we use the analysis of proofs and inferences provided by linear logic in order to define a fine-grained notion of group reasoning that allows for studying collective rationality with respect to a number of logics. We analyse the well-known paradoxes (...) in judgement aggregation and we pinpoint the reasoning steps that trigger the inconsistencies. Moreover, we extend the map of possibility and impossibility results in judgement aggregation by discussing the case of substructural logics. In particular, we show that there exist fragments of linear logic for which general possibility results can be obtained. (shrink)

Should we use the same standard of proof to adjudicate guilt for murder and petty theft? Why not tailor the standard of proof to the crime? These relatively neglected questions cut to the heart of central issues in the philosophy of law. This paper scrutinises whether we ought to use the same standard for all criminal cases, in contrast with a flexible approach that uses different standards for different crimes. I reject consequentialist arguments for a radically flexible standard (...) of proof, instead defending a modestly flexible approach on non-consequentialist grounds. The system I defend is one on which we should impose a higher standard of proof for crimes that attract more severe punishments. This proposal, although apparently revisionary, accords with a plausible theory concerning the epistemology of legal judgments and the role they play in society. (shrink)

While the existence of horrendous evils has generally been taken to be evidence against the existence of God, some philosophers have suggested that it may be evidence for the existence of God. This paper introduces three main kinds of theistic arguments from horrendous evils: the argument from objectively horrifying evils, the pragmatic argument from evil, and an argument from reasonable responses. For each of these arguments, I will first reconstruct a standard version of the argument, before suggesting ways the (...) argument may be challenged, or further developed. (shrink)

This essay concerns the causation involved in divine sustenance—the “pressure of the will of God” that continually upholds things in existence and supplies them with their properties and powers. My aim is to consolidate the theological doctrine of sustenance and a metaphysical theory of properties. Towards that end, I develop and motivate two consolidatory proposals, which together secure a more parsimonious theistic ontology and integrate the doctrine of sustenance and a theory of properties in a mutually enhancing way. The (...) bulk of the essay concerns the first proposal, which I explain and motivate in the first three sections. In the last two sections I explain and motivate the second proposal. (shrink)

Is God a person, like you and me eventually, but only much better and without our human deficiencies? When you read some of the philosophers of religion, including Richard Swinburne, Alvin Plantinga, or Open Theists, God appears as such a person, in a sense closer to Superman than to the Creator of Heaven and Earth. It is also a theory that a Christian pastoral theology today tends to impose, insisting that God is close to us and attentive to all of (...) us. But this modern account of God could be a deep and even tragic mistake. One God in three persons, the formula of the Trinity, does not mean that God is a person. On this matters we need an effort in the epistemology of theology to examine more precisely what we can pretend to know about God, and especially how we could pretend to know that God is person. (shrink)

Which rules for aggregating judgments on logically connected propositions are manipulable and which not? In this paper, we introduce a preference-free concept of non-manipulability and contrast it with a preference-theoretic concept of strategy-proofness. We characterize all non-manipulable and all strategy-proof judgment aggregation rules and prove an impossibility theorem similar to the Gibbard--Satterthwaite theorem. We also discuss weaker forms of non-manipulability and strategy-proofness. Comparing two frequently discussed aggregation rules, we show that “conclusion-based voting” is less vulnerable to manipulation than “premise-based (...) voting”, which is strategy-proof only for “reason-oriented” individuals. Surprisingly, for “outcome-oriented” individuals, the two rules are strategically equivalent, generating identical judgments in equilibrium. Our results introduce game-theoretic considerations into judgment aggregation and have implications for debates on deliberative democracy. (shrink)

In this dissertation, we shall investigate whether Tennant's criterion for paradoxicality(TCP) can be a correct criterion for genuine paradoxes and whether the requirement of a normal derivation(RND) can be a proof-theoretic solution to the paradoxes. Tennant’s criterion has two types of counterexamples. The one is a case which raises the problem of overgeneration that TCP makes a paradoxical derivation non-paradoxical. The other is one which generates the problem of undergeneration that TCP renders a non-paradoxical derivation paradoxical. Chapter 2 deals (...) with the problem of undergeneration and Chapter 3 concerns the problem of overgeneration. Chapter 2 discusses that Tenant’s diagnosis of the counterexample which applies CR−rule and causes the undergeneration problem is not correct and presents a solution to the problem of undergeneration. Chapter 3 argues that Tennant’s diagnosis of the counterexample raising the overgeneration problem is wrong and provides a solution to the problem. Finally, Chapter 4 addresses what should be explicated in order for RND to be a proof-theoretic solution to the paradoxes. (shrink)

A. E. Taylor states the widely held view that Plato’s Euthyphro posed a question which figured prominently in later ethical controversies: “It amounts to asking whether acts of piety, or more generally virtuous acts, derive their character of being right from the mere fact of being commanded or are commanded because they are antecedently intrinsically right.” I argue against this characterization of the Euthyphro. The argument Socrates deploys against Euthyphro’s third and most serious definition of holiness or piety (to hosion) (...) is not the opening round in the debate over divine command theory nor is a discussion of the nature of holiness ipso facto an exercise in ethical theory. (shrink)

I explore, from a proof-theoretic perspective, the hierarchy of classical and paraconsistent logics introduced by Barrio, Pailos and Szmuc in (Journal o f Philosophical Logic,49, 93-120, 2021). First, I provide sequent rules and axioms for all the logics in the hierarchy, for all inferential levels, and establish soundness and completeness results. Second, I show how to extend those systems with a corresponding hierarchy of validity predicates, each one of which is meant to capture “validity” at a different inferential level. (...) Then, I point out two potential philosophical implications of these results. (i) Since the logics in the hierarchy differ from one another on the rules, I argue that each such logic maintains its own distinct identity (contrary to arguments like the one given by Dicher and Paoli in 2019). (ii) Each validity predicate need not capture “validity” at more than one metainferential level. Hence, there are reasons to deny the thesis (put forward in Barrio, E., Rosenblatt, L. & Tajer, D. (Synthese, 2016)) that the validity predicate introduced in by Beall and Murzi in (Journal o f Philosophy,110(3), 143–165, 2013) has to express facts not only about what follows from what, but also about the metarules, etc. (shrink)

This paper discusses proof-theoretic semantics, the project of specifying the meanings of the logical constants in terms of rules of inference governing them. I concentrate on Michael Dummett’s and Dag Prawitz’ philosophical motivations and give precise characterisations of the crucial notions of harmony and stability, placed in the context of proving normalisation results in systems of natural deduction. I point out a problem for defining the meaning of negation in this framework and prospects for an account of the meanings (...) of modal operators in terms of rules of inference. (shrink)

In this paper, I present the recently much discussed Value Challenge for Theories of Knowledge and formulate Generic Theistic reliabilism as a theory, which can answer this challenge, with respect to Theism and the proposition ”God exists’.

The standard of proof in criminal trials in many liberal democracies is proof beyond a reasonable doubt, the BARD standard. It is customary to describe it, when putting a number on it, as requiring that the fact finder be at least 90% certain, after considering the evidence, that the defendant is guilty. Strikingly, no good reason has yet been offered in defense of using that standard. A number of non-consequentialist justifications that aim to support an even higher standard (...) have been offered; all are morally unsound. Meanwhile, consequentialist arguments plausibly support a substantially lower standard — in some cases so low as to undermine the idea that punishment is what is at stake. In this paper, I offer a new retributive justification that supports excluding the instrumental benefits of punishment from the balance that sets the standard. The resulting balance supports a standard arguably in the ballpark of the customary understanding of BARD: a standard requiring that the fact finder have a high, though not maximally high, degree of confidence that the defendant is guilty. (shrink)

Christ, who is the Creator and source of all knowledge, is the ultimate goal of all those seeking truth in any discipline. It is difficult to know God with the puny tools of science. As we get closer and closer to the truth, our science must merge with our theology otherwise we will be following a false end of our scientific inquiry. I think Max Planck said it best: “God is the beginning of every religion and at the end of (...) the natural sciences.” All scientists who have any depth to their work will find the hand of God in nature or else a mystery that they refuse to identify with God. (shrink)

Prawitz conjectured that proof-theoretic validity offers a semantics for intuitionistic logic. This conjecture has recently been proven false by Piecha and Schroeder-Heister. This article resolves one of the questions left open by this recent result by showing the extensional alignment of proof-theoretic validity and general inquisitive logic. General inquisitive logic is a generalisation of inquisitive semantics, a uniform semantics for questions and assertions. The paper further defines a notion of quasi-proof-theoretic validity by restricting proof-theoretic validity to (...) allow double negation elimination for atomic formulas and proves the extensional alignment of quasi-proof-theoretic validity and inquisitive logic. (shrink)

Theistic metaethics usually places one key restriction on the explanation of moral facts, namely: every moral fact must ultimately be explained by some fact about God. But the widely held belief that moral truths are necessary truths seems to undermine this claim. If a moral truth is necessary, then it seems like it neither needs nor has an explanation. Or so the objection typically goes. Recently, two proponents of theistic metaethics — William Lane Craig and Mark Murphy — (...) have argued that this objection is flawed. They claim that even if a truth is necessary, it does not follow that it neither needs nor has an explanation. In this article, I challenge Craig and Murphy’s reasoning on three main grounds. First, I argue that the counterexamples they use to undermine the necessary truth objection to theistic metaethics are flawed. While they may provide some support for the notion that necessary truths can be explained, they do not provide support for the notion that necessary moral truths can be explained. Second, I argue that the principles of explanation that Murphy and Craig use to support theistic metaethics are either question-begging (in the case of Murphy) or improperly motivated (in the case of Craig). And third, I provide a general defence of the claim that necessary moral truths neither need nor have an explanation. (shrink)

This paper considers proof-theoretic semantics for necessity within Dummett's and Prawitz's framework. Inspired by a system of Pfenning's and Davies's, the language of intuitionist logic is extended by a higher order operator which captures a notion of validity. A notion of relative necessary is defined in terms of it, which expresses a necessary connection between the assumptions and the conclusion of a deduction.

It is shown how the schema of equivalence can be used to obtain short proofs of tautologies A , where the depth of proofs is linear in the number of variables in A .

This paper is an English version of the paper that was published in German under the title: "Über die Aussichten erfolgreicher Beweise für Theismus oder Atheismus". My English paper was translated into German by Gabriele Schlegel. -/- The aim of this paper is to examine the prospects for proofs or successful arguments for the existence or non-existence of God.

In mathematics, any form of probabilistic proof obtained through the application of a probabilistic method is not considered as a legitimate way of gaining mathematical knowledge. In a series of papers, Don Fallis has defended the thesis that there are no epistemic reasons justifying mathematicians’ rejection of probabilistic proofs. This paper identifies such an epistemic reason. More specifically, it is argued here that if one adopts a conception of mathematical knowledge in which an epistemic subject can know a mathematical (...) proposition based solely on a probabilistic proof, one is then forced to admit that such an epistemic subject can know several lottery propositions based solely on probabilistic evidence. Insofar as knowledge of lottery propositions on the basis of probabilistic evidence alone is denied by the vast majority of epistemologists, it is concluded that this constitutes an epistemic reason for rejecting probabilistic proofs as a means of acquiring mathematical knowledge. (shrink)

This paper discusses a range of modal ontological arguments. It is claimed that these modal ontological arguments fail because they depend upon controversial assumptions about the nature of modal space.

In what follows I offer an explanation for the evils in our world that should be a live option for theists who accept middle knowledge. My explanation depends on the possibility of a multiverse of radically different kinds of universes. Persons must pass through various universes, the sequence being chosen by God on an individual basis, until reaching God’s goal for them. Our universe is depicted as governed much by chance, and I give a justification, in light of my thesis, (...) for why God would have people pass through a universe of just such a sort. (shrink)

A question, long discussed by legal scholars, has recently provoked a considerable amount of philosophical attention: ‘Is it ever appropriate to base a legal verdict on statistical evidence alone?’ Many philosophers who have considered this question reject legal reliance on bare statistics, even when the odds of error are extremely low. This paper develops a puzzle for the dominant theories concerning why we should eschew bare statistics. Namely, there seem to be compelling scenarios in which there are multiple sources of (...) incriminating statistical evidence. As we conjoin together different types of statistical evidence, it becomes increasingly incredible to suppose that a positive verdict would be impermissible. I suggest that none of the dominant views in the literature can easily accommodate such cases, and close by offering a diagnosis of my own. (shrink)

In a series of papers, Don Fallis points out that although mathematicians are generally unwilling to accept merely probabilistic proofs, they do accept proofs that are incomplete, long and complicated, or partly carried out by computers. He argues that there are no epistemic grounds on which probabilistic proofs can be rejected while these other proofs are accepted. I defend the practice by presenting a property I call ‘transferability’, which probabilistic proofs lack and acceptable proofs have. I also consider what this (...) says about the similarities between mathematics and, on the one hand natural sciences, and on the other hand philosophy. (shrink)

Should we use the same standard of proof to adjudicate guilt for murder and petty theft? Why not tailor the standard of proof to the crime? These relatively neglected questions cut to the heart of central issues in the philosophy of law. This paper scrutinises whether we ought to use the same standard for all criminal cases, in contrast with a flexible approach that uses different standards for different crimes. I reject consequentialist arguments for a radically flexible standard (...) of proof, instead defending a modestly flexible approach on non-consequentialist grounds. The system I defend is one on which we should impose a higher standard of proof for crimes that attract more severe punishments. This proposal, although apparently revisionary, accords with a plausible theory concerning the epistemology of legal judgments and the role they play in society. (shrink)

In this paper we give some formal examples of ideas developed by Penco in two papers on the tension inside Frege's notion of sense (see Penco 2003). The paper attempts to compose the tension between semantic and cognitive aspects of sense, through the idea of sense as proof or procedure – not as an alternative to the idea of sense as truth condition, but as complementary to it (as it happens sometimes in the old tradition of procedural semantics).

Kurt Gödel wrote (1964, p. 272), after he had read Husserl, that the notion of objectivity raises a question: “the question of the objective existence of the objects of mathematical intuition (which, incidentally, is an exact replica of the question of the objective existence of the outer world)”. This “exact replica” brings to mind the close analogy Husserl saw between our intuition of essences in Wesensschau and of physical objects in perception. What is it like to experience a mathematical proving (...) process? What is the ontological status of a mathematical proof? Can computer assisted provers output a proof? Taking a naturalized world account, I will assess the relationship between mathematics, the physical world and consciousness by introducing a significant conceptual distinction between proving and proof. I will propose that proving is a phenomenological conscious experience. This experience involves a combination of what Kurt Gödel called intuition, and what Husserl called intentionality. In contrast, proof is a function of that process — the mathematical phenomenon — that objectively self-presents a property in the world, and that results from a spatiotemporal unity being subject to the exact laws of nature. In this essay, I apply phenomenology to mathematical proving as a performance of consciousness, that is, a lived experience expressed and formalized in language, in which there is the possibility of formulating intersubjectively shareable meanings. (shrink)

Writing strategic documents is a major practice of many actors striving to see their educational ideas realised in the curriculum. In these documents, arguments are systematically developed to create the legitimacy of a new educational goal and competence to make claims about it. Through a qualitative analysis of the writing strategies used in these texts, I show how two of the main actors in the Czech educational discourse have developed a proof that a new educational goal is needed. I (...) draw on the connection of the relational approach in the sociology of education with Lyotard’s analytical semantics of instances in the event. The comparison of the writing strategies in the two documents reveals differences in the formation of a particular pattern of justification. In one case the texts function as a herald of pure reality, and in the other case as a messenger of other witnesses. This reveals different regimens of proof, although both of them were written as prescriptive directives – normative models of the educational world. (shrink)

The guise of the good doctrine is the view that whatever we desire, we desire it under the guise of the good, i.e. it appears good to us in some way. In this paper I first clarify the role that the doctrine of the guise of the good plays in the first step of J. S. Mill’s proof of the principle of utility (in which he shows that one’s happiness is desirable as an end). Then I provide textual evidence (...) in favour of ascribing the doctrine to Mill, arguing that he commits to it to the extent that he equates finding something pleasant and thinking it desirable. Finally I counter two potential sources of evidence against ascribing the guise of the good to Mill: apparent desires based on ‘fixed ideas’, and those habitual desires which are no longer associated with finding their objects pleasant. I argue that ‘fixed ideas’ do not feed actual desires, and that the habitual desires which seem to escape the guise of the good, even if not uncommon, have a secondary status as desires. (shrink)

We introduce translations between display calculus proofs and labeled calculus proofs in the context of tense logics. First, we show that every derivation in the display calculus for the minimal tense logic Kt extended with general path axioms can be effectively transformed into a derivation in the corresponding labeled calculus. Concerning the converse translation, we show that for Kt extended with path axioms, every derivation in the corresponding labeled calculus can be put into a special form that is translatable to (...) a derivation in the associated display calculus. A key insight in this converse translation is a canonical representation of display sequents as labeled polytrees. Labeled polytrees, which represent equivalence classes of display sequents modulo display postulates, also shed light on related correspondence results for tense logics. (shrink)

In this paper I consider an understudied form of the design argument which focuses on the beauty of the natural world and which argues, on that basis, that the world requires a divine Artist in order to explain its beauty. Against this view, one might raise a question concerning the beauty of, and in, this divine Artist. What explains the divine beauty? This kind of explanatory regress objection is exactly like that used by Philo in Hume’s Dialogues to undercut standard (...) versions of the design argument focused on the orderliness of the world. Here I argue that Philo’s explanatory regress objection likewise significantly undercuts versions of the design argument focusing on the beauty of the world. (shrink)