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)

In this paper, I propose that 'true’ is polysemous, and thus ambiguous. I suggest that the semantic paradoxes both motivates taking 'true’ to be polysemous and shows that the concept truth is indefinitely extensible. In doing so, I explain that 'true’ is polysemous between the meanings corresponding to the subconcepts of the concept truth generated by such indefinite extensibility. I conclude that the proposal provides satisfying solutions to the semantic paradoxes.

Bertrand Russell offered an influential paradox of propositions in Appendix B of The Principles of Mathematics, but there is little agreement as to what to conclude from it. We suggest that Russell's paradox is best regarded as a limitative result on propositional granularity. Some propositions are, on pain of contradiction, unable to discriminate between classes with different members: whatever they predicate of one, they predicate of the other. When accepted, this remarkable fact should cast some doubt upon some of the (...) uses to which modern descendente of Russell's paradox of propositions have been put in recent literature. (shrink)

The notion of more truth, or of more truth and less falsehood, is central to epistemology. Yet, I argue, we have no idea what this consists in, as the most natural or obvious thing to say—that more truth is a matter of a greater number of truths, and less falsehood is a matter of a lesser number of falsehoods—is ultimately implausible. The issue is important not merely because the notion of more truth and less falsehood is central to epistemology, but (...) because an implicit, false picture of what this consists in underpins and gives shape to much contemporary epistemology. (shrink)

Toward the end of his classic treatise An Essay on Free Will, Peter van Inwagen offers a modal argument against the Principle of Sufficient Reason which he argues shows that the principle “collapses all modal distinctions.” In this paper, a critical flaw in this argument is shown to lie in van Inwagen’s beginning assumption that there is such a thing as the conjunction of all contingently true propositions. This is shown to follow from Cantor’s theorem and a property of conjunction (...) with respect to contingent propositions. Given the failure of this assumption, van Inwagen’s argument against the Principle of Sufficient Reason cannot succeed, at least not without the addition of some remarkable and previously unacknowledged qualifications. (shrink)

In this paper I present two new arguments against the possibility of an omniscient being. My new arguments invoke considerations of cardinality and resemble several arguments originally presented by Patrick Grim. Like Grim, I give reasons to believe that there must be more objects in the universe than there are beliefs. However, my arguments will rely on certain mereological claims, namely that Classical Extensional Mereology is necessarily true of the part-whole relation. My first argument is an instance of a problem (...) first noted by Gideon Rosen and requires an additional assumption about the mereological structure of certain beliefs. That assumption is that an omniscient being’s beliefs are mereological simples. However, this assumption is dropped when I present my second argument. Thus, I hope to show that if Classical Extensional Mereology is true of the part-whole relation, there cannot be an omniscient being. (shrink)

I formulate and defend two sceptical theses on specific parts of our modal knowledge (unqualified and absolute modalities). My main point is that unqualified modal sentences are defective in that they fail to belong unambiguously to specific modal kinds and thus cannot be evaluated; hence, we must be sceptical of beliefs involving them.

The question of what truths are necessary in the broadest possible sense is a difficult one to answer, as is the question of what the limits are to what is possible. (Most people would see these two questions as different sides of the same coin, of course, since many think the question of what is possible is just the question of what is not necessarily ruled out). We have three general sorts of strategies for determining whether something is necessary (or (...) possible). We can identify it in a class that we were previously sure was a class of things that are necessary – we might show it is a theorem of a logical system that we have confidence in, or that the sentence appears to be true simply in virtue of the meanings of the words, or that it is a true statement involving names or about natural kinds of the “necessary a posteriori” sort discussed by Kripke and Putnam, and there are perhaps other classes of claims which we are prepared to accept are necessary if true.1 Likewise, we might establish the possibility of something occurring by reference to a class of well-established or uncontroversial possibilities: e.g. we are inclined to think that it is possible (in the broadest sense) for an event to occur in the future if one of the same kind has occurred in the past. (shrink)

Bringsjord (1985) argues that the definition W of possible worlds as maximal possible sets of propositions is incoherent. Menzel (1986a) notes that Bringsjord’s argument depends on the Powerset axiom and that the axiom can be reasonably denied. Grim (1986) counters that W can be proved to be incoherent without Powerset. Grim was right. However, the argument he provided is deeply flawed. The purpose of this note is to detail the problems with Grim’s argument and to present a sound alternative argument (...) for his conclusion – basically the argument Russell gave to establish a well-known paradox in The Principles of Mathematics. (shrink)

In Modal Logic as Metaphysics, Timothy Williamson claims that the possibilism-actualism (P-A) distinction is badly muddled. In its place, he introduces a necessitism-contingentism (N-C) distinction that he claims is free of the confusions that purportedly plague the P-A distinction. In this paper I argue first that the P-A distinction, properly understood, is historically well-grounded and entirely coherent. I then look at the two arguments Williamson levels at the P-A distinction and find them wanting and show, moreover, that, when the N-C (...) distinction is broadened (as per Williamson himself) so as to enable necessitists to fend off contingentist objections, the P-A distinction can be faithfully reconstructed in terms of the N-C distinction. However, Williamson’s critique does point to a genuine shortcoming in the common formulation of the P-A distinction. I propose a new definition of the distinction in terms of essential properties that avoids this shortcoming. (shrink)

It can be shown by means of a paradox that, given the Principle of Sufficient Reason, there is no conjunction of all contingent truths. The question is, or ought to be, how to interpret that result: _Quid sibi velit?_ A celebrated argument against PSR due to Peter van Inwagen and Jonathan Bennett in effect interprets the result to mean that PSR entails that there are no contingent truths. But reflection on parallels in philosophy of mathematics shows it can equally be (...) interpreted either as a proof that there are "too many" contingent truths to combine in a single conjunction or as a proof that the concept _contingent truth_ is indefinitely extensible and there is no such thing as "all contingent truths." Either interpretation would reconcile PSR with contingent truth, but the natural rationales of those interpretations are at odds. This essay argues that the second interpretation is a more satisfactory explanation of why, if PSR is true, there should be no conjunction of all contingent truths. This sheds new light on the nature of the explanatory demand embedded in PSR and uncovers a number of surprising implications for the commitments of rationalism. (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)

In a recent article, P. Roger Turner and Justin Capes argue that no one is, or ever was, even partly morally responsible for certain world-indexed truths. Here we present our reasons for thinking that their argument is unsound: It depends on the premise that possible worlds are maximally consistent states of affairs, which is, under plausible assumptions concerning states of affairs, demonstrably false. Our argument to show this is based on Bertrand Russell’s original ‘paradox of propositions’. We should then opt (...) for a different approach to explain world-indexed truths whose upshot is that we may be morally responsible for some of them. The result to the effect that there are no maximally consistent states of affairs is independently interesting though, since this notion motivates an account of the nature of possible worlds in the metaphysics of modality. We also register in this article, independently of our response to Turner and Capes, and in the spirit of Russell’s aforementioned paradox and many other versions thereof, a proof of the claim that there is no set of all true propositions one can render false. (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)

We present a new puzzle about logical truth, necessity, and moral responsibility. We defend one solution to the puzzle. A corollary of our preferred solution is that prominent arguments for the incompatibility of determinism and moral responsibility are invalid.

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.

Existentialism concerning singular propositions is the thesis that singular propositions ontologically depend on the individuals they are directly about in such a way that necessarily, those propositions exist only if the individuals they are directly about exist. Haecceitism is the thesis that what non-qualitative facts there are fails to supervene on what purely qualitative facts there are. I argue that existentialism concerning singular propositions entails the denial of haecceitism and that this entailment has interesting implications for debates concerning the philosophy (...) of language, the nature of propositions, and the metaphysics of modality. (shrink)

RESUMO Este artigo é dedicado ao argumento contra o Requisito de Existência fornecido por Takashi Yagisawa. Argumentamos que o cerne do argumento de Yagisawa – a Forte Iterabilidade – não pode ser inferido pela ideia de contingente a priori (Kripke) e é incompatível com a ideia de @-transformação (Plantinga). Assim, essas ideias, contrariamente a Yagisawa, não podem servir de base metodológica da Forte Iterabilidade. Também argumentamos que a Forte Iterabilidade é incompatível com o Princípio Constitutivo. Finalmente, mostramos que o conceito (...) de propriedades indexadas pelo mundo (o argumento de Yagisawa se fa na ideia de propriedades indexadas pelo mundo) é inconsistente e, mesmo que o defensor da Forte Iterabilidade possa resistir a esta objeção, a Forte Iterabilidade deve ser abandonada. (shrink)

This collection of essays explores the philosophy of human knowledge from a multitude of perspectives, with a particular emphasis upon the justification component of the classical analysis of knowledge and with an excursion along the way to explore the role of knowledge in Texas Hold ‘Em poker. An important theme of the collection is the role of knowledge in religion, including a detailed argument for agnosticism. A number of the essays touch upon issues in philosophical logic, among them a fascinating (...) new counter-example to Modus Ponens. The collection is rounded out with essays on causality and the philosophy of mind. The author’s perspective on the philosophy of human knowledge is fresh and challenging, as evidenced by essays entitled “On Epistemic Preferability;” “On Being Unjustified;” “The Logic of ‘Unless’” and “Is ‘This sentence is true.’ True?” An interesting feature of The Logic of Philosophy: Pesky Essays is the inclusion of responses to several of its key essays, contributed by such prominent contemporary philosophers as Roderick Chisholm, Ted Sider and Tomas Kapitan. (shrink)

This thesis comprises three main chapters—each comprising one relatively standalone paper. The unifying theme is fragmentalism about truth, which is the view that the predicate “true” either expresses distinct concepts or expresses distinct properties. -/- In Chapter 1, I provide a formal development of alethic pluralism. Pluralism is the view that there are distinct truth properties associated with distinct domains of subject matter, where a truth property satisfies certain truth-characterizing principles. On behalf of pluralists, I propose an account of logic (...) and semantics that shows how they can answer central conceptual and logical challenges for their view. -/- In Chapter 2, I motivate and develop a modal account of propositions on the basis of an iterative conception of propositions, where the modality is logico-mathematical. The modal account of propositions takes the conception to motivate an inherently potential hierarchy of propositions. I show that the account helps provide satisfying solutions to the intensional paradoxes of Russell-Myhill, Kaplan, and Prior. -/- In Chapter 3, I propose that “true” is polysemous. I suggest that “true” is initially polysemous between correspondence truth and disquotational truth, and further polysemous between the meanings corresponding to the subconcepts of the concept truth generated by the indefinite extensibility of that concept. I show that the proposal provides satisfying solutions to the semantic paradoxes. (shrink)

A critical reflection on John Woods's new monograph, Truth in Fiction – Rethinking its Logic. I focus in particular on Woods’s world-inheritance thesis (what others have variously called ‘background,’ ‘the principle of minimal departure,’ and ‘the reality assumption,’ and which replaces Woods’s earlier ‘fill-conditions’) and its interplay with auctorial say-so, arguing that world-inheritance actually constrains auctorial say-so in ways Woods has not anticipated.

There is a common approach to metaphysical disputes, which takes language as its starting point, and leads to a view about the range of acceptable metaphysical positions in any such dispute. I argue that this approach rests on accepting what I call the Strong Linguistic Thesis (SLT). In the metaphysical debate about time I argue that the new B-theory has rejected SLT, and for good reasons. The metaphysical debate about modality parallels the early metaphysical debate about time. I argue that (...) a position analogous to the new B-theory of time is available in the modal debate, and has some advantages over its rivals. (shrink)