We often speak as if there are merely possible people—for example, when we make such claims as that most possible people are never going to be born. Yet most metaphysicians deny that anything is both possibly a person and never born. Since our unreflective talk of merely possible people serves to draw non-trivial distinctions, these metaphysicians owe us some paraphrase by which we can draw those distinctions without committing ourselves to there being merely possible people. We show that such paraphrases (...) are unavailable if we limit ourselves to the expressive resources of even highly infinitary first-order modal languages. We then argue that such paraphrases are available in higher-order modal languages only given certain strong assumptions concerning the metaphysics of properties. We then consider alternative paraphrase strategies, and argue that none of them are tenable. If talk of merely possible people cannot be paraphrased, then it must be taken at face value, in which case it is necessary what individuals there are. Therefore, if it is contingent what individuals there are, then the demands of paraphrase place tight constraints on the metaphysics of properties: either (i) it is necessary what properties there are, or (ii) necessarily equivalent properties are identical, and having properties does not entail even possibly being anything at all. (shrink)
This paper is a study of higher-order contingentism – the view, roughly, that it is contingent what properties and propositions there are. We explore the motivations for this view and various ways in which it might be developed, synthesizing and expanding on work by Kit Fine, Robert Stalnaker, and Timothy Williamson. Special attention is paid to the question of whether the view makes sense by its own lights, or whether articulating the view requires drawing distinctions among possibilities that, according to (...) the view itself, do not exist to be drawn. The paper begins with a non-technical exposition of the main ideas and technical results, which can be read on its own. This exposition is followed by a formal investigation of higher-order contingentism, in which the tools of variable-domain intensional model theory are used to articulate various versions of the view, understood as theories formulated in a higher-order modal language. Our overall assessment is mixed: higher-order contingentism can be fleshed out into an elegant systematic theory, but perhaps only at the cost of abandoning some of its original motivations. (shrink)
According to the structured theory of propositions, if two sentences express the same proposition, then they have the same syntactic structure, with corresponding syntactic constituents expressing the same entities. A number of philosophers have recently focused attention on a powerful argument against this theory, based on a result by Bertrand Russell, which shows that the theory of structured propositions is inconsistent in higher order-logic. This paper explores a response to this argument, which involves restricting the scope of the claim that (...) propositions are structured, so that it does not hold for all propositions whatsoever, but only for those which are expressible using closed sentences of a given formal language. We call this restricted principle Closed Structure, and show that it is consistent in classical higher-order logic. As a schematic principle, the strength of Closed Structure is dependent on the chosen language. For its consistency to be philosophically significant, it also needs to be consistent in every extension of the language which the theorist of structured propositions is apt to accept. But, we go on to show, Closed Structure is in fact inconsistent in a very natural extension of the standard language of higher-order logic, which adds resources for plural talk of propositions. We conclude that this particular strategy of restricting the scope of the claim that propositions are structured is not a compelling response to the argument based on Russell’s result, though we note that for some applications, for instance to propositional attitudes, a restricted thesis in the vicinity may hold some promise. (shrink)
Epistemic two-dimensional semantics is a theory in the philosophy of language that provides an account of meaning which is sensitive to the distinction between necessity and apriority. While this theory is usually presented in an informal manner, I take some steps in formalizing it in this paper. To do so, I define a semantics for a propositional modal logic with operators for the modalities of necessity, actuality, and apriority that captures the relevant ideas of epistemic two-dimensional semantics. I also describe (...) some properties of the logic that are interesting from a philosophical perspective, and apply it to the so-called nesting problem. (shrink)
This paper is concerned with a propositional modal logic with operators for necessity, actuality and apriority. The logic is characterized by a class of relational structures defined according to ideas of epistemic two-dimensional semantics, and can therefore be seen as formalizing the relations between necessity, actuality and apriority according to epistemic two-dimensional semantics. We can ask whether this logic is correct, in the sense that its theorems are all and only the informally valid formulas. This paper gives outlines of two (...) arguments that jointly show that this is the case. The first is intended to show that the logic is informally sound, in the sense that all of its theorems are informally valid. The second is intended to show that it is informally complete, in the sense that all informal validities are among its theorems. In order to give these arguments, a number of independently interesting results concerning the logic are proven. In particular, the soundness and completeness of two proof systems with respect to the semantics is proven (Theorems 2.11 and 2.15), as well as a normal form theorem (Theorem 3.2), an elimination theorem for the actuality operator (Corollary 3.6), and the decidability of the logic (Corollary 3.7). It turns out that the logic invalidates a plausible principle concerning the interaction of apriority and necessity; consequently, a variant semantics is briefly explored on which this principle is valid. The paper concludes by assessing the implications of these results for epistemic two-dimensional semantics. (shrink)
According to propositional contingentism, it is contingent what propositions there are. This paper presents two ways of modeling contingency in what propositions there are using two classes of possible worlds models. The two classes of models are shown to be equivalent as models of contingency in what propositions there are, although they differ as to which other aspects of reality they represent. These constructions are based on recent work by Robert Stalnaker; the aim of this paper is to explain, expand, (...) and, in one aspect, correct Stalnaker's discussion. (shrink)
Certain passages in Kaplan’s ‘Demonstratives’ are often taken to show that non-vacuous sentential operators associated with a certain parameter of sentential truth require a corresponding relativism concerning assertoric contents: namely, their truth values also must vary with that parameter. Thus, for example, the non-vacuity of a temporal sentential operator ‘always’ would require some of its operands to have contents that have different truth values at different times. While making no claims about Kaplan’s intentions, we provide several reconstructions of how such (...) an argument might go, focusing on the case of time and temporal operators as an illustration. What we regard as the most plausible reconstruction of the argument establishes a conclusion similar enough to that attributed to Kaplan. However, the argument overgenerates, leading to absurd consequences. We conclude that we must distinguish assertoric contents from compositional semantic values, and argue that once they are distinguished, the argument fails to establish any substantial conclusions. We also briefly discuss a related argument commonly attributed to Lewis, and a recent variant due to Weber. (shrink)
Propositional quantifiers are added to a propositional modal language with two modal operators. The resulting language is interpreted over so-called products of Kripke frames whose accessibility relations are equivalence relations, letting propositional quantifiers range over the powerset of the set of worlds of the frame. It is first shown that full second-order logic can be recursively embedded in the resulting logic, which entails that the two logics are recursively isomorphic. The embedding is then extended to all sublogics containing the logic (...) of so-called fusions of frames with equivalence relations. This generalizes a result due to Antonelli and Thomason, who construct such an embedding for the logic of such fusions. (shrink)
An argument going back to Russell shows that the view that propositions are structured is inconsistent in standard type theories. Here, it is shown that such type theories may nevertheless provide entities which can serve as proxies for structured propositions. As an illustration, such proxies are applied to the case of grounding, as standard views of grounding require a degree of propositional structure which suffices for a version of Russell’s argument. While this application solves some of the problems grounding faces, (...) it introduces problematic limitations: it becomes impossible to quantify unrestrictedly over the relata of ground. The proposed proxies may thus not save grounding, but they shed light on what exactly Russell’s argument does and does not show. (shrink)
The models of contingency in what propositions, properties and relations there are developed in Part 1 are related to models of contingency in what propositions there are due to Robert Stalnaker. It is shown that some but not all of the classes of models of Part 1 agree with Stalnaker’s models concerning the patterns of contingency in what propositions there are they admit. Further structural connections between the two kinds of models are explored.
I consider the first-order modal logic which counts as valid those sentences which are true on every interpretation of the non-logical constants. Based on the assumptions that it is necessary what individuals there are and that it is necessary which propositions are necessary, Timothy Williamson has tentatively suggested an argument for the claim that this logic is determined by a possible world structure consisting of an infinite set of individuals and an infinite set of worlds. He notes that only the (...) cardinalities of these sets matters, and that not all pairs of infinite sets determine the same logic. I use so-called two-cardinal theorems from model theory to investigate the space of logics and consequence relations determined by pairs of infinite sets, and show how to eliminate the assumption that worlds are individuals from Williamson’s argument. (shrink)
Timothy Williamson has argued that in the debate on modal ontology, the familiar distinction between actualism and possibilism should be replaced by a distinction between positions he calls contingentism and necessitism. He has also argued in favor of necessitism, using results on quantified modal logic with plurally interpreted second-order quantifiers showing that necessitists can draw distinctions contingentists cannot draw. Some of these results are similar to well-known results on the relative expressivity of quantified modal logics with so-called inner and outer (...) quantifiers. The present paper deals with these issues in the context of quantified modal logics with generalized quantifiers. Its main aim is to establish two results for such a logic: Firstly, contingentists can draw the distinctions necessitists can draw if and only if the logic with inner quantifiers is at least as expressive as the logic with outer quantifiers, and necessitists can draw the distinctions contingentists can draw if and only if the logic with outer quantifiers is at least as expressive as the logic with inner quantifiers. Secondly, the former two items are the case if and only if all of the generalized quantifiers are first-order definable, and the latter two items are the case if and only if first-order logic with these generalized quantifiers relativizes. (shrink)
Existential claims are widely held to be grounded in their true instances. However, this principle is shown to be problematic by arguments due to Kit Fine. Stephan Krämer has given an especially simple form of such an argument using propositional quantifiers. This note shows that even if a schematic principle of existential grounds for propositional quantifiers has to be restricted, this does not immediately apply to a corresponding non-schematic principle in higher-order logic.
Two expressive limitations of an infinitary higher-order modal language interpreted on models for higher-order contingentism – the thesis that it is contingent what propositions, properties and relations there are – are established: First, the inexpressibility of certain relations, which leads to the fact that certain model-theoretic existence conditions for relations cannot equivalently be reformulated in terms of being expressible in such a language. Second, the inexpressibility of certain modalized cardinality claims, which shows that in such a language, higher-order contingentists cannot (...) express what is communicated using various instances of talk of ‘possible things’, such as ‘there are uncountably many possible stars’. (shrink)
Robert Stalnaker has recently advocated propositional contingentism, the claim that it is contingent what propositions there are. He has proposed a philosophical theory of contingency in what propositions there are and sketched a possible worlds model theory for it. In this paper, such models are used to interpret two propositional modal languages: one containing an existential propositional quantifier, and one containing an existential propositional operator. It is shown that the resulting logic containing an existential quantifier is not recursively axiomatizable, as (...) it is recursively isomorphic to second-order logic, and a natural candidate axiomatization for the resulting logic containing an existential operator is shown to be incomplete. (shrink)
This article explores the connection between two theses: the principle of conditional excluded middle for the counterfactual conditional, and the claim that it is a contingent matter which (coarse grained) propositions there are. Both theses enjoy wide support, and have been defended at length by Robert Stalnaker. We will argue that, given plausible background assumptions, these two principles are incompatible, provided that conditional excluded middle is understood in a certain modalized way. We then show that some (although not all) arguments (...) for conditional excluded middle can in fact be extended to motivate this modalized version of the principle. (shrink)
A formal result is proved which is used in Juhani Yli-Vakkuri’s ‘Epistemicism and Modality’ to argue that certain two-dimensional possible world models are inadequate for a language with operators for ‘necessarily’, ‘actually’, and ‘definitely’.
The impossibility theorem of Dekel, Lipman and Rustichini has been thought to demonstrate that standard state-space models cannot be used to represent unawareness. We first show that Dekel, Lipman and Rustichini do not establish this claim. We then distinguish three notions of awareness, and argue that although one of them may not be adequately modeled using standard state spaces, there is no reason to think that standard state spaces cannot provide models of the other two notions. In fact, standard space (...) models of these forms of awareness are attractively simple. They allow us to prove completeness and decidability results with ease, to carry over standard techniques from decision theory, and to add propositional quantifiers straightforwardly. (shrink)
In his book The Boundary Stones of Thought, Ian Rumfitt considers five arguments in favour of intuitionistic logic over classical logic. Two of these arguments are based on reflections concerning the meaning of statements in general, due to Michael Dummett and John McDowell. The remaining three are more specific, concerning statements about the infinite and the infinitesimal, statements involving vague terms, and statements about sets.Rumfitt is sympathetic to the premisses of many of these arguments, and takes some of them to (...) be effective challenges to Bivalence, the following principle: Each statement is either true or false.However, he argues that counterexamples to Bivalence do not immediately lead to counterexamples to Excluded Middle, and so do not immediately refute classical logic; here, Excluded Middle is taken to be the following principle: For each statement A, is true.Much... (shrink)
Well-known results due to David Makinson show that there are exactly two Post complete normal modal logics, that in both of them, the modal operator is truth-functional, and that every consistent normal modal logic can be extended to at least one of them. Lloyd Humberstone has recently shown that a natural analog of this result in congruential modal logics fails, by showing that not every congruential modal logic can be extended to one in which the modal operator is truth-functional. As (...) Humberstone notes, the issue of Post completeness in congruential modal logics is not well understood. The present article shows that in contrast to normal modal logics, the extent of the property of Post completeness among congruential modal logics depends on the background set of logics. Some basic results on the corresponding properties of Post completeness are established, in particular that although a congruential modal logic is Post complete among all modal logics if and only if its modality is truth-functional, there are continuum many modal logics Post complete among congruential modal logics. (shrink)
Two-dimensional semantics is a theory in the philosophy of language that provides an account of meaning which is sensitive to the distinction between necessity and apriority. Usually, this theory is presented in an informal manner. In this thesis, I take first steps in formalizing it, and use the formalization to present some considerations in favor of two-dimensional semantics. To do so, I define a semantics for a propositional modal logic with operators for the modalities of necessity, actuality, and apriority that (...) captures the relevant ideas of two-dimensional semantics. I use this to show that some criticisms of two-dimensional semantics that claim that the theory is incoherent are not justified. I also axiomatize the logic, and compare it to the most important proposals in the literature that define similar logics. To indicate that two-dimensional semantics is a plausible semantic theory, I give an argument that shows that all theorems of the logic can be philosophically justified independently of two-dimensional semantics. (shrink)
This essay examines how Michel Henry's and Jean‐Luc Marion's continuation of phenomenology's turn to the invisible relates to painting, aesthetics, and theology. First, it discusses Henry and Marion's redefinition of phenomenality. Second, it explores Henry's “Kandinskian” description of abstract painting as expressing “Life.” Third, it explicates Marion's “Rothkoian” rehabilitation of the idol and renewed zeal for the icon—both phenomena exemplify “givenness.” Fourth, it unpacks my thesis: Henry's phenomenology, theologically applied, exercises an inadequate Kantian apophasis, characterized by a sublime sacrifice of (...) the imagination; although Marion's work sometimes evidences a similar tendency, its prevailing momentum offers theology a fully catholic scope. (shrink)
Rahner's Mariology and theology of the saints exemplify his respect for the universality of the Catholic ethos. The article’s three parts substantiate this claim. First, it analyzes Rahner's placement of Mary outside his theology's center, while he resists marginalizing her. This analysis involves contrasting Rahner with Hans Urs von Balthasar. Second, it reads Rahner's theology of Mary's Assumption as an exercise in fundamental-eschatological theology. He takes a similar approach in his theology of the saints. Third, it considers Rahner's thoughts on (...) devotion to Mary and the saints, relating these practices to his fundamental-eschatological theology. Rahner’s contextualization of Mary and the saints within the wideness of all history, to which eschatology attests, reflects his holding open of the universal Catholic ethos. This sets him apart from other Catholics, who fix Mary and the saints firmly at Catholicism’s center, thus potentially restricting the Catholic ethos. Today’s Catholics must learn from Rahner’s holism. (shrink)
I want to look at recent developments of representing AGM-style belief revision in dynamic epistemic logics and the options for doing something similar for ranking theory. Formally, my aim will be modest: I will define a version of basic dynamic doxastic logic using ranking functions as the semantics. I will show why formalizing ranking theory this way is useful for the ranking theorist first by showing how it enables one to compare ranking theory more easily with other approaches to belief (...) revision. I will then use the logic to state an argument for defining ranking functions on larger sets of ordinals than is customary. Secondly, I will argue that the only way to extend the account of belief revision given by ranking theory to higher-order beliefs and revisions is by continuing the approach taken by me and defining ranking theoretical equivalents of dynamic epistemic logics. For proponents of dynamic epistemic logic, such logics will naturally be of interest provided they are convinced of the revision operator defined by ranking theory. (shrink)
Humanism and the Death of God is a critical exploration of secular humanism and its discontents. Through close readings of three exemplary nineteenth-century philosophical naturalists or materialists, who perhaps more than anyone set the stage for our contemporary quandaries when it comes to questions of human nature and moral obligation, Ronald E. Osborn argues that "the death of God" ultimately tends toward the death of liberal understandings of the human as well. Any fully persuasive defense of humanistic values - including (...) the core humanistic concepts of inviolable dignity, rights, and equality attaching to each individual - requires an essentially religious vision of personhood. Osborn shows such a vision is found in an especially dramatic and historically consequential way in the scandalous particularity of the Christian narrative of God becoming a human. He does not attempt to provide logical proofs for the central claims of Christian humanism along the lines some philosophers might demand. Instead, this study demonstrates how philosophical naturalism or materialism, and secular humanisms and anti-humanisms, might be persuasively read from the perspective of a classically orthodox Christian faith. (shrink)
This article argues that Karl Rahner’s theme of “eschatological ignorance” should be retrieved to facilitate and to fortify the enactment of Catholic theology’s prophetic commitments in a U.S. context. First, the article presents and defends Rahner’s famous distinction between eschatology and apocalyptic. Second, it characterizes Rahner’s distinction as representative of his conviction of a need for docta ignorantia futuri, which stems from his theology of God as Absolute Mystery, and which, though Rahner recommends it to twentieth-century Europeans, seems particularly well (...) suited for theological application in the twenty-first-century United States. Third, it suggests how Rahner’s eschatological ignorance might make a prophetic impact on the American socio-religio-political climate. (shrink)
Things could have been different, but could it also have been different what things there are? It is natural to think so, since I could have failed to be born, and it is natural to think that I would then not have been anything. But what about entities like propositions, properties and relations? Had I not been anything, would there have been the property of being me? In this thesis, I formally develop and assess views according to which it is (...) both contingent what individuals there are and contingent what propositions, properties and relations there are. I end up rejecting these views, and conclude that even if it is contingent what individuals there are, it is necessary what propositions, properties and relations there are. -/- Call the view that it is contingent what individuals there are first-order contingentism, and the view that it is contingent what propositions, properties and relations there are higher-order contingentism. I bring together the three major contributions to the literature on higher-order contingentism, which have been developed largely independently of each other, by Kit Fine, Robert Stalnaker, and Timothy Williamson. I show that a version of Stalnaker's approach to higher-order contingentism was already explored in much more technical detail by Fine, and that it stands up well to the major challenges against higher-order contingentism posed by Williamson. -/- I further show that once a mistake in Stalnaker's development is corrected, each of his models of contingently existing propositions corresponds to the propositional fragment of one of Fine's more general models of contingently existing propositions, properties and relations, and vice versa. I also show that Stalnaker's theory of contingently existing propositions is in tension with his own theory of counterfactuals, but not with one of the main competing theories, proposed by David Lewis. -/- Finally, I connect higher-order contingentism to expressive power arguments against first-order contingentism. I argue that there are intelligible distinctions we draw with talk about "possible things", such as the claim that there are uncountably many possible stars. Since first-order contingentists hold that there are no possible stars apart from the actual stars, they face the challenge of paraphrasing such talk. I show that even in an infinitary higher-order modal logic, the claim that there are uncountably many possible stars can only be paraphrased if higher-order contingentism is false. I therefore conclude that even if first-order contingentism is true, higher-order contingentism is false. (shrink)
Can conjunctive propositions be identical without their conjuncts being identical? Can universally quantified propositions be identical without their instances being identical? On a common conception of propositions, on which they inherit the logical structure of the sentences which express them, the answer is negative both times. Here, it will be shown that such a negative answer to both questions is inconsistent, assuming a standard type-theoretic formalization of theorizing about propositions. The result is not specific to conjunction and universal quantification, but (...) applies to any binary operator and propositional quantifier. It is also shown that the result essentially arises out of giving a negative answer to both questions, as each negative answer is consistent by itself. (shrink)
Robert Stalnaker recently proposed a simple theory of propositions using the notion of a set of propositions being consistent, and conjectured that this theory is equivalent to the claim that propositions form a complete atomic Boolean algebra. This paper clarifies and confirms this conjecture. Stalnaker also noted that some of the principles of his theory may be given up, depending on the intended notion of proposition. This paper therefore also investigates weakened constraints on consistency and the corresponding classes of Boolean (...) algebras. (shrink)
This article explores how Jean-Luc Nancy attempts to gain critical traction on Christianity by proscribing thinking of completion. First, it describes Nancy's deconstruction of Christianity as stemming from his aesthetic redirection of Heidegger's thinking of finitude. Second, it further details Nancy's noetic declension of Heidegger via Kant and Lyotard, where the imagination and aesthetic communication are deemed impossible. Third, it examines Nancy's treatment of paintings of the Virgin Mary who, for Nancy, exemplifies his brand of incompletion. Nancy's work on Mary (...) reveals both the oversights and the insights of his deconstruction of Christianity, which Catholic theology should seriously engage. (shrink)
