In the philosophy of artificial intelligence (AI) we are often warned of machines built with the best possible intentions, killing everyone on the planet and in some cases, everything in our light cone. At the same time, however, we are also told of the utopian worlds that could be created with just a single superintelligent mind. If we’re ever to live in that utopia (or just avoid dystopia) it’s necessary we solve the control problem. The control problem asks how humans (...) would be able to control an AI arbitrarily. Nick Bostrom and other AI researchers have proposed different theoretical solutions to the control problem. In this paper, I will not look at the empirical question of how to solve the control problem. Instead, I will ask if we can solve it at all, a critical assumption most AI researchers have made is that we can. I propose, in fact, that we have a priori grounds for believing it is logically impossible to solve the control problem, since all superintelligent minds are, by definition, uncontrollable. (shrink)

Can there be grounding without necessitation? Can a fact obtain wholly in virtue of metaphysically more fundamental facts, even though there are possible worlds at which the latter facts obtain but not the former? It is an orthodoxy in recent literature about the nature of grounding, and in first-order philosophical disputes about what grounds what, that the answer is no. I will argue that the correct answer is yes. I present two novel arguments against grounding necessitarianism, and show that grounding (...) contingentism is fully compatible with the various explanatory roles that grounding is widely thought to play. (shrink)

There are three main accounts of scientific progress: 1) the epistemic account, according to which an episode in science constitutes progress when there is an increase in knowledge; 2) the semantic account, according to which progress is made when the number of truths increases; 3) the problem-solving account, according to which progress is made when the number of problems that we are able to solve increases. Each of these accounts has received several criticisms in the last decades. Nevertheless, some authors (...) think that the epistemic account is to be preferred if one takes a realist stance. Recently, Dellsén proposed the noetic account, according to which an episode in science constitutes progress when scientists achieve increased understanding of a phenomenon. Dellsén claims that the noetic account is a more adequate realist account of scientific progress than the epistemic account. This paper aims precisely at assessing whether the noetic account is a more adequate realist account of progress than the epistemic account. (shrink)

The paper discusses the arguments for and against animalism and concludes that a pluralist position which rejects animalism and embraces a multiplicity of thinkers is the best option.

Coincidence comes in two varieties – permanent and temporary. Moderate monism is the position that permanent coincidence, but not temporary coincidence, entails identity. Extreme monism is the position that even temporary coincidence entails identity. Pluralists are opponents of monism tout court. The intuitively obvious, commonsensical position is moderate monism. It is therefore important to see if it can be sustained.

In his influential article ‘Essence and Modality’, Fine proposes a definition of necessity in terms of the primitive essentialist notion ‘true in virtue of the nature of’. Fine’s proposal is suggestive, but it admits of different interpretations, leaving it unsettled what the precise formulation of an Essentialist definition of necessity should be. In this paper, four different versions of the definition are discussed: a singular, a plural reading, and an existential variant of Fine’s original suggestion and an alternative version proposed (...) by Correia which is not based on Fine’s primitive essentialist notion. The first main point of the paper is that the singular reading is untenable. The second that given plausible background assumptions, the remaining three definitions are extensionally equivalent. The third is that, this equivalence notwithstanding, Essentialists should adopt Correia’s version of the definition, since both the existential variant, which has de facto been adopted as the standard version of the definition in the literature, and the plural reading suffer from problems connected to Fine’s primitive essentialist notion. (shrink)

I consider whether the self-ascription theory can succeed in providing a tenseless (B-theoretic) account of tensed belief and timely action. I evaluate an argument given by William Lane Craig for the conclusion that the self-ascription account of tensed belief entails a tensed theory (A-theory) of time. I claim that how one formulates the selfascription account of tensed belief depends upon whether one takes the subject of selfascription to be a momentary person-stage or an enduring person. I provide two different formulations (...) of the self-ascription account of tensed belief, one that is compatible with a perdurantist account of persons and the other that is compatible with an endurantist account of persons. I argue that a self-ascription account of tensed beliefs for enduring subjects most plausibly involves the self-ascription of relations rather than properties. I argue that whether one takes the subject of self-ascription to be a momentary personstage or an enduring person, the self-ascription theory provides a plausible B-theoretic account of how tensed belief and timely action are possible. (shrink)

In this paper I consider two strategies for providing tenseless truth-conditions for tensed sentences: the token-reflexive theory and the date theory. Both theories have faced a number of objections by prominent A-theorists such as Quentin Smith and William Lane Craig. Traditionally, these two theories have been viewed as rival methods for providing truth-conditions for tensed sentences. I argue that the debate over whether the token-reflexive theory or the date theory is true has arisen from a failure to distinguish between conditions (...) for the truth of tensed tokens and conditions for the truth of propositions expressed by tensed tokens. I demonstrate that there is a true formulation of the token-reflexive theory that provides necessary and sufficient conditions for the truth of tensed tokens, and there is a true formulation of the date theory that provides necessary and sufficient conditions for the truth of propositions expressed by tensed tokens. I argue that once the views are properly formulated, the A-theorist’s objections fail to make their mark. However, I conclude by claiming that even though there is a true formulation of the token-reflexive theory and a true formulation of the date theory, the New B-theory nonetheless fails to provide a complete account of the truth and falsity of tensed sentences. (shrink)

When do objects at different times compose a further object? This is the question of diachronic composition. The universalist answers, ‘under any conditions whatsoever’. Others argue for restrictions on diachronic composition: composition occurs only when certain conditions are met. Recently, some philosophers have argued that restrictions on diachronic compositions are motivated by our best physical theories. In Persistence and Spacetime and elsewhere, Yuri Balashov argues that diachronic compositions are restricted in terms of causal connections between object stages. In a recent (...) article, Nikk Effingham argues that the standard objections to views that endorse restrictions on composition do not apply to a view that restricts composition according to compliance with the laws of nature. On the face of it, such restrictions on diachronic composition preserve our common-sense ontology while eliminating from it scientifically revisionary objects that travel faster than the speed of light. I argue that these attempts to restrict diachronic composition by appealing to either causal or nomological constraints face insurmountable difficulties within the context of special relativity. I discuss how the universalist should best respond to Hudson’s argument for superluminal objects, and in doing so, I present and defend a new sufficient condition for motion that does not entail that such objects are in superluminal motion. 1 Introduction2 Diachronic Composition3 Diachronic Composition and Superluminal Objects4 Restricting Diachronic Composition5 Causal and Nomological Restrictions on Composition in a Relativistic Context6 Superluminal Objects and Motion7 Conclusion. (shrink)

This paper examines "moderate modal skepticism", a form of skepticism about metaphysical modality defended by Peter van Inwagen in order to blunt the force of certain modal arguments in the philosophy of religion. Van Inwagen’s argument for moderate modal skepticism assumes Yablo's (1993) influential world-based epistemology of possibility. We raise two problems for this epistemology of possibility, which undermine van Inwagen's argument. We then consider how one might motivate moderate modal skepticism by relying on a different epistemology of possibility, which (...) does not face these problems: Williamson’s (2007: ch. 5) counterfactual-based epistemology. Two ways of motivating moderate modal skepticism within that framework are found unpromising. Nevertheless, we also find a way of vindicating an epistemological thesis that, while weaker than moderate modal skepticism, is strong enough to support the methodological moral van Inwagen wishes to draw. (shrink)

This article surveys recent developments in the epistemology of modality.

It is often thought that endowing a demonstrative with a Fregean sense leaves no room for maintaining that it is also a rigid designator. In addition, some philosophers claim that indexicals - surely the paradigms of singular reference - pose a serious threat to the Fregean sense/ reference approach as they do not comply with the view that singular terms have Fregean senses. In this paper I argue that neither of these is true.

The paper argues against Peacocke's moderate rationalism in modality. In the first part, I show, by identifying an argumentative gap in its epistemology, that Peacocke's account has not met the Integration Challenge. I then argue that we should modify the account's metaphysics of modal concepts in order to avoid implausible consequences with regards to their possession conditions. This modification generates no extra explanatory gap. Yet, once the minimal modification that avoids those implausible consequences is made, the resulting account cannot support (...) Peacocke's moderate rationalism. (shrink)

That believing truly as a matter of luck does not generally constitute knowing has become epistemic commonplace. Accounts of knowledge incorporating this anti-luck idea frequently rely on one or another of a safety or sensitivity condition. Sensitivity-based accounts of knowledge have a well-known problem with necessary truths, to wit, that any believed necessary truth trivially counts as knowledge on such accounts. In this paper, we argue that safety-based accounts similarly trivialize knowledge of necessary truths and that two ways of responding (...) to this problem for safety, issuing from work by Williamson and Pritchard, are of dubious success. (shrink)

David Lewis defends the following "non-circular definition of personhood": "something is a continuant person if and only if it is a maximal R-interrelated aggregate of person-stages. That is: if and only if it is an aggregate of person-stages, each of which is R-related to all the rest (and to itself), and it is a proper part of no other such aggregate." I give a counterexample, involving a person who is a part of another, much larger person, with a separate mental (...) life. I then offer an easy repair, which preserves the virtues of Lewis's definition without introducing any new vices. (shrink)

In this paper I propose a new solution to the problem of change: situationalism. According to this view, parts of reality fundamentally disagree about what is the case and reality as a whole is unsettled (i.e. metaphysically indeterminate). When something changes, parts of the world irreconcilably disagree about what properties it has. From this irreconcilable disagreement, indeterminacy arises. I develop this picture using situations, which are parts of possible worlds; this gives it the name situationalism. It allows a B-theory endurance (...) view on which there is genuine incompatibility when things change. There are costs to the view, which are explored, but it is a novel approach which offers a distinct explanation of what happens when things exist through change. (shrink)

In this paper I will examine the infinite regress arguments pertaining to the unreality of relations that are presented in Francis Herbert Bradley’s paper, Appearance and Reality. Then I will suggest two argumentative strategies one can take to undermine Bradley’s regress argument. The first option concerns plainly rejecting the regress by stating that Bradley is viewing relations as kinds of objects that are in need of being related, whereas the second option is in regards to adopting an existential-dependence view between (...) objects and their properties to refute the need for relations. I will conclude this paper by comparing these two strategies against each other, alluding to each of their ramifications. (shrink)

// tl;dr A Proposition is a Way of Thinking // -/- This chapter is about type-theoretic approaches to propositional content. Type-theoretic approaches to propositional content originate with Hintikka, Stalnaker, and Lewis, and involve treating attitude environments (e.g. "Nate thinks") as universal quantifiers over domains of "doxastic possibilities" -- ways things could be, given what the subject thinks. -/- This chapter introduces and motivates a line of a type-theoretic theorizing about content that is an outgrowth of the recent literature on epistemic (...) modality, according to which contentful thought is broadly "informational" in its nature and import. The general idea here is that an object of thought is not a way *the world* could be, but rather a way *one's perspective* could be (with respect to a relevant representational question). I will spend the middle part of this chapter motivating and developing a version of this strategy that is, I’ll argue, well-suited to explaining clear phenomena concerning the attribution of perspectival attitudes -- in particular, attitudes towards loosely information-sensitive propositions -- with which extant approaches struggle. My overarching goal here will be to motivate a distinctive version of the "informational" approach -- the "Flexible Types" approach, which is based on the theory proposed in Charlow (2020). According to the Flexible Types approach, propositional attitude verbs are quantifiers over sets of possibilities, but a possibility is a type-flexible notion -- sometimes a possible world, sometimes a perspective, sometimes a set of possible worlds, sometimes a set of perspectives. -/- After introducing the Flexible Types approach, this chapter circles back to more traditional concerns for the analysis of propositions as types of possibilities -- Frege's Puzzle and the problem of Logical Omniscience. Here too the Flexible Types approach bears fruit. Although there are certainly significant differences -- I note some in the concluding section -- the gist of this theory is Hinitkkan or Lewisian in spirit (if not quite in letter). We can make progress on addressing the challenges for the analysis of propositional content in terms of types of possibilities, through empirically driven refinement of our notion of what kind of thing a "doxastic possibility" is. (shrink)

Writers in the propositions literature consider the Benacerraf objection serious, often decisive. The objection figures heavily in dismissing standard theories of propositions of the past, notably set-theoretic theories. I argue that the situation is more complicated. After explicating the propositional Benacerraf problem, I focus on a classic set-theoretic theory of propositions, the possible worlds theory, and argue that methodological considerations influence the objection’s success.

A and B continue their conversation concerning the Identity of Indiscernibles. Both are aware of recent critiques of the principle that haven’t received replies; B summarizes those critiques, and A offers the replies that are due. B then raises a new worry.

ABSTRACT Quine insisted that the satisfaction of an open modalised formula by an object depends on how that object is described. Kripke's ‘objectual’ interpretation of quantified modal logic, whereby variables are rigid, is commonly thought to avoid these Quinean worries. Yet there remain residual Quinean worries for epistemic modality. Theorists have recently been toying with assignment-shifting treatments of epistemic contexts. On such views an epistemic operator ends up binding all the variables in its scope. One might worry that this yields (...) the undesirable result that any attempt to ‘quantify in’ to an epistemic environment is blocked. If quantifying into the relevant constructions is vacuous, then such views would seem hopelessly misguided and empirically inadequate. But a famous alternative to Kripke's semantics, namely Lewis' counterpart semantics, also faces this worry since it also treats the boxes and diamonds as assignment-shifting devices. As I'll demonstrate, the mere fact that a variable is bound is no obstacle to binding it. This provides a helpful lesson for those modelling de re epistemic contexts with assignment sensitivity, and perhaps leads the way toward the proper treatment of binding in both metaphysical and epistemic contexts: Kripke for metaphysical modality, Lewis for epistemic modality. (shrink)

This paper provides an analysis of the intrinsic/extrinsic distinction, as applied both to properties and to relations. In contrast to other accounts, the approach taken here locates the source of a property’s intrinsicality or extrinsicality in the manner in which that property is ‘logically constituted’, and thus – plausibly – in its nature or essence, rather than in e.g. its modal profile. Another respect in which the present proposal differs from many extant analyses lies in the fact that it does (...) not seek to analyse the ‘global’ distinction between intrinsic and extrinsic properties on the basis of the ‘local’ distinction between having a property intrinsically and having it extrinsically. Instead, the latter distinction is explicated on the basis of the former. (shrink)

Fictionalists maintain that possible worlds, numbers or composite objects exist only according to theories which are useful but false. Hale, Divers and Woodward have provided arguments which threaten to show that fictionalists must be prepared to regard the theories in question as contingently, rather than necessarily, false. If warranted, this conclusion would significantly limit the appeal of the fictionalist strategy rendering it unavailable to anyone antecedently convinced that mathematics and metaphysics concern non-contingent matters. I try to show that their arguments (...) can be resisted by developing and defending a strategy suggested by Rosen, Nolan and Dorr, according to which the fiction-operator is to be analysed in terms of a counterfactual that admits of non-trival truth-values even when the antecedent is impossible. (shrink)

The dynamics of general relativity is encoded in a set of ten differential equations, the so-called Einstein field equations. It is usually believed that Einstein's equations represent a physical law describing the coupling of spacetime with material fields. However, just six of these equations actually describe the coupling mechanism: the remaining four represent a set of differential relations known as Bianchi identities. The paper discusses the physical role that the Bianchi identities play in general relativity, and investigates whether these identities (...) --qua part of a physical law-- highlight some kind of a posteriori necessity in a Kripkean sense. The inquiry shows that general relativistic physics has an interesting bearing on the debate about the metaphysics of the laws of nature. (shrink)

There is more than one way to say that composition is identity. Yi has distinguished the Weak Composition thesis from the Strong Composition thesis and attributed the former to David Lewis while noting that Lewis associates something like the latter with me. Weak Composition is the thesis that the relation between the parts collectively and their whole is closely analogous to identity. Strong Composition is the thesis that the relation between the parts collectively and their whole is identity. Yi is (...) right that Strong Composition does not fully reflect my view. We must recognize further what, borrowing Lewis's characterization, could be called the "stronger, and stranger" Composition thesis, or what I'll call the Stronger Composition thesis for short. On Strong Composition, it is only collectively that the parts are identical with the whole. On Stronger Composition, they are individually identical with it as well. I will explain and motivate this thesis. (shrink)

Quantifier variance is a well-known view in contemporary metaontology, but it remains very widely misunderstood by critics. Here we briefly and clearly explain the metasemantics of quantifier variance and distinguish between modest and strong forms of variance (Section I), explain some key applications (Section II), clear up some misunderstandings and address objections (Section III), and point the way toward future directions of quantifier-variance-related research (Section IV).

semantic minimalism and moderte contextualism.

From García-Carpintero and Kölbel, eds, Relative Truth.

This paper develops a novel problem for representationalism (also known as "intentionalism"), a popular contemporary account of perception. We argue that representationalism is incompatible with supervaluationism, the leading contemporary account of vagueness. The problem generalizes to naive realism and related views, which are also incompatible with supervaluationism.

I focus on a key argument for global external world scepticism resting on the underdetermination thesis: the argument according to which we cannot know any proposition about our physical environment because sense evidence for it equally justifies some sceptical alternative (e.g. the Cartesian demon conjecture). I contend that the underdetermination argument can go through only if the controversial thesis that conceivability is per se a source of evidence for metaphysical possibility is true. I also suggest a reason to doubt that (...) conceivability is per se a source of evidence for metaphysical possibility, and thus to doubt the underdetermination argument. (shrink)

The notion of existence is a very puzzling one philosophically. Often philosophers have appealed to linguistic properties of sentences stating existence. However, the appeal to linguistic intuitions has generally not been systematic and without serious regard of relevant issues in linguistic semantics. This paper has two aims. On the one hand, it will look at statements of existence from a systematic linguistic point of view, in order to try to clarify what the actual semantics of such statements in fact is. (...) On the other hand, it will explore what sort of ontology such statements reflect. The first aim is one of linguistic semantics; the second aim is one of descriptive metaphysics. Philosophically, existence statements appear to reflect the distinction between endurance and perdurance as well as particular notions of abstract states and of kinds. Linguistically, statements of existence involve a particular way of drawing the distinction between eventive and stative verbs and between individual-level and stage-level predicates as well as a particular approach to the semantics of bare plurals and mass nouns. (shrink)

This book present a unified semantic theory of expressions involving the notions of part and whole. It develops a theory of part structures which differs from traditional (extensional) mereological theories in that the notion of an integrated whole plays a central role and in that the part structure of an entity is allowed to vary across different situations, perspectives, and dimensions. The book presents a great range of empirical generalizations involving plurals, mass nouns, adnominal and adverbial modifiers such as 'whole', (...) 'together', and 'alone', nominal and adverbial quanitfiers ranging over parts, and expressions of completion such as 'completely' and 'partly'. (shrink)

In Reasons and Persons, Parfit (1984) posed a challenge: provide a satisfying normative account that solves the Non-Identity Problem, avoids the Repugnant and Absurd Conclusions, and solves the Mere-Addition Paradox. In response, some have suggested that we look toward person-affecting views of morality for a solution. But the person-affecting views that have been offered so far have been unable to satisfy Parfit's four requirements, and these views have been subject to a number of independent complaints. This paper describes a person-affecting (...) account which meets Parfit's challenge. The account satisfies Parfit's four requirements, and avoids many of the criticisms that have been raised against person-affecting views. (shrink)

This paper extends the definition of strong supervenience to cover classes of relations of any adicity, including transworld relations. It motivates that project by showing that not all interesting supervenience claims involving relations are global supervenience claims. The proposed definition has five welcome features: it reduces to the familiar definition in the special case where the classes contain only monadic properties; it equips supervenience with the expected formal properties, such as transitivity and monotonicity; it entails that a relation supervenes on (...) its converse; it classifies certain paradigms correctly; it makes distinctions even in the realm of the non-contingent, as witnessed by the fact that identity does not supervene on any class of relations. Finally, the paper applies the defined concept, and the related concept of orthogonality, to the study of internal and external relations. (shrink)

In this book, William Brant inquires how violence is reduced. Social causes of violence are exposed. War, sexual domination, leadership, propagandizing and comedy are investigated. Legal systems are explored as reducers and implementers of violence and threats.

This book offers an historically-informed critical assessment of Dummett's account of abstract objects, examining in detail some of the Fregean presuppositions whilst also engaging with recent work on the problem of abstract entities.

Let us distinguish two kinds of contingentism: entity contingentism and metaphysical contingentism. Here, I use ‘entity’ very broadly to include anything over which we can quantify—objects (abstract and concrete), properties, and relations. Then entity contingentism about some entity, E, is the view that E exists contingently: that is, that E exists in some possible worlds and not in others. By contrast, entity necessitarianism about E is the view that E exists of necessity: that is, that E exists in all possible (...) worlds. We can distinguish two views: global entity contingentism and global entity necessitarianism. Global entity contingentism is the view that for any possible E, E exists contingently. Global entity necessitarianism is the view that for any possible E, E exists necessarily. While entity contingentism and entity necessitarianism are views about the modal status of entities, metaphysical contingentism and necessitarianism are views about the modal status of metaphysical principles. Metaphysical contingentism about some metaphysical principle, P, is the view that P is contingent: it is true in some worlds, and false in others. Metaphysical necessitarianism about P is the view that P is necessary: either P is true in every world, or false in every world. We can then distinguish two views: global metaphysical contingentism and global metaphysical necessitarianism. Global metaphysical contingentism is the view that for any internally coherent metaphysical principle P, P is contingent: P is true in some worlds and false in others. Global metaphysical necessitarianism is the view that for any internally coherent metaphysical principle, P, P is necessary: it is either true in every world, or false in every world. This chapter principally focuses on metaphysical rather than entity contingentism, though §2 briefly discusses the latter. As we will see, (§2), both global entity contingentism and global entity necessitarianism are controversial views, and most philosophers fall somewhere between these two extremes, holding that some, but not all, entities exist necessarily—a view we can call entity moderatism. By contrast, global metaphysical necessitarianism has, until recently, largely been the default view. It is only recently that some philosophers have argued that we should be metaphysical contingentists about at least some metaphysical principles—a view we can call metaphysical moderatism. §3 considers why global metaphysical necessitarianism has hitherto been so persuasive, then evaluates (§3.1) some arguments for the view before considering more recent arguments in favour of the contingency of (at least some) metaphysical principles (§3.2). (shrink)

Thing ontologies are ontologies that consider the universe to be made up of a plurality of discrete objects. Non-thing ontologies can take the form of ontologies of discrete objects, too, but not necessarily so: they can also be conceived as ontologies of one continuous object. The paper considers the central versions of ontologies of discrete objects first, starting with thing ontologies, moving from there to non-thing ontologies of discrete objects and finally ontologies of one continuous object.

At several points in his later writings Wittgenstein discusses imaginary forms of life and ways of thinking that appear queer or alien from our point of view; concepts so different from ours that those who think from within them seem to be alternatives to us. In this paper I argue that reflection on the notions of difference and possibility in play here shows that imaginary cases of alien conceptual schemes or forms of life such as those considered by Wittgenstein are (...) not all cases of concepts that are entirely unintelligible for us; rather they may represent possible, albeit distant, ways of thinking for us. Such cases serve to aid imaginative reflection on our own case(s). By making us appreciate the possibility of the strange, they help us better to appreciate the arbitrariness of the familiar. I end the paper by considering what the implications of this reading of Wittgenstein’s position might be for Donald Davidson’s rejection of conceptual relativism. (shrink)

This paper aims to provide two abductive considerations adducing in favor of the thesis of Necessitism in modal ontology. I demonstrate how instances of the Barcan formula can be witnessed, when the modal operators are interpreted 'naturally' -- i.e., as including geometric possibilities -- and the quantifiers in the formula range over a domain of natural, or concrete, entities and their contingently non-concrete analogues. I argue that, because there are considerations within physics and metaphysical inquiry which corroborate modal relationalist claims (...) concerning the possible geometric structures of spacetime, and dispositional properties are actual possible entities, the condition of being grounded in the concrete is consistent with the Barcan formula; and thus -- in the geometric setting -- merits adoption by the Necessitist. (shrink)

The paper defends the philosophical method of "regimentation" by example, especially in relation to the theory of mind. The starting point is the Place-Smart after-image argument: A green after-image will not be located outside the skull, but if we cracked open your skull, we won't find anything green in there either. (If we did, you'd have some disturbing medical news.) So the after-image seems not to be in physical space, suggesting that it is non-physical. In response, I argue that the (...) green blob is a fictional object, while assuming a weak sort of realism about fictional objects (where they exist as mind-dependent objects). This view can look like dualism, however, but I try to interpret it not as implying metaphysical dualism, but rather as reflecting a dualism of theory. Roughly, there can be a theory of mind-independent objects, and a theory of mind-dependent objects. Yet there are principled reasons why we cannot integrate the two into a consistent whole, for reasons related to Russell's vicious circle principle. Most of the paper motivates this by an analogy between the physicalist's theory of the world, and drawing a map with a complete representation of the map itself. Regimentation unearths the inconsistencies that arise, when trying to represent as part of a model the very representations used to define the model. (shrink)

This paper aims to contribute to the analysis of the nature of mathematical modality and hyperintensionality, and to the applications of the latter to absolute decidability. Rather than countenancing the interpretational type of mathematical modality as a primitive, I argue that the interpretational type of mathematical modality is a species of epistemic modality. I argue, then, that the framework of two-dimensional semantics ought to be applied to the mathematical setting. The framework permits of a formally precise account of the priority (...) and relation between epistemic mathematical modality and metaphysical mathematical modality. The discrepancy between the modal systems governing the parameters in the two-dimensional intensional setting provides an explanation of the difference between the metaphysical possibility of absolute decidability and our knowledge thereof. I also advance a topic-sensitive epistemic two-dimensional truthmaker semantics, if hyperintensional approaches are to be preferred to possible worlds semantics. I examine the relation between two-dimensional hyperintensional states and epistemic set theory, providing two-dimensional hyperintensional formalizations of the modal logic of ZFC, large cardinal axioms, $\Omega$-logic, and the Epistemic Church-Turing Thesis. (shrink)