At the heart of the Stoic theory of modality is a strict commitment to bivalence, even for future contingents. A commitment to both future truth and contingency has often been thought paradoxical. This paper argues that the Stoic retreat from necessity is successful. it maintains that the Stoics recognized three distinct senses of necessity and possibility: logical, metaphysical and providential. Logical necessity consists of truths that are knowable a priori. Metaphysical necessity consists of truths that are knowable (...) a posteriori, a world order according to certain metaphysical principles and natures that god crafts within the constraints of matter. Finally, what is providentially necessary is what occurs according to the chain of fate, but only once it is in process or past. -/- The method of the paper is a close reading of Diogenes Laertius 7.75, adducing broad textual evidence along the way, to show that the Stoic theory of modality embraces Philonian possibility, both that which is capable of being true as a matter of logical consistency, and that which is possible according to the bare fitness of the entity. What differentiates the Stoics from Philo is their additional commitment to possibility as opportunity, resisting the collapse of determinism into necessity. (shrink)

ABSTRACT: An introduction to Stoic logic. Stoic logic can in many respects be regarded as a fore-runner of modern propositional logic. I discuss: 1. the Stoic notion of sayables or meanings (lekta); the Stoic assertibles (axiomata) and their similarities and differences to modern propositions; the time-dependency of their truth; 2.-3. assertibles with demonstratives and quantified assertibles and their truth-conditions; truth-functionality of negations and conjunctions; non-truth-functionality of disjunctions and conditionals; language regimentation and ‘bracketing’ devices; Stoic basic (...) principles of propositional logic; 4. Stoic modal logic; 5. Stoic theory of arguments: two premisses requirement; validity and soundness; 6. Stoic syllogistic or theory of formally valid arguments: a reconstruction of the Stoic deductive system, which consisted of accounts of five types of indemonstrable syllogisms, which function as nullary argumental rules that identify indemonstrables or axioms of the system, and four deductive rules (themata) by which certain complex arguments can be reduced to indemonstrables and thus shown to be formally valid themselves; 7. arguments that were considered as non-syllogistically valid (subsyllogistic and unmethodically concluding arguments). Their validity was explained by recourse to formally valid arguments. (shrink)

ABSTRACT: A detailed presentation of Stoic logic, part one, including their theories of propositions (or assertibles, Greek: axiomata), demonstratives, temporal truth, simple propositions, non-simple propositions(conjunction, disjunction, conditional), quantified propositions, logical truths, modal logic, and general theory of arguments (including definition, validity, soundness, classification of invalid arguments).

Sources for Stoicism present conflicting accounts of the Stoic principles. Some suggest that the principles are inseparable from each other. Others suggest that they are separable. To resolve this apparent interpretive dilemma, I distinguish between the functions of the principles and the bodies that realize those functions. Although the principles cannot separate when realizing their roles, the Stoic theory of blending entails that the bodies that realize those roles are physically separable. I present a strategy for further (...) work on the principles in light of this interpretation. (shrink)

Discrimination is a central epistemic capacity but typically, theories of discrimination only use discrimination as a vehicle for analyzing knowledge. This paper aims at developing a self-contained theory of discrimination. Internalist theories of discrimination fail since there is no compelling correlation between discriminatory capacities and experiences. Moreover, statistical reliabilist theories are also flawed. Only a modal theory of discrimination is promising. Versions of sensitivity and adherence that take particular alternatives into account provide necessary and sufficient conditions on (...) discrimination. Safety in contrast is not sufficient for discrimination as there are cases of safety that are clearly instances of discrimination failure. The developed account of discrimination between objects will be extended to discrimination between kinds and between types. (shrink)

The function of a trait token is usually defined in terms of some properties of other (past, present, future) tokens of the same trait type. I argue that this strategy is problematic, as trait types are (at least partly) individuated by their functional properties, which would lead to circularity. In order to avoid this problem, I suggest a way to define the function of a trait token in terms of the properties of the very same trait token. To able to (...) allow for the possibility of malfunctioning, some of these properties need to be modal ones: a function of a trait is to do F just in case its doing F would contribute to the inclusive fitness of the organism whose trait it is. Function attributions have modal force. Finally, I explore whether and how this theory of biological function could be modified to cover artifact function. (shrink)

In a series of papers, Bence Nanay has recently put forward and defended a new theory of function, which he calls the ‘Modal Theory of Function’. In this article, I critically address this theory and argue that it fails to fulfill some key desiderata that a satisfactory theory of function must comply with. As a result, I conclude that, whatever property Nanay’s notion of function refers to, it is not the property having the function that (...) is standardly attributed in science. (shrink)

Relative to any reasonable frame, satisfiability of modal quantificational formulae in which “= ” is the sole predicate is undecidable; but if we restrict attention to satisfiability in structures with the expanding domain property, satisfiability relative to the familiar frames (K, K4, T, S4, B, S5) is decidable. Furthermore, relative to any reasonable frame, satisfiability for modal quantificational formulae with a single monadic predicate is undecidable ; this improves the result of Kripke concerning formulae with two monadic predicates.

This paper investigates the prospects for a semantic theory that treats disjunction as a modal operator. Potential motivation for such a theory comes from the way in which modals embed within disjunctions. After reviewing some of the relevant data, I go on to distinguish a variety of modal theories of disjunction. I analyze these theories by considering pairs of conflicting desiderata, highlighting some of the tradeoffs they must face.

Arguments concerning central issues of contemporary Medical Ethics often not only bear similarities, but also derive their sheer essence from notions which belong to the celebrated history of Ethics. Thus, argumentation pro euthanasia and assisted suicide which focus on the detainment of dignity and the ensuring of posthumous reputation on behalf of the moral agent is shown to echo stoic views on arête and the subordination of life to the primary human goal, namely the achievement of virtue. The progress (...) made in palliative care when seen alongside the — steadily increasing — requests for suicide, is indicative of the fact that, though pain now days can be effectively controlled, moral agents often consider the preservation of their life detrimental to the detainment of virtue or posthumous reputation. The stoic view is considered to justify elective death as a personal choice, but is deemed inadequate as well as inconsistent in the broader context of a coherent value theory. (shrink)

Philosophers and psychologists widely hold that artifact categories – just like biological categories – are individuated by their function. But recent empirical findings in psychology question this assumption. My proposal is to suggest a way of squaring these findings with the central role function should play in individuating artifact categories. But in order to do so, we need to give up on the standard account of artifact function, according to which function is fixed by design, and replace it with a (...) more context-sensitive account, according to which function attributions depend on the explanatory context and, as a result, categorization also depends on the explanatory context, just as the empirical findings from psychology suggest. I argue that the recent ‘modal theory of function’ originally proposed to explain biological function, is capable of providing such an account of artifact function. (shrink)

I provide an examination and comparison of modal theories for underwriting different non-modal theories of sets. I argue that there is a respect in which the `standard' modal theory for set construction---on which sets are formed via the successive individuation of powersets---raises a significant challenge for some recently proposed `countabilist' modal theories (i.e. ones that imply that every set is countable). I examine how the countabilist can respond to this issue via the use of regularity (...) axioms and raise some questions about this approach. I argue that by comparing them with the `standard' uncountabilist theory, a new approach that brings in arbitrariness rather than the strict controls of forcing is desirable. (shrink)

Some philosophers of fiction – most famously Jerold Levinson1 - have tried to argue that fictional narrators can never be identified with real authors. This argument relies on the claim that narration involves genuine assertion (not just the pretense of assertion that lacks truthfulness) and that real authors are not in a position to assert anything about beings on the fictional plain - given that they don’t rationally believe in their existence. This debate on the status of narrators depends on (...) the idea that fictional beings and beings in the real worlds reside, as it were, at different levels. The assumption that there is a gap separating the levels of fiction and reality serves as a rationale for the claim that real authors could not possibly be en rapport with the fictional characters that they create (e.g. entertain beliefs about them, etc.). (shrink)

This paper contends that Stoic logic (i.e. Stoic analysis) deserves more attention from contemporary logicians. It sets out how, compared with contemporary propositional calculi, Stoic analysis is closest to methods of backward proof search for Gentzen-inspired substructural sequent logics, as they have been developed in logic programming and structural proof theory, and produces its proof search calculus in tree form. It shows how multiple similarities to Gentzen sequent systems combine with intriguing dissimilarities that may enrich contemporary (...) discussion. Much of Stoic logic appears surprisingly modern: a recursively formulated syntax with some truth-functional propositional operators; analogues to cut rules, axiom schemata and Gentzen’s negation-introduction rules; an implicit variable-sharing principle and deliberate rejection of Thinning and avoidance of paradoxes of implication. These latter features mark the system out as a relevance logic, where the absence of duals for its left and right introduction rules puts it in the vicinity of McCall’s connexive logic. Methodologically, the choice of meticulously formulated meta-logical rules in lieu of axiom and inference schemata absorbs some structural rules and results in an economical, precise and elegant system that values decidability over completeness. (shrink)

A lump theorist claims that ordinary objects are spread out across possible worlds, much like many of us think that tables are spread out across space. We are not wholly located in any one particular world, the lump theorist claims, just as we are not wholly spatially located where one’s hand is. We are modally spread out, a trans-world mereological sum of world-bound parts. We are lump sums of modal parts. And so are all other ordinary objects. In this (...) paper, I explore lump theory and investigate five arguments against it. These arguments may be the primary reasons why lump theory has not been widely accepted––or extensively explored––until now. I maintain that these arguments can be answered, and moreover, that accepting lump theory has distinct advantages, making it a competitive view in its own right. (shrink)

We reply to various arguments by Otavio Bueno and Edward Zalta (‘Object Theory and Modal Meinongianism’) against Modal Meinongianism, including that it presupposes, but cannot maintain, a unique denotation for names of fictional characters, and that it is not generalizable to higher-order objects. We individuate the crucial difference between Modal Meinongianism and Object Theory in the former’s resorting to an apparatus of worlds, possible and impossible, for the representational purposes for which the latter resorts to (...) a distinction between two kinds of predication, exemplification and encoding. We show that encoding has fewer forerunners in the history of philosophy than Bueno and Zalta want, and that there’s a reason why the notion has been found baffling by some. (shrink)

This paper motivates and develops a novel semantic framework for deontic modals. The framework is designed to shed light on two things: the relationship between deontic modals and substantive theories of practical rationality and the interaction of deontic modals with conditionals, epistemic modals and probability operators. I argue that, in order to model inferential connections between deontic modals and probability operators, we need more structure than is provided by classical intensional theories. In particular, we need probabilistic structure that interacts directly (...) with the compositional semantics of deontic modals. However, I reject theories that provide this probabilistic structure by claiming that the semantics of deontic modals is linked to the Bayesian notion of expectation. I offer a probabilistic premise semantics that explains all the data that create trouble for the rival theories. (shrink)

Provisional draft, pre-production copy of my book “The Modal Future” (forthcoming with Cambridge University Press).

How did the Stoics conceive of a polis and statehood? What happens when these ideas meet different biographies and changing historical environments? To answer these questions, 'The Stoics and the State' combines close philological reading of original source texts and fine-grained conceptual analysis with wide-ranging contextualisation, which is both thematic and diachronic. A systematic account elucidates extant definitions, aspects of statehood (territory, institutions, population and state objectives) and the constitutive function of the common law. The book’s diachronic part investigates how (...) Stoics from Zeno to Marcus Aurelius used their theory of the state to assess particular states, explain the origin of political communities and shape their own political practice. A glimpse at modern adaptations from Justus Lipsius to Martha C. Nussbaum explains the peculiarities of Stoic notions and their basis in a conception of human nature as not only political but essentially sociable and beneficent. (shrink)

Philosophical debate about the meaning of normative terms has long been pulled in two directions by the apparently competing ideas: (i) ‘ought’s do not describe what is actually the case but rather prescribe possible action, thought, or feeling, (ii) all declarative sentences deserve the same general semantic treatment, e.g. in terms of compositionally specified truth conditions. In this paper, I pursue resolution of this tension by rehearsing the case for a relatively standard truth-conditionalist semantics for ‘ought’ conceived as a necessity (...) modal and proposing a revision to it motivated by the distinctively prescriptive character of some deontic modals. In my view, this puts pressure on a popular conception of one of the core debates of metanormative theory between realists and antirealists. To make good on this claim, I go on to explore two very general ways we might interpret the results of compositional semantics—“representationalism” and “inferentialism”—in order to argue that, contrary to what is generally assumed, both can capture the special prescriptivity of ‘ought’ and both can countenance compositionally specified and informative truth-conditions for ought-sentences. Hence, my main thesis is that the deciding factor between them should not be which of ideas (i) and (ii) we are more impressed by but rather what we think of the relative merits of how representationalism and inferentialism respect these ideas. I’m inclined to favor an antirealist form of inferentialism, but the task I’ve set myself here is mainly to articulate the view in the context of metanormative theory and the semantics of deontic modals rather than try to defend it fully. To this purpose, towards the end I also briefly compare and contrast inferentialism with a third “ideationalist” metasemantic view, which may be an attractive home for some sophisticated versions of metanormative expressivism. Depending on how expressivism is worked out, it may be completely compatible with and so perhaps usefully combined with inferentialism or it may offer a competing way to respect ideas (i) and (ii). (shrink)

This article presents an overview of the basic philosophical motivations for, and some recent work in, modal set theory.

Say that the Moving Spotlight Theory (MST) combines the following three theses: A-THEORY : There is an absolute distinction between present and non-present time.

It is a commonsense thesis that unactualized possibilities are not parts of actuality. To keep his modal realism in line with this thesis, David Lewis employed his indexical account of the term “actual.” I argue that the addition of counterpart theory to Lewis’s modal realism undermines his strategy for respecting the commonsense thesis. The case made here also reveals a problem for Lewis’s attempt to avoid haecceitism.

In Stoic physics, blending (κρᾶσις) is the relation between active pneuma and passive matter; natural bodies from rocks and logs to plants, animals and the cosmos itself are blends of pneuma and matter. Blending structures the Stoic cosmos. I develop a new interpretation of the Stoic theory of blending, based on passages from Hierocles. The theory of blending, I argue, has been misunderstood. Hierocles allows us to see in detail how the theory is supposed (...) to work and how it fits into Stoic physics. (shrink)

In this paper, we consider recent attempts to metaphysically explain agentive modality in terms of conditionals. We suggest that the best recent accounts face counterexamples, and more worryingly, they take some agentive modality for granted. In particular, the ability to perform basic actions features as a primitive in these theories. While it is perfectly acceptable for a semantics of agentive modal claims to take some modality for granted in getting the extension of action claims correct, a metaphysical explanation of (...) agentive modality cannot, at least not in the way that conditional approaches to agentive modality do. We argue that this problem was present even in the classical conditional analysis. By a pessimistic induction, we suggest that, probably, no conditional approach to agentive modality will succeed. (shrink)

If ordinary particulars are bundles of properties, and if properties are said to be universals, then three well-known objections arise : no particular can change, all particulars have all of their properties essentially (even the most insignificant ones), and there cannot be two numerically distinct but qualitatively indiscernible particulars. In this paper, I try to make a little headway on these issues and see how the objections can be met, if one accepts a certain view about persistence through time and (...) across possible worlds – namely, four-dimensionalism and its modal analogue. The paper is especially devoted to the second and third of the three objections. (shrink)

Bundle theories identify material objects with bundles of properties. On the traditional approach, these are the properties possessed by that material object. That view faces a deep problem: it seems to say that all of an object’s properties are essential to it. Essential bundle theory attempts to overcome this objection, by taking the bundle as a specification of the object’s essential properties only. In this paper, I show that essential bundle theory faces a variant of the objection. To (...) avoid the problem, the theory must accept the contingency of identity. I show how this can be achieved in a coherent and well-motivated way, a way that isn’t available to traditional bundle theories. (shrink)

ABSTRACTRecent debate over the semantics and pragmatics of epistemic modals has focused on intuitions about cross-contextual truth-value assessments. In this paper, we advocate a different approach to evaluating theories of epistemic modals. Our strategy focuses on judgments of the incompatibility of two different epistemic possibility claims, or two different truth value assessments of a single epistemic possibility claim. We subject the predictions of existing theories to empirical scrutiny, and argue that existing contextualist and relativist theories are unable to account for (...) the full pattern of observed judgments. As a way of illustrating the theoretical upshot of these results, we conclude by developing a novel theory of epistemic modals that is able to predict the results. (shrink)

Here I propose an interpretation of the ancient Stoic psychological theory on which (i) the concepts that an adult human possesses affect the content of the perceptual impressions (φαντασίαι αἰσθητικαί) she forms, and (ii) the content of such impressions is exhausted by an ‘assertible’ (ἀξίωμα) of suitable complexity. What leads the Stoics to accept (i) and (ii), I argue, is their theory of assent and belief formation, which requires that the perceptual impression communicate information suitable to serve (...) as the content of belief. In arguing for (i), I reject a rival interpretation on which conceptualization occurs subsequently to the formation of a perceptual impression. In arguing for (ii), I deny that perceptual impressions have two kinds of content: one formulated in an assertible, the other sensory, featuring independently of this assertible. I explore the implications of (i) and (ii) for the Stoic theory of emotions, expertise, and rationality, and argue that they shed new light on the workings of impression, assent, and belief. (shrink)

This book concerns the foundations of epistemic modality and hyperintensionality and their applications to the philosophy of mathematics. I examine the nature of epistemic modality, when the modal operator is interpreted as concerning both apriority and conceivability, as well as states of knowledge and belief. The book demonstrates how epistemic modality and hyperintensionality relate to the computational theory of mind; metaphysical modality and hyperintensionality; the types of mathematical modality and hyperintensionality; to the epistemic status of large cardinal axioms, (...) undecidable propositions, and abstraction principles in the philosophy of mathematics; to the modal and hyperintensional profiles of the logic of rational intuition; and to the types of intention, when the latter is interpreted as a hyperintensional mental state. Chapter 2 argues for a novel type of expressivism based on the duality between the categories of coalgebras and algebras, and argues that the duality permits of the reconciliation between modal cognitivism and modal expressivism. I also develop a novel topic-sensitive truthmaker semantics for dynamic epistemic logic, and develop a novel dynamic epistemic two-dimensional hyperintensional semantics. Chapter 3 provides an abstraction principle for epistemic (hyper-)intensions. Chapter 4 advances a topic-sensitive two-dimensional truthmaker semantics, and provides three novel interpretations of the framework along with the epistemic and metasemantic. Chapter 5 applies the fixed points of the modal μ-calculus in order to account for the iteration of epistemic states in a single agent, by contrast to availing of modal axiom 4 (i.e. the KK principle). The fixed point operators in the modal μ-calculus are rendered hyperintensional, which yields the first hyperintensional construal of the modal μ-calculus in the literature and the first application of the calculus to the iteration of epistemic states in a single agent instead of the common knowledge of a group of agents. Chapter 6 advances a solution to the Julius Caesar problem based on Fine's `criterial' identity conditions which incorporate conditions on essentiality and grounding. Chapter 7 provides a ground-theoretic regimentation of the proposals in the metaphysics of consciousness and examines its bearing on the two-dimensional conceivability argument against physicalism. The topic-sensitive epistemic two-dimensional truthmaker semantics developed in chapters 2 and 4 are availed of in order for epistemic states to be a guide to metaphysical states in the hyperintensional setting. -/- Chapters 8-12 provide cases demonstrating how the two-dimensional hyperintensions of hyperintensional, i.e. topic-sensitive epistemic two-dimensional truthmaker, semantics, solve the access problem in the epistemology of mathematics. Chapter 8 examines the interaction between my hyperintensional semantics and the axioms of epistemic set theory, large cardinal axioms, the Epistemic Church-Turing Thesis, the modal axioms governing the modal profile of Ω-logic, Orey sentences such as the Generalized Continuum Hypothesis, and absolute decidability. These results yield inter alia the first hyperintensional Epistemic Church-Turing Thesis and hyperintensional epistemic set theories in the literature. Chapter 9 examines the modal and hyperintensional commitments of abstractionism, in particular necessitism, and epistemic hyperintensionality, epistemic utility theory, and the epistemology of abstraction. I countenance a hyperintensional semantics for novel epistemic abstractionist modalities. I suggest, too, that observational type theory can be applied to first-order abstraction principles in order to make first-order abstraction principles recursively enumerable, i.e. Turing machine computable, and that the truth of the first-order abstraction principle for hyperintensions is grounded in its being possibly recursively enumerable and the machine being physically implementable. Chapter 10 examines the philosophical significance of hyperintensional Ω-logic in set theory and discusses the hyperintensionality of metamathematics. Chapter 11 provides a modal logic for rational intuition and provides a hyperintensional semantics. Chapter 12 avails of modal coalgebras to interpret the defining properties of indefinite extensibility, and avails of hyperintensional epistemic two-dimensional semantics in order to account for the interaction between the interpretational and objective modalities and truthmakers thereof. This yields the first hyperintensional category theory in the literature. I invent a new mathematical trick in which first order structures are treated as categories, and Vopenka's principle can be satisfied because of the elementary embeddings between the categories and generate Vopenka cardinals while bypassing the category of Set in category theory. Chapter 13 examines modal responses to the alethic paradoxes. Chapter 14 examines, finally, the modal and hyperintensional semantics for the different types of intention and the relation of the latter to evidential decision theory. (shrink)

We introduce a realist, unextravagant interpretation of quantum theory that builds on the existing physical structure of the theory and allows experiments to have definite outcomes but leaves the theory’s basic dynamical content essentially intact. Much as classical systems have specific states that evolve along definite trajectories through configuration spaces, the traditional formulation of quantum theory permits assuming that closed quantum systems have specific states that evolve unitarily along definite trajectories through Hilbert spaces, and our interpretation (...) extends this intuitive picture of states and Hilbert-space trajectories to the more realistic case of open quantum systems despite the generic development of entanglement. We provide independent justification for the partial-trace operation for density matrices, reformulate wave-function collapse in terms of an underlying interpolating dynamics, derive the Born rule from deeper principles, resolve several open questions regarding ontological stability and dynamics, address a number of familiar no-go theorems, and argue that our interpretation is ultimately compatible with Lorentz invariance. Along the way, we also investigate a number of unexplored features of quantum theory, including an interesting geometrical structure—which we call subsystem space—that we believe merits further study. We conclude with a summary, a list of criteria for future work on quantum foundations, and further research directions. We include an appendix that briefly reviews the traditional Copenhagen interpretation and the measurement problem of quantum theory, as well as the instrumentalist approach and a collection of foundational theorems not otherwise discussed in the main text. (shrink)

In our everyday discourse, most of us use modal statements to express possibility, necessity, or contingency. Logicians, linguists, and philosophers of language tend to use the possible world discourse to analyse the semantics of this kind of sentences. There is a disadvantage of this method: in the usual Quinean meta-ontology it commits the users to the existence of possible worlds. Even though there are many theories on metaphysics of these possible worlds, I will focus on the fictionalist approach, which (...) aims to suspend the undesired ontological commitment. Therefore it is an anti-realist theory. The fictionalist strategy is based on the idea that according to our common-sense ontology, fictions and fictional entities do not exist, and one can treat the possible world discourse as a fiction, and the possible worlds as fictional entities. However, in the last two decades, realist theories about fictions and fictional entities have arisen, especially the abstract artefact theory. In this paper I try to revise the fictionalist approach to modality by keeping the main idea that possible worlds are fictional entities, while accepting that fictional entities are abstract artefacts. The result is a new realist theory of modal fictionalism. (shrink)

Even the most cursory reader of Husserl’s writings must be struck by the frequent references to essences (“Wesen”, “Essenzen”), Ideas (“Idee”), kinds, natures, types and species and to necessities, possibilities, impossi- bilities, necessary possibilities, essential necessities and essential laws. What does Husserl have in mind in talking of essences and modalities? What did he take the relation between essentiality and modality to be? In the absence of answers to these questions it is not clear that a reader of Husserl can (...) be said to understand him. (shrink)

I clarify some of the details of the modal theory of function I outlined in Nanay (2010): (a) I explicate what it means that the function of a token biological trait is fixed by modal facts; (b) I address an objection to my trait type individuation argument against etiological function and (c) I examine the consequences of replacing the etiological theory of function with a modal theory for the prospects of using the concept of (...) biological function to explain mental content. (shrink)

This paper shows the ways in which Kant’s notions of the feeling of life and the feeling of the promotion of life may be influenced by Epicurus’ theory of pleasure and the Stoic notion of oikeiôsis, respectively. Accordingly, getting a clear picture of Epicurus’ theory of pleasure and the Stoic notion of oikeiôsis will help us (i) understand why Kant introduces these notions in the third Critique and (ii) why he identifies aesthetic pleasure with the feeling (...) of the promotion of life. As I will demonstrate, the feeling of life allows us to be conscious of the harmonious interaction of our faculties with each other while the feeling of the promotion of life allows us to be aware of the harmonious relationship between our faculties and nature. Hence, the feeling of the promotion of life indicates the well-being of the subject in its relation to its environment. (shrink)

Void is at the heart of Stoic metaphysics. As the incorporeal par excellence, being defined purely in terms of lacking body, it brings into sharp focus the Stoic commitment to non-existent Somethings. This article argues that Stoic void, far from rendering the Stoic system incoherent or merely ad hoc, in fact reflects a principled and coherent physicalism that sets the Stoics apart from their materialist predecessors and atomist neighbors.

Shelly Kagan has recently defended the view that it is morally worse for a human being to suffer some harm than it is for a lower animal (such as a dog or a cow) to suffer a harm that is equally severe (ceteris paribus). In this paper, I argue that this view receives rather less support from our intuitions than one might at first suppose. According to Kagan, moreover, an individual’s moral status depends partly upon her ‘modal capacities.’ In (...) this paper, I argue that the most natural strategy for justifying Kagan’s theory faces some important challenges. More generally, I argue that philosophers who wish to defend the view that human beings have a higher moral status than that of the lower animals face a dilemma. Either their theory of moral status will imply (unacceptably) that some severely cognitively impaired human beings have a significantly lower moral status than that of typical human beings, or these philosophers will be forced to ground moral status in a set of properties so far removed from a subject’s actual capacities that it will become difficult to see why these kinds of properties should have such moral importance. (shrink)

At least since Aristotle's famous discussion of the sea-battle tomorrow in On Interpretation 9, philosophers have been fascinated by a rich set of interconnecte.

We argue that the extant evidence for Stoic logic provides all the elements required for a variable-free theory of multiple generality, including a number of remarkably modern features that straddle logic and semantics, such as the understanding of one- and two-place predicates as functions, the canonical formulation of universals as quantified conditionals, a straightforward relation between elements of propositional and first-order logic, and the roles of anaphora and rigid order in the regimented sentences that express multiply general propositions. (...) We consider and reinterpret some ancient texts that have been neglected in the context of Stoic universal and existential propositions and offer new explanations of some puzzling features in Stoic logic. Our results confirm that Stoic logic surpasses Aristotle’s with regard to multiple generality, and are a reminder that focusing on multiple generality through the lens of Frege-inspired variable-binding quantifier theory may hamper our understanding and appreciation of pre-Fregean theories of multiple generality. (shrink)

ABSTRACT: For the Stoics, a syllogism is a formally valid argument; the primary function of their syllogistic is to establish such formal validity. Stoic syllogistic is a system of formal logic that relies on two types of argumental rules: (i) 5 rules (the accounts of the indemonstrables) which determine whether any given argument is an indemonstrable argument, i.e. an elementary syllogism the validity of which is not in need of further demonstration; (ii) one unary and three binary argumental rules (...) which establish the formal validity of non-indemonstrable arguments by analysing them in one or more steps into one or more indemonstrable arguments (cut type rules and antilogism). The function of these rules is to reduce given non-indemonstrable arguments to indemonstrable syllogisms. Moreover, the Stoic method of deduction differs from standard modern ones in that the direction is reversed (similar to tableau methods). The Stoic system may hence be called an argumental reductive system of deduction. In this paper, a reconstruction of this system of logic is presented, and similarities to relevance logic are pointed out. (shrink)

The study of reference often leads to addressing fundamental issues in semantics, metaphysics and epistemology; this suggests that reference is closely linked to the three realms. The overall purpose of this study is to elucidate the structure of some of these links, through a close examination of the “mechanism” of reference. As in many other enquiries, considering the possible (i.e., the modal,) in addition to the actual proves very helpful in clarifying and explicating insights. The reference of a term (...) with respect to possible worlds is commonly called “intension”; so this is a study of intensions. The main contribution of the study is an outline for a “calculator” of intensions. It is argued that the intension of a term is a function of three variables: (a) the way in which the term “picks out” its referent in different possible worlds (semantics); (b) criteria of identity (metaphysics); and (c) the actual state of affairs (actuality). While considering different possible values for these variables, it is demonstrated how the variables combine to generate the term’s intension. In other words, the result is a calculator that when provided with the required values, yields the reference of the term in different possible worlds. By taking into account the possible gap between what we take the values of these variables to be and what they may in fact be, we also gain important insights into the epistemic aspect of reference. In addition, since a rigid designator is a term with constant intension, the proposed thesis provides an elaborate account of rigidity. The first chapter is devoted to the development of the calculator of intensions. Each of the following three chapters elaborates on one aspect of intensions, namely, the semantic, metaphysical and epistemic aspects. In the course of these chapters, various familiar puzzles pertaining to the respective philosophical realms are addressed (many of these puzzles are discussed in Kripke’s Naming and Necessity – a work that considerably inspired this study). In the fifth and last chapter the analysis of intensions is applied to two case-studies from relatively recent philosophical literature: the Kripke-Lewis debate over the identity theory of mind, and the debate over the significance of Donnellan’s referential/attributive distinction. The novel accounts that these applications generate purport to illustrate the importance and originality of the proposed thesis. (shrink)

This paper explains and defends the idea that metaphysical necessity is the strongest kind of objective necessity. Plausible closure conditions on the family of objective modalities are shown to entail that the logic of metaphysical necessity is S5. Evidence is provided that some objective modalities are studied in the natural sciences. In particular, the modal assumptions implicit in physical applications of dynamical systems theory are made explicit by using such systems to define models of a modal temporal (...) logic. Those assumptions arguably include some necessitist principles. -/- Too often, philosophers have discussed ‘metaphysical’ modality — possibility, contingency, necessity — in isolation. Yet metaphysical modality is just a special case of a broad range of modalities, which we may call ‘objective’ by contrast with epistemic and doxastic modalities, and indeed deontic and teleological ones (compare the distinction between objective probabilities and epistemic or subjective probabilities). Thus metaphysical possibility, physical possibility and immediate practical possibility are all types of objective possibility. We should study the metaphysics and epistemology of metaphysical modality as part of a broader study of the metaphysics and epistemology of the objective modalities, on pain of radical misunderstanding. Since objective modalities are in general open to, and receive, natural scientific investigation, we should not treat the metaphysics and epistemology of metaphysical modality in isolation from the metaphysics and epistemology of the natural sciences. -/- In what follows, Section 1 gives a preliminary sketch of metaphysical modality and its place in the general category of objective modality. Section 2 reviews some familiar forms of scepticism about metaphysical modality in that light. Later sections explore a few of the many ways in which natural science deals with questions of objective modality, including questions of quantified modal logic. (shrink)

In the substitutional framework, validity is truth under all substitutions of the nonlogical vocabulary. I develop a theory where □ is interpreted as substitutional validity. I show how to prove soundness and completeness for common modal calculi using this definition.

Lewis (1968) claims that his language of Counterpart Theory (CT) interprets modal discourse and he adverts to a translation scheme from the language of Quantifed Modal Logic (QML) to CT. However, everybody now agrees that his original translation scheme does not always work, since it does not always preserve the ‘intuitive’ meaning of the translated QML-formulas. Lewis discusses this problem with regard to the Necessitist Thesis, and I will extend his discourse to the analysis of the Converse (...) Barcan Formula. Everyone also agrees that there are CT-formulas that can express the QMLcontent that gets lost through the translation. The problem is how we arrive to them. In this paper, I propose new translation rules from QML to CT, based on a suggestion by Kaplan. However, I will claim that we cannot have ‘the’ translation scheme from QML to CT. The reason being that de re modal language is ambiguous. Accordingly, there are diferent sorts of QML, depending on how we resolve such ambiguity. Therefore, depending on what sort of QML we intend to translate into CT, we need to use the corresponding translation scheme. This suggests that all the translation problems might just disappear if we do what Lewis did not: begin with a fully worked out QML that tells us how to understand de re modal discourse. (shrink)

It is widely agreed that the intelligibility of modal metaphysics has been vindicated. Quine's arguments to the contrary supposedly confused analyticity with metaphysical necessity, and rigid with non-rigid designators.2 But even if modal metaphysics is intelligible, it could be misconceived. It could be that metaphysical necessity is not absolute necessity – the strictest real notion of necessity – and that no proposition of traditional metaphysical interest is necessary in every real sense. If there were nothing otherwise “uniquely metaphysically (...) significant” about metaphysical necessity, then paradigmatic metaphysical necessities would be necessary in one sense of “necessary”, not necessary in another, and that would be it. The question of whether they were necessary simpliciter would be like the question of whether the Parallel Postulate is true simpliciter – understood as a pure mathematical conjecture, rather than as a hypothesis about physical spacetime. In a sense, the latter question has no objective answer. In this article, I argue that paradigmatic questions of modal metaphysics are like the Parallel Postulate question. I then discuss the deflationary ramifications of this argument. I conclude with an alternative conception of the space of possibility. According to this conception, there is no objective boundary between possibility and impossibility. Along the way, I sketch an analogy between modal metaphysics and set theory. (shrink)

This essay considers how ancient Stoic cosmopolitanism – roughly, the claim all human beings are members of the same “cosmopolis”, or universal city, and so are entitled to moral concern in virtue of possessing reason – informs Stoic thinking about how we ought to treat non-human entities in the environment. First, I will present the Stoic justification for the thesis that there are only rational members of the cosmopolis – and so that moral concern does not extend (...) to any non-human part of the natural world – and explore the foundations of these views in Stoic physics. Next, I will show that, like other anthropocentric theories, Stoic cosmopolitanism allows for environmental preservation and protection of non-human entities, so long as these activities ultimately benefit human beings. However, because the Stoics include the appreciation of natural beauty as a component of the happy life, this justification is not as feeble as it might seem. Humans are naturally set up to contemplate the order and complexity of the universe, and so environmental degradation and species loss, in marring this harmonious system, frustrates the achievement of the human goal. After exploring these facets of Stoic philosophy, and assessing to what extent they might justify environmental conservation, I close with a critical appraisal of Stoic theory – specifically, of the claims that (i) only humans possess reason and (ii) only rational creatures are deserving of moral concern. (shrink)

What does 'might' mean? One hypothesis is that 'It might be raining' is essentially an avowal of ignorance like 'For all I know, it's raining'. But it turns out these two constructions embed in different ways, in particular as parts of larger constructions like Wittgenstein's 'It might be raining and it's not' and Moore's 'It's raining and I don't know it', respectively. A variety of approaches have been developed to account for those differences. All approaches agree that both Moore sentences (...) and Wittgenstein sentences are classically consistent. In this paper I argue against this consensus. I adduce a variety of new data which I argue can best be accounted for if we treat Wittgenstein sentences as being classically inconsistent. This creates a puzzle, since there is decisive reason to think that 'Might p' is classically consistent with 'Not p'. How can it also be that 'Might p and not p' and 'Not p and might p' are classically inconsistent? To make sense of this situation, I propose a new theory of epistemic modals and their interaction with embedding operators. This account makes sense of the subtle embedding behavior of epistemic modals, shedding new light on their meaning and, more broadly, the dynamics of information in natural language. -/- . (shrink)

The paper begins with a clarification of the notions of intuition (and, in particular, modal intuition), modal error, conceivability, metaphysical possibility, and epistemic possibility. It is argued that two-dimensionalism is the wrong framework for modal epistemology and that a certain nonreductionist approach to the theory of concepts and propositions is required instead. Finally, there is an examination of moderate rationalism’s impact on modal arguments in the philosophy of mind -- for example, Yablo’s disembodiment argument and (...) Chalmers’s zombie argument. A less vulnerable style of modal argument is defended, which nevertheless wins the same anti-materialist conclusions sought by these other arguments. (shrink)

This essay proposes a new theory of agentive modals: ability modals and their duals, compulsion modals. After criticizing existing approaches—the existential quantificational analysis, the universal quantificational analysis, and the conditional analysis—it presents a new account that builds on both the existential and conditional analyses. On this account, the act conditional analysis, a sentence like ‘John can swim across the river’ says that there is some practically available action that is such that if John tries to do it, he swims (...) across the river. The essay argues that the act conditional analysis avoids the problems faced by existing accounts of agentive modality and shows how the act conditional analysis can be extended to an account of generic agentive modal claims. The upshot is a new vantage point on the role of agentive modal ascriptions in practical discourse: ability ascriptions serve as a kind of hypothetical guarantee, and compulsion ascriptions as a kind of nonhypothetical guarantee. (shrink)