I present a case for a rapprochement between aspects of rationalism and scientific realism, by way of a general framework employing modal epistemology and elements of 2-dimensional semantics (2DS). My overall argument strategy is meta-inductive: The bulk of this paper establishes a “base case,” i.e., a concretely constructive example by which I demonstrate this linkage. The base case or constructive example acts as the exemplar for generating, in a constructively ‘bottom-up’ fashion, a more generally rigorous case for rationalism-realism qua (...) modal epistemology. The exemple I choose in D. Chalmers’ (2002) modal rationalism and R. Giere’s (1985, 1988) constructive realism. I show by way of a thorough analysis how Giere’s claims concerning modal scope are characterized as instances of Chalmers’ modal rationalism, both weak and strong. In essence, as I demonstrate via Chalmers’ notions, ceteris paribus the constructive realist ultimately opts for a comparatively wider gate, characterized by modal reasoning, to lead from the rooms of conceivability qua thought experiments and models, to the pastures of metaphysical possibility. Chalmers likewise tries to erect such a wider gate, in his general conceivability-possibility theses. Anti-realists, on the other hand, see a narrower passage and my contention herein is that they suffer from modal myopia, which hopefully the ‘corrective vision’ of Chalmers’ modal rationalism can restore. In the introduction and concluding sections I sketch out suggestions of constructing ‘inductive steps’ from my base case, to generate more extensively general claims regarding realism qua rationalism. -/- . (shrink)

The paper explores the project of an ambitious modal epistemology that attempts to combine the a priori methods of Chalmers’ 2D semantics with Kripke’s modal metaphysics. I argue that such a project is not viable. The ambitious modal epistemology involves an inconsistent triad composed of (1) Modal Monism, (2) Two-Dimensionalism, and what I call (3) “Metaphysical Kripkeanism”. I present the three theses and show how only two of those can be true at a time. There is (...) a fundamental incompatibility between Chalmers’ Modal Rationalism and Kripke’s modal metaphysics. Specifically, Chalmers’ conceivability entails possibilities that a Kripkean rejects as genuinely metaphysical. However, three positive stances in modal epistemology emerge from the combinations that the triad allows. One of those offers a promising way forward for 2D modal epistemologies. But it comes with a cost, as it requires abandoning modal monism and reshaping the scope of what a priori conceivability can give us access to. (shrink)

This dissertation contains four independent essays addressing a cluster of related topics in the philosophy of mind. Chapter 1: “Fundamentality Physicalism” argues that physicalism can usefully be conceived of as a thesis about fundamentality. The chapter explores a variety of other potential formulations of physicalism (particularly modal formulations), contrasts fundamentality physicalism with these theses, and offers reasons to prefer fundamentality physicalism over these rivals. Chapter 2:“Modal Rationalism and the Demonstrative Reply to the Master Argument Against Physicalism” introduces the (...) Master Argument Against Physicalism and investigates its crucial premise: the inference from an a priori gap between the physical and consciousness to a lack of necessitation between the two. I argue against the strong form of modal rationalism that underwrites the master argument and offer a more moderate rationalist view. I offer a novel demonstrative reply to the master argument, according to which a connection between conscious experience and demonstratives, not dualism, is the source of the epistemic gap between consciousness and the physical. Chapter 3: “Conceptual Mastery and the Knowledge Argument” argues that Frank Jackson’s famous anti-physicalist knowledge argument featuring Mary, a brilliant neuroscientist raised in a black and white room, founders on a dilemma. Either (i) Mary cannot know the relevant experiential truths because of trivial obstacles that have no bearing on the truth of physicalism or (ii) once the obstacles have been removed, Mary can know the relevant truths. Chapter 4: “Toward a Theory of Conceptual Mastery” investigates the question “Under what conditions does a thinker fully understand, or have mastery of, a concept?” I argue against three views of conceptual mastery, according to which conceptual mastery is a matter of holding certain beliefs, being disposed to make certain inferences, or having certain intuitions. I propose and respond to objections to my own “meaning postulate view” of the conditions under which a thinker has mastery of a concept. (shrink)

The co-evolutionary concept of tri-modal stable evolutionary strategy (SESH) of Homo sapiens is developed. The concept based on the principle of evolutionary complementarity of anthropogenesis: value of evolutionary risk and evolutionary path of human evolution are defined by descriptive (evolutionary efficiency) and creative-teleological (evolutionary correctness) parameters simultaneously, that cannot be instrumental reduced to others ones. Resulting volume of both parameters define the vectors of human evolution by two gear mechanism ˗ genetic and cultural co-evolution and techno-humanitarian balance. Explanatory model (...) and methodology of evaluation of creatively teleological evolutionary risk component of NBIC technological complex is proposed. The mechanism of influence of each module on the evolution of the two remaining modules of SESH a priori can be twofold: (1) informational co-evolution (direct selective pressure); (2) semantic co-evolution (time-varying semantic code, the compliance of the biological, socio- cultural and techno-rationalist adaptive modules of human stable evolutionary strategy). More rapidly evolving autonomous element of the co-evolutionary pair becomes making sense factor for the partner. Semantic co-evolution is the discrete acquisition of adaptive significance of individual alleles by changing socio-cultural types, manifested as an increase in the genetic variability of populations of Homo sapiens, and domesticated species parallel to socio-culturogenesis. The socio- cultural landscape leads to drastically difference of direction in biological evolution of Atlantic and East-Slavic ethnicities/civilizations. (shrink)

It used to be thought that rational coherence and metaphysical possibility went hand in hand. Kripke and Putnam put a spanner in the works by proposing examples of propositions which seem to violate this principle. I will propose a nuanced form of modal rationalism consistent with the Kripke/putnam cases. The rough idea is that rational coherence entails possibility when you grasp the essential nature of what you’re conceiving of.

The objection from the insolvability of principle-based modal disagreements appears to support the claim that there are no objective modal facts, or at the very least modal facts cannot be accounted for by modal rationalist theories. An idea that resurfaced fairly recently in the literature is that the use of ordinary empirical statements presupposes some prior grasp of modal notions. If this is correct, then the idea that we may have a total agreement concerning empirical (...) facts and disagree on modal facts, which is the starting point of the objection from the insolvability of modal disagreement, is undercut. This paper examines the no-separation thesis and shows that some of the arguments against the classical (empiricist) distinction between empirical and modal statements fail to be conclusive if they are taken to defend a strong notion of metaphysical possibility. The no-separation thesis appears to work only in theoretical frameworks where metaphysical modalities are considered (broadly) conceptual. For these reasons, the no-separation thesis cannot save modal rationalism from the insolvability of modal disagreement. (shrink)

In this chapter, it is suggested that our epistemic access to metaphysical modality generally involves rationalist, a priori elements. However, these a priori elements are much more subtle than ‘traditional’ modal rationalism assumes. In fact, some might even question the ‘apriority’ of these elements, but I should stress that I consider a priori and a posteriori elements especially in our modal inquiry to be so deeply intertwined that it is not easy to tell them apart. Supposed metaphysically necessary (...) identity statements involving natural kind terms are a good example: the fact that empirical input is crucial in establishing their necessity has clouded the role and content of the a priori input, as I have previously argued. For instance, the supposed metaphysically necessary identity statement involving water and its microstructure can only be established with the help of a controversial a priori principle concerning the determination of chemical properties by microstructure. The Kripke-Putnam framework of modal epistemology fails precisely because it is unclear whether the required a priori element is present. My positive proposal builds on E. J. Lowe’s work. Lowe holds that our knowledge of metaphysical modality is based on our knowledge of essence. Lowe’s account strives to offer a uniform picture of modal epistemology: essence is the basis of all our modal knowledge. This is the basis of Lowe’s modal rationalism. I believe that Lowe’s proposal is on the right lines in the case of abstract objects, but I doubt that it can be successfully applied to the case of natural kinds. Accordingly, the case of natural kinds will be my main focus and I will suggest that modal rationalism, at least as it is traditionally understood, falls short of explaining modal knowledge concerning natural kinds. Yet, I think that Lowe has identified something of crucial importance for modal epistemology, namely the essentialist, a priori elements present in our modal inquiry. The upshot is that rather than moving all the way from modal rationalism to modal empiricism, a type of hybrid approach, ‘empirically-informed modal rationalism ’, can be developed. (shrink)

The co-evolutionary concept of three-modal stable evolutionary strategy of Homo sapiens is developed. The concept based on the principle of evolutionary complementarity of anthropogenesis: value of evolutionary risk and evolutionary path of human evolution are defined by descriptive (evolutionary efficiency) and creative-teleological (evolutionary correctness) parameters simultaneously, that cannot be instrumental reduced to other ones. Resulting volume of both parameters define the vectors of biological, social, cultural and techno-rationalistic human evolution by two gear mechanism — genetic and cultural co-evolution and (...) techno-humanitarian balance. Explanatory model and methodology of evaluation of creatively teleological evolutionary risk component of NBIC technological complex is proposed. Integral part of the model is evolutionary semantics (time-varying semantic code, the compliance of the biological, socio-cultural and techno-rationalist adaptive modules of human stable evolutionary strategy). (shrink)

In this paper, I discuss the main characteristics of the epistemology of modal rationalism by proceeding from the critical investigation of Peacocke’s theory of modality. I build on arguments by Crispin Wright and Sonia Roca-Royes, which are generalised and supplemented by further analysis, in order to show that principle-based accounts have little prospects of succeeding in their task of providing an integrated account of the metaphysics and the epistemology of modality. I argue that it is unlikely that we will (...) able to develop an exhaustive and accurate principle-based account that discriminates objectively between correct and deviant modal knowledge. Even if such an account can be formulated, a non-circular way of justifying its necessity also seems to be out of our reach. (shrink)

This paper argues for contrastivism about the deontic modals, 'ought', 'must', and 'may'. A simple contrastivist semantics that predicts the desired entailment relations among these modals is offered.

ABSTRACT: This chapter offers a revenge-free solution to the liar paradox (at the centre of which is the notion of Gestalt shift) and presents a formal representation of truth in, or for, a natural language like English, which proposes to show both why -- and how -- truth is coherent and how it appears to be incoherent, while preserving classical logic and most principles that some philosophers have taken to be central to the concept of truth and our use of (...) that notion. The chapter argues that, by using a truth operator rather than truth predicate, it is possible to provide a coherent, model-theoretic representation of truth with various desirable features. After investigating what features of liar sentences are responsible for their paradoxicality, the chapter identifies the logic as the normal modal logic KT4M (= S4M). Drawing on the structure of KT4M (=S4M), the author proposes that, pace deflationism, truth has content, that the content of truth is bivalence, and that the notions of both truth and bivalence are semideterminable. (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)

In this paper the propositional logic LTop is introduced, as an extension of classical propositional logic by adding a paraconsistent negation. This logic has a very natural interpretation in terms of topological models. The logic LTop is nothing more than an alternative presentation of modal logic S4, but in the language of a paraconsistent logic. Moreover, LTop is a logic of formal inconsistency in which the consistency and inconsistency operators have a nice topological interpretation. This constitutes a new proof (...) of S4 as being "the logic of topological spaces", but now under the perspective of paraconsistency. (shrink)

The article argues against attempts to combine ontological realism about modality with the rejection of modal rationalism and it suggests that modal realism requires modal rationalism. /// El artículo da argumentos en contra de que se intente combinar el realismo ontológico sobre la modalidad con el rechazo del racionalismo modal y sugiere que el realismo modal exige racionalismo modal.

This essay aims to provide a modal logic for rational intuition. Similarly to treatments of the property of knowledge in epistemic logic, I argue that rational intuition can be codified by a modal operator governed by the modal $\mu$-calculus. Via correspondence results between fixed point modal propositional logic and the bisimulation-invariant fragment of monadic second-order logic, a precise translation can then be provided between the notion of 'intuition-of', i.e., the cognitive phenomenal properties of thoughts, and the (...) modal operators regimenting the notion of 'intuition-that'. I argue that intuition-that can further be shown to entrain conceptual elucidation, by way of figuring as a dynamic-interpretational modality which induces the reinterpretation of both domains of quantification and the intensions and hyperintensions of mathematical concepts that are formalizable in monadic first- and second-order formal languages. Hyperintensionality is countenanced via a topic-sensitive epistemic two-dimensional truthmaker semantics. (shrink)

The epistemic modal auxiliaries must and might are vehicles for expressing the force with which a proposition follows from some body of evidence or information. Standard approaches model these operators using quantificational modal logic, but probabilistic approaches are becoming increasingly influential. According to a traditional view, must is a maximally strong epistemic operator and might is a bare possibility one. A competing account—popular amongst proponents of a probabilisitic turn—says that, given a body of evidence, must \ entails that (...) \\) is high but non-maximal and might \ that \\) is significantly greater than 0. Drawing on several observations concerning the behavior of must, might and similar epistemic operators in evidential contexts, deductive inferences, downplaying and retractions scenarios, and expressions of epistemic tension, I argue that those two influential accounts have systematic descriptive shortcomings. To better make sense of their complex behavior, I propose instead a broadly Kratzerian account according to which must \ entails that \ = 1\) and might \ that \ > 0\), given a body of evidence and a set of normality assumptions about the world. From this perspective, must and might are vehicles for expressing a common mode of reasoning whereby we draw inferences from specific bits of evidence against a rich set of background assumptions—some of which we represent as defeasible—which capture our general expectations about the world. I will show that the predictions of this Kratzerian account can be substantially refined once it is combined with a specific yet independently motivated ‘grammatical’ approach to the computation of scalar implicatures. Finally, I discuss some implications of these results for more general discussions concerning the empirical and theoretical motivation to adopt a probabilisitic semantic framework. (shrink)

Expressivists about epistemic modals deny that ‘Jane might be late’ canonically serves to express the speaker’s acceptance of a certain propositional content. Instead, they hold that it expresses a lack of acceptance. Prominent expressivists embrace pragmatic expressivism: the doxastic property expressed by a declarative is not helpfully identified with that sentence’s compositional semantic value. Against this, we defend semantic expressivism about epistemic modals: the semantic value of a declarative from this domain is the property of doxastic attitudes it canonically serves (...) to express. In support, we synthesize data from the critical literature on expressivism—largely reflecting interactions between modals and disjunctions—and present a semantic expressivism that readily predicts the data. This contrasts with salient competitors, including: pragmatic expressivism based on domain semantics or dynamic semantics; semantic expressivism à la Moss [2015]; and the bounded relational semantics of Mandelkern [2019]. (shrink)

According to Amie Thomasson’s modal normativism, the function of modal discourse is to convey semantic rules. But what is a "semantic rule"? I raise three worries according to which there is no conception of a semantic rule that can serve the needs of a modal normativist. The first worry focuses on de re and a posteriori necessities. The second worry concerns Thomasson's inferential specification of the meaning of modal terms. The third worry asks about the normative (...) status of semantic rules. (shrink)

This paper gives an outline of truthmaker semantics for natural language against the background of standard possible-worlds semantics. It develops a truthmaker semantics for attitude reports and deontic modals based on an ontology of attitudinal and modal objects and on a semantic function of clauses as predicates of such objects. It also présents new motivations for 'object-based truthmaker semantics' from intensional transitive verbs such as ‘need’, ‘look for’, ‘own’, and ‘buy’ and gives an outline of their semantics. This paper (...) is a commissioned 'target' article, with commentaries by W. Davis, B. Arsenijevic, K. Moulton, K. Liefke, M. Kaufmann, R. Matthews, P. Portner and A. Rubinstein, P. Elliott, G. Ramchand and my reply. (shrink)

I propose a unified solution to two puzzles: Ross's puzzle and free choice permission. I begin with a pair of cases from the decision theory literature illustrating the phenomenon of act dependence, where what an agent ought to do depends on what she does. The notion of permissibility distilled from these cases forms the basis for my analysis of 'may' and 'ought'. This framework is then combined with a generalization of the classical semantics for disjunction — equivalent to Boolean disjunction (...) on the diagonal, but with a different two-dimensional character — that explains the puzzling facts in terms of semantic consequence. (shrink)

According to Amie Thomasson's Modal Normativism (MN), knowledge of metaphysical modality is to be explained in terms of a speaker’s mastery of semantic rules, as opposed to one’s epistemic grasp of independent modal facts. In this chapter, I outline (MN)'s account of modal knowledge (§1) and argue that more than semantic mastery is needed for knowledge of metaphysical modality. Specifically (§2), in reasoning aimed at gaining such knowledge, a competent speaker needs to further deploy essentialist principles and (...) information. In response, normativists might contend that a competent speaker will only need to appeal to specific independence counterfactuals, on analogy with quasi-realism about morality. These conditionals fix the meaning of our terms at the actual world, independently of the particular context in which a statement is evaluated. However, I show that this strategy causes several problems for the account (§3). While those problems might perhaps be avoided by endorsing a certain picture of modal metaphysics (Modal Monism), such a picture involves notorious issues that normativists will have to address (§4). It is thus doubtful that (MN) can explain knowledge of metaphysical modality. Still, it may explain some modal knowledge without committing to Modal Monism. As I show (§5), semantic mastery may suffice for gaining knowledge of logical-conceptual modality or analyticity. (shrink)

The standard account of modal expressions in natural language analyzes them as quantifiers over a set of possible worlds determined by the evaluation world and an accessibility relation. A number of authors have recently argued for an alternative account according to which modals are analyzed as quantifying over a domain of possible worlds that is specified directly in the points of evaluation. But the new approach only handles the data motivating it if it is supplemented with a non-standard account (...) of attitude verbs and conditionals. It can be shown the the relational account handles the same data equally well if it too is supplemented with a non-standard account of such expressions. (shrink)

I argue that the two-dimensional hyperintensions of epistemic topic-sensitive two-dimensional truthmaker semantics provide a compelling solution to the access problem. I countenance an abstraction principle for epistemic hyperintensions based on Voevodsky's Univalence Axiom and function type equivalence in Homotopy Type Theory. I apply, further, modal rationalism in modal epistemology to solve the access problem. Epistemic possibility and hyperintensionality, i.e. conceivability, can be a guide to metaphysical possibility and hyperintensionality, when (i) epistemic worlds or epistemic hyperintensional states are interpreted (...) as being centered metaphysical worlds or hyperintensional states, i.e. indexed to an agent, when (ii) the epistemic (hyper-)intensions and metaphysical (hyper-)intensions for a sentence coincide, i.e. the hyperintension has the same value irrespective of whether the worlds in the argument of the functions are considered as epistemic or metaphysical, and when (iii) sentences are said to consist in super-rigid expressions, i.e. rigid expressions in all epistemic worlds or states and in all metaphysical worlds or states. I argue that (i) and (ii) obtain in the case of the access problem. (shrink)

Over the last fifteen years, linguists and philosophers of language have reexamined the canonical, Kratzerian semantics for modal expressions, with special attention paid to their epistemic and deontic uses. This article is an overview of the literature on deontic modal expressions. Section 1 provides an overview of the canonical semantics, noting some of its main advantages. Section 2 introduces a set of desiderata that have achieved the status of fixed points in the debates about whether the canonical semantics (...) is correct. These include the observations that deontic modal sentences have both deliberative and evaluative readings and both information-sensitive and -insensitive readings. Adequate resolutions of certain puzzles in deontic logic and resolving the Frege-Geach problem for Expressivism have also achieved this status. The third section provides an opinionated overview of some of the main extant rivals to the canonical semantics, including Cariani, Kaufmann, and Kaufmann’s (2013) complex contextualism , Yalcin’s (2012) Expressivism, Willer’s (2014) dynamic semantics, and Starr’s (2016) dynamic Expressivism. Section 4 provides an assessment of each of the views discussed in terms of the desiderata introduced in section 2. Section 5 is an overview of remaining issues that require more attention in the literature. (shrink)

Possible worlds semantics faces a range of difficulties for at least certain types of modals, especially deontic modals with their distinction between heavy and light permissions and obligations. This paper outlines a new semantics of modals that aims to overcome some of those difficulties. The semantics is based on an a novel ontology of modal objects, entities like obligations, permissions, needs, as well as epistemic states, abilities, and essences. Moreover, it is based on truthmaking, in the sense of Fine’s (...) recent truthmaker semantics. (shrink)

The integration challenge for modality states that metaphysical theories of modality tend to fail in one of two ways: either they render the meanings of modal sentences mysterious, or they render modal knowledge mysterious. I argue that there are specific semantic and epistemic constraints on metaphysics implied by the integration challenge and that a plausible metaphysical theory of modality will satisfy both of them. I further argue that no popular metaphysical theory of modality simultaneously satisfies both of the (...) constraints. Therefore, a new metaphysical theory of modality is needed, one that can offer a clear response to the integration challenge. I attempt to supply the needed theory and show that it satisfies the constraints of the integration challenge. The overall result is an argument for a new and unique metaphysical theory of modality that I call constructionism. (shrink)

In proof-theoretic semantics, meaning is based on inference. It may be seen as the mathematical expression of the inferentialist interpretation of logic. Much recent work has focused on base-extension semantics, in which the validity of formulas is given by an inductive definition generated by provability in a ‘base’ of atomic rules. Base-extension semantics for classical and intuitionistic propositional logic have been explored by several authors. In this paper, we develop base-extension semantics for the classical propositional modal systems K, KT (...) , K4, and S4, with □ as the primary modal operator. We establish appropriate soundness and completeness theorems and establish the duality between □ and a natural presentation of ♢. We also show that our semantics is in its current form not complete with respect to euclidean modal logics. Our formulation makes essential use of relational structures on bases. (shrink)

Dugundji proved in 1940 that most parts of standard modal systems cannot be characterized by a single finite deterministic matrix. In the eighties, Ivlev proposed a semantics of four-valued non-deterministic matrices (which he called quasi-matrices), in order to characterize a hierarchy of weak modal logics without the necessitation rule. In a previous paper, we extended some systems of Ivlev’s hierarchy, also proposing weaker six-valued systems in which the (T) axiom was replaced by the deontic (D) axiom. In this (...) paper, we propose even weaker systems, by eliminating both axioms, which are characterized by eight-valued non-deterministic matrices. In addition, we prove completeness for those new systems. It is natural to ask if a characterization by finite ordinary (deterministic) logical matrices would be possible for all those Ivlev-like systems. We will show that finite deterministic matrices do not characterize any of them. (shrink)

This paper outlines a semantic account of attitude reports and deontic modals based on cognitive and illocutionary products, mental states, and modal products, as opposed to the notion of an abstract proposition or a cognitive act.

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

ABSTRACT: This 1974 paper builds on our 1969 paper (Corcoran-Weaver [2]). Here we present three (modal, sentential) logics which may be thought of as partial systematizations of the semantic and deductive properties of a sentence operator which expresses certain kinds of necessity. The logical truths [sc. tautologies] of these three logics coincide with one another and with those of standard formalizations of Lewis's S5. These logics, when regarded as logistic systems (cf. Corcoran [1], p. 154), are seen to be (...) equivalent; but, when regarded as consequence systems (ibid., p. 157), one diverges from the others in a fashion which suggests that two standard measures of semantic complexity may not be as closely linked as previously thought. -/- This 1974 paper uses the linear notation for natural deduction presented in [2]: each two-dimensional deduction is represented by a unique one-dimensional string of characters. Thus obviating need for two-dimensional trees, tableaux, lists, and the like—thereby facilitating electronic communication of natural deductions. The 1969 paper presents a (modal, sentential) logic which may be thought of as a partial systematization of the semantic and deductive properties of a sentence operator which expresses certain kinds of necessity. The logical truths [sc. tautologies] of this logic coincides those of standard formalizations of Lewis’s S4. Among the paper's innovations is its treatment of modal logic in the setting of natural deduction systems--as opposed to axiomatic systems. The author’s apologize for the now obsolete terminology. For example, these papers speak of “a proof of a sentence from a set of premises” where today “a deduction of a sentence from a set of premises” would be preferable. 1. Corcoran, John. 1969. Three Logical Theories, Philosophy of Science 36, 153–77. J P R -/- 2. Corcoran, John and George Weaver. 1969. Logical Consequence in Modal Logic: Natural Deduction in S5 Notre Dame Journal of Formal Logic 10, 370–84. MR0249278 (40 #2524). 3. Weaver, George and John Corcoran. 1974. Logical Consequence in Modal Logic: Some Semantic Systems for S4, Notre Dame Journal of Formal Logic 15, 370–78. MR0351765 (50 #4253). (shrink)

In 1988, J. Ivlev proposed some (non-normal) modal systems which are semantically characterized by four-valued non-deterministic matrices in the sense of A. Avron and I. Lev. Swap structures are multialgebras (a.k.a. hyperalgebras) of a special kind, which were introduced in 2016 by W. Carnielli and M. Coniglio in order to give a non-deterministic semantical account for several paraconsistent logics known as logics of formal inconsistency, which are not algebraizable by means of the standard techniques. Each swap structure induces naturally (...) a non-deterministic matrix. The aim of this paper is to obtain a swap structures semantics for some Ivlev-like modal systems proposed in 2015 by M. Coniglio, L. Fariñas del Cerro and N. Peron. Completeness results will be stated by means of the notion of Lindenbaum–Tarski swap structures, which constitute a natural generalization to multialgebras of the concept of Lindenbaum–Tarski algebras. (shrink)

It is often argued that inferential role semantics (IRS) entails semantic holism as long as theorists fail to answer the question about which inferences, among the many, are meaning-constitutive. Since analyticity, as truth in virtue of meaning, is a widely dismissed notion in indicating which inferences determine meaning, it seems that holism follows. Semantic holism is often understood as facing problems with the stability of content and many usual explanations of communication. Thus, we should choose between giving up IRS, to (...) avoid these holistic entailments, and defending holism against this charge, to rescue IRS. I try to pursue the second goal by analyzing certain patterns of counterfactual reasoning. Wilfrid Sellars and Robert Brandom claim that, to defend IRS, content-constitutive inferences are those counterfactually robust. While it is difficult to assess the goodness of such a view, it nonetheless entails that counterfactually non-robust inferences (which I call “modally ruled out inferences”) are not content-constitutive. If this is true, and if we take certain remarks about the grasp of concepts on board, there is a way to restrict the scope of the holism entailed by IRS to the extent of reshaping problems with the stability of content. (shrink)

Possible worlds are commonly seen as an interpretation of modal operators such as "possible" and "necessary". Here, we develop possible world semantics (PWS) which can be expressed in basic set theory and first-order logic, thus offering a reductionist account of modality. Specifically, worlds are understood as complete sets of statements and possible worlds are sets whose statements are consistent with a set of conceptual laws. We introduce the construction calculus (CC), a set of axioms and rules for truth, possibility, (...) worldness and consistency. We show that CC allows to prove fundamental theorems about necessity, possibility, impossibility and contigency, thus demonstrating prima-facie plausibility of PWS. Finally, we discuss the explanatory power of our approach and draw connections between our account and established philosophical conceptions of possible worlds. (shrink)

A new proof style adequate for modal logics is defined from the polynomial ring calculus. The new semantics not only expresses truth conditions of modal formulas by means of polynomials, but also permits to perform deductions through polynomial handling. This paper also investigates relationships among the PRC here defined, the algebraic semantics for modal logics, equational logics, the Dijkstra???Scholten equational-proof style, and rewriting systems. The method proposed is throughly exemplified for S 5, and can be easily extended (...) to other modal logics. (shrink)

Epistemic modal operators give rise to something very like, but also very unlike, Moore's paradox. I set out the puzzling phenomena, explain why a standard relational semantics for these operators cannot handle them, and recommend an alternative semantics. A pragmatics appropriate to the semantics is developed and interactions between the semantics, the pragmatics, and the definition of consequence are investigated. The semantics is then extended to probability operators. Some problems and prospects for probabilistic representations of content and context are (...) explored. (shrink)

Intellectual humility can be broadly construed as being conscious of the limits of one’s existing knowledge and capable to acquire more knowledge, which makes it a key virtue of the information age. However, the claim “I am (intellectually) humble” seems paradoxical in that someone who has the disposition in question would not typically volunteer it. There is an explanatory gap between the meaning of the sentence and the meaning the speaker ex- presses by uttering it. We therefore suggest analyzing intellectual (...) humility semantically, using a psycholexical approach that focuses on both synonyms and antonyms of ‘intellectual humili- ty’. We present a thesaurus-based methodology to map the semantic space of intellectual hu- mility and the vices it opposes as a heuristic to support philosophical and psychological anal- ysis of this disposition. We performed the mapping both in English and German in order to test for possible cultural differences in the understanding of intellectual humility. In both lan- guages, we find basically the same three semantic dimensions of intellectual humility (sensi- bility, discreetness, and knowledge dimensions) as well as three dimensions of its related vic- es (self-overrating, other-underrating and dogmatism dimensions). The resulting semantic clusters were validated in an empirical study with English (n=276) and German (n=406) par- ticipants. We find medium to high correlations (0.54-0.72) between thesaurus similarity and perceived similarity, and we can validate the labels of the three dimensions identified in the study. But we also find indications of the limitations of the thesaurus methodology in terms of cluster plausibility. We conclude by discussing the importance of these findings for construct- ing psychometric scales for intellectual humility. (shrink)

Metaphysical rationalism, the doctrine which affirms the Principle of Sufficient Reason (the PSR), is out of favor today. The best argument against it is that it appears to lead to necessitarianism, the claim that all truths are necessarily true. Whatever the intuitive appeal of the PSR, the intuitive appeal of the claim that things could have been otherwise is greater. This problem did not go unnoticed by the great metaphysical rationalists Spinoza and Leibniz. Spinoza’s response was to embrace necessitarianism. Leibniz’s (...) response was to argue that, despite appearances, rationalism does not lead to necessitarianism. This paper examines the debate between these two rationalists and concludes that Leibniz has persuasive grounds for his opinion. This has significant implications both for the plausibility of the PSR and for our understanding of modality. (shrink)

This paper is a study of a distinctively chemical notion of possibility. This is the notion of possibility that occurs in chemical discourses when chemists speak of the possibility or impossibility of achieving a given result through chemical means. This notion pertains to the possibility of processes, not of compounds, so it differs from the kind of chemical possibility mentioned in Wittgenstein's Philosophical Investigations or the kinds discussed in the literature on Putnam's Twin Earth argument. I argue that this process-oriented (...) notion of possibility cannot be reduced in a simple way to physical possibility, and that standard possible worlds semantics does not allow a natural analysis of this notion. I suggest an extension of possible worlds semantics that may overcome this limitation. I finish by pointing out some open questions about chemical possibility. (shrink)

Against the background of standard possible-worlds semantics, this paper outlines a truthmaker approach to the semantics of attitude reports and modal sentences based on an ontology of attitudinal and modal objects.

This article proposes a way of blocking the zombie argument against materialism. The central idea—which can be motivated in various ways, but which I will motivate by drawing on recent work by Wolfgang Schwarz—is that sentences reporting conscious experience are modally inert, roughly in the sense that adding them to a description of a metaphysically possible scenario always results in a description of a metaphysically possible scenario. This is notable in that it leads to a way of blocking the zombie (...) argument, which is perfectly compatible with modal rationalism and with the view that conceivability entails possibility. (shrink)

The paper argues against a commitment to metaphysical necessity, semantic modalities are enough. The best approaches to elucidate the semantic modalities are (still) versions of lingustic ersatzism and fictionalism, even if only developed in parts. Within these necessary properties and the difference between natural and semantic laws can be accounted for. The proper background theory for this is an updated version of Logical Empiricism, which is congenial to recent trends in Structural Realism. The anti-metaphysical attitude of Logical Empiricism deserves revitalization. (...) Another target besides metaphysical necessity are substantial forms of iterated modalities, as used, for instance, in the philosophy of religion. (shrink)

In a previous work we introduced the algorithm \SQEMA\ for computing first-order equivalents and proving canonicity of modal formulae, and thus established a very general correspondence and canonical completeness result. \SQEMA\ is based on transformation rules, the most important of which employs a modal version of a result by Ackermann that enables elimination of an existentially quantified predicate variable in a formula, provided a certain negative polarity condition on that variable is satisfied. In this paper we develop several (...) extensions of \SQEMA\ where that syntactic condition is replaced by a semantic one, viz. downward monotonicity. For the first, and most general, extension \SSQEMA\ we prove correctness for a large class of modal formulae containing an extension of the Sahlqvist formulae, defined by replacing polarity with monotonicity. By employing a special modal version of Lyndon's monotonicity theorem and imposing additional requirements on the Ackermann rule we obtain restricted versions of \SSQEMA\ which guarantee canonicity, too. (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)

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)