The paper proposes a way for adherents of Fregean, structured propositions to designate propositions and other complex senses/concepts using a special kind of functor. I consider some formulations from Peacocke's works and highlight certain problems that arise as we try to quantify over propositional constituents while referring to propositions using "that"-clauses. With the functor notation, by contrast, we can quantify over senses/concepts with objectual, first-order quantifiers and speak without further ado about their involvement in propositions. The functor notation also turns (...) out to come with an important kind of expressive strengthening, and is shown to be neutral on several controversial issues. (shrink)

Esta enciclopédia abrange, de uma forma introdutória mas desejavelmente rigorosa, uma diversidade de conceitos, temas, problemas, argumentos e teorias localizados numa área relativamente recente de estudos, os quais tem sido habitual qualificar como «estudos lógico-filosóficos». De uma forma apropriadamente genérica, e apesar de o território teórico abrangido ser extenso e de contornos por vezes difusos, podemos dizer que na área se investiga um conjunto de questões fundamentais acerca da natureza da linguagem, da mente, da cognição e do raciocínio humanos, bem (...) como questões acerca das conexões destes com a realidade não mental e extralinguística. A razão daquela qualificação é a seguinte: por um lado, a investigação em questão é qualificada como filosófica em virtude do elevado grau de generalidade e abstracção das questões examinadas (entre outras coisas); por outro, a investigação é qualificada como lógica em virtude de ser uma investigação logicamente disciplinada, no sentido de nela se fazer um uso intenso de conceitos, técnicas e métodos provenientes da disciplina de lógica. O agregado de tópicos que constitui a área de estudos lógico-filosóficos é já visível, pelo menos em parte, no Tractatus Logico-Philosophicus de Ludwig Wittgenstein, uma obra publicada em 1921. E uma boa maneira de ter uma ideia sinóptica do território disciplinar abrangido por esta enciclopédia, ou pelo menos de uma porção substancial dele, é extrair do Tractatus uma lista dos tópicos mais salientes aí discutidos; a lista incluirá certamente tópicos do seguinte género, muitos dos quais se podem encontrar ao longo desta enciclopédia: factos e estados de coisas; objectos; representação; crenças e estados mentais; pensamentos; a proposição; nomes próprios; valores de verdade e bivalência; quantificação; funções de verdade; verdade lógica; identidade; tautologia; o raciocínio matemático; a natureza da inferência; o cepticismo e o solipsismo; a indução; as constantes lógicas; a negação; a forma lógica; as leis da ciência; o número. (shrink)

The doctrine of the Trinity is central to mainstream Christianity. But insofar as it posits “three persons” (Father, Son and Holy Spirit), who are “one God,” it appears as inconsistent as the claim that 1+1+1=1. -/- Much of the literature on “The Logical Problem of the Trinity,” as this has been called, attacks or defends Trinitarianism with little regard to the fourth century theological controversies and the late Hellenistic and early Medieval philosophical background in which it took shape. I argue (...) that this methodol- ogy, which I call “the Puzzle Approach,” produces obviously invalid arguments, and it is unclear how to repair it without collapsing into my preferred method- ology, “the Historical Approach,” which sees history as essential to the debate. I also discuss “mysterianism,” arguing that, successful or not, it has a different goal from the other approaches. I further argue that any solution from the His- torical Approach satisfies the concerns of the Puzzle Approach and mysterianism anyway. -/- I then examine the solution to the Logical Problem of the Trinity found in St. Gregory of Nyssa’s writings, both due to his place in the history of the doctrine, and his clarity in explicating what I call “the metaphysics of synergy.” I recast his solution in standard predicate logic and provide a formal proof of its consistency. I end by considering the possibilities for attacking the broader philosophical context of his defense and conclude that the prospects for doing so are dim. In any case, if there should turn out to be any problem with the doctrine of the Trinity at all, it will not be one of mere logical inconsistency in saying that “These Three are One.”. (shrink)

Externalist representationalism is touted as a superior rival to naïve realism, and yet a careful analysis of the externalist representationalist's analysis of our ordinary perceptual experiences shows the view to be far closer to naïve realism than we might have expected. One of the central advertised benefits of representationalist views in general is that they are compatible with the idea that ordinary, illusory and hallucinatory perceptual experiences are of the same fundamental kind. Naïve realists are forced to deny the ‘common (...) fundamental kind claim’ and adopt disjunctivism. However, I argue that externalist representationalism is also a version of disjunctivism. Consequently, one of the main rivals to naïve realism turns out not to be a rival at all. (shrink)

This paper aims to vindicate the thesis that cognitive computational properties are abstract objects implemented in physical systems. I avail of the equivalence relations countenanced in Homotopy Type Theory, in order to specify an abstraction principle for epistemic intensions. The homotopic abstraction principle for epistemic intensions provides an epistemic conduit into our knowledge of intensions as abstract objects. I examine, then, how intensional functions in Epistemic Modal Algebra are deployed as core models in the philosophy of mind, Bayesian perceptual psychology, (...) and the program of natural language semantics in linguistics, and I argue that this provides abductive support for the truth of homotopic abstraction. Epistemic modality can thus be shown to be both a compelling and a materially adequate candidate for the fundamental structure of mental representational states, comprising a fragment of the Language of Thought. (shrink)

This paper is an investigation of the general logic of "identifications", claims such as 'To be a vixen is to be a female fox', 'To be human is to be a rational animal', and 'To be just is to help one's friends and harm one's enemies', many of which are of great importance to philosophers. I advocate understanding such claims as expressing higher-order identity, and discuss a variety of different general laws which they might be thought to obey. [New version: (...) Nov. 4th, 2016]. (shrink)

Semantics in the Montagovian tradition combines two basic tenets. One tenet is that the semantic value of a sentence is an intension, a function from points of evaluations into truth-values. The other tenet is that the semantic value of a composite expression is the result of applying the function denoted by one component to arguments denoted by the other components. Many philosophers object to intensional semantics on the grounds that intensionally equivalent sentences do not substitute salva veritate into attitude ascriptions. (...) They propose instead that the semantic values of sentences must be structured propositions. In rejecting intensional semantics, philosophers who endorse structured propositions also usually reject functional compositionality, undermining both tenets of the Montagovian programme. I defend a semantic theory that incorporates both structured propositions and functional compositionality. I argue that this semantic theory can preserve many explanatory benefits of Montague semantics. Finally, I show how treating composition functional application can resolve core problems internal to a theory of structured propositions. (shrink)

An epistemology of art has seemed problematic mainly because of arguments claiming that an essential element of a theory of knowledge, truth, has no place in aesthetic contexts. For, if it is objectively true that something is beautiful, it seems to follow that the predicate “is beautiful” expresses a property – a view asserted by Plato but denied by Hume and Kant. But then, if the belief that something is beautiful is not objectively true, we cannot be said to know (...) that something is beautiful and the path to an epistemology of art is effectively blocked. The article places the existence aesthetic properties in the proper context; presents a logically correct argument for the existence of such properties; identifies strategies for responding to this argument; explains why objections by Hume, Kant, and several other philosophers fail; and sketches a realization account of beauty influenced by Hogarth. (shrink)

Commonplace syntactic constructions in natural language seem to generate ontological commitments to a dazzling array of metaphysical categories - aggregations, sets, ordered n-tuples, possible worlds, intensional entities, ideal objects, species, intensive and extensive quantities, stuffs, situations, states, courses of events, nonexistent objects, intentional and discourse objects, general objects, plural objects, variable objects, arbitrary objects, vague kinds and concepts, fuzzy sets, and so forth. But just because a syntactic construction in some natural language appears to invoke a new category of entity, (...) are we theoreticians epistemically justified in holding that there are such entities? This would hardly seem sufficient. To be epistemically justified, the ontology to which we theoreticians are committed must pass strict standards: the entities must be of the sort required by our best comprehensive theory of the world. The thesis of this paper is that fine-grained type-free intensional entities are like this. If the thesis is right, these entities have a special objective status perhaps not possessed by some of the other ontological categories associated with special syntactic constructions in natural language. In fact, it is plausible to hold that fine-grained type-free intensional entities provide the proper minimal framework for constructing logical and linguistic theories. In this paper my strategy will be to survey the competing conceptions of fine-grained type-free intensionality and to present arguments in support of one of them. Following this narrowing down process, I will go on to the indicated epistemological considerations. (shrink)

The purpose of this paper is to lay out the algebraic approach to propositions and then to show how it can be implemented in new solutions to Frege's puzzle and a variety of related puzzles about content.

Kit Fine has reawakened a puzzle about variables with a long history in analytic philosophy, labeling it “the antinomy of the variable”. Fine suggests that the antinomy demands a reconceptualization of the role of variables in mathematics, natural language semantics, and first-order logic. The difficulty arises because: (i) the variables ‘x’ and ‘y’ cannot be synonymous, since they make different contributions when they jointly occur within a sentence, but (ii) there is a strong temptation to say that distinct variables ‘x’ (...) and ‘y’ are synonymous, since sentences differing by the total, proper substitution of ‘x’ for ‘y’ always agree in meaning. We offer a precise interpretation of the challenge posed by (i) and (ii). We then develop some neglected passages of Tarski to show that his semantics for variables has the resources to resolve the antinomy without abandoning standard compositional semantics. (shrink)

According to the traditional bundle theory, particulars are bundles of compresent universals. I think we should reject the bundle theory for a variety of reasons. But I will argue for the thesis at the core of the bundle theory: that all the facts about particulars are grounded in facts about universals. I begin by showing how to meet the main objection to this thesis (which is also the main objection to the bundle theory): that it is inconsistent with the possibility (...) of distinct qualitative indiscernibles. Here, the key idea appeals to a non-standard theory of haecceities as non-well-founded properties of a certain sort. I will then defend this theory from a number of objections, and finally argue that we should accept it on the basis of considerations of parsimony about the fundamental. (shrink)

The purpose of this paper can be described as follows. The contemporary philosophical logic cannot work without using some terms well-known from mathematics and logic. Among such terms that play an important role in logical and philosophical analyses of language, meaning and the like we can find function, procedure and construction. One problem is that various authors use these terms in various ways, another problem consists in the well-known fact that many philosophers do not have any idea of what those (...) and similar terms could mean. The present paper tries to explain why an exact explication of the three mentioned terms can contribute to understanding and even solving many problems with semantics of natural language, which a philosopher should be interested in. (shrink)

The Problem of Doxastic Shift may be stated as a dilemma: on the one hand, the distribution of nominal complements of the form `the ψ that p’ strongly suggests that `that’-clauses cannot be univocally assigned propositionaldenotations; on the other hand, facts about quantification strongly suggest that `that’-clauses must be assigned univocal denotations. I argue that the Problem may be solved by defining the extension of a proposition to be a set of facts or, more generally, conditions. Given this, the logical (...) operation of descriptive predication can be introduced in a way that resolves the dilemma withoutsacrificing the singular term analysis of `that’-clauses. (shrink)

According to foundationalism, some beliefs are justified but do not depend for their justification on any other beliefs. According to access internalism, a subject is justified in believing some proposition only if that subject is aware of or has access to some reason to think that the proposition is true or probable. In this paper I discusses a fundamental challenge to internalist foundationalism often referred to as the Sellarsian dilemma. I consider three attempts to respond to the dilemma – phenomenal (...) conservatism, BonJour’s classical foundationalism, and Fumerton’s classical foundationalism. I argue that, of these three, only the last seems to avoid getting impaled on one or the other horn of the dilemma. I end by responding to some concerns with Fumerton’s account. (shrink)

Propositionalism is the view that intentional attitudes, such as belief, are relations to propositions. Propositionalists argue that propositionalism follows from the intuitive validity of certain kinds of inferences involving attitude reports. Jubien (2001) argues powerfully against propositions and sketches some interesting positive proposals, based on Russell’s multiple relation theory of judgment, about how to accommodate “propositional phenomena” without appeal to propositions. This paper argues that none of Jubien’s proposals succeeds in accommodating an important range of propositional phenomena, such as the (...) aforementioned validity of attitude-report inferences. It then shows that the notion of a predication act-type, which remains importantly Russellian in spirit, is sufficient to explain the range of propositional phenomena in question, in particular the validity of attitude-report inferences. The paper concludes with a discussion of whether predication act-types are really just propositions by another name. (shrink)

In philosophical logic necessity is usually conceived as a sentential operator rather than as a predicate. An intensional sentential operator does not allow one to express quantified statements such as 'There are necessary a posteriori propositions' or 'All laws of physics are necessary' in first-order logic in a straightforward way, while they are readily formalized if necessity is formalized by a predicate. Replacing the operator conception of necessity by the predicate conception, however, causes various problems and forces one to reject (...) many philosophical accounts involving necessity that are based on the use of operator modal logic. We argue that the expressive power of the predicate account can be restored if a truth predicate is added to the language of first-order modal logic, because the predicate 'is necessary' can then be replaced by 'is necessarily true'. We prove a result showing that this substitution is technically feasible. To this end we provide partial possible-worlds semantics for the language with a predicate of necessity and perform the reduction of necessities to necessary truths. The technique applies also to many other intensional notions that have been analysed by means of modal operators. (shrink)

Conceptualism is the thesis that, for any perceptual experience E, (i) E has a Fregean proposition as its content and (ii) a subject of E must possess a concept for each item represented by E. We advance a framework within which conceptualism may be defended against its most serious objections (e.g., Richard Heck's argument from nonveridical experience). The framework is of independent interest for the philosophy of mind and epistemology given its implications for debates regarding transparency, relationalism and representationalism, demonstrative (...) thought, phenomenal character, and the speckled hen objection to modest foundationalism. (shrink)

In this paper we (i) identify the notion of ‘essentially non-conceptual content’ by critically analyzing the recent and contemporary debate about non-conceptual content, (ii) work out the basics of broadly Kantian theory of essentially non-conceptual content in relation to a corresponding theory of conceptual content, and then (iii) demonstrate one effective application of the Kantian theory of essentially non-conceptual content by using this theory to provide a ‘minimalist’ solution to the problem of perceptual self-knowledge which is raised by Strong Externalism.

In this paper, I argue that there are universals. I begin (Sect. 1) by proposing a sufficient condition for a thing’s being a universal. I then argue (Sect. 2) that some truths exist necessarily. Finally, I argue (Sects. 3 and 4) that these truths are structured entities having constituents that meet the proposed sufficient condition for being universals.

This paper embeds a theory of proper names in a general approach to singular reference based on type‐free property theory. It is proposed that a proper name “N” is a sortal common noun whose meaning is essentially tied to the linguistic type “N”. Moreover, “N” can be singularly referring insofar as it is elliptical for a definite description of the form the “N” Following Montague, the meaning of a definite description is taken to be a property of properties. The proposed (...) theory fulfils the major desiderata stemming from Kripke's works on proper names. (shrink)

Online collection of papers by Devitt, Dretske, Guarino, Hochberg, Jackson, Petitot, Searle, Tye, Varzi and other leading thinkers on philosophy and the foundations of cognitive Science. Topics dealt with include: Wittgenstein and Cognitive Science, Content and Object, Logic and Foundations, Language and Linguistics, and Ontology and Mereology.

There are two broad approaches to theorizing about ontological categories. Quineans use first-order quantifiers to generalize over entities of each category, whereas type theorists use quantification on variables of different semantic types to generalize over different categories. Does anything of import turn on the difference between these approaches? If so, are there good reasons to go type-theoretic? I argue for positive answers to both questions concerning the category of propositions. I also discuss two prominent arguments for a Quinean conception of (...) propositions, concerning their role in natural language semantics and apparent quantification over propositions within natural language. It will emerge that even if these arguments are sound, there need be no deep question about Quinean propositions’ true nature, contrary to much recent work on the metaphysics of propositions. (shrink)

Cognition is not, and could not possibly be, entirely representational in character. There is also a phenomenal form of cognitive expression that registers the intrinsic properties of mental states themselves. Arguments against the reality of this intrinsic phenomenal dimension to mental experience have focused either on its supposed impossibility, or secondly, the non-appearance of any such qualities to introspection. This paper argues to the contrary, that the registration of cognitive state properties does take place independently of representational content; and necessarily (...) so, since it supports an independent function—self-management. Given the fact that unlike a computer, the brain must, of necessity, operate itself, it needs to be in touch with itself to do so. Intrinsic phenomenal forms of cognitive expression allow the brain to do just that by registering characteristics of the cognitive states themselves. Self-management might well prove to constitute the prime reason for the emergence of subjectivity itself. (shrink)

In truth theory one aims at general formal laws governing the attribution of truth to statements. Gupta’s and Belnap’s revision-theoretic approach provides various well-motivated theories of truth, in particular T* and T#, which tame the Liar and related paradoxes without a Tarskian hierarchy of languages. In property theory, one similarly aims at general formal laws governing the predication of properties. To avoid Russell’s paradox in this area a recourse to type theory is still popular, as testified by recent work in (...) formal metaphysics by Williamson and Hale. There is a contingent Liar that has been taken to be a problem for type theory. But this is because this Liar has been presented without an explicit recourse to a truth predicate. Thus, type theory could avoid this paradox by incorporating such a predicate and accepting an appropriate theory of truth. There is however a contingent paradox of predication that more clearly undermines the viability of type theory. It is then suggested that a type-free property theory is a better option. One can pursue it, by generalizing the revision-theoretic approach to predication, as it has been done by Orilia with his system P*, based on T*. Although Gupta and Belnap do not explicitly declare a preference for T# over T*, they show that the latter has some advantages, such as the recovery of intuitively acceptable principles concerning truth and a better reconstruction of informal arguments involving this notion. A type-free system based on T# rather than T* extends these advantages to predication and thus fares better than P* in the intended applications of property theory. (shrink)

I formulate an account, in terms of essence and ground, that explains why atomic Russellian propositions have the truth conditions they do. The key ideas are that (i) atomic propositions are just 0-adic relations, (ii) truth is just the 1-adic version of the instantiation (or, as I will say, holding) relation (Menzel 1993: 86, note 27), and (iii) atomic propositions have the truth conditions they do for basically the same reasons that partially plugged relations, like being an x and a (...) y such that Philip gave x to y, have the holding conditions they do. The account is meant to be mainly of intrinsic interest, but I hope that it goes some distance toward answering an objection to classical theories of propositions put forward by King (2014), who writes that ‘since the classical conception of propositions as things that have truth conditions by their very natures and independently of minds and languages is incapable of explaining how or why propositions have truth conditions, it is unacceptable’ (2014: 47). Propositions do have their truth conditions ‘by their very natures’ and ‘independently of minds and languages’. But a fact about a given entity can hold by the very nature of that entity without being a fundamental fact. I argue that this is plausibly the case for atomic Russellian propositions and the facts about their truth conditions. A fact about the truth conditions of such a proposition holds by the very nature of the given proposition but is metaphysically grounded in facts about that proposition’s parts and their essences. If my account is correct, then the supposedly intractable problem of explaining why the given propositions have the truth conditions they do reduces to the problem of explaining why relations have the holding essences they do, which few seem to have found worrisome . (shrink)

Informally, structural properties of mathematical objects are usually characterized in one of two ways: either as properties expressible purely in terms of the primitive relations of mathematical theories, or as the properties that hold of all structurally similar mathematical objects. We present two formal explications corresponding to these two informal characterizations of structural properties. Based on this, we discuss the relation between the two explications. As will be shown, the two characterizations do not determine the same class of mathematical properties. (...) From this observation we draw some philosophical conclusions about the possibility of a ‘correct’ analysis of structural properties. (shrink)

This paper is the twin of (Duží and Jespersen, in submission), which provides a logical rule for transparent quantification into hyperprop- ositional contexts de dicto, as in: Mary believes that the Evening Star is a planet; therefore, there is a concept c such that Mary be- lieves that what c conceptualizes is a planet. Here we provide two logical rules for transparent quantification into hyperpropositional contexts de re. (As a by-product, we also offer rules for possible- world propositional contexts.) One (...) rule validates this inference: Mary believes of the Evening Star that it is a planet; therefore, there is an x such that Mary believes of x that it is a planet. The other rule validates this inference: the Evening Star is such that it is believed by Mary to be a planet; therefore, there is an x such that x is believed by Mary to be a planet. Issues unique to the de re variant include partiality and existential presupposition, sub- stitutivity of co-referential (as opposed to co-denoting or synony- mous) terms, anaphora, and active vs. passive voice. The validity of quantifying-in presupposes an extensional logic of hyperinten- sions preserving transparency and compositionality in hyperinten- sional contexts. This requires raising the bar for what qualifies as co-denotation or equivalence in extensional contexts. Our logic is Tichý’s Transparent Intensional Logic. The syntax of TIL is the typed lambda calculus; its highly expressive semantics is based on a procedural redefinition of, inter alia, functional abstraction and application. The two non-standard features we need are a hyper- intension (called Trivialization) that presents other hyperintensions and a four-place substitution function (called Sub) defined over hy- perintensions. (shrink)

The paper has two parts: First, I describe a relatively popular thesis in the philosophy of propositional attitudes, worthy of the name ‘taking tense seriously’; and I distinguish it from a family of views in the metaphysics of time, namely, the A-theories (or what are sometimes called ‘tensed theories of time’). Once the distinction is in focus, a skeptical worry arises. Some A-theorists maintain that the difference between past, present, and future, is to be drawn in terms of what exists: (...) growing-block theorists eschew ontological commitment to future entities; presentists, to future and past entities. Others think of themselves as A-theorists but exclude no past or future things from their ontology. The metaphysical skeptic suspects that their attempt to articulate an ‘eternalist’ version of the A-theory collapses into merely ‘taking tense seriously’– a thesis that does not imply the A-theory. The second half of the paper is the search for a stable eternalist A-theory. It includes discussion of temporary intrinsics, temporal parts, and truth. (shrink)

This book concerns the foundations of epistemic modality and hyperintensionality and their applications to the philosophy of mathematics. David Elohim examines 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 \textbf{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 and hyperintensional cognitivism and modal and hyperintensional expressivism. Elohim develops a novel, topic-sensitive truthmaker semantics for dynamic epistemic logic, and develops a novel, dynamic two-dimensional semantics grounded in two-dimensional hyperintensional Turing machines. Chapter \textbf{3} provides an abstraction principle for two-dimensional (hyper-)intensions. Chapter \textbf{4} advances a topic-sensitive two-dimensional truthmaker semantics, and provides three novel interpretations of the framework along with the epistemic and metasemantic. Chapter \textbf{5} applies the fixed points of the modal $\mu$-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 $\mu$-calculus are rendered hyperintensional, which yields the first hyperintensional construal of the modal $\mu$-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 \textbf{6} advances a solution to the Julius Caesar problem based on Fine's `criterial' identity conditions which incorporate conditions on essentiality and grounding. Chapter \textbf{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 \textbf{2} and \textbf{4} is availed of in order for epistemic states to be a guide to metaphysical states in the hyperintensional setting. -/- Chapters \textbf{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 \textbf{8} examines the interaction between Elohim's 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 $\Omega$-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 \textbf{9} examines the modal and hyperintensional commitments of abstractionism, in particular necessitism, and epistemic hyperintensionality, epistemic utility theory, and the epistemology of abstraction. Elohim countenances a hyperintensional semantics for novel epistemic abstractionist modalities. Elohim suggests, too, that higher 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 two-dimensional hyperintensions is grounded in its being possibly recursively enumerable and the machine being physically implementable. Chapter \textbf{10} examines the philosophical significance of hyperintensional $\Omega$-logic in set theory and discusses the hyperintensionality of metamathematics. Chapter \textbf{11} provides a modal logic for rational intuition and provides a hyperintensional semantics. Chapter \textbf{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 interpretational and objective modalities and the truthmakers thereof. This yields the first hyperintensional category theory in the literature. Elohim invents 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 in the category of Set in category theory. Chapter \textbf{13} examines modal responses to the alethic paradoxes. Elohim provides a counter-example to epistemic closure for logical deduction. Chapter \textbf{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)

Resumen En una serie de escritos Timothy Williamson ha argumentado a favor del necesitismo, esto es, la tesis de que es necesario que todo exista necesariamente. Este trabajo discute el necesitismo de segundo orden, esto es, la tesis de que es necesario que toda propiedad exista necesariamente, considerando líneas de argumentación semejantes a las desplegadas en primer orden. Se examinan tres de estos argumentos: el carácter necesario de ser una propiedad, la aparición de las propiedades en proposiciones, y los compromisos (...) ontológicos del metalenguaje en el que se formula la semántica. Se argumenta que ninguno de ellos es realmente convincente. La justificación del necesitismo de segundo orden parece requerir más metafísica sustantiva que resultados formales, al menos si es que los resultados formales de que se trata son aquellos discutidos aquí.In a series of writings Timothy Williamson has argued for necessitism, i. e. the thesis that it is necessary that everything exists necessarily. This work discusses second-order necessitism, i. e. the thesis that it is necessary that every property exists necessarily, considering lines of argument similar to those displayed on first-order. Three of those arguments are examined. the necessary character ofbeing a property, the occurrence of properties in propositions, and the ontological commitments of the metalanguage where the semantics is formulated. It is argued that none of them are compelling. The justification for second-order necessitism seems to require more substantive metaphysics than formal results, at least if the formal results in view are those discussed here. (shrink)

It is argued that although George Bealer's influential ‘Self-Consciousness argument’ refutes standard versions of reductive functionalism (RF), it fails to generalize in the way Bealer supposes. To wit, he presupposes that any version of RF must take the content of ‘pain’ to be the property of being in pain (and so on), which is expressly rejected in independently motivated versions of conceptual role semantics (CRS). Accordingly, there are independently motivated versions of RF, incorporating CRS, which avoid Bealer's main type of (...) refutation. I focus particularly on one such theory, which takes concepts to be event types that are individuated by their psychological roles, which has the resources of responding to each of the more specific worries Bealer expresses. (shrink)

I try to lay bare some of the conceptual space in which one may be a Social Trinitarian. I organize the paper around answers to five questions. These are: (1) How do the three Persons of the Trinity relate to the Godhead? (2) How many divine beings or gods are there? (3) How many distinct centers of consciousness are there in the Godhead? (4) How many omnicompetent beings are there? (5) How are the Persons of the Trinity individuated? I try (...) to make clear costs and benefits of various answers to these questions. (shrink)

My first aim in this paper is to show that the transparency claim cannot serve the purpose to which it is assigned; that is, the idea that perceptual experience is transparent is no help whatsoever in motivating an externalist account of phenomenal character. My second aim is to show that the internalist qualia theorist's response to the transparency idea has been unnecessarily concessive to the externalist. Surprisingly, internalists seem to allow that much of the phenomenal character of perceptual experience depends (...) essentially (and not just causally) upon externally located properties. They argue that we can also be aware of internal, non-intentional qualia. I present an alternative response the internalist can make to the transparency claim: phenomenal character is wholly internal, and seeming to be aware of externally located properties just is being aware of internally constituted experiential features. (shrink)

Speaks defends the view that propositions are properties: for example, the proposition that grass is green is the property being such that grass is green. We argue that there is no reason to prefer Speaks's theory to analogous but competing theories that identify propositions with, say, 2-adic relations. This style of argument has recently been deployed by many, including Moore and King, against the view that propositions are n-tuples, and by Caplan and Tillman against King's view that propositions are facts (...) of a special sort. We offer our argument as an objection to the view that propositions are unsaturated relations. (shrink)

It is commonplace for philosophers to distinguish mere truths from truths that perspicuously represent the world's structure. According to a popular view, the perspicuous truths are supposed to be metaphysically revelatory and to play an important role in the accounts of law-hood, confirmation, and linguistic interpretation. Yet, there is no consensus about how to characterize this distinction. I examine strategies developed by Lewis and by Sider in his Writing the Book of the World which purport to explain this distinction in (...) terms of vocabulary: the truths that represent the world perspicuously have better, joint-carving vocabulary. I argue that the distinction between a perspicuous and mere truth concerns both the vocabulary of the sentence and its grammar. I then show that the collective motivations for distinguishing perspicuous from mere truths do not allow Lewis and Sider to properly impose constraints on grammar. (shrink)

According to traditional theism, God alone exists a se, independent of all other things, and all other things exist ab alio, i.e., God both creates them and sustains them in existence. On the face of it, divine "aseity" is inconsistent with classical Platonism, i.e., the view that there are objectively existing, abstract objects. For according to the classical Platonist, at least some abstract entities are wholly uncreated, necessary beings and, hence, as such, they also exist a se. The thesis of (...) theistic activism purports to reconcile divine aseity with a robust Platonism. Specifically, the activist holds that God creates the abstract objects no less than the contingent concrete objects of the physical universe and hence that, like all created things, they exist ab alio after all, their necessity notwithstanding. But many philosophers believe a severe roadblock for activism remains — a problem known as the bootstrapping objection. Despite widespread faith in the deliverances of this argument, in this paper I show that the bootstrapping objection is open to significant objections on several fronts. (shrink)

Revised and reprinted in Handbook of Philosophical Logic, volume 10, Dov Gabbay and Frans Guenthner (eds.), Dordrecht: Kluwer, (2003). -- Two sorts of property theory are distinguished, those dealing with intensional contexts property abstracts (infinitive and gerundive phrases) and proposition abstracts (‘that’-clauses) and those dealing with predication (or instantiation) relations. The first is deemed to be epistemologically more primary, for “the argument from intensional logic” is perhaps the best argument for the existence of properties. This argument is presented in the (...) course of discussing generality, quantifying-in, learnability, referential semantics, nominalism, conceptualism, realism, type-freedom, the first-order/higher-order controversy, names, indexicals, descriptions, Mates’ puzzle, and the paradox of analysis. Two first-order intensional logics are then formulated. Finally, fixed-point type-free theories of predication are discussed, especially their relation to the question whether properties may be identified with propositional functions. (shrink)

The paper presents a two-level approach to an assessment of meaning theories. To begin with, language is distinguished from lan guage-model and, analogously, meaning is discerned from a model of meaning. The first level of a theory assessment is presented as dealing with the relation of a model of meaning to intra-theoretical aims and assumptions of a theory with specific language-model. The second level of assessment concerns ontological, epistemological, logical and other assumptions underlying the respective language-model. Finally, several questions are (...) set forth as methodological directives for elucidating hidden assumptions behind the theories of meaning. (shrink)

Most contemporary philosophical discussions of intentionality start and end with a treatment of the propositional attitudes. In fact, many theorists hold that all attitudes are propositional attitudes. Our folk-psychological ascriptions suggest, however, that there are non-propositional attitudes: I like Sally, my brother fears snakes, everyone loves my grandmother, and Rush Limbaugh hates Obama. I argue that things are as they appear: there are non-propositional attitudes. More specifically, I argue that there are attitudes that relate individuals to non-propositional objects and do (...) so not in virtue of relating them to propositions. I reach this conclusion by not only showing that attempted analyses of apparently non-propositional attitudes in terms of the propositional fail, but that some non-propositional attitudes don’t even supervene on propositional attitudes. If this is correct, then the common discussions of intentionality that address only propositional attitudes are incomplete and those who hold that all intentional states are propositional are mistaken. (shrink)

Fitch's basic logic is an untyped illative combinatory logic with unrestricted principles of abstraction effecting a type collapse between properties (or concepts) and individual elements of an abstract syntax. Fitch does not work axiomatically and the abstraction operation is not a primitive feature of the inductive clauses defining the logic. Fitch's proof that basic logic has unlimited abstraction is not clear and his proof contains a number of errors that have so far gone undetected. This paper corrects these errors and (...) presents a reasonably intuitive proof that Fitch's system K supports an implicit abstraction operation. Some general remarks on the philosophical significance of basic logic, especially with respect to neo-logicism, are offered, and the paper concludes that basic logic models a highly intensional form of logicism. (shrink)

The paper raises some difficulties for the typical motivations behind set reductionism, the view that sets are reducible to entities identified independently of set theory.

Arguments are given against the thesis that properties and propositional functions are identical. The first shows that the familiar extensional treatment of propositional functions -- that, for all x, if f(x) = g(x), then f = g -- must be abandoned. Second, given the usual assumptions of propositional-function semantics, various propositional functions (e.g., constant functions) are shown not to be properties. Third, novel examples are given to show that, if properties were identified with propositional functions, crucial fine-grained intensional distinctions would (...) be lost. (shrink)

This paper begins with a brief summary of the Self-consciousness Argument, developed in the author’s paper “Self-consciousness.” (This argument is designed to refute the extant versions of functionalism -- American functionalism, Australian functionalism, and language-of-thought functionalism.) After this summary is given, two thesis are defended. The first is that the Self-consciousness Argument is not guilty of a Fregean equivocation regarding embedded occurrences of mental predicates, as has been suggested by many commentators, including Mark McCullagh. The second thesis is that the (...) Self-consciousness Argument cannot be avoided by weakening the psychological theory upon which Ramsified functional definitions are based. Specifically, it does no good to excise psychological principles involving embedded mental predicates. Why? Because functional definitions based on the resulting sparse theories are exposed to an interesting new family of counterexamples. (shrink)

A logical empiricist “baseline statement” can formalize some propositions established by a body of evidence or set of observations. However, it may not necessarily capture, of two propositions it entails, whether all the subsets of the evidence that establish one proposition also establish the other, vice versa, or neither. Yet, according to this paper, which obtains should sometimes matter for confirmation. It illustrates by showing how this “evidential dependence” can be used to address problems with generalizations of grue-like predicates, and (...) do so still within a very simple broadly Hempelian framework. (shrink)

This paper sets out a predicative response to the Russell-Myhill paradox of propositions within the framework of Church’s intensional logic. A predicative response places restrictions on the full comprehension schema, which asserts that every formula determines a higher-order entity. In addition to motivating the restriction on the comprehension schema from intuitions about the stability of reference, this paper contains a consistency proof for the predicative response to the Russell-Myhill paradox. The models used to establish this consistency also model other axioms (...) of Church’s intensional logic that have been criticized by Parsons and Klement: this, it turns out, is due to resources which also permit an interpretation of a fragment of Gallin’s intensional logic. Finally, the relation between the predicative response to the Russell-Myhill paradox of propositions and the Russell paradox of sets is discussed, and it is shown that the predicative conception of set induced by this predicative intensional logic allows one to respond to the Wehmeier problem of many non-extensions. (shrink)

We may wonder about the status of logical accounts of the meaning of language. When does a particular proposal count as a theory? How do we judge a theory to be correct? What criteria can we use to decide whether one theory is “better” than another? Implicitly, many accounts attribute a foundational status to set theory, and set-theoretic characterisations of possible worlds in particular. The goal of a semantic theory is then to find a translation of the phenomena of interest (...) into a set-theoretic model. Such theories may be deemed to have “explanatory” or “predictive” power if a mapping can found into expressions of set-theory that have the appropriate behaviour by virtue of the rules of set-theory (for example Montague 1973; Montague1974). This can be contrasted with an approach in which we can help ourselves to “new” primitives and ontological categories, and devise logical rules and axioms that capture the appropriate inferential behaviour (as in Turner 1992). In general, this alternative approach can be criticised as being mere “descriptivism”, lacking predictive or explanatory power. Here we will seek to defend the axiomatic approach. Any formal account must assume some normative interpretation, but there is a sense in which such theories can provide a more honest characterisation (cf. Dummett 199). In contrast, the set-theoretic approach tends to conflate distinct ontological notions. Mapping a pattern of semantic behaviour into some pre-existing set-theoretic behaviour may lead to certain aspects of that behaviour being overlooked, or ignored (Chierchia & Turner 1988; Bealer 1982). Arguments about the explanatory and predictive power of set-theoretic interpretations can also be questioned (see Benacerraf 1965, for example). We aim to provide alternative notions for evaluating the quality of a formalisation, and the role of formal theory. Ultimately, claims about the methodological and conceptual inadequacies of axiomatic accounts compared to set-theoretic reductions must rely on criteria and assumptions that lie outside the domain of formal semantics as such. (shrink)