Hylomorphically complex objects are things that change their parts or matter or that might have, or have had, different parts or matter. Often ontologists analyze such objects in terms of sets (or functions, understood set-theoretically) or other extensional entities such as mereological fusions or quantities of matter. I urge two reasons for being wary of any such analyses. First, being extensional, such things as sets are ill-suited to capture the characteristic modal and temporal flexibility of hylomorphically complex (...) objects. Secondly, sets are often appealed to because they seem to contain their members. But the idea that sets do contain their members, in the ordinary sense of containment, is a substantive metaphysical position that makes analyses that rely on that idea for their plausibility much more metaphysically committing than is generally thought. (shrink)

In this paper, we present an extensional system of mereology suitable to account for the intuitive distinction between heaplike and non-heaplike entities. Since the need to capture this distinction has been a key motivation for non-extensional mereologies, we first assess the main non-extensional systems advanced in the last years and highlight some mereological and metaphysical difficulties they involve. We then advance a novel program, according to which the distinction between heaplike and non-heaplike entities can be (...) accounted for by bringing together the parthood relation characterized by classical extensional mereology and an Aristotelian extensional notion of potential parthood. Thus, while rejecting the thesis of mereological monism, our proposal is consistent with the thesis of mereological extensionalism. We show that within this framework it is possible to characterize the above-mentioned distinction, to define the relation of material constitution, and to capture three fundamental standpoints in metaphysics. (shrink)

Ethical extensionism is a common argument pattern in environmental and animal ethics, which takes a morally valuable trait already recognized in us and argues that we should recognize that value in other entities such as nonhuman animals. I exposit ethical extensionism’s core argument, argue for its validity and soundness, and trace its history to 18th century progressivist calls to expand the moral community and legal franchise. However, ethical extensionism has its critics. The bulk of the paper responds to recent (...) criticisms, including (1) environmental ethicists’ objection against its austere conception of moral value (2), feminist ethicists’ claim that extensionism fails to account for the moral significance of difference, (3) disability theorists’ concern that ethical extensionist arguments are offensive, and (4) animal rights theorists’ lament that extensionism is a practical failure. While something is to be gained from each criticism, I argue that they ultimately fail and that extensionism remains compelling. (shrink)

I argue that 'c' occurs extensionally in 'c caused e' and 'D' occurs extensionally in 'c caused e because c is D'. I claim that this has been insufficiently appreciated because the two contexts are often run together and because it has not been clear that the description D of c is among the referents of an explanatory argument. I argue as well that Hume's analysis of causation is consistent with taking causation to be a relation between single events, and (...) that even if events are eliminated as virtual entities, extensionality holds for all terms in the resulting context. (shrink)

Neo-Fregean approaches to set theory, following Frege, have it that sets are the extensions of concepts, where concepts are the values of second-order variables. The idea is that, given a second-order entity $X$, there may be an object $\varepsilon X$, which is the extension of X. Other writers have also claimed a similar relationship between second-order logic and set theory, where sets arise from pluralities. This paper considers two interpretations of second-order logic—as being either extensional or intensional—and whether either (...) is more appropriate for this approach to the foundations of set theory. Although there seems to be a case for the extensional interpretation resulting from modal considerations, I show how there is no obstacle to starting with an intensional second-order logic. I do so by showing how the $\varepsilon$ operator can have the effect of “extensionalizing” intensional second-order entities. (shrink)

In his 2000 book Logical Properties Colin McGinn argues that predicates denote properties rather than sets or individuals. I support the thesis, but show that it is vulnerable to a type-incongruity objection, if properties are (modelled as) functions, unless a device for extensionalizing properties is added. Alternatively, properties may be construed as primitive intensional entities, as in George Bealer. However, I object to Bealer’s construal of predication as a primitive operation inputting two primitive entities and outputting a third (...) primitive entity. Instead I recommend we follow Pavel Tichý in construing both predication and extensionalization as instances of the primitive operation of functional application. (shrink)

This paper examines whether classical extensional mereology is adequate for formalizing the whole–parts relation in quantum chemical systems. Although other philosophers have argued that classical extensional and summative mereology does not adequately formalize whole–parts relation within organic wholes and social wholes, such critiques often assume that summative mereology is appropriate for formalizing the whole–parts relation in inorganic wholes such as atoms and molecules. However, my discussion of atoms and molecules as they are conceptualized in quantum chemistry will establish (...) that standard mereology cannot adequately fulfill this task, since the properties and behavior of such wholes are context-dependent and cannot simply be reduced to the summative properties of their parts. To the extent that philosophers of chemistry have called for the development of an alternative mereology for quantum chemical systems, this paper ends by proposing behavioral mereology as a promising step in that direction. According to behavioral mereology, considerations of what constitutes a part of a whole is dependent upon the observable behavior displayed by these entities. Thus, relationality and context-dependence are stipulated from the outset and this makes behavioral mereology particularly well-suited as a mereology of quantum chemical wholes. The question of which mereology is appropriate for formalizing the whole–parts relation in quantum chemical systems is relevant to contemporary philosophy of chemistry, since this issue is related to the more general questions of the reducibility of chemical wholes to their parts and of the reducibility of chemistry to physics, which have been of central importance within the philosophy of chemistry for several decades. More generally, this paper puts contemporary discussions of mereology within the philosophy of chemistry into a broader historical and philosophical context. In doing so, this paper also bridges the gap between formal mereology, conceived as a branch of formal ontology, and “applied” mereology, conceived as a branch of philosophy of science. (shrink)

The problems that Millikan addresses in theories of concepts arise from an extensional view of concepts and word meaning. If instead one assumes that concepts are psychological entities intended to explain human behavior and thought, many of these problems dissolve.

Extensional articulations of physicalism define what it means to be physical relative to the properties of a set of entities, such that physicalism is true if the fundamental properties which compose the entities in this set are the same sorts of fundamental properties which compose everything that exists. Here I present a novel problem for these articulations of physicalism: they are consistent with phenomenal idealism, which is the view that only phenomenal properties exist. Under this view, paradigm (...) physical objects such as tables and chairs are constructed out of more basic phenomenal properties. Since this view says that everything—including paradigm physical entities—is ultimately constituted by phenomenal properties, it follows that this view is consistent with extensional definitions of physicalism, since such definitions only require that there be no fundamental difference between paradigm physical entities and everything else. Yet a good definition of physicalism should not be consistent with phenomenal idealism. (shrink)

In this paper, I introduce the idea that some important parts of contemporary pure mathematics are moving away from what I call the extensional point of view. More specifically, these fields are based on criteria of identity that are not extensional. After presenting a few cases, I concentrate on homotopy theory where the situation is particularly clear. Moreover, homotopy types are arguably fundamental entities of geometry, thus of a large portion of mathematics, and potentially to all mathematics, (...) at least according to some speculative research programs. (shrink)

E.J. Lowe is one of the few philosophers who defend both the existence of spatially coincident entities and the Principle of Weak Extensionality that no two objects which have proper parts have exactly the same proper parts at the same time. Lowe maintains that when spatially coincident things like the statue and the lump of bronze are in a constitution relation, the constituted entity (the statue) has parts that the constituting entity (the lump) doesn’t, hence the compatibility with Weak (...) Extensionality. My contention is that his argument for why the statue has parts the lump of bronze lacks can also be used to show that the lump of bronze has parts the statue doesn’t. This will mean that there is no basis for saying the statue and the lump are in a constitution relation. I argue for accepting a modified account of constitution and abandoning the Principle of Weak Extensionality. (shrink)

The distinction between norms and norm-formulations commits legal theorists to treating legal norms as entities. In this article, I first explore the path from meaning to entities built by some analytical philosophers of language. Later, I present a set of problems produced by treating norms as entities. Whatever type of entities we deal with calls for a clear differentiation between the identification and individuation criteria of such entities. In the putative case of abstract entities, (...) the differentiation collapses. By changing the notions of the intension and extension of words by extensional and intensional aspects of what we talk about, I outline a methodological programme for Law and Legal Theory. That programme is based in the identification of normativity. (shrink)

Extensionalism, as I understand it here, is the view that physical reality consists exclusively of extensional entities. On this view, intensional entitities must either be eliminated in favor of an ontology of extensional entities, or be reduced to such an ontology, or otherwise be admitted as non-physical. In this paper I argue that extensionalism is a misguided philosophical doctrine. First, I argue that intensional phenomena are not confined to the realm of language and thought. Rather, the (...) ontology of such phenomena is intimately entwined with the ontology of properties. After providing some evidence to the popularity of extensionalism in contemporary analytic philosophy, I investigate the motivating reasons behind it. Considering several explanations, I argue that the main motivating reason is rooted in the identification of matter with extension, an identification which is one of the hallmarks of the mechanistic conception of nature inherited from the founding fathers of our modern scientific outlook. I then argue that such a conception is not only at odds with a robust ontology of properties but is also at odds with our best contemporary physics. Rather than vindicating extensionalism contemporary science undermines the position, and the lesson to be drawn from this surprising fact is that extensionalism needs no longer be espoused as a regulative ideal of naturalistic philosophy. I conclude by showing that the ontological approach to intensional phenomena advocated throughout the paper also gains support from an examination of the historical context within which ‘intension’ was first introduced as a semantic notion. (shrink)

Recent work in philosophy of language has raised significant problems for the traditional theory of propositions, engendering serious skepticism about its general workability. These problems are, I believe, tied to fundamental misconceptions about how the theory should be developed. The goal of this paper is to show how to develop the traditional theory in a way which solves the problems and puts this skepticism to rest. The problems fall into two groups. The first has to do with reductionism, specifically attempts (...) to reduce propositions to extensional entities-either extensional functions or sets. The second group concerns problems of fine grained content-both traditional 'Cicero'/'Tully' puzzles and recent variations on them which confront scientific essentialism. After characterizing the problems, I outline a non-reductionist approach-the algebraic approach-which avoids the problems associated with reductionism. I then go on to show how the theory can incorporate non-Platonic (as well as Platonic) modes of presentation. When these are implemented nondescriptively, they yield the sort of fine-grained distinctions which have been eluding us. The paper closes by applying the theory to a cluster of remaining puzzles, including a pair of new puzzles facing scientific essentialism. (shrink)

The author puts forth an approach to propositional attitude contexts based upon the view that one does not have beliefs of ordinary extensional entitiessimpliciter. Rather, one has beliefs of such entities as presented in various manners. Roughly, these are treated as beliefs of ordered pairs — the first member of which is the ordinary extensional entity and the second member of which is a predicate that it satisfies. Such an approach has no difficulties with problems involving identity, (...) such as of The Morning Star and The Evening Star (section 1). Given the second members of the pairs, the modes of presentation, it is quite natural to allow exportation everywhere. There is no need for essentialism. (One also can have non-essentialistic modal logic if one grants analyticity or the like.) (section 2). Given that the second member of the pair need only be one that is satisfied by the entity that is the first member (and need not be specificative), the method has no difficulties when one is concerned only with discriminations (and not specifications) (section 3). When this method is combined with the Frege-Carnap method of descriptions, fictional entities can be accommodated; Goodman''s unicorn-picture and the like can be brought within a Tarskian semantics; and Geach''s difficulties with intentional identity appear to be handled (section 4). Given the author''s ordered pair construals, there appears to be no additional need for notional construals; i.e., the author''s one unified method appears satisfactory for dealing with both traditionalde re (relational) andde dicto (notional) construals. The Paradox of the Knower and the like do not appear formulatable against the author''s approach. (section 5). The author also argues against the basic principles behind the Church-Langford translation argument (section 6). (shrink)

The topic of this special issue of Synthese is hyperintensionality. This introduction offers a brief survey of the very notion of hyperintensionality followed by a summary of each of the papers in this collection. The papers are foundational studies of hyperintensionality accompanied by ample philosophical applications.Hyperintensionality concerns the individuation of non-extensional entities such as propositions and properties, relations-in-intension and individual roles, as well as, for instance, proofs and judgments and computational procedures, in case these do not reduce to (...) any of the former. Hyperintensional individuation is frequently also referred to as ‘fine-grained’ or sometimes simply ‘intensional’ individuation, when ‘intensional’ is not understood in the specific sense of possible-world semantics or in the pejorative sense of flouting various logical rules of extensional logic. A principle of individuation qualifies as hyperintensional as soon as it is finer than necessary .. (shrink)

This paper defendsintensional essentialism: a property (intensional entity) is not essential relative to an individual (extensional entity), but relative to other properties (or intensional entities). Consequently, an individual can have a property only accidentally, but in virtue of having that property the individual has of necessity other properties. Intensional essentialism is opposed to various aspects of the Kripkean notion of metaphysical modality, eg, varying domains, existence as a property of individuals, and its category of properties which are both (...) empirical and essential with respect to particular individuals and natural kinds. The key notion of intensional essentialism isrequisite. A requisite is explicated as a relation-in-extension between two intensions (functions from possible worlds and moments of time)X, Y such that wherever and wheneverX is instantiatedY is also instantiated. We predict three readings of the sentence. Every wooden table is necessarily wooden , one involving modalityde re and the other two modalityde dicto. The first reading claims that no individual which is a wooden table is necessarily wooden. The claim is backed up by bare particular anti-essentialism. The two other interpretations claim that it is necessary that whatever is a wooden table is wooden. However, as we try to show, one is logically far more perspicuous thanks to the concept of requisite and thus preferable to more standardde dicto formalizations. (shrink)

This publication of the proceedings of the first of a new series of colloquia to be held at the University of Western Ontario contains an opening address on existence and quantification by W. V. Quine and three symposia. The paper discussed in the first of these symposia, "Descartes' Ontological Argument" by Anthony Kenny, follows closely one chapter of Kenny's recent book on Descartes. Kenny's paper contains both an interesting account of Descartes' views and some challenging remarks about ontological arguments in (...) general. His paper is discussed in separate commentaries by Norman Malcolm and Terence Penelhum. An interesting feature of this volume is that some comments from the floor are recorded and included along with the regular commentaries. Ernest Sosa and Bernard Williams comment on Kenny's paper along with Malcolm and Penelhum. Kenny responds to all four commentators. The other two symposia follow a similar format. The second, "On Events and Event-descriptions," features a paper by R. M. Martin which focuses on the logic of event descriptions and their role in scientific explanation. Events for Martin are extensional entities, unlike facts, but like facts they are "fictitious in the sense of being handled on virtually." His views are discussed by Donald Davidson, R. J. Butler and Wesley Salmon. In the third symposium on "Existence Assumptions in Practical Thinking," Stephan Körner elaborates on his view of effective choice, relating his account to those of Hume, Kant, and Peirce on the specific topic of the relationship of choice and natural necessity. The commentaries of J. J. Thomson and Bernard Williams are helpful here in getting Körner to clarify his interesting views. In sum, this first colloquium at the University of Western Ontario features genuine philosophical communication on some important issues.--R. H. K. (shrink)

We demonstrate how to validly quantify into hyperintensional contexts involving non-propositional attitudes like seeking, solving, calculating, worshipping, and wanting to become. We describe and apply a typed extensional logic of hyperintensions that preserves compositionality of meaning, referential transparency and substitutivity of identicals also in hyperintensional attitude contexts. We specify and prove rules for quantifying into hyperintensional contexts. These rules presuppose a rigorous method for substituting variables into hyperintensional contexts, and the method will be described. We prove the following. First, (...) it is always valid to quantify into hyperintensional attitude contexts and over hyperintensional entities. Second, factive empirical attitudes validate, furthermore, quantifying over intensions and extensions, and so do non-factive attitudes, both empirical and non-empirical , provided the entity to be quantified over exists. We focus mainly on mathematical attitudes, because they are uncontroversially hyperintensional. (shrink)

Standard approaches to proper names, based on Kripke's views, hold that the semantic values of expressions are (set-theoretic) functions from possible worlds to extensions and that names are rigid designators, i.e.\ that their values are \emph{constant} functions from worlds to entities. The difficulties with these approaches are well-known and in this paper we develop an alternative. Based on earlier work on a higher order logic that is \emph{truly intensional} in the sense that it does not validate the axiom scheme (...) of Extensionality, we develop a simple theory of names in which Kripke's intuitions concerning rigidity are accounted for, but the more unpalatable consequences of standard implementations of his theory are avoided. The logic uses Frege's distinction between sense and reference and while it accepts the rigidity of names it rejects the view that names have direct reference. Names have constant denotations across possible worlds, but the semantic value of a name is not determined by its denotation. (shrink)

In Entities and Indices, M. J. Cresswell argued that a first-order modal language can reach the expressive power of natural-language modal discourse only if we give to the formal language a semantics with indices containing infinite possible worlds and we add to it an infinite collection of operators $${{\varvec{actually}}}_n$$ actually n and $$ Ref _n$$ R e f n which store and retrieve worlds. In the fourth chapter of the book, Cresswell gave a proof that the resulting intensional language, (...) which he called $${\mathscr {L}}^*$$ L ∗, is as expressive as an extensional variant of it, called $${\mathscr {L}}$$ L, which has full quantification over worlds. In both linguistics and philosophy, Cresswell’s book has been viewed as offering a compelling argument for preferring extensional systems in the study of natural language. In this paper, after providing a model-theoretic definition of the relation being as expressive as that can be applied to Cresswell’s languages $${\mathscr {L}}$$ L and $${\mathscr {L}}^*$$ L ∗, we show that the intensional language $${\mathscr {L}}^*$$ L ∗ is not as expressive as the extensional language $${\mathscr {L}}$$ L. This result, we claim, undermines Cresswell’s argument to the effect that English modal discourse has the power of explicit quantification over worlds. Additionally, we show that $${\mathscr {L}}^*$$ L ∗ does become as expressive as $${\mathscr {L}}$$ L when we add Cresswell’s operator of universal modality $$\square $$ □ to $${\mathscr {L}}^*$$ L ∗, which provides an extra amount of expressive power. Recently, I. Yanovich has advocated a view that is similar to ours in important respects. At the end of the paper we offer a short discussion of his formalism. (shrink)

The core entities of computer science include formal languages, spec-ifications, models, programs, implementations, semantic theories, type inference systems, abstract and physical machines. While there are conceptual questions concerning their nature, and in particular ontological ones (Turner 2018), our main focus here will be on the relationships between them. These relationships have an extensional aspect that articulates the propositional connection between the two entities, and an intentional one that fixes the direction of governance. An analysis of these two (...) aspects will drive our investigation; an investigation that will touch upon some of the central concerns of the philosophy of computer science (Turner 2017). (shrink)

In the last few decades of the twentieth century there was a revolution in metaphysics: the intensional revolution. Many metaphysicians rejected the doctrine, associated with Quine and Davidson, that extensional analyses and theoretical resources were the only acceptable ones. Metaphysicians embraced tools like modal and counterfactual analyses, claims of modal and counterfactual dependence, and entities such as possible worlds and intensionally individuated properties and relations. The twenty-first century is seeing a hypterintensional revolution. Theoretical tools in common use carve (...) more finely than by necessary equivalence: two pieces of language can apply to the same entities across all possible worlds but not be equivalent; thoughts can be necessarily equivalent in truth value but not synonymous. This paper argues that hyperintensional resources are valuable in metaphysics outside theories of representation, and discusses some promising areas of hyperintensional metaphysics. (shrink)

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

Which categories of entities qualify as ontological categories? Which combinations of categories qualify as adequate systems of ontological categories? These are the two questions the author focuses on in this article. Contrary to the usual praxis in contemporary ontological literature, he addresses both questions conjointly. First, the author presents some problems of characterizing ontological categories in purely extensional terms, i.e. as widely inclusive natural classes. Second, he introduces the transversality requirement: ontological categories should be individually and naturally domain-transversal, (...) i.e. ontological categories must be neutral concerning different scientific disciplines like physics, biology and mathematics. As a result, ontological categories must have instances in any domain of reality. Finally, the author checks the adequacy of some systems of ontological categories according to this criterion and meets some possible objections. (shrink)

It has been maintained by such philosophers as Quine and Goodman that purely ‘extensional’ language suffices for all the purposes of properly formalized scientific discourse. Those entities that were traditionally called ‘universals’ — properties, concepts, forms, etc. — are rejected by these extensionalist philosophers on the ground that ‘the principle of individuation is not clear’. It is conceded that science requires that we allow something tantamount to quantification over non-particulars (or, anyway, over things that are not material objects, (...) not space-time points, not physical fields, etc.), but, the extensionalists contend, quantification over sets serves the purposes nicely. The ‘ontology’ of modern science, at least as Quine formalizes it, comprises material objects (or, alternatively, space-time points), sets of material objects, sets of sets of material objects,... but no properties, concepts,or forms. Let us thus examine the question: Can the principle of individuation for properties ever be made clear? (shrink)

Sometimes mereologists have problems with counting. We often don't want to count the parts of maximally connected objects as full-fledged objects themselves, and we don't want to count discontinuous objects as parts of further, full-fledged objects. But whatever one takes "full-fledged object" to mean, the axioms and theorems of classical, extensional mereology commit us to the existence both of parts and of wholes – all on a par, included in the domain of quantification – and this makes mereology look (...) counterintuitive to various philosophers. In recent years, a proposal has been advanced to solve the tension between mereology and familiar ways of counting objects, under the label of Minimalist View . The Minimalist View may be summarized in the slogan: "Count x as an object iff it does not overlap with any y you have already counted as an object". The motto seems prima facie very promising but, we shall argue, when one looks at it more closely, it is not. On the contrary, the Minimalist View involves an ambiguity that can be solved in quite different directions. We argue that one resolution of the ambiguity makes it incompatible with mereology. This way, the Minimalist View can lend no support to mereology at all. We suggest that the Minimalist View can become compatible with mereology once its ambiguity is solved by interpreting it in what we call an epistemic or conceptual fashion: whereas mereology has full metaphysical import, the Minimalist View may account for our ways of selecting "conceptually salient" entities. But even once it is so disambiguated, it is doubtful that the Minimalist View can help to make mereology more palatable, for it cannot make it any more compatible with commonsensical ways of counting objects. (shrink)

Turing and Church formulated two different formal accounts of computability that turned out to be extensionally equivalent. Since the accounts refer to different properties they cannot both be adequate conceptual analyses of the concept of computability. This insight has led to a discussion concerning which account is adequate. Some authors have suggested that this philosophical debate—which shows few signs of converging on one view—can be circumvented by regarding Church’s and Turing’s theses as explications. This move opens up the possibility that (...) both accounts could be adequate, albeit in their own different ways. In this paper, I focus on the question of whether Church’s thesis can be seen as an explication in the precise Carnapian sense. Most importantly, I address an additional constraint that Carnap puts on the explicative power of axiomatic systems—an axiomatisation explicates when it is clear which mathematical entities form the theory’s intended model—and that implicitly applies to axiomatisations of recursion theory used in Church’s account of computability. To overcome this difficulty, I propose two possible clarifications of the pre-systematic concept of “computability” that can both be captured in recursion theory, and I show how both clarifications avoid an objection arising from Carnap’s constraint. (shrink)

Many contemporary philosophers accept Hume's Dictum, according to which there are no metaphysically necessary connections between distinct, intrinsically typed entities. Tacit in Lewis 's work is a potential motivation for HD, according to which one should accept HD as presupposed by the best account of the range of metaphysical possibilities---namely, a combinatorial account, applied to spatiotemporal fundamentalia. Here I elucidate and assess this Ludovician motivation for HD. After refining HD and surveying its key, recurrent role in Lewis ’s work, (...) I present Lewis ’s appeal to HD as providing a broadly axiomatic generating basis for the space of metaphysical modality, and canvas the prima facie advantages of the resulting combinatorial principle---HD ---as being principled, extensionally adequate and modally reductive. Most criticisms of Lewis 's combinatorialism have targeted seeming ways in which the theory overgenerates the desired space; I rather argue that HD seriously undergenerates the desired space in three different ways. For each way I argue that available means of overcoming the undergeneration either fail to close the gap, undermine the claim that HD is a principled generator of metaphysical modal space, undermine the reductive status of Lewis 's combinatorialism, or call into question the truth of HD. (shrink)

Stephen Neale presents, in Facing Facts (Oxford: Clarendon Press, 2001), one convenient package containing his reasoned complaints against theories of facts and non-extensional connectives. The slingshot is a powerful argument (or better, it is a powerful family of arguments) which constrains theories of facts, propositions and non-extensional connectives by showing that some of these theories are rendered trivial. This book is the best place to find the state of the art on the slingshot and its implications for logic, (...) language and metaphysics. It provides a useful starting point for anyone who has wondered what all of the fuss about the slingshot amounts to. Neale shows that the fuss does amount to something, and that theories of facts must “face facts” and present an adequate response to the slingshot. However, Neale’s evaluation of the state of play for theories of facts is too pessimistic. As the book draws near to a close, Neale writes: As I have stressed, Russell’s Theory of Facts, according to which facts have properties as components, is safe. It is certainly tempting to draw the moral that if one wants non-collapsing facts one needs properties as components of facts. I have not attempted to prove this here, but I suspect it will be proved in due course. (page 210) Neale concludes that while theories which take facts to be structured entities are safe from slingshot arguments, and he suspects that this is the only kind of fact theory safe from slingshot-style collapse. If this were the case, then theories such as situation theories or accounts of truthmakers may well be threatened. However, Neale’s suspicion is ill-founded, as I shall soon show. Not only do Russellian theories of facts survive the slingshot unscathed, but so can theories of facts which take them to be unstructured entities. Furthermore, the way that this may be not only argued for, but proved can provide a new weapon in the armoury of the theorist investigating fact theories. (shrink)

Many contemporary philosophers accept a strong generalization of Hume's denial of necessary causal connections, in the form of Hume's dictum (HD), according to which there are no metaphysically necessary connections between distinct, intrinsically typed entities. Hume's version of his dictum occurs during his investigation into the source of the idea of causal connection. The most powerful role that HD plays in Lewis's system concerns its providing a basis for, as Lewis puts it, a "principle of plentitude" that will guarantee (...) "that the worlds are abundant, and logical space is somehow complete". Lewis's combinatorialism promises to provide a principled, extensionally adequate, and reductive generator of metaphysical modal space. Beyond combinatorialism, there are many other accounts of metaphysical modality that need to be considered, not just with an eye to extensional adequacy but also to the clear desideratum to provide an account of the space of metaphysical modality that is principled. (shrink)

The „Paradox of the Concept Horse" arises on the assumption of the Reference Principle: that co-referential expressions should be cross-substitutable salva veritate in extensional contexts and salva congruitate in all. Accordingly no singular term can co-refer with an unsaturated expression. The paper outlines a number of desiderata for a satisfactory response to the problem and argues that recent treatments by Dummett and Wiggins fall short by their lights. It is then pointed out that a more consistent perception of the (...) requirements of the Reference Principle leads not to the Paradox but to the result that Frege had no business extending the notion of Bedeutung to unsaturated expressions in the first place. Rather the relation between, e.g., predicates and the entities that comprise the range of higher-order logical variables must be logically unlike that between singular terms and their referents; the way is therefore opened for singular terms to refer to entities of the former kind after all. The Concept Horse is a concept (and a Fregean object too.). (shrink)

This book offers a comprehensive primer for the study of intensionality. It explores and assesses those key theories of intensionality which have been developed in the twentieth and early twenty-first centuries. Each of the examined theories is tested as to whether it can account for the problems associated with the intersubstitution salva veritate of co-extensional expressions, and existential generalisation. All of these theories are subsequently compared so as to determine which of them comes closest to successfully solving these problems. (...) The book examines four kinds of intensionalist approaches: the Fregean approach ; the possible-worlds approaches of Carnap, Montague and Cresswell; the theory of properties relations and propositions devised by Bealer; and the Meinongian approaches put forward by Zalta and Priest. The book also proposes an alternative to intensionalism: sententialism. Sententialists argue that the problems of intensionality could be solved by appealing to linguistic items rather than intensional entities. Drawing on the works of Quine, Davidson, Scheffler and R. M. Martin, it explores the viability and value of sententialism as an alternative to intensionalism. (shrink)

Abstractionism in the philosophy of mathematics aims at deriving large fragments of mathematics by combining abstraction principles (i.e. the abstract objects $\S e_1, \S e_2$, are identical if, and only if, an equivalence relation $Eq_\S$ holds between the entities $e_1, e_2$) with logic. Still, as highlighted in work on the semantics for relevant logics, there are different ways theories might be combined. In exactly what ways must logic and abstraction be combined in order to get interesting mathematics? In this (...) paper, we investigate the matter by deriving the axioms of second-order Peano Arithmetic from Frege's Basic Law V (the extension of $F$ is identical with the extension of $G$ if, and only if, $F$ and $G$ are extensionally equivalent) in the presence of a relevant higher-order logic. The results are interesting. Not only must we take on logic as true, and not only must we apply our logic to abstraction principles, but also we have to apply our theory of abstraction back to the logic in order to arrive at arithmetic. Thus, what Abstractionism gives us is not simply what we get from abstraction via logic, but also what we get from logic via abstraction. (shrink)

In this paper, we outline an approach to giving extensional truth-theoretic semantics for what have traditionally been seen as opaque sentential contexts. We outline an approach to providing a compositional truth-theoretic semantics for opaque contexts which does not require quantifying over intensional entities of any kind, and meets standard objections to such accounts. The account we present aims to meet the following desiderata on a semantic theory T for opaque contexts: (D1) T can be formulated in a first-order (...) extensional language; (D2) T does not require quantification over intensional entities­i.e., meanings, propositions, properties, relations, or the like­in its treatment of opaque contexts; (D3) T captures the entailment relations that hold in virtue of form between sentences in the language for which it is a theory; (D4) T has a finite number of axioms. If the approach outlined here is correct, it resolves a longstanding complex of problems in metaphysics, the philosophy of mind and the philosophy of language. (shrink)

This paper defends two claims about the criterion of commitment of W.V.O Quine. The first claim is that the criterion can be made extensional. The second is that a proper formulation becomes an analytic truth. We spend a few preliminary sections clarifying our intended notion of ontological commitment. We will not go very far in our investigation of the criterion if we do not distinguish the things a theory postulates, what its adherents, or anybody else, believe in, and which (...) of these entities we have compelling reasons to accept. A look at [Quine 1953] shows that the criterion concerned the postulation of entities by theories, but it is often misread as an attempt to say something about either or. The core of the paper is an exposition of two formulations of the criterion. I first state a schema improving on that of [Scheffler and Chomsky 1959]. The second formulation is a single principle and construes commitment as a relation between theories and predicates: ontological commitment to the entities that satisfy a given predicate. Both criteria are extensional and are formulated for constructional systems, in the sense of [Carnap 1928] and [Goodman 1951], rather than for theories construed as interpreted sets of sentences. This solves a problem raised by [Halvorson 2019]. Their analyticity is substantiated by showing that their most controversial consequences are instances of Tarski’s Convention. (shrink)

The problem with model-theoretic modal semantics is that it provides only the formal beginnings of an account of the semantics of modal languages. In the case of non-modal language, we bridge the gap between semantics and mere model theory, by claiming that a sentence is true just in case it is true in an intended model. Truth in a model is given by the model theory, and an intended model is a model which has as domain the actual objects of (...) discourse, and which relates these objects in an appropriate manner. However, the same strategy applied to the modal case seems to require an intended modal model whose domain includes mere possibilia. Building on recent work by Christopher Menzel (Synthese 85 (1990)), I give an account of model-theoretic semantics for modal languages which does not require mere possibilia or intensional entities of any kind. Menzel has offered a representational account of model-theoretic modal semantics that accords with actualist scruples, since it does not require possibilia. However, Menzel's view is in the company of other actualists who seek to eliminate possible worlds, but whose accounts tolerate other sorts of abstract, intensional entities, such as possible states of affairs. Menzel's account crucially depends on the existence of properties and relations in intension. I offer a purely extensional, representational account and prove that it does all the work that Menzel's account does. The result of this endeavor is an account of model theoretic semantics for modal languages requiring nothing but pure sets and the actual objects of discourse. Since ontologically beyond what is prima facie presupposed by the model theory itself. Thus, the result is truly an ontology-free model-theoretic semantics for modal languages. That is to say, getting genuine modal semantics out of the model theory is ontologically cost-free. Since my extensional account is demonstrably no less adequate, and yet is at the same time more ontologically frugal, it is certainly to be preferred. (shrink)

Trust is a central dimension in the relation between human beings and technologies. In many discourses about technology, the relation between human beings and technologies is conceptualized as an external relation: a relation between pre-given entities that can have an impact on each other but that do not mutually constitute each other. From this perspective, relations of trust can vary between _reliance_, as is present for instance in technological extensionism, and _suspicion_, as in various precautionary approaches in ethics that (...) focus on technological risks. Against these two interpretations of trust, this article develops a third one. Based on a more internal account of the relations between human beings and technologies, it becomes possible to see that every technological development puts at stake what it means to be a human being. Using technologies, then, implies trusting ourselves _to_ technologies. We argue that this does not imply an uncritical subjection to technology. Rather, recognizing that technologies help to constitute human subjectivity implies that human beings can get actively involved in processes of technological mediation. Trust then has the character of _confidence_: deliberately trusting oneself _to_ technology. (shrink)

Noneism a is form of Meinongianism, proposed by Richard Routley and developed and improved by Graham Priest in his widely discussed book Towards Non-Being. Priest's noneism is based upon the double move of building a worlds semantics including impossible worlds, besides possible ones, and admitting a new comprehension principle for objects, differerent from the ones proposed in other kinds of neo-Meinongian theories, such as Parsons' and Zalta's. The new principle has no restrictions on the sets of properties that can deliver (...) objects, but parameterizes the having of properties by objects to worlds. Modality is therefore explicitly built in - so the approach can be conveniently labeled as "modal noneism". In this paper, I put modal noneism to work by testing it against classical issues in modal logic and semantics. It turns out that - perhaps surprisingly - the theory performs well in problems of transworld identity, which are frequently considered to be the difficult ones in the literature; faces a limitation, albeit not a severe one, when one comes to transworld individuation, which is often taken as an easy issue, if not a pseudo-problem; and may stumble upon a real trouble when dealing with what I shall call 'extensionally indiscernible entities' - particular nonexistent objects modal noneism is committed to. (shrink)

It is a widely held view in philosophy that propositions perform a plethora of different theoretical roles. Amongst other things, they are believed to be the semantic values of sentences in contexts, the objects of attitudes, the contents of illocutionary acts, and the referents of that-clauses. This assumption is often combined with the claim that propositions have their truth-values eternally. In this paper I aim to show that these two assumptions are incompatible: propositions cannot both fulfill the mentioned roles and (...) be eternally true or false. Following Kaplan and Lewis’s Operator Argument, I argue that compositional semantic values of sentences in contexts do not correspond to eternal propositions. Thus, either we regard the non-eternal entities that in fact realize the semantic role of propositions as also fulfilling the remaining propositional roles, or we abandon the assumption that there is a unique realizer of all the roles. The Operator Argument has recently come under attack, mainly for its tense-logical assumptions. However, rejecting these assumptions is not a sufficient defense of the compatibility of the two claims, since the extensional alternative to the tense-logical framework does not allow us to universally retain eternal propositions as compositional semantic values of sentences either. (shrink)

There are three families of solutions to the traditional Amputation Paradox: Eliminativism, Contingent Identity Theories, and Theories of Coincident Entities. Theories of Coincident Entities challenge our common understanding of the relation between identity and parthood, since they accept that two things can be mereologically coincident without being identical. The contemporary discussion of the Amputation Paradox tends to mention only one theory of Coincident Entities, namely the Constitution View, which violates the mereological principle of Extensionality. But in fact, (...) there is another theory, namely the Unique Part View, which violates another mereological principle. In this paper, I argue that the contemporary focus on the Constitution View is unmotivated, at least when we are confronted with the Amputation Paradox, and that a balanced comparison of the two views should favour the Unique Part View. (shrink)

It is plausible that the universe exists: a thing such that absolutely everything is a part of it. It is also plausible that singular, structured propositions exist: propositions that literally have individuals as parts. Furthermore, it is plausible that for each thing, there is a singular, structured proposition that has it as a part. Finally, it is plausible that parthood is a partial ordering: reflexive, transitive, and anti-symmetric. These plausible claims cannot all be correct. We canvass some costs of denying (...) each claim and conclude that parthood is not a partial ordering. Provided that the relevant entities exist, parthood is not anti-symmetric and proper parthood is neither asymmetric nor transitive. (shrink)

In this essay I offer a theory of the outward directedness of intentional states, namely, an account of what makes intentional states directed at their respective intentional objects. The theory is meant to be complementary to the canonical interactivist account of mental content in that the latter emphasizes the predicative, intensional, and internal aspects of representation whereas here I shall focus on its denotative, extensional, and external aspects. Thus, the aim is to establish that the two projects are not (...) only consistent but mutually supportive. Further, it is hoped that supplementing the interactivist conception of representation with a theory of intentional directedness along such lines will increase its overall appeal to critical readers. Based on the core idea that the directedness of a representation is a function of the manner in which it is constructed within, and contributes to the ongoing unfolding of a dynamical interactive loop connecting information to focused action, the theory is subsequently extended to cover many problem domains familiarly associated with representation and reference. (shrink)

The standard definition of atomicity—the thesis that everything is ultimately composed of entities that lack proper parts—is satisfied by a model that is not atomistic. The standard definition is therefore an incorrect characterization of atomicity. I show that the model satisfies the axioms of all but the strongest mereology and therefore that the standard definition of atomicity is only adequate given some controversial metaphysical assumptions. I end by proposing a new definition of atomicity that does not require extensionality or (...) unrestricted summation. (shrink)

Classical mereology is a particularly strong theory about the part–whole relation. Not only does it ensure that any collection of entities composes a whole, or ‘fusion’, it also states that this object is unique: no two entities have the same parts. Recently, Claudio Calosi (dialectica 68(1):121–139, 2014) has argued that this extensional aspect makes classical mereology incompatible with multilocated entities. Calosi’s argument is arguably the most precise one from a whole battery of arguments to the effect (...) that some mereological principle is at odds with multilocation. Still, I show that Calosi’s arguments fail and that classical mereology is a safe space for multilocation. Moreover, I argue that the question of extensionality is orthogonal to the question of multilocation. (shrink)

This thesis promotes a therapeutic revision of fundamental assumptions in contemporary ontological thought. I show that none of the extant standard theories of objects provides a viable account of the numerical, qualitative, and trans-temporal identity of objects, and that this is due to certain substance-ontological premises. I argue that in order to state the identity conditions of objects we must abandon these premises, together with the idea that objects enjoy ontological primacy. ;I follow a methodological program of formally criticizing an (...) ontological framework by demonstrating that each of the theories developed within this framework is incoherent, i.e., either inconsistent or subject to vicious regress. I proceed in three steps. First, I show that the substance-ontological paradigm cannot be characterized in terms of its basic entities, since there is no extensional, intensional, or functional definition of the notion of substance common to all extant substance ontologies; consequently, I propose to describe the substance-ontological paradigm in terms of its basic assumptions. ;Second, I analyze the contemporary discussion of the problem of individuality, the problem of universals, and the problem of persistence, and uncover 22 characteristic implicit assumptions of substance ontology. I show on the basis of representative examples that, due to their commitment to substance-ontological presuppositions, all extant types of solutions to the three mentioned problems are incoherent. In particular, I take issue with the bare particular view, the qualified particular view, and the bundle view of individuality; different varieties of platonist and nominalist theories of universals and of relational and functional theories of predication; and the endurance and perdurance approaches to persistence. ;Third, while historical process-ontological schemes have dropped some of the revealed substance-ontological presuppositions, I finally explore the result of rejecting all of them and sketch a scheme based on dynamic masses which promises to yield coherent explanations of the ontological features of those complex processes which we commonly consider to be objects. (shrink)

Despite its central role in our cognitive lives, rational belief revision has received relatively little attention from epistemologists. This dissertation begins to fill that absence. In particular, we explore the phenomenon of defeasible epistemic justification, i.e., justification that can be lost as well as gained by epistemic agents. We begin by considering extant theories of defeat, according to which defeaters are whatever cause a loss of justification or things that somehow neutralize one's reasons for belief. Both of these theories are (...) both extensionally and explanatorily inadequate and, so, are rejected. We proceed to develop a novel theory of defeat according to which defeaters are reasons against belief. According to this theory, the dynamics of justification are explained by the competition between reasons for and reasons against belief. We find that this theory not only handles the counter-examples that felled the previous theories but also does a fair job in explaining the various aspects of the phenomenon of defeat. Furthermore, this theory accomplishes this without positing any novel entities or mechanisms; according to this theory, defeaters are epistemic reasons against belief, the mirror image of our epistemic reasons for belief, rather than sui generis entities. (shrink)

We prove how to validly quantify into hyperpropositional contexts de dicto in Transparent Intensional Logic. Hyperpropositions are sentential meanings and attitude complements individuated more finely than up to logical equivalence. A hyperpropositional context de dicto is a context in which only co-hyperintensional propositions can be validly substituted. A de dicto attitude ascription is one that preserves the attributee’s perspective when one complement is substituted for another. Being an extensional logic of hyperintensions, Transparent Intensional Logic validates all the rules of (...) extensional logic, including existential quantification. Yet the rules become more exacting when applied to hyperintensional contexts. The rules apply to only some types of entities, because the existence of only some types of entities is entailed by a hyperpropositional attitude de dicto. The insight that the paper offers is how a particular logic of hyperintensions is capable of validating quantifying-in in a principled and rigorous manner. This result advances the community-wide understanding of how to logically manipulate hyperintensions. (shrink)

Some tools introduced by Linnebo to show that mathematical entities are thin objects can also be applied to non-mathematical entities, which have been thought to be thin as well for a variety of reasons. In this paper, I discuss some difficulties and opportunities concerning the application of abstraction and interpretational modalities to mereological sums. In particular, I show that on one hand some prima facie attractive candidates for the role of an explanatory plural abstraction principle for mereological sums (...) (in terms of pluralities of summed entities) are not really explanatory; on the other hand, singular abstraction principles (in terms of single summed entities) are materially inadequate. Nonetheless, explanatory criteria of identity and conditions of existence for mereological sums are provided by classical extensional mereology independent of abstraction principles. Thus, given classical extensional mereology, the reasons why, according to Linnebo, mathematical abstracted entities are thin also hold for mereological sums. Finally, I contend that interpretational modalities can be used to characterise the process by which a subject adds sums of previously admitted entities to the domain of quantification. (shrink)

In his recent article, ``Self-Consciousness'’, George Bealer has set outa novel and interesting argument against functionalism in the philosophyof mind. I shall attempt to show, however, that Bealer's argument cannotbe sustained.In arguing for this conclusion, I shall be defending three main theses.The first is connected with the problem of defining theoreticalpredicates that occur in theories where the following two features arepresent: first, the theoretical predicate in question occurswithin both extensional and non-extensional contexts; secondly, thetheory in question asserts that (...) the relevant theoretical states enterinto causal relations. What I shall argue is that a Ramsey-styleapproach to the definition of such theoretical terms requires twodistinct quantifiers: one which ranges over concepts, and theother which ranges over properties in the world.My second thesis is a corollary: since the theories on whichBealer is focusing have both of the features just mentioned, and sincethe method that he employs to define theoretical terms in his argumentagainst functionalism does not involve both quantifiers that range overproperties and quantifiers that range over concepts, that method isunsound.My final thesis is that when a sound method is used, Bealer's argumentagainst functionalism no longer goes through.The structure of my discussion is as follows. I begin by setting out twoarguments – the one, a condensed version of Bealer's argument, andthe other, an argument that parallels Bealer's argument very closely.The parallel argument leads to a conclusion, however, that, rather thanbeing merely somewhat surprising, seems very implausible indeed. Forwhat the second argument establishes, if sound, is that there can betheoretical terms that apply to objects by virtue of their first-orderphysical properties, but whose meaning cannot be defined via aRamsey-style approach.Having set out the two parallel arguments, I then go on to focus uponthe second, to determine what is wrong with it. My diagnosis will bethat the problem with the argument arises from the fact that it involvesdefining a theoretical term that occurs both inside and outside ofopaque contexts, for the method employed fails to take into account thefact that the types of entities that are involved in the relevanttruthmakers are different when a sentence occurs within an extensionalcontext from those involved when a sentence occurs within anon-extensional context.I then go on to discuss how one should define a theoretical term thatoccurs within such theories, and I argue that in such a case one needstwo quantifiers, ranging over different types of entities – on theone hand, over properties and relations, and the other, over concepts. Ithen show that, when such an approach is followed, the argument inquestion collapses.I then turn to Bealer's argument against functionalism, and I show,first, that precisely the same method of defining theoretical terms canbe applied there, and, secondly, that, when this is done, it turns outthat that argument is also unsound.Next, I consider two responses that Bealer might make to my argument,and I argue that those responses would not succeed.Finally, I conclude by asking exactly where the problem lies in the caseof Bealer's argument. My answer will be that it is not simply the factthat one is dealing with a theoretical term that occurs in bothextensional and non-extensional contexts. It is rather the combinationof that feature together with the fact that the theory in questionasserts that the relevant type of theoretical state enters into causalrelations. For the first of these features means that the Ramseysentence for the theory must involve quantification over concepts, whilethe presence of the second feature means that the Ramsey sentence mustinvolve quantification over properties in the world, and so no attemptto offer a Ramsey-style account of the meaning of the relevanttheoretical term can succeed unless one employs both quantification overconcepts and quantification over properties. Bealer, however, in hisargument against functionalism, uses a method of defining theoreticalterms that does not involve both types of quantification, and it isprecisely because of this that his argument does not in the end succeed. (shrink)