A report of a person's desire can be true even if its embedded clause underspecifies the content of the desire that makes the report true. It is true that Fiona wants to catch a fish even if she has no desire that is satisfied if she catches a poisoned minnow. Her desire is satisfied only if she catches an edible, meal-sized fish. The content of her desire is more specific than the propositional content of the embedded clause in our true (...) report of her desires. Standard semantic accounts of belief reports require, however, that the embedded clause of a true belief report specify precisely the content of the belief that makes it true. Such accounts of belief reports therefore face what I call "the problem of underspecification" if they are extended to desire reports. Such standard accounts are sometimes refined by requiring that a belief report can be true not only if its subject has a belief with precisely the propositional content specified by its embedded clause, but also only if its subject grasps that content in a particular way. Such refinements do not, however, help to address the problem of underspecification for desire reports. (shrink)

One reason to think that names have a predicate-type semantic value is that they naturally occur in count-noun positions: ‘The Michaels in my building both lost their keys’; ‘I know one incredibly sharp Cecil and one that's incredibly dull’. Predicativism is the view that names uniformly occur as predicates. Predicativism flies in the face of the widely accepted view that names in argument position are referential, whether that be Millian Referentialism, direct-reference theories, or even Fregean Descriptivism. But names are predicates (...) in all of their occurrences; they are predicates that are true of their bearers. When a name appears as a bare singular in argument position, it really occupies the predicate position of what in this essay is called a denuded definite description: a definite description with an unpronounced definite article. Sloat provided good evidence for this. The definite article is sometimes pronounced with names in the singular: ‘The Ivan we all love doesn't feel well’. Sloat proposed a disjunctive generalization of when the definite article must be pronounced with a singular name. This essay shows that by slightly revising Sloat's generalization, we arrive at a simple, nondisjunctive, syntactic rule that governs the overt appearance of the definite article with singular names. But Ivan does not necessarily bear the name ‘Ivan’, so one might worry that the sentence “Ivan might not have had ‘Ivan’ as a name” would incorrectly be predicted false. This essay shows that Predicativism does not have this consequence by showing that incomplete definite descriptions in general and incomplete denuded descriptions, such as ‘Øthe Ivan’, in particular are rigid designators. (shrink)

Russell’s theory of memory as acquaintance with the past seems to square uneasily with his definition of acquaintance as the converse of the relation of presentation of an object to a subject. We show how the two views can be made to cohere under a suitable construal of ‘presentation’, which has the additional appeal of bringing Russell’s theory of memory closer to contemporary views on direct reference and object-dependent thinking than is usually acknowledged. The drawback is that memory as acquaintance (...) with the past falls short of fulfilling Russell’s requirement that knowledge by acquaintance be discriminating knowledge – a shortcoming shared by contemporary externalist accounts of knowledge from memory. (shrink)

This article examines Cohen’s “transcendental method”, Windelband’s “critical method”, the neo-Kantian distinctions between natural science and the humanities (i. e., human or cultural sciences), and Weber’s account of ideal-typical explanations. The Marburg and the Southwest Schools of neo-Kantianism have in common that their respective philosophies of science focused on method, but they substantially differ in their approaches. Cohen advanced the “transcendental method”, which was taken up and transformed by Natorp and Cassirer; later, it became influential in neo-Kantian approaches to 20th (...) century physics. Windelband distinguished between facts and values, linking the former to the “genetic” method of history and the latter to the “critical” method of philosophy; and between the “nomothetic” and “idiographic” methods of the empirical sciences, a distinction further elaborated by Rickert. The distinction does not give rise to a sharp discrimination but is rather what Weber would later call an ideal type. All these approaches contribute in different ways to understanding the structure of scientific knowledge, focusing on different aspects of the general path of the empirical sciences between rationalism and empiricism. (shrink)

There is some consensus among orthodox category theorists that the concept of adjoint functors is the most important concept contributed to mathematics by category theory. We give a heterodox treatment of adjoints using heteromorphisms that parses an adjunction into two separate parts. Then these separate parts can be recombined in a new way to define a cognate concept, the brain functor, to abstractly model the functions of perception and action of a brain. The treatment uses relatively simple category theory and (...) is focused on the interpretation and application of the mathematical concepts. (shrink)

Soames (Philos Top 15:44–87, 1987 , J Philos Logic 37:267–276, 2008 ) has argued that propositions cannot be sets of truth-supporting circumstances. This argument is criticized for assuming that various singular terms are directly referential when in fact there are good grounds to doubt this.

The problem, or cluster of problems, of the unity of the proposition, along with the cluster of problems that tend to go under the name of Bradley’s regress, has recently again become a going concern for philosophers, after having for some time been regarded as primarily of historical interest. In this paper, I distinguish between the different problems that tend to be brought up under the heading of the unity of the proposition, and between different related regress arguments. I present (...) my favored solutions to these problems. (shrink)

One of the many ways that ‘deflationary’ and ‘inflationary’ theories of truth are said to differ is in their attitude towards truth qua property. This difference used to be very easy to delineate, with deflationists denying, and inflationists asserting, that truth is a property, but more recently the debate has become a lot more complicated, owing primarily to the fact that many contemporary deflationists often do allow for truth to be considered a property. Anxious to avoid inflation, however, these deflationists (...) are at pains to point out that the truth property, on their view, is not a property of any significant interest. Correspondingly, inflationists have seen this as an opportunity to refine what kind of property they think truth is, which—according to them—moves their views beyond deflationism. The upshot of this is that there are number of different accounts in the literature of what distinguishes an inflationary truth property from a deflationary one, or—as it is sometimes put—what distinguishes a ‘substantive’ property from an ‘insubstantive’ one. This has made it hard to pin down exactly what is at issue at the metaphysical level between deflationists and inflationists, which makes it increasingly hard to see how debates between them are properly phrased. Given that these positions represent the two central attitudes towards truth in contemporary debates, this makes for a serious obstacle for the project of discerning the correct theory of truth. The aim of this paper is to discern the best way to distinguish between substantive and insubstantive properties, and thus to restore some focus to these debates. I argue that the three central distinctions in the literature fail, and offer what I take to be a more promising distinction in terms of a graded distinction between abundant and sparse properties. (shrink)

This paper deals with two issues. First, it identifies structured propositions with logical procedures. Second, it considers various rigorous definitions of the granularity of procedures, hence also of structured propositions, and comes out in favour of one of them. As for the first point, structured propositions are explicated as algorithmically structured procedures. I show that these procedures are structured wholes that are assigned to expressions as their meanings, and their constituents are sub-procedures occurring in executed mode. Moreover, procedures are not (...) mere aggregates of their parts; rather, procedural constituents mutually interact. As for the second point, there is no universal criterion of the structural isomorphism of meanings, hence of co-hyperintensionality, hence of synonymy for every kind of language. The positive result I present is an ordered set of rigorously defined criteria of fine-grained individuation in terms of the structure of procedures. Hence procedural semantics provides a solution to the problem of the granularity of co-hyperintensionality. (shrink)

Frege held that logical objects are objective but not wirklich, and that psychologism follows from the mistake of believing whatever is not wirklich to be subjective. It has been suggested that Frege's use of the terms ?objective? and ?wirklich? is in line with that found in Lotze's Logic; from this it has been inferred that Frege's doctrines have been misinterpreted as being ontological in character, but that they really belong to epistemology. In fact, Lotze held that something may be the (...) same for all thinkers, and yet may exist only in thought, not independently of it. For Frege, by contrast, there is nothing intermediate between the content of a single consciousness and what exists independently of being thought at all. This crucial disagreement underlies the divergence between Frege's realism and Lotze's idealism. (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)

Non-symmetric relations like loves or between can apply to the same relata in non-equivalent ways. For example, loves may apply to Abelard and Eloise either by Abelard’s loving Eloise or by Eloise’s loving Abelard. On the standard account of relations, different applications of a relation to fixed relata are distinguished by the direction in which the relation applies to the relata. But neither Directionalism nor its most popular rival, Positionalism, offer accounts of differential application that generalize to relations of arbitrary (...) symmetry structure. Here, I develop an alternative account, Relative Positionalism, which distinguishes different applications of a relation to fixed relata in terms of the ways in which the relata are characterized relative to one another. In presenting and defending Relative Positionalism, this paper covers some of the same ground as my [2016], but avoids the latter’s algebraic approach and focuses on interpretative issues—in particular, how to make sense of relative property instantiation—that were not addressed in the earlier paper. (shrink)

Maureen Donnelly’s (2016) relative positionalism correctly handles any fixed arity relation with any symmetry such a relation can have, yielding the intuitively correct way(s) in which that relation can apply. And it supplies an explanation of what is going on in the world that makes this the case. But it has at least one potential shortcoming — one that its opponents are likely to seize upon: it can only handle relations with fixed arities. It is unable to handle relations with (...) variable arities. I argue that, all else being equal, relative positionalism ought nonetheless to be preferred to its closest competitors — at least to the extent that the explanation it supplies of relational application is plausible — even though those competitors can handle variable arity relations in addition to fixed arity relations. (shrink)

What is the relation between metaphysical necessity and essence? This paper defends the view that the relation is one of identity: metaphysical necessity is a special case of essence. My argument consists in showing that the best joint theory of essence and metaphysical necessity is one in which metaphysical necessity is just a special case of essence. The argument is made against the backdrop of a novel, higher-order logic of essence, whose core features are introduced in the first part of (...) the paper. The second part investigates the relation between metaphysical necessity and essence in the context of HLE. Reductive hypotheses are among the most natural hypotheses to be explored in the context of HLE. But they also have to be weighed against their non-reductive rivals. I investigate three different reductive hypotheses and argue that two of them fare better than their non-reductive rivals: they are simpler, more natural, and more systematic. Specifically, I argue that one candidate reduction, according to which metaphysical necessity is truth in virtue of the nature of all propositions, is superior to the others, including one proposed by Kit Fine, according to which metaphysical necessity is truth in virtue of the nature of all objects. The paper concludes by offering some reasons to think that the best joint theory of essence and metaphysical necessity is one in which the logic of metaphysical necessity includes S4, but not S5. (shrink)

Poincaré was a persistent critic of logicism. Unlike most critics of logicism, however, he did not focus his attention on the basic laws of the logicists or the question of their genuinely logical status. Instead, he directed his remarks against the place accorded to logical inference in the logicist's conception of mathematical proof. Following Leibniz, traditional logicist dogma (and this is explicit in Frege) has held that reasoning or inference is everywhere the same — that there are no principles of (...) inference specific to a given local topic. Poincaré, a Kantian, disagreed with this. Indeed, he believed that the use of non-logical reasoning was essential to genuinely mathematical reasoning (proof). In this essay, I try to isolate and clarify this idea and to describe the mathematical epistemology which underlies it. Central to this epistemology (which is basically Kantian in orientation, and closely similar to that advocated by Brouwer) is a principle of epistemic conservation which says that knowledge of a given type cannot be extended by means of an inference unless that inference itself constitutes knowledge belonging to the given type. (shrink)

A feature of Frege's philosophy of arithmetic that has elicited a great deal of attention in the recent secondary literature is his contention that numbers are ‘self‐subsistent’ objects. The considerable interest in this thesis among the contemporary philosophy of mathematics community stands in marked contrast to Kreisel's folk‐lore observation that the central problem in the philosophy of mathematics is not the existence of mathematical objects, but the objectivity of mathematics. Although Frege was undoubtedly concerned with both questions, a goal of (...) the present paper is to argue that his success in securing the objectivity of arithmetic depends on a less contentious commitment to numbers as objects than either he or his critics have supposed. As such, this paper is an articulation and defense of both Frege's analysis of arithmetic and Kreisel's observation. (shrink)

What is logical relevance? Anderson and Belnap say that the “modern classical tradition [,] stemming from Frege and Whitehead-Russell, gave no consideration whatsoever to the classical notion of relevance.” But just what is this classical notion? I argue that the relevance tradition is implicitly most deeply concerned with the containment of truth-grounds, less deeply with the containment of classes, and least of all with variable sharing in the Anderson–Belnap manner. Thus modern classical logicians such as Peirce, Frege, Russell, Wittgenstein, and (...) Quine are implicit relevantists on the deepest level. In showing this, I reunite two fields of logic which, strangely from the traditional point of view, have become basically separated from each other: relevance logic and diagram logic. I argue that there are two main concepts of relevance, intensional and extensional. The first is that of the relevantists, who overlook the presence of the second in modern classical logic. The second is the concept of truth-ground containment as following from in Wittgenstein’s Tractatus. I show that this second concept belongs to the diagram tradition of showing that the premisses contain the conclusion by the fact that the conclusion is diagrammed in the very act of diagramming the premisses. I argue that the extensional concept is primary, with at least five usable modern classical filters or constraints and indefinitely many secondary intensional filters or constraints. For the extensional concept is the genus of deductive relevance, and the filters define species. Also following the Tractatus, deductive relevance, or full truth-ground containment, is the limit of inductive relevance, or partial truth-ground containment. Purely extensional inductive or partial relevance has its filters or species too. Thus extensional relevance is more properly a universal concept of relevance or summum genus with modern classical deductive logic, relevantist deductive logic, and inductive logic as its three main domains. (shrink)

We discuss the concept of a cardinal number and its history, focussing on Cantor's work and its reception. J'ay fait icy peu pres comme Euclide, qui ne pouvant pas bien >faire< entendre absolument ce que c'est que raison prise dans le sens des Geometres, definit bien ce que c'est que memes raisons. (Leibniz) 1.

The paper offers a survey of four key moments in which symbolisms for quantification were first introduced: §§11–2 of Frege’s Begriffsschrift ; Peirce’s ‘Algebra of Logic’ ; Peano’s ‘St...

The article concerns the treatment of the so-called denoting phrases, of the forms ?every A?, ?any A?, ?an A? and ?some A?, in Russell's Principles of Mathematics. An initially attractive interpretation of what Russell's theory was has been proposed by P.T. Geach, in his Reference and Generality (1962). A different interpretation has been proposed by P. Dau (Notre Dame Journal, 1986). The article argues that neither of these is correct, because both credit Russell with a more thought-out theory than he (...) actually had. The conclusion is mainly negative: at this date Russell has no coherent theory of these phrases. An appendix notes that his understanding of the quantifiers in predicate logic is also, at this date, not entirely secure. (shrink)

According to act theories, propositions are structured cognitive act‐types. Act theories appear to make propositions inherently representational and truth‐evaluable, and to provide solutions to familiar problems with alternative theories, including Frege’s and Russell’s problems, and the third‐realm and unity problems. Act theories have critical problems of their own, though: acts as opposed to their objects are not truth evaluable, not structured in the right way, not expressed by sentences, and not the objects of propositional attitudes. I show how identifying propositions (...) with other cognitive event‐types, namely thoughts, has the perceived virtues of act theories without the defects. (shrink)

The relativistic revolution led to varieties of neo-Kantianism in which constitutive principles define the object of scientific knowledge in a domain-dependent and historically mutable manner. These principles are a priori insofar as they are necessary premises for the formulation of empirical laws in a given domain, but they lack the self-evidence of Kant’s a priori and they cannot be identified without prior knowledge of the theory they purport to frame. In contrast, the rationalist endeavors of a few masters of theoretical (...) physics have led to comprehensibility conditions that are easily admitted in a given domain and yet suffice to generate the theory of this domain. The purpose of this essay is to compare these two kinds of relativized a priori, to discuss the nature of the comprehensibility conditions, and to demonstrate their effectiveness in a modular conception of physical theories. (shrink)

Causal slingshots are formal arguments advanced by proponents of an event ontology of token-level causation which, in the end, are intended to show two things: (i) The logical form of statements expressing causal dependencies on token level features a binary predicate ‘‘... causes ...’’ and (ii) that predicate takes events as arguments. Even though formalisms are only revealing with respect to the logical form of natural language statements, if the latter are shown to be adequately captured within a corresponding formalism, (...) proponents of slingshots usually take the adequacy of their formalizations for granted without justifying it. The first part of this paper argues that the most discussed version of a causal slingshot, viz. the one e.g. presented by Davidson (Essays on actions and events. Oxford, Clarendon Press, 1980), can indeed be refuted for relying on an inadequate formal apparatus. In contrast, the formal means of Gödel’s (The philosophy of Betrand Russell. New York, Tudor, 1944) often neglected slingshot are shown to stand on solid ground in the second part of the paper. Nonetheless, I contend that Gödel’s slingshot does only half the work friends of event causation would like it to do. It provides good reasons for (i) but not for (ii). (shrink)

It is widely held that there is a problem of talking about or otherwise representing things that not exist. But what exactly is this problem? This paper presents a formulation of the problem in terms of the conflict between the fact that there are truths about non-existent things and the fact that truths must be answerable to reality, how things are. Given this, the problem of singular negative existential statements is no longer the central or most difficult aspect of the (...) problem of non-existence, despite what some philosophers say. (shrink)

This paper discusses the history of the confusion and controversies over whether the definition of consequence presented in the 11-page 1936 Tarski consequence-definition paper is based on a monistic fixed-universe framework?like Begriffsschrift and Principia Mathematica. Monistic fixed-universe frameworks, common in pre-WWII logic, keep the range of the individual variables fixed as the class of all individuals. The contrary alternative is that the definition is predicated on a pluralistic multiple-universe framework?like the 1931 Gödel incompleteness paper. A pluralistic multiple-universe framework recognizes multiple (...) universes of discourse serving as different ranges of the individual variables in different interpretations?as in post-WWII model theory. In the early 1960s, many logicians?mistakenly, as we show?held the ?contrary alternative? that Tarski 1936 had already adopted a Gödel-type, pluralistic, multiple-universe framework. We explain that Tarski had not yet shifted out of the monistic, Frege?Russell, fixed-universe paradigm. We further argue that between his Principia-influenced pre-WWII Warsaw period and his model-theoretic post-WWII Berkeley period, Tarski's philosophy underwent many other radical changes. (shrink)

Prior Analytics by the Greek philosopher Aristotle (384 – 322 BCE) and Laws of Thought by the English mathematician George Boole (1815 – 1864) are the two most important surviving original logical works from before the advent of modern logic. This article has a single goal: to compare Aristotle’s system with the system that Boole constructed over twenty-two centuries later intending to extend and perfect what Aristotle had started. This comparison merits an article itself. Accordingly, this article does not discuss (...) many other historically and philosophically important aspects of Boole’s book, e.g. his confused attempt to apply differential calculus to logic, his misguided effort to make his system of ‘class logic’ serve as a kind of ‘truth-functional logic’, his now almost forgotten foray into probability theory, or his blindness to the fact that a truth-functional combination of equations that follows from a given truth-functional combination of equations need not follow truth-functionally. One of the main conclusions is that Boole’s contribution widened logic and changed its nature to such an extent that he fully deserves to share with Aristotle the status of being a founding figure in logic. By setting forth in clear and systematic fashion the basic methods for establishing validity and for establishing invalidity, Aristotle became the founder of logic as formal epistemology. By making the first unmistakable steps toward opening logic to the study of ‘laws of thought’—tautologies and laws such as excluded middle and non-contradiction—Boole became the founder of logic as formal ontology. (shrink)

Prior Analytics by the Greek philosopher Aristotle and Laws of Thought by the English mathematician George Boole are the two most important surviving original logical works from before the advent of modern logic. This article has a single goal: to compare Aristotle's system with the system that Boole constructed over twenty-two centuries later intending to extend and perfect what Aristotle had started. This comparison merits an article itself. Accordingly, this article does not discuss many other historically and philosophically important aspects (...) of Boole's book, e.g. his confused attempt to apply differential calculus to logic, his misguided effort to make his system of ‘class logic’ serve as a kind of ‘truth-functional logic’, his now almost forgotten foray into probability theory, or his blindness to the fact that a truth-functional combination of equations that follows from a given truth-functional combination of equations need not follow truth-functionally. One of the main conclusions is that Boole's contribution widened logic and changed its nature to such an extent that he fully deserves to share with Aristotle the status of being a founding figure in logic. By setting forth in clear and systematic fashion the basic methods for establishing validity and for establishing invalidity, Aristotle became the founder of logic as formal epistemology. By making the first unmistakable steps toward opening logic to the study of ‘laws of thought’—tautologies and laws such as excluded middle and non-contradiction—Boole became the founder of logic as formal ontology.… using mathematical methods … has led to more knowledge about logic in one century than had been obtained from the death of Aristotle up to … when Boole's masterpiece was published.Paul Rosenbloom 1950. (shrink)

What is the Bare Particular Theory? Is it committed, like the Bundle Theory, to a constituent ontology: according to which a substance’s qualities—and according to the Bare Particular Theory, its substratum also—are proper parts of the substance? I argue that Bare Particularists need not, should not, and—if a recent objection to ‘the Bare Particular Theory’ succeeds—cannot endorse a constituent ontology. There is nothing, I show, in the motivations for Bare Particularism or the principles that distinguish Bare Particularism from rival views (...) that entails a constituent ontology. I outline a version of Bare Particularism that in rejecting a constituent ontology avoids the New Objection. I argue against Theodore Sider that this really is a distinct theory to the version of Bare Particularism that endorses a constituent ontology, and not a mere terminological variant. I show that this, the best version of the Bare Particular Theory, is also defensible against the old objections. (shrink)

In this article, I pay special expository attention to two pieces of philosophically relevant Wittgenstein–Russell correspondence from the period leading up to the ultimate demise of Russell's Theory of Knowledge manuscript (in June 1913). This is done in the hopes of shedding light on Wittgenstein's notoriously obscure criticisms of Russell's multiple relation theory of judgement. I argue that these two pieces of correspondence (the first, a letter from Wittgenstein to Russell dated January 1913, and the second, a letter from Russell (...) to Ottoline Morrell, reporting a tense confrontation with Wittgenstein on 26 May 1913) each refer to what is more or less the same approach to problems concerning the unity and well-formedness of propositions or judgements. However, the view advanced in Wittgenstein's January letter to Russell nevertheless differs in a key respect from the view of Russell's referred to in the May letter to Morrell. The difference involves Wittgenstein's incorporating qualities and relations as unsaturated parts of the copulae of atomic complexes, where these copulae are in turn conceived as logical forms. Because such an approach to logical form (and more specifically, to relations) was philosophically unpalatable to Russell, he undertook an alternative theoretical correction in the context of his 1913 Theory of Knowledge manuscript. This theoretical correction was discussed with Wittgenstein during the tense confrontation on 26 May, and involved deploying a supplemental significance constraint on judgements. It was this significance constraint on judgements, moreover, which was the ‘premiss’ alluded to by Wittgenstein in the context of a June 1913 letter to Russell, wherein he claims to express his objection to Russell's theory ‘exactly.’. (shrink)

In his “Space, supervenience and substantivalism”, Le Poidevin proposes a substantivalism in which space is discrete, implying that there are unmediated spatial relations between neighboring primitive points. This proposition is motivated by his concern that relationism suffers from an explanatory lacuna and that substantivalism gives rise to a vicious regress. Le Poidevin implicitly requires that the relationist be committed to the “only x and y ” principle regarding spatial relations. It is not obvious that the relationist is committed to this (...) principle in such a context. An additional motivation for Le Poidevin's argument, that space should be considered to be discrete, is that he believes that substantivalists are committed to a vicious regress. I show that the regress is in fact not of the vicious variety. These two main arguments show that Le Poidevin's suggestion that we drop the density postulate for space is unnecessary. (shrink)

Two topics figure prominently in recent discussions of mathematical structuralism: challenges to the purported metaphysical insight provided by sui generis structuralism and the significance of category theory for understanding and articulating mathematical structuralism. This article presents an overview of central themes related to these topics.

We characterize abstraction in computer science by first comparing the fundamental nature of computer science with that of its cousin mathematics. We consider their primary products, use of formalism, and abstraction objectives, and find that the two disciplines are sharply distinguished. Mathematics, being primarily concerned with developing inference structures, has information neglect as its abstraction objective. Computer science, being primarily concerned with developing interaction patterns, has information hiding as its abstraction objective. We show that abstraction through information hiding is a (...) primary factor in computer science progress and success through an examination of the ubiquitous role of information hiding in programming languages, operating systems, network architecture, and design patterns. (shrink)

A semantic analysis of mass nouns is given in terms of a logic of classes as many. In previous work it was shown that plural reference and predication for count nouns can be interpreted within this logic of classes as many in terms of the subclasses of the classes that are the extensions of those count nouns. A brief review of that account of plurals is given here and it is then shown how the same kind of interpretation can also (...) be given for mass nouns. (shrink)

The problematic features of Quine's set theories NF and ML are a result of his replacing the higher-order predicate logic of type theory by a first-order logic of membership, and can be resolved by returning to a second-order logic of predication with nominalized predicates as abstract singular terms. We adopt a modified Fregean position called conceptual realism in which the concepts (unsaturated cognitive structures) that predicates stand for are distinguished from the extensions (or intensions) that their nominalizations denote as singular (...) terms. We argue against Quine's view that predicate quantifiers can be given a referential interpretation only if the entities predicates stand for on such an interpretation are the same as the classes (assuming extensionality) that nominalized predicates denote as singular terms. Quine's alternative of giving predicate quantifiers only a substitutional interpretation is compared with a constructive version of conceptual realism, which with a logic of nominalized predicates is compared with Quine's description of conceptualism as a ramified theory of classes. We argue against Quine's implicit assumption that conceptualism cannot account for impredicative concept-formation and compare holistic conceptual realism with Quine's class Platonism. (shrink)

Mathematical apriorists usually defend their view by contending that axioms are knowable a priori, and that the rules of inference in mathematics preserve this apriority for derived statements—so that by following the proof of a statement, we can trace the apriority being inherited. The empiricist Philip Kitcher attacked this claim by arguing there is no satisfactory theory that explains how mathematical axioms could be known a priori. I propose that in analyzing Ernest Sosa’s model of intuition as an intellectual virtue, (...) we can construct an “intuition–virtue” that could supply the missing explanation for the apriority of axioms. I first argue that this intuition–virtue qualifies as an a priori warrant according to Kitcher’s account, and then show that it could produce beliefs about mathematical axioms independent of experience. If my argument stands, this paper could provide insight on how virtue epistemology could help defend mathematical apriorism on a larger scale. (shrink)

If one examines the sky at sunset on a clear night, one seems to see a continuum of colors from reds, oranges and yellows to a deep blue-black. Between any two colored points in the sky there seem to be other colored points. Furthermore, the changes in color across the sky appear to be continuous. Although the colors at the zenith and the horizon are obviously distinct, nowhere in the sky can one see any color borders, and every sufficiently small (...) region of the sky is made up of regions that all seem to be of the same color. (shrink)

Drawing on the findings of neuroscience, this text proposes and defends the hypothesis that the various modalities of sensation share a generic form that the author, Austen Clark, calls feature-placing.

The aim of this paper is to discuss the philosophical premises of Whitehead's definition of time in _The Concept of Nature and other works of the same period. Whitehead probably introduced this definition, which depends on what he calls the "method of extensive abstraction," in 1913, just after the publication of the _Principia Mathematica with Russell. He only published his results in 1919. However, Russell takes up the method, with slight modifications, after personal communication with Whitehead, as soon as 1914, (...) in _Our Knowledge of the External World. It is also carefully studied by G. Mead, in particular in _Philosophy of the Present, and by Merleau-Ponty, in his lectures at the Collège de France. (edited). (shrink)

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.

Aim of the paper is to revise Boolos’ reinterpretation of second-order monadic logic in terms of plural quantification ([4], [5]) and expand it to full second order logic. Introducing the idealization of plural acts of choice, performed by a suitable team of agents, we will develop a notion of plural reference . Plural quantification will be then explained in terms of plural reference. As an application, we will sketch a structuralist reconstruction of second-order arithmetic based on the axiom of infinite (...) à la Dedekind, as the unique non-logical axiom. We will also sketch a virtual interpretation of the classical continuum involving no other infinite than a countable plurality of individuals. (shrink)

During the first months of 1887, while completing the drafts of his Mitteilungen zur Lehre vom Transfiniten, Georg Cantor maintained a continuous correspondence with Benno Kerry. Their exchange essentially concerned two main topics in the philosophy of mathematics, namely, (a) the concept of natural number and (b) the infinitesimals. Cantor's and Kerry's positions turned out to be irreconcilable, mostly because of Kerry's irremediably psychologistic outlook, according to Cantor at least. In this study, I will examine and reconstruct the main points (...) in the discussion around (a) and (b) and stress some interesting aspects of the philosophical and mathematical thought of Benno Kerry. (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)