We investigate a construction schema for first-order logical systems, called “form logic”. Form logic allows us to overcome the dualistic commitment of predicate logic to individual constants and predicates. Dualism is replaced by a pluralism of terms of different “logical forms”. Individual form-logical systems are generated by the determination of a range of logical forms and of the formbased syntax rules for combining terms into formulas. We develop a generic syntax and semantics for such systems and provide a completeness proof (...) for them. To illustrate the idea of form logic, and the possibilities it facilitates, we discuss three particular systems, one of which is the form-logical reconstruction of standard first-order predicate logic. (shrink)

The paradox of the concept horse has often been taken to be devastating for Frege’s ontological distinction between objects and concepts. I argue that if we consider how the concept-object distinction is supposed to account for the unity of linguistic meaning, it transpires that the paradox is in fact not paradoxical.

Evidence is drawn together to connect sources of inconsistency that Frege discerned in his foundations for arithmetic with the origins of the paradox derived by Russell in "Basic Laws" I and then with antinomies, paradoxes, contradictions, riddles associated with modal and intensional logics. Examined are: Frege's efforts to grasp logical objects; the philosophical arguments that compelled Russell to adopt a description theory of names and a eliminative theory of descriptions; the resurfacing of issues surrounding reference, descriptions, identity, substitutivity, paradox in (...) the debates concerning modal and intensional logics; the development of the New Theory of Reference. I consider this to be the philosophical ground upon which the debates regarding that theory should take place. (shrink)

In this paper I argue for a view of groups, things like teams, committees, clubs and courts. I begin by examining features all groups seem to share. I formulate a list of six features of groups that serve as criteria any adequate theory of groups must capture. Next, I examine four of the most prominent views of groups currently on offer—that groups are non-singular pluralities, fusions, aggregates and sets. I argue that each fails to capture one or more of the (...) criteria. Last, I develop a view of groups as realizations of structures. The view has two components. First, groups are entities with structure. Second, since groups are concreta, they exist only when a group structure is realized. A structure is realized when each of its functionally defined nodes or places are occupied. I show how such a view captures the six criteria for groups, which no other view of groups adequately does, while offering a substantive answer to the question, “What are groups?”. (shrink)

The main task of this paper is to understand if and how static images like photographs can represent and/or depict temporal extension (duration). In order to do this, a detour will be necessary to understand some features of the nature of photographic representation and depiction in general. This important detour will enable us to see that photographs (can) have a narrative content, and that the skilled photographer can 'tell a story' in a very clear sense, as well as control and (...) guide the attention of the spectator of the photograph. The understanding and defence of this claim is a secondary aim of this paper, and it will then allow us to provide a good treatment of the particular case of photographic representation and depiction of temporal extension. (shrink)

This paper will argue that the puzzles about instantaneous velocity, and rates of change more generally, are the result of a failure to recognize an ambiguity in the concept of an instant, and therefore of an instantaneous state. We will conclude that there are two distinct conceptions of a temporal instant: (i) instants conceived as fundamentally distinct zero-duration temporal atoms and (ii) instants conceived as the boundary of, or between,temporally extended durations. Since the concept of classical instantaneous velocity is well- (...) defined only on the second conception of instants, we will conclude that this distinction allows us to avoid the above dilemma. If instantaneous velocity is well-defined then the states of a system at various instants are not logically distinct and thus we cannot generate Zeno’s paradox. However, if we assume that the instants are metaphysically distinct, then instantaneous velocity is not well-defined and thus the second horn of the dilemma about the causal-explanatory role of instantaneous velocity cannot be generated. (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)

Let serious propositional contingentism (SPC) be the package of views which consists in (i) the thesis that propositions expressed by sentences featuring terms depend, for their existence, on the existence of the referents of those terms, (ii) serious actualism—the view that it is impossible for an object to exemplify a property and not exist—and (iii) contingentism—the view that it is at least possible that some thing might not have been something. SPC is popular and compelling. But what should we say (...) about possible worlds, if we accept SPC? Here, I first show that a natural view of possible worlds, well-represented in the literature, in conjunction with SPC is inadequate. Though I note various alternative ways of thinking about possible worlds in response to the first problem, I then outline a second more general problem—a master argument—which generally shows that any account of possible worlds meeting very minimal requirements will be inconsistent with compelling claims about mere possibilia which the serious propositional contingentist should accept. (shrink)

This dialogue explores the question of whether intentionality—the “ofness”, “aboutness”, or “directedness” of mental states—is a relation. We explore three views: the Naive View, on which intentionality is a relation to ordinary, everyday objects, facts, and other such items; the Abstract Contents View, on which intentionality is a relation to mind-independent abstract entities that are our contents; and the Aspect View, on which intentionality is a matter of having intentional states with particular (non-relational) aspects that are our contents. We consider (...) the challenges facing these views, which include empirical challenges in accounting for all the contents our intentional states can represent, metaphysical challenges in making sense of how contents can be entertained or otherwise represented by us and how they can play a psychological role in the mental economy, and challenges in making sense of how intentionality connects us to the world—if at all. Along the way, we consider the question of how consciousness is related to intentionality and how this affects one’s choice of views. (shrink)

In the language of second-order logic, first- and second-order variables are distinguished syntactically and cannot be grammatically substituted. According to a prominent argument for the deployment of these languages, these substitution failures are necessary to block the derivation of paradoxes that result from attempts to generalize over predicate interpretations. I first examine previous approaches which interpret second-order sentences using expressions of natural language and argue that these approaches undermine these syntactic restrictions. I then examine Williamson’s primitivist approach according to which (...) second-order sentences are not offered readings in a previously understood language. I argue that the syntactic restrictions alone do not block the derivation of the paradox, unless they are backed by a principled reason that the language cannot be expanded to allow the grammatical substitution of first- and second- order variables. I argue that there is neither a syntactic nor a semantic principle that prohibits such an expansion. (shrink)

W. V. Quine famously defended two theses that have fallen rather dramatically out of fashion. The first is that intensions are “creatures of darkness” that ultimately have no place in respectable philosophical circles, owing primarily to their lack of rigorous identity conditions. However, although he was thoroughly familiar with Carnap’s foundational studies in what would become known as possible world semantics, it likely wouldn’t yet have been apparent to Quine that he was fighting a losing battle against intensions, due in (...) large measure to developments stemming from Carnap’s studies and culminating in the work of Kripke, Hintikka, and Bayart. These developments undermined Quine’s crusade against intensions on two fronts. First, in the context of possible world semantics, intensions could after all be given rigorous identity conditions by defining them (in the simplest case) as functions from worlds to appropriate extensions, a fact exploited to powerful and influential effect in logic and linguistics by the likes of Kaplan, Montague, Lewis, and Cresswell. Second, the rise of possible world semantics fueled a strong resurgence of metaphysics in contemporary analytic philosophy that saw properties and propositions widely, fruitfully, and unabashedly adopted as ontological primitives in their own right. This resurgence — happily, in my view — continues into the present day. -/- For a time, at any rate, Quine experienced somewhat better success with his second thesis: that higher-order logic is, at worst, confused and, at best, a quirky notational alternative to standard first-order logic. However, Quine notwithstanding, a great deal of recent work in formal metaphysics transpires in a higher-order logical framework in which properties and propositions fall into an infinite hierarchy of types of (at least) every finite order. Initially, the most philosophically compelling reason for embracing such a framework since Russell first proposed his simple theory of types was simply that it provides a relatively natural explanation of the paradoxes. However, since the seminal work of Prior there has been a growing trend to consider higher-order logic to be the most philosophically natural framework for metaphysical inquiry, many of the contributors to this volume being among the most important and influential advocates of this view. Indeed, this is now quite arguably the dominant view among formal metaphysicians. -/- In this paper, and against the current tide, I will argue in §1 that there are still good reasons to think that Quine’s second battle is not yet lost and that the correct framework for logic is first-order and type-free — properties and propositions, logically speaking, are just individuals among others in a single domain of quantification — and that it arises naturally out of our most basic logical and semantical intuitions. The data I will draw upon are not new and are well-known to contemporary higher-order metaphysicians. However, I will try to defend my thesis in what I believe is a novel way by suggesting that these basic intuitions ground a reasonable distinction between “pure” logic and non-logical theory, and that Russell-style semantic paradoxes of truth and exemplification arise only when we move beyond the purely logical and, hence, do not of themselves provide any strong objection to a type-free conception of properties and propositions. -/- Most of my arguments in §1 are largely independent of any specific account of the nature of properties and propositions beyond their type-freedom. However, I will in addition argue that there are good reasons to take propositions, at least, to be very fine-grained. My arguments are thus bolstered significantly if it can be shown that there are in fact well-defined examples of logics that are not only type-free but which comport with such a conception of propositions. It is the purpose of §2 to lay out a logic of this sort in some detail, drawing especially upon work by George Bealer and related work of my own. With the logic in place, it will be possible to generalize the line of argument noted above regarding Russell-style paradoxes and, in §3, apply it to two propositional paradoxes — the Prior-Kaplan paradox and the Russell-Myhill paradox — that are often taken to threaten the sort of account developed here. (shrink)

In this paper a symmetry argument against quantity absolutism is amended. Rather than arguing against the fundamentality of intrinsic quantities on the basis of transformations of basic quantities, a class of symmetries defined by the Π-theorem is used. This theorem is a fundamental result of dimensional analysis and shows that all unit-invariant equations which adequately represent physical systems can be put into the form of a function of dimensionless quantities. Quantity transformations that leave those dimensionless quantities invariant are empirical and (...) dynamical symmetries. The proposed symmetries of the original argument fail to be both dynamical and empirical symmetries and are open to counterexamples. The amendment of the original argument requires consideration of the relationships between quantity dimensions. The discussion raises a pertinent issue: what is the modal status of the constants of nature which figure in the laws? Two positions, constant necessitism and constant contingentism, are introduced and their relationships to absolutism and comparativism undergo preliminary investigation. It is argued that the absolutist can only reject the amended symmetry argument by accepting constant necessitism. I argue that the truth of an epistemically open empirical hypothesis would make the acceptance of constant necessitism costly: together they entail that the facts are nomically necessary. (shrink)

Several natural languages such as English contain prima facie different kinds of referential and quantificational expressions. In particular, natural languages.

In the paper, Jan Łukasiewicz’s program of the logicization of philosophy is presented and discussed. Łukasiewicz, known mostly for his invention of trivalent logic as well as his achievements in propositional calculus and metalogic, had always been concerned with the methodological condition of philosophy. He finally found “the measure of exactness” in mathematical logic. According to him, only the use of logical tools may provide philosophical investigations with an appropriate level of exactness. He expressed his views most firmly and directly (...) in the paper, “A call for the method of Philosophy”. Łukasiewicz proposed giving philosophical theories the form of axiomatic systems by indicating the primitive terms of their language, selecting suitable axioms, and explicitly determining the applied rules of inference. All the theses of these systems should be consequences of the accepted axioms and confronted with the data of experience and the results of science. Łukasiewicz’s program is presented together with its inspirations and prospects. (shrink)

The question of ontological foundation has undergone a noteworthy revival in recent years: metaphysicians today quarrel about how exactly to understand the asymmetrical and hyperintensional relationship of grounding. One of the reasons for this revival is that the old quantificationalist meta-ontology inherited from Quine has been effectively criticised by leading philosophers favourable to a meta-ontology, the aim of which is to come to know “which facts/items ground (constitute the base of) which other facts/items”, thus to examine the relation of ontological (...) dependence between beings (e.g. chemical properties depend on physical properties, the economic situation on the behaviour of individuals etc.), i.e. to explore the hierarchical structure of reality. I shall not discuss here the relationship of grounding in itself, but make some historical-formal remarks on the properties of the ultimate ontological foundational item itself and its aporetic nature. To do so I explore various more or less exotic philosophical ecosystems in the following order: Heidegger (Seyn), Plato (ἕν), Wáng Bi (道, dào). On the way I shall propose a new interpretation both of certain hypotheses in the Parmenides and of the nature of the opposition between Wáng Bì and Guō Xiàng in regard to the logical grammar of the expression “nothing (無, wú)” (transl. J. Dudley). (shrink)

This paper consists of an investigation of three debates concerning propositional identity: the tension between structured propositions and higher-order logic, the principle Only Logical Circles, and Kaplan’s Paradox. The literature at large has mistaken the consequences of each of these debates. Structuralists are not committed to the claim that identical properties have different extensions; rather, they are committed to existence monism. Only Logical Circles does not preclude the identification of green in terms of grue; some further (and, as of yet, (...) undisclosed) principle is required for that result. And Kaplan’s Paradox does not count against the possible-worlds conception of propositions; it applies to every account of propositions whatsoever. (shrink)

It has been argued recently that classical theism and Lewisian modal realism are incompatible theses. The most substantial argument to this effect takes the form of a trilemma. It argues that no sense can be made of God’s being a necessary being in the modal realistic picture, on pain of, among other things, modal collapse. The question of this essay is: Is that so? My goal here is to detail the reasons that have been offered in support of this contention (...) and then defend the coherence of theistic modal realism from the trilemma. I call my reply to the argument an “Anselmian-Thomistic” defense, since it appeals to resources from classical medieval philosophy, especially from Anselm and Aquinas. (shrink)

Platonists affirm the existence of abstract mathematical objects, and Nominalists deny the existence of abstract mathematical objects. While there are standard arguments in favor of Nominalism, these arguments fail to account for the necessity of Nominalism. Furthermore, these arguments do nothing to explain why Nominalism is true. They only point to certain theoretical vices that might befall the Platonist. The goal of this paper is to formulate and defend a simple, valid argument for the necessity of Nominalism that seeks to (...) precisify the widespread intuition that mathematical objects are somehow ‘spooky’ or ‘mysterious’. (shrink)

In computational complexity theory, decision problems are divided into complexity classes based on the amount of computational resources it takes for algorithms to solve them. In theoretical computer science, it is commonly accepted that only functions for solving problems in the complexity class P, solvable by a deterministic Turing machine in polynomial time, are considered to be tractable. In cognitive science and philosophy, this tractability result has been used to argue that only functions in P can feasibly work as computational (...) models of human cognitive capacities. One interesting area of computational complexity theory is descriptive complexity, which connects the expressive strength of systems of logic with the computational complexity classes. In descriptive complexity theory, it is established that only first-order (classical) systems are connected to P, or one of its subclasses. Consequently, second-order systems of logic are considered to be computationally intractable, and may therefore seem to be unfit to model human cognitive capacities. This would be problematic when we think of the role of logic as the foundations of mathematics. In order to express many important mathematical concepts and systematically prove theorems involving them, we need to have a system of logic stronger than classical first-order logic. But if such a system is considered to be intractable, it means that the logical foundation of mathematics can be prohibitively complex for human cognition. In this paper I will argue, however, that this problem is the result of an unjustified direct use of computational complexity classes in cognitive modelling. Placing my account in the recent literature on the topic, I argue that the problem can be solved by considering computational complexity for humanly relevant problem solving algorithms and input sizes. (shrink)

The philosophical investigation of perceptual illusions can generate fruitful insights in the study of subjective time consciousness. However, the way illusions are interpreted is often controversial. Recently, proponents of the so-called dynamic snapshot theory have appealed to the Waterfall Illusion, a kind of motion aftereffect, to support a particular view of temporal consciousness according to which experience is structured as a series of instantaneous snapshots with dynamic qualities. This dynamism is meant to account for familiar features of the phenomenology of (...) time, such as succession, continuity, and change. Previous theories have typically appealed to a subjective present occupying an interval of time; that is, a “specious present.” I argue, through analysis of motion aftereffect illusions and the rare condition of akinetopsia, i.e. motion-blindness, that the Waterfall Illusion fails to support the dynamic snapshot theory as intended. Furthermore, I suggest that future theories of subjective time should see temporal phenomenology as the result of non-localised processes closely tied to the mechanism underlying consciousness generally. (shrink)

A principle, according to which any scientific theory can be mathematized, is investigated. Social science, liberal arts, history, and philosophy are meant first of all. That kind of theory is presupposed to be a consistent text, which can be exhaustedly represented by a certain mathematical structure constructively. In thus used, the term “theory” includes all hypotheses as yet unconfirmed as already rejected. The investigation of the sketch of a possible proof of the principle demonstrates that it should be accepted rather (...) a metamathematical axiom about the relation of mathematics and reality. The main statement is formulated as follows: Any scientific theory admits isomorphism to some mathematical structure in a way constructive. Its investigation needs philosophical means. Husserl’s phenomenology is what is used, and then the conception of “bracketing reality” is modelled to generalize Peano arithmetic in its relation to set theory in the foundation of mathematics. The obtained model is equivalent to the generalization of Peano arithmetic by means of replacing the axiom of induction with that of transfinite induction. The sketch of the proof is organized in five steps: a generalization of epoché; involving transfinite induction in the transition between Peano arithmetic and set theory; discussing the finiteness of Peano arithmetic; applying transfinite induction to Peano arithmetic; discussing an arithmetical model of reality. Accepting or rejecting the principle, two kinds of mathematics appear differing from each other by its relation to reality. Accepting the principle, mathematics has to include reality within itself in a kind of Pythagoreanism. These two kinds are called in paper correspondingly Hilbert mathematics and Gödel mathematics. The sketch of the proof of the principle demonstrates that the generalization of Peano arithmetic as above can be interpreted as a model of Hilbert mathematics into Gödel mathematics therefore showing that the former is not less consistent than the latter, and the principle is an independent axiom. The present paper follows a pathway grounded on Husserl’s phenomenology and “bracketing reality” to achieve the generalized arithmetic necessary for the principle to be founded in alternative ontology, in which there is no reality external to mathematics: reality is included within mathematics. That latter mathematics is able to self-found itself and can be called Hilbert mathematics in honour of Hilbert’s program for self-founding mathematics on the base of arithmetic. The principle of universal mathematizability is consistent to Hilbert mathematics, but not to Gödel mathematics. Consequently, its validity or rejection would resolve the problem which mathematics refers to our being; and vice versa: the choice between them for different reasons would confirm or refuse the principle as to the being. An information interpretation of Hilbert mathematics is involved. It is a kind of ontology of information. The Schrödinger equation in quantum mechanics is involved to illustrate that ontology. Thus the problem which of the two mathematics is more relevant to our being is discussed again in a new way A few directions for future work can be: a rigorous formal proof of the principle as an independent axiom; the further development of information ontology consistent to both kinds of mathematics, but much more natural for Hilbert mathematics; the development of the information interpretation of quantum mechanics as a mathematical one for information ontology and thus Hilbert mathematics; the description of consciousness in terms of information ontology. (shrink)

Ontological pluralism is the view that there are different fundamental ways of being. Trenton Merricks has recently raised three objections to combining pluralism with a generic way of being enjoyed by absolutely everything there is: first, that the resulting view contradicts the pluralist’s core intuition; second, that it is especially vulnerable to the charge—due to Peter van Inwagen—that it posits a difference in being where there is simply a difference in kind; and, third, that it is in tension with various (...) historically influential motivations for pluralism. I reply to each of these objections in turn. My replies will help to bring out the true nature of the pluralist’s basic commitments. (shrink)

Intuitivamente, la realidad está formada por entidades y hechos existentes y concretos. Sin embargo, nuestro lenguaje y pensamiento versa también sobre hechos meramente posibles, sobre cosas inexistentes y entidades abstractas. ¿Cómo es esto posible? ¿Significa ello que cuando hablamos y pensamos de estas otras cosas no hablamos de nada real? ¿o mas bien la realidad está mas poblada de lo que pensábamos y hay diferentes maneras de formar parte de la realidad además de la de existir de manera positiva y (...) concreta? En este libro trataremos de arrojar luz a estas y otras preguntas similares, poniendo atención a las estrategias argumentativas generales que suelen esgrimirse en esta rama de la filosofía. (shrink)

This paper deals with Natorp’s version of the Marburg mathematical philosophy of science characterized by the following three features: The core of Natorp’s mathematical philosophy of science is contained in his “knowledge equation” that may be considered as a mathematical model of the “transcendental method” conceived by Natorp as the essence of the Marburg Neo-Kantianism. For Natorp, the object of knowledge was an infinite task. This can be elucidated in two different ways: Carnap, in the Aufbau, contended that this endeavor (...) can be divided into two distinct parts, namely, a finite “constitution” of the object of knowledge and an infinite incompletable empirical description. In contrast, and more in the original spirit of Cohen and Natorp, the physicist and philosopher Margenau in The Nature of Physical Reality (Margenau. 1950) conceived the infinity of this “Aufgabe” as an infinite dialectical process, in which relative “data” and “conceptual constructs” determine each other. This dialectical process eliminates the dichotomy between Anschauung and Begriff that distinguished the Marburg Neo-Kantianism from Kantian orthodoxy, namely, the abandonment of the difference between intuition and concept. Finally, the paper deals with the non-Archimedean geometrical systems that played a central role in Natorp’s defence of Cohen’s “infinitesimal” metaphysics. (shrink)

Penelope Maddy has recently addressed the set-theoretic multiverse, and expressed reservations on its status and merits ([Maddy, 2017]). The purpose of the paper is to examine her concerns, by using the interpretative framework of set-theoretic naturalism. I first distinguish three main forms of 'multiversism', and then I proceed to analyse Maddy's concerns. Among other things, I take into account salient aspects of multiverse-related mathematics , in particular, research programmes in set theory for which the use of the multiverse seems to (...) be crucial, and show how one may provide responses to Maddy's concerns based on a careful analysis of 'multiverse practice'. (shrink)

A. J. Ayer’s Language, Truth, and Logic had been responsible for introducing the Vienna Circle’s ideas, developed within a Germanophone framework, to an Anglophone readership. Inevitably, this migration from one context to another resulted in the alteration of some of the concepts being transmitted. Such alterations have served to facilitate a number of false impressions of Logical Empiricism from which recent scholarship still tries to recover. In this paper, I will attempt to point to the ways in which LTL has (...) helped to foster the various mistaken stereotypes about Logical Empiricism which were combined into the received view. I will begin by examining Ayer’s all too brief presentation of an Anglocentric lineage for his ideas. This lineage, as we shall see, simply omits the major 19th century Germanophone influences on the rise of analytic philosophy. The Germanophone ideas he presents are selectively introduced into an Anglophone context, and directed towards various concerns that arose within that context. I will focus on the differences between Carnap’s version of the overcoming of metaphysics, and Ayer’s reconfiguration into what he calls the elimination of metaphysics. Having discussed the above, I will very briefly outline the consequences that Ayer’s radicalisation of the Vienna Circle’s doctrines had on the subsequent Anglophone reception of Logical Empiricism. (shrink)

ABSTRACT This paper reveals David Hilbert’s position in the philosophy of mathematics, circa 1900, to be a form of non-eliminative structuralism, predating his formalism. I argue that Hilbert withstands the pressing objections put to him by Frege in the course of the Frege-Hilbert controversy in virtue of this early structuralist approach. To demonstrate that this historical position deserves contemporary attention I show that Hilbertian structuralism avoids a recent wave of objections against non-eliminative structuralists to the effect that they cannot distinguish (...) between structurally identical but importantly distinct mathematical objects, such as the complex roots of $-1$. (shrink)

Eternalists believe that there is no ontological difference between the past, present and future. Thus, a challenge arises: in virtue of what does time have a direction? Some eternalists, Oaklander and Tegtmeier ) argue that the direction of time is primitive. A natural response to positing primitive directionality is the suspicion that said posit is too mysterious to do any explanatory work. The aim of this paper is to relieve primitive directionality of some of its mystery by offering a novel (...) way to understand the phenomenon in terms of the recently popularised notion of grounding. (shrink)

Aquinas’ theory of being has received a growing amount of attention from contemporary scholars, both from a historic and a philosophical point of view. An important source of this attention is Geach’s seminal Form and Existence. In it, Geach argues that Aquinas subscribes to a tensed notion of existence and a theory of time according to which past and future entities do not exist in act. Subsequent commentators, such as Kenny in his Aquinas on Being, have agreed with Geach on (...) both points. In this paper, I argue that in several passages of his corpus, most notably those in which he is concerned with God’s knowledge of future contingents, Aquinas implicitly subscribes to a theory of being and time according to which: past and future entities are attributed existence in act, there is theoretical need for introducing a tenseless notion of existence. (shrink)

I begin by giving reasons to accept the block-universe view, the strongly supported by physics view that we live in a four-dimensional world. According to it, the past and the future are as real as the present. As a result, it seems that the future is determined in the sense that what will be the case will necessarily be the case. In the dissertation, I examine whether we have to accept this consequence. I show that we do not have to (...) bite the bullet: the future might be both real and contingent. I first start to consider modal realism (possible futures are real) as a possible solution. However, I propose then another account, actualist (positing the reality of only one possible world: the space-time we live in). This solution relies on a conventionalist theory about metaphysical modality (Sidelle, 1989). It states that modal modality is purely conventional. In combination with a realist interpretation of natural modality (causal and/or nomological), this framework allows me to propose that the future is conventionally closed and naturally contingent. In this view, the necessity of the future holds in virtue of linguistic conventions and then is conventionally necessary. But this is a distinct phenomenon from the natural contingency of the future: the future is naturally contingent because there are mind-independent probabilistic relations holding between the present and the future. This solution has strong consequences: most importantly, an anti-realist view about ordinary objects and physical particles. I end up by presenting and arguing in favour of the general image of the world that comes out from these views. (shrink)

Stojnić et al. (2013, 2017) argue that the reference of demonstratives is fixed without any contribution from the extra-linguistic context. On their `prominence/coherence' theory, the reference of a demonstrative expression depends only on its context-independent linguistic meaning. Here, we argue that Stojnić et al.’s striking claims can be maintained in only the thinnest technical sense. Instead of eliminating appeals to the extra-linguistic context, we show how the prominence/coherence theory merely suppresses them. Then we ask why one might be tempted to (...) try and offer such a view. Since we are rather sympathetic to the motivations we find, we close by sketching a more plausible alternative. (shrink)

The perceptual system estimates distal conditions based upon proximal sensory input. It typically exploits information from multiple cues across and within modalities: it estimates shape based upon visual and haptic cues; it estimates depth based upon convergence, binocular disparity, motion parallax, and other visual cues; and so on. Bayesian models illuminate the computations through which the perceptual system combines sensory cues. I review key aspects of these models. Based on my review, I argue that we should posit co-referring perceptual representations (...) corresponding to distinct sensory cues. For example, the perceptual system represents a distal size using a representation canonically linked with vision and a distinct representation canonically linked with touch. Distinct co-referring perceptual representations represent the same denotation, but they do so under different modes of presentation. Bayesian cue combination models demonstrate that psychological explanation of perception should attend to mode of presentation and not simply to denotation. (shrink)

Recently, various people have maintained that one must revise either the externalistically-based notion of singular thought or the naïve realism-inspired notion of relational particularity, as respectively applied to some thoughts and to some perceptual experiences. In order to do so, one must either provide a broader notion of singular thought or flank the notion of relational particularity with a broader notion of phenomenal particularity. I want to hold that there is no need of that revision. For the original notions can (...) still play the role for which they were invoked. This requires that (i) both the first and the second notion respectively involve a dependence on and a metaphysical relation to the intentional objects of certain mental states once we are ontologically committed to such objects; (ii) both that object-dependence and that metaphysical relation are interpreted in terms of a substantive individuation of the relevant mental state via the object it is about: that object constitutes the state. (shrink)

Despite the importance of the variational principles of physics, there have been relatively few attempts to consider them for a realistic framework. In addition to the old teleological question, this paper continues the recent discussion regarding the modal involvement of the principle of least action and its relations with the Humean view of the laws of nature. The reality of possible paths in the principle of least action is examined from the perspectives of the contemporary metaphysics of modality and Leibniz's (...) concept of essences or possibles striving for existence. I elaborate a modal interpretation of the principle of least action that replaces a classical representation of a system's motion along a single history in the actual modality by simultaneous motions along an infinite set of all possible histories in the possible modality. This model is based on an intuition that deep ontological connections exist between the possible paths in the principle of least action and possible quantum histories in the Feynman path integral. I interpret the action as a physical measure of the essence of every possible history. Therefore only one actual history has the highest degree of the essence and minimal action. To address the issue of necessity, I assume that the principle of least action has a general physical necessity and lies between the laws of motion with a limited physical necessity and certain laws with a metaphysical necessity. (shrink)

Building on recent work by Delia Graff Fara and Ora Matushansky on appellative constructions like ‘Mirka called Roger handsome’, I argue that if Millianism about proper names is true, then the quantifier ‘something’ in ‘Mirka called Roger something’ is best understood as a kind of substitutional quantifier. Any adequate semantics for such quantifiers must explain both the logical behavior of ‘Mirka called Roger something’ and the acceptability of ‘so’-anaphora in ‘Mirka called Roger something, and everyone so called is handsome’. Millianism (...) about proper names is inconsistent with such quantifiers being standard non-substitutional second-order quantifiers. But this is not the only option for Millianism: I provide two different propositional semantics for substitutional quantification, each of which is adequate in the sense above, given Millianism. One of these is based on Tobias Rosefeldt’s work on non-nominal quantification, and I identify in what way Rosefeldt’s semantics is substitutional. (shrink)

How is Frege able to claim that the notion of judgement is essential to his logic without introducing a form of psychologism? I argue first that Frege’s logical notion of judgement is to be distinguished from an empirical notion of judgement, that it cannot be understood as an abstract, idealized notion, and that there are doubts concerning a transcendental reading of Frege’s writings. Then, I explain that the logical notion of judgement has to be understood from a first-person perspective, to (...) be contrasted with a third-person perspective, in which judgement is understood as an empirical, psychological phenomenon. Frege’s logic is essentially a first-person engagement, as each of us can make use of the ideography as a science of logic only if we ourselves have made the relevant judgements. Finally, I claim that the judging agent as conceived by Frege can, after all, be understood as a transcendental ego. (shrink)

On all sides, one hears appeals to objectivity and exhortations to be objective. These admonitions are usually made by scientifically-minded people. Laudable as these appeals may be, they are sometimes so framed as to give the impression that objectivity is a quality or property of events that is immediately recognizable. It is thus, a finality, an ultimate for knowledge, which, when recognized, is taken as given. Ulterior questions, as to what constitutes the objective character of fact, are considered spurious meanderings (...) of minds intent on weaving a cosy scheme of the universe.[...]. (shrink)

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

Peter Hanks and Scott Soames both defend pragmatic solutions to the problem of the unity of the proposition. According to them, what ties together Tim and baldness in the singular proposition expressed by ‘Tim is bald’ is an act of the speaker : the act of predicating baldness of Tim. But Soames construes that act as force neutral and noncommittal while, for Hanks, it is inherently assertive and committal. Hanks answers the Frege–Geach challenge by arguing that, in complex sentences, the (...) force inherent in the content of an embedded sentence is cancelled. Indrek Reiland has recently objected to Hanks’s proposal that it faces a dilemma: either force cancellation dissolves the unity of the proposition secured by the cancelled act of assertion, or Hanks’s proposal reduces to Soames’s. In this paper, I respond to Reiland by offering an analysis of force cancellation which gets rid of the alleged dilemma. The proposal is based on a set of distinctions from speech act theory : between two senses of ’force’, two types of act, and two types of context. The role of simulation in force cancellation is emphasized, and connections drawn to broader issues such as the evolution of complex language. (shrink)

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

This paper is about the meaning and function of identity statements involving proper names. There are two prominent views on this topic, according to which identity statements ascribe a relation: the object-view, on which identity statements ascribe a relation borne by all objects to themselves, and the name-view, on which an identity statement 'a is b' says that the names 'a' and 'b' codesignate. The object- and name-views may seem to exhaust the field. I make a case for treating identity (...) statements as sui generis instead of attempting to explain them by means of the idea that they ascribe a relation. My contention is that once we do this, no analysis is required. -/- I do not wish to insist that we stop saying that identity statements ascribe a relation. The point is that there is a fundamental disanalogy between identity statements and other two-termed statements which we overlook to our peril. This will be seen to parallel the more recognized disanalogy between existence statements and other one-termed statements. One way of registering the fundamental disanalogy is to say that identity statements are not relational, but this is not essential. Following my negative arguments in section 2, I employ some simple diagrammatical models in section 3 to exhibit the fundamental disanalogy. In a final section I respond to some possible objections which may be raised against this kind of approach. (shrink)

Although the economic thought of Marshall and Pigou was united by ethical positions broadly considered utilitarian, differences in their intellectual milieu led to degrees of difference between their respective philosophical visions. This change in milieu includes the influence of the little understood period of transition from the early idealist period in Great Britain, which provided the context to Marshall’s intellectual formation, and the late British Idealist period, which provided the context to Pigou’s intellectual formation. During this latter period, the pervading (...) Hegelianism and influences of naturalism arising from the ideas of Charles Darwin and Herbert Spencer were challenged by Hermann Lotze, a key transitional thinker influencing the Neo-Kantian movement, who recognised significant limits of naturalism, on the one hand, and the metaphysical tenor of absolute idealism, on the other, and attempted to provide a balance between the two. The goal of this paper is to make the provisional case for the argument that Pigou’s views on ethics were not only directly influenced by utilitarian thinkers like Mill and Sidgwick, but they were also indirectly influenced by Hermann Lotze, via the influence of the Neo- Kantian movement on late British idealism. To that end, Pigou’s essays in The Trouble with Theism (1908), including his sympathetic consideration of the ethics of Friedrich Nietzsche, reflect the influence of Lotze indirectly through the impact at Cambridge of: James Ward’s critique of associationist psychology, and consideration of the limits of naturalism including the critique of evolutionary ethics; Bertrand Russell’s rejection of neo-Hegelianism and, together with Alfred North Whitehead, the development of Logicism; and G.E. Moore’s critique of utilitarian ethics on the basis of the naturalistic fallacy and the development of his own intuitionist system of ethics. (shrink)

A lengthy reply to 13 critical discussions of _Meaning in Life: An Analytic Study_ collected in an e-book and reprinted from the _Journal of Philosophy of Life_. The contributors are from a variety of philosophical traditions, including the Anglo-American, Continental and East Asian (especially Buddhist and Japanese) ones.

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)