Indispensablists contend that accepting scientific realism while rejecting mathematical realism involves a double standard. I refute this contention by developing an enhanced version of scientific realism, which I call interactive realism. It holds that interactively successful theories are typically approximately true, and that the interactive unobservable entities posited by them are likely to exist. It is immune to the pessimistic induction while mathematical realism is susceptible to it.

I defend a new position in philosophy of mathematics that I call mathematical inferentialism. It holds that a mathematical sentence can perform the function of facilitating deductive inferences from some concrete sentences to other concrete sentences, that a mathematical sentence is true if and only if all of its concrete consequences are true, that the abstract world does not exist, and that we acquire mathematical knowledge by confirming concrete sentences. Mathematical inferentialism has several advantages over mathematical realism and fictionalism.

I develop two problems, which I call the problem of divine location and the problem of divine age, to challenge the theist belief that God created the universe. The problem of divine location holds that it is not clear where God existed before he created the universe. The problem of divine age holds that it is not clear how old God was when he created the universe. I explore several theist responses to these two problems, and argue that all of (...) them are problematic under the existing conceptions of space and time in physics. The philosophical magnitudes of these two problems are equal to that of the problem of evil. (shrink)

Intuition is sometimes derided as an abstruse or esoteric phenomenon akin to crystal-ball gazing. Such derision appears to be fuelled primarily by the suggestion, evidently endorsed by traditional rationalists such as Plato and Descartes, that intuition is a kind of direct, immediate apprehension akin to perception. This paper suggests that although the perceptual analogy has often been dismissed as encouraging a theoretically useless metaphor, a quasi-perceptualist view of intuition may enable rationalists to begin to meet the challenge of supplying a (...) theoretically satisfying treatment of their favoured epistemic source. It is argued, first, that intuitions and perceptual experiences are at a certain level of abstraction the same type of mental state, presentations, which are distinct from beliefs, hunches, inclinations, attractions, and seemings. The notion of a presentation is given a positive explication, which identifies its characteristic features, accounts for several of its substantive psychological roles, and systematically locates it in a threefold division among types of contentful states. Subsequently, it is argued that presentations, intuitive no less than sensory, are by their nature poised to play a distinctive epistemic role. Specifically, in the case of intuition, we encounter an intellectual state that is so structured as to provide justification without requiring justification in turn—something which may, thus, be thought of as ‘given’. (shrink)

This essay explores the use of platonist and nominalist concepts, derived from the philosophy of mathematics and metaphysics, as a means of elucidating the debate on spacetime ontology and the spatial structures endorsed by scientific realists. Although the disputes associated with platonism and nominalism often mirror the complexities involved with substantivalism and relationism, it will be argued that a more refined three-part distinction among platonist/nominalist categories can nonetheless provide unique insights into the core assumptions that underlie spatial ontologies, but it (...) also assists in critiquing alternative uses of nominalism, platonism, and both ontic and epistemic structural realism. (shrink)

Physicalism, if it is to be a significant thesis, should differentiate itself from key metaphysical contenders which endorse the existence of platonic entities, emergent properties, Cartesian souls, angels, and God. Physicalism can never be true in worlds where things of these kinds exist. David Papineau, David Spurrett, and Barbara Montero have recently developed and defended two influential conceptions of physicalism. One is derived from a conception of the physical as the non-mentally-and-non-biologically identifiable. The other is derived from a conception of (...) the physical as the non-sui-generis-mental. The paper looks at the resources available to those conceptions, but argues that each is insufficient to yield a conception of physicalism that differentiates it from key anti-physicalist positions. According to these conceptions, if we lived in a world full of things that clearly cannot be physical, we would still live in a physical world. Thus, such conceptions of physicalism are of little theoretical interest. (shrink)

There has been much discussion of late on what exactly the Problem of Universals is and is not. Of course answers to these questions and many more like it depend on what is supposed to be explained by a solution to the Problem of Universals. In this paper, I seek to establish two claims: first, that when the facts (explanada) to be explained and the kind of explanation needed are elucidated, it will be shown that the Problem of Universals is (...) a real metaphysical problem, not a pseudo problem; secondly, the facts whose explanation posed the problem in the Problem of Universals still provide reason to think realism regarding universals is true, even if God exists. (shrink)

Many philosophers posit abstract entities – where something is abstract if it is acausal and lacks spatio-temporal location. Theories, types, characteristics, meanings, values and responsibilities are all good candidates for abstractness. Such things raise an epistemological puzzle: if they are abstract, then how can we have any epistemic access to how they are? If they are invisible, intangible and never make anything happen, then how can we ever discover anything about them? In this article, I critically examine epistemological objections to (...) belief in abstract objects offered by Paul Benacerraf, Colin Cheyne and Hartry Field. (shrink)

This thesis provides an account of acquaintance with abstract objects. The notion of acquaintance is integral to theorising on reference and singular thought, since it is generally taken to be the relation that must exist between a subject and an object, in order for the subject to refer to, and entertain singular thoughts about the object. The most common way of understanding acquaintance is as a form of causal connection. However, this implies a problem. We seem to be able to (...) refer and have singular thoughts about abstract objects. But given that abstract objects are causally inert, this would mean that we are unable to become acquainted with them. This problem shall be the focus of this thesis. I first argue that these traditional causal interpretations of acquaintance are lacking. Instead, I show that acquaintance is dependent to some degree on factors internal to the subject, namely the skills that they possess. From doctors to sommeliers to mathematicians (and possibly even philosophers!) – these subjects seem to succeed in becoming acquainted with certain objects precisely in virtue of their respective skills. Thus, building off from Evans’ The Varieties of Reference, I present a novel account of acquaintance, which I term as Skill-based Acquaintance (SBA). On SBA, a subject is said to be acquainted with an object when they possess discriminating knowledge of that object, gained through the use of their capacities and skills. The SBA account is applied to virtual (Ch.3), fictional (Ch.4), and mathematical objects (Ch.5), as well as God (Ch.6). SBA is successful in explaining how subjects can indeed become acquainted with these problematic categories of objects - some of which are abstract – thus being able to refer and entertain singular thoughts about them. Overall, then, SBA is shown to have greater explanatory power than competing accounts and should thus be preferred. (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)

Hutto and Myin have proposed an account of radically enactive (or embodied) cognition (REC) as an explanation of cognitive phenomena, one that does not include mental representations or mental content in basic minds. Recently, Zahidi and Myin have presented an account of arithmetical cognition that is consistent with the REC view. In this paper, I first evaluate the feasibility of that account by focusing on the evolutionarily developed proto-arithmetical abilities and whether empirical data on them support the radical enactivist view. (...) I argue that although more research is needed, it is at least possible to develop the REC position consistently with the state-of-the-art empirical research on the development of arithmetical cognition. After this, I move the focus to the question whether the radical enactivist account can explain the objectivity of arithmetical knowledge. Against the realist view suggested by Hutto, I argue that objectivity is best explained through analyzing the way universal proto-arithmetical abilities determine the development of arithmetical cognition. (shrink)

Commentators regularly attribute to Frege realist, idealist, and quietist responses to metaphysical questions concerning the abstract objects he calls ‘thoughts’. But despite decades of effort, the evidence offered on behalf of these attributions remains unconvincing. I argue that Frege deliberately avoids commitment to any of these positions, as part of a metaphysical separatist policy motivated by the fact that logic is epistemologically autonomous from metaphysics. Frege’s views and arguments prove relevant to current attempts to argue for epistemological autonomy, particularly that (...) of ethics. (shrink)

This paper is an investigation into the metaphysics of social objects such as political borders, states, and organizations. I articulate a metaphysical puzzle concerning such objects and then propose a novel account of social objects that provides a solution to the puzzle. The basic idea behind the puzzle is that under appropriate circumstances, seemingly concrete social objects can apparently be created by acts of agreement, decree, declaration, or the like. Yet there is reason to believe that no concrete object can (...) be created in this way. The central idea of my positive account is that social objects have a normative component to them, and seemingly concrete social objects have both normative and material components. I develop this idea more rigorously using resources from the Aristotelian hylomorphic tradition. The resulting normative hylomorphic account, I argue, solves the puzzle by providing a satisfying explanation of creation-by-agreement and the like, while also avoiding the difficulties facing extant accounts of social objects. (shrink)

This dissertation is centered around a set of apparently conflicting intuitions that we may have about mathematics. On the one hand, we are inclined to believe that the theorems of mathematics are true. Since many of these theorems are existence assertions, it seems that if we accept them as true, we also commit ourselves to the existence of mathematical objects. On the other hand, mathematical objects are usually thought of as abstract objects that are non-spatiotemporal and causally inert. This makes (...) it difficult to understand how we can have knowledge of them and how they can have any relevance for our mathematical theories. I begin by characterizing a realist position in the philosophy of mathematics and discussing two of the most influential arguments for that kind of view. Next, after highlighting some of the difficulties that realism faces, I look at a few alternative approaches that attempt to account for our mathematical practice without making the assumption that there exist abstract mathematical entities. More specifically, I examine the fictionalist views developed by Hartry Field, Mark Balaguer, and Stephen Yablo, respectively. A common feature of these views is that they accept that mathematics interpreted at face value is committed to the existence of abstract objects. In order to avoid this commitment, they claim that mathematics, when taken at face value, is false. I argue that the fictionalist idea of mathematics as consisting of falsehoods is counter-intuitive and that we should aim for an account that can accommodate both the intuition that mathematics is true and the intuition that the causal inertness of abstract mathematical objects makes them irrelevant to mathematical practice and mathematical knowledge. The solution that I propose is based on Rudolf Carnap's distinction between an internal and an external perspective on existence. I argue that the most reasonable interpretation of the notions of mathematical truth and existence is that they are internal to mathematics and, hence, that mathematical truth cannot be used to draw the conclusion that mathematical objects exist in an external/ontological sense. (shrink)

Christian Platonism and Divine Simplicity remain the most commonly discussed views with respect to the way in which Christians ought to conceive of God’s nature and properties. In this essay, I suggest that we ought to consider seriously two versions of a quite different view, namely, what I call “the Nominalized Composite God View.” Both versions of the Nominalized Composite God View share two features: (1) they treat God as metaphysically composite, in opposition to Divine Simplicity, and (2) they deny (...) that God has God’s properties in virtue of instantiating abstractly existing universals, in opposition to Christian Platonism. (shrink)

Anderson and Welty have recently advanced an argument for the claim that the laws of logic are ontologically dependent upon a necessarily existent mind, i.e. God. In this paper I argue that a key premise of Anderson and Welty’s argument—viz., a premise which asserts that \(x\) is intrinsically intentional only if \(x\) is mind-dependent—is false, for on a broadly Fregean account of propositions, propositions are intrinsically intentional but not mind-dependent.

We examine the philosophical disputes among computer scientists concerning methodological, ontological, and epistemological questions: Is computer science a branch of mathematics, an engineering discipline, or a natural science? Should knowledge about the behaviour of programs proceed deductively or empirically? Are computer programs on a par with mathematical objects, with mere data, or with mental processes? We conclude that distinct positions taken in regard to these questions emanate from distinct sets of received beliefs or paradigms within the discipline: – The rationalist (...) paradigm, which was common among theoretical computer scientists, defines computer science as a branch of mathematics, treats programs on a par with mathematical objects, and seeks certain, a priori knowledge about their ‘correctness’ by means of deductive reasoning. – The technocratic paradigm, promulgated mainly by software engineers and has come to dominate much of the discipline, defines computer science as an engineering discipline, treats programs as mere data, and seeks probable, a posteriori knowledge about their reliability empirically using testing suites. – The scientific paradigm, prevalent in the branches of artificial intelligence, defines computer science as a natural (empirical) science, takes programs to be entities on a par with mental processes, and seeks a priori and a posteriori knowledge about them by combining formal deduction and scientific experimentation. We demonstrate evidence corroborating the tenets of the scientific paradigm, in particular the claim that program-processes are on a par with mental processes. We conclude with a discussion in the influence that the technocratic paradigm has been having over computer science. (shrink)

A perspective in the philosophy of mathematics is developed from a consideration of the strengths and limitations of both logicism and platonism, with an early focus on Frege’s work. Importantly, although many set-theoretic structures may be developed each of which offers limited isomorphism with the system of natural numbers, no one of them may be identified with it. Furthermore, the timeless, ever present nature of mathematical concepts and results itself offers direct access, in the face of a platonist account which (...) generates a supposed problem of access. Crucially too, pure mathematics has its own distinctive method of confirming or validating results - mathematical proof - which supplies a higher level of confidence and objectivity than that available elsewhere. The dichotomy of invention and discovery is too jejune a framework for analysing creative mathematical activity. The Gödelian platonist perspective is evaluated and queried through scrutiny of the part played by mathematical resources and constraints in relation to human activity. It appears that there can be non-causal mathematical explanations and mathematical constraint on purely natural processes. Valuable implications of Quine’s naturalism are explored, but one must be cautious of his thesis of confirmational holism. The distinction between algebraic and non-algebraic mathematical theories usefully contributes to our understanding of the internally differentiated nature of the subject. (shrink)

In this paper I argue, that if it is metaphysically possible for it to have been the case that nothing existed, then it follows that the right modal logic cannot extend D, ruling out popular modal logics S4 and S5. I provisionally defend the claim that it is possible for nothing to have existed. I then consider the various ways of resisting the conclusion that the right modal logic is weaker than D.

Contemporary philosophy’s three main naturalisms are methodological, ontological and epistemological. Methodological naturalism states that the only authoritative standards are those of science. Ontological and epistemological naturalism respectively state that all entities and all valid methods of inquiry are in some sense natural. In philosophy of mathematics of the past few decades methodological naturalism has received the lion’s share of the attention, so we concentrate on this. Ontological and epistemological naturalism in the philosophy of mathematics are discussed more briefly in section (...) 6. (shrink)

El nominalisme té almenys dues varietats. Una consisteix en el rebuig dels objectes abstractes; l’altra, en el rebuig dels universals. Les dues varietats del nominalisme són independents entre si i cadascuna pot defensar-se consistentment sense l’altra, per bé que comparteixen algunes motivacions i arguments. Aquest article exposa les teories nominalistes de les dues varietats.