This book develops a naturalistic aesthetic theory that accounts for aesthetic phenomena in mathematics in the same terms as it accounts for more traditional aesthetic phenomena. Building upon a view advanced by James McAllister, the assertion is that beauty in science does not confine itself to anecdotes or personal idiosyncrasies, but rather that it had played a role in shaping the development of science. Mathematicians often evaluate certain pieces of mathematics using words like beautiful, elegant, or even ugly. Such evaluations (...) are prevalent, however, rigorous investigation of them, of mathematical beauty, is much less common. The volume integrates the basic elements of aesthetics, as it has been developed over the last 200 years, with recent findings in neuropsychology as well as a good knowledge of mathematics. The volume begins with a discussion of the reasons to interpret mathematical beauty in a literal or non-literal fashion, which also serves to survey historical and contemporary approaches to mathematical beauty. The author concludes that literal approaches are much more coherent and fruitful, however, much is yet to be done. In this respect two chapters are devoted to the revision and improvement of McAllister’s theory of the role of beauty in science. These antecedents are used as a foundation to formulate a naturalistic aesthetic theory. The central idea of the theory is that aesthetic phenomena should be seen as constituting a complex dynamical system which the author calls the aesthetic as process theory. The theory comprises explications of three central topics: aesthetic experience, aesthetic value and aesthetic judgment. The theory is applied in the final part of the volume and is used to account for the three most salient and often used aesthetic terms often used in mathematics: beautiful, elegant and ugly. This application of the theory serves to illustrate the theory in action, but also to further discuss and develop some details and to showcase the theory’s explanatory capabilities. (shrink)

This volume, The Brazilian Studies in the Philosophy and History of Science, is the first attempt to present to a general audience, works from Brazil on this subject. The included papers are original, covering a remarkable number of relevant topics of philosophy of science, logic and on the history of science. The Brazilian community has increased in the last years in quantity and in quality of the works, most of them being published in respectable international journals on the subject. The (...) chapters of this volume are forwarded by a general introduction, which aims to sketch not only the contents of the chapters, but it is conceived as a historical and conceptual guide to the development of the field in Brazil. The introduction intends to be useful to the reader, and not only to the specialist, helping them to evaluate the increase in production of this country within the international context. (shrink)

The book is about logical analysis of natural language. Since we humans communicate by means of natural language, we need a tool that helps us to understand in a precise manner how the logical and formal mechanisms of natural language work. Moreover, in the age of computers, we need to communicate both with and through computers as well. Transparent Intensional Logic is a tool that is helpful in making our communication and reasoning smooth and precise. It deals with all kinds (...) of linguistic context in a fully compositional and anti-contextual way. (shrink)

In recent years the philosophy of information has emerged as an important area of research in philosophy. However, until now information’s philosophical history has been largely overlooked. Information and the History of Philosophy is the first comprehensive investigation of the history of philosophical questions around information, including work from before the Common Era to the twenty-first century. It covers scientific and technology-centred notions of information; views of human information processing, as well as socio-political topics such as the control and use (...) of information in societies. Organised into five parts, nineteen chapters by an international team of contributors cover the following topics and more: Information before 500 CE, including ancient Chinese, Greek and Roman approaches to information Early theories of information processing, sources of information and cognition Information and computation in Leibniz, visualised scientific information, copyright and social reform The nineteenth century, including biological information, knowledge economies, and information’s role in empire and eugenics Recent and contemporary philosophy of information, including racialized information, Shannon information, and the very idea of an information revolution. Information and the History of Philosophy is a landmark publication in this emerging field. As such, it is essential reading for students and researchers in the history of philosophy, philosophy of science and technology, and library and information studies. It is also a valuable resource for those working in subjects such as the history of science, media and communication studies, and intellectual history. (shrink)

A Série Investigação Filosófica é uma série de livros de traduções de verbetes da Enciclopédia de Filosofia da Stanford (Stanford Encyclopedia of Philosophy) e de outras plataformas internacionalmente reconhecidas, que intenciona servir tanto como material didático para os professores das diferentes sub-áreas e níveis da Filosofia quanto como material de estudo para a pesquisa e para concursos da área. Nós, professores, sabemos o quão difícil é encontrar bom material em português para indicarmos. E há uma certa deficiência na graduação brasileira (...) de filosofia, principalmente em localizações menos favorecidas, com relação ao conhecimento de outras línguas, como o inglês e o francês. Tentamos, então, suprir essa deficiência, ao introduzirmos essas traduções ao público de língua portuguesa, sem nenhuma finalidade comercial e meramente pela glória da filosofia. (shrink)

What is the source of logical and mathematical truth? This book revitalizes conventionalism as an answer to this question. Conventionalism takes logical and mathematical truth to have their source in linguistic conventions. This was an extremely popular view in the early 20th century, but it was never worked out in detail and is now almost universally rejected in mainstream philosophical circles. Shadows of Syntax is the first book-length treatment and defense of a combined conventionalist theory of logic and mathematics. It (...) argues that our conventions, in the form of syntactic rules of language use, are perfectly suited to explain the truth, necessity, and a priority of logical and mathematical claims, as well as our logical and mathematical knowledge. (shrink)

The book provides a historical and systematic exposition of the semantic theory of truth formulated by Alfred Tarski in the 1930s. This theory became famous very soon and inspired logicians and philosophers. It has two different, but interconnected aspects: formal-logical and philosophical. The book deals with both, but it is intended mostly as a philosophical monograph. It explains Tarski’s motivation and presents discussions about his ideas as well as points out various applications of the semantic theory of truth to philosophical (...) problems. (shrink)

This book is in honour of Professor Anna-Sofia Maurin on her 50th birthday. It consists of eighteen essays on metaphysical issues written by Swedish and international scholars.

I discuss a puzzle that shows there is a need to develop a new metaphysical interpretation of mathematical theories, because all well-known interpretations conflict with important aspects of mathematical activities. The new interpretation, I argue, must authenticate the ontological commitments of mathematical theories without curtailing mathematicians' freedom and authority to creatively introduce mathematical ontology during mathematical problem-solving. Further, I argue that these two constraints are best met by a metaphysical interpretation of mathematics that takes mathematical entities to be constitutively constructed (...) by human activity in a manner similar to the constitutive construction of the US Supreme Court by certain legal and political activities. Finally, I outline some of the philosophical merits of metaphysical interpretations of mathematical theories of this type. (shrink)

'Reason, Causation and Compatibility with the Phenomena' strives to give answers to the philosophical problem of the interplay between realism, explanation and experience. This book is a compilation of essays that recollect significant conceptions of rival terms such as determinism and freedom, reason and appearance, power and knowledge. This title discusses the progress made in epistemology and natural philosophy, especially the steps that led from the ancient theory of atomism to the modern quantum theory, and from mathematization to analytic philosophy. (...) Moreover, it provides possible gateways from modern deadlocks of theory either through approaches to consciousness or through historical critique of intellectual authorities. This work will be of interest to those either researching or studying in colleges and universities, especially in the departments of philosophy, history of science, philosophy of science, philosophy of physics and quantum mechanics, history of ideas and culture. Greek and Latin Literature students and instructors may also find this book to be both a fascinating and valuable point of reference. (shrink)

This volume is the first ever collection devoted to the field of proof-theoretic semantics. Contributions address topics including the systematics of introduction and elimination rules and proofs of normalization, the categorial characterization of deductions, the relation between Heyting's and Gentzen's approaches to meaning, knowability paradoxes, proof-theoretic foundations of set theory, Dummett's justification of logical laws, Kreisel's theory of constructions, paradoxical reasoning, and the defence of model theory. The field of proof-theoretic semantics has existed for almost 50 years, but the term (...) itself was proposed by Schroeder-Heister in the 1980s. Proof-theoretic semantics explains the meaning of linguistic expressions in general and of logical constants in particular in terms of the notion of proof. This volume emerges from presentations at the Second International Conference on Proof-Theoretic Semantics in Tübingen in 2013, where contributing authors were asked to provide a self-contained description and analysis of a significant research question in this area. The contributions are representative of the field and should be of interest to logicians, philosophers, and mathematicians alike. (shrink)

In this paper I present and critically discuss Simon Evnine’s account of hylomorphically complex objects (as presented in his 2016 book Making Objects and Events). On the one hand, I object to the account he gives of how artifacts (which are for him the paradigmatic cases of hylomorphically complex objects) allegedly acquire their existence and identity conditions. I elaborate on two problems I see for this account: first, that it seems unable to explain our knowledge of the kinds to which (...) artifacts belong; second, that it cannot offer a plausible solution to the grounding problem for coincident objects. I also object to the way in which he tries to adapt the sort of account he gave for artifacts to the case of organisms (in my view this fails because both cases are dissimilar at crucial points), and finally I also object to his attempt to extend that account, in a fictional way, to the case of natural non-organic objects (as I try to show, both his arguments to the effect that there are no such objects, and his positive fictionalist proposal to account for our talk about them, are flawed). (shrink)

I argue that attempts to demarcation ethics from science are not jeopardized by the fact that conjunctions of moral claims may have empirically verifiable logical consequences.

Philosophers have often wanted to state a principled way of demarcating empirical from non-empirical thought. This was a major concern of the Vienna Circle. In my view, this is an important intellectual project. Although it is not so common now to address the issue directly, it hovers in the background of many discussions. Non-empirical thought comes in different kinds. Perhaps some is a priori. Common candidates are mathematical, logical, modal and moral thought. Some non-empirical thought might be non-cognitive. Common candidates (...) are moral, aesthetic and religious thought. Or some non-empirical thought might be pseudo-empirical. Common candidates are astrological, theistic, Marxist or psychoanalytic thought; such thought masquerades as empirical, but in fact is not. These are all ways that thought can fail to be empirical. Here I shall focus for the most part on the case of morality, where there has been a lively debate about the empirical status of moral thought. I shall probe the prospects for a demarcation principle that can be used to decide whether or not moral thought is empirical. Some philosophers have recently presented what seems like a compelling case for thinking that moral thought is empirical, and so engaging with their arguments will raise the issue of what the empirical/nonempirical distinction amounts to, and also the issue of how to tell which forms of thought are empirical and which are not. (shrink)

In the 1920s, David Hilbert proposed a research program with the aim of providing mathematics with a secure foundation. This was to be accomplished by first formalizing logic and mathematics in their entirety, and then showing---using only so-called finitistic principles---that these formalizations are free of contradictions. ;In the area of logic, the Hilbert school accomplished major advances both in introducing new systems of logic, and in developing central metalogical notions, such as completeness and decidability. The analysis of unpublished material presented (...) in Chapter 2 shows that a completeness proof for propositional logic was found by Hilbert and his assistant Paul Bernays already in 1917--18, and that Bernays's contribution was much greater than is commonly acknowledged. Aside from logic, the main technical contribution of Hilbert's Program are the development of formal mathematical theories and proof-theoretical investigations thereof, in particular, consistency proofs. In this respect Wilhelm Ackermann's 1924 dissertation is a milestone both in the development of the Program and in proof theory in general. Ackermann gives a consistency proof for a second-order version of primitive recursive arithmetic which, surprisingly, explicitly uses a finitistic version of transfinite induction up to www . He also gave a faulty consistency proof for a system of second-order arithmetic based on Hilbert's &egr;-substitution method. Detailed analyses of both proofs in Chapter 3 shed light on the development of finitism and proof theory in the 1920s as practiced in Hilbert's school. ;In a series of papers, Charles Parsons has attempted to map out a notion of mathematical intuition which he also brings to bear on Hilbert's finitism. According to him, mathematical intuition fails to be able to underwrite the kind of intuitive knowledge Hilbert thought was attainable by the finitist. It is argued in Chapter 4 that the extent of finitistic knowledge which intuition can provide is broader than Parsons supposes. According to another influential analysis of finitism due to W. W. Tait, finitist reasoning coincides with primitive recursive reasoning. The acceptance of non-primitive recursive methods in Ackermann's dissertation presented in Chapter 3, together with additional textual evidence presented in Chapter 4, shows that this identification is untenable as far as Hilbert's conception of finitism is concerned. Tait's conception, however, differs from Hilbert's in important respects, yet it is also open to criticisms leading to the conclusion that finitism encompasses more than just primitive recursive reasoning. (shrink)

Is a mathematical theorem proved because provable, or provable because proved? If Brouwer’s intuitionism is accepted, we’re committed, it seems, to the latter, which is highly problematic. Or so I will argue. This and other consequences of Brouwer’s attempt to found mathematics on the intuition of a move of time have heretofore been insufficiently appreciated. Whereas the mathematical anomalies of intuitionism have received enormous attention, too little time, I’ll try to show, has been devoted to some of the temporal anomalies (...) that Brouwer has invited us to introduce into mathematics. (shrink)

This article attempts to motivate a new approach to anti-realism (or nominalism) in the philosophy of mathematics. I will explore the strongest challenges to anti-realism, based on sympathetic interpretations of our intuitions that appear to support realism. I will argue that the current anti-realistic philosophies have not yet met these challenges, and that is why they cannot convince realists. Then, I will introduce a research project for a new, truly naturalistic, and completely scientific approach to philosophy of mathematics. It belongs (...) to anti-realism, but can meet those challenges and can perhaps convince some realists, at least those who are also naturalists. (shrink)

I argue that the most popular versions of naturalism imply nominalism in philosophy of mathematics. In particular, there is a conflict in Quine's philosophy between naturalism and realism in mathematics. The argument starts from a consequence of naturalism on the nature of human cognitive subjects, physicalism about cognitive subjects, and concludes that this implies a version of nominalism, which I will carefully characterize. The indispensability of classical mathematics for the sciences and semantic/confirmation holism does not affect the argument. The disquotational (...) theory of reference and truth is discussed but rejected. This argument differs from the Benacerrafian arguments against realism, because it does not rely on any specific assumption about the nature of knowledge or reference. It differs from the popular objections to the indispensability argument for realism as well, because it can admit both indispensability and holism. This argument motivates a new, radically naturalistic and nominalistic approach to philosophy of mathematics. (shrink)

The indispensability argument for abstract mathematical entities has been an important issue in the philosophy of mathematics. The argument relies on several assumptions. Some objections have been made against these assumptions, but there are several serious defects in these objections. Ameliorating these defects leads to a new anti-realistic philosophy of mathematics, mainly: first, in mathematical applications, what really exist and can be used as tools are not abstract mathematical entities, but our inner representations that we create in imagining abstract mathematical (...) entities; second, the thoughts that we create in imagining infinite mathematical entities are bounded by external conditions. (shrink)

There are two general questions which many views in the philosophy of mathematics can be seen as addressing: what are mathematical objects, and how do we have knowledge of them? Naturally, the answers given to these questions are linked, since whatever account we give of how we have knowledge of mathematical objects surely has to take into account what sorts of things we claim they are; conversely, whatever account we give of the nature of mathematical objects must be accompanied by (...) a corresponding account of how it is that we acquire knowledge of those objects. The connection between these problems results in what is often called "Benacerraf's Problem", which is a dilemma that many philosophical views about mathematical objects face. It will be my goal here to present a view, attributed to Richard Dedekind, which approaches the initial questions in a different way than many other philosophical views do, and in doing so, avoids the dilemma given by Benacerraf's problem. (shrink)

Over the past few decades the notion of symmetry has played a major role in physics and in the philosophy of physics. Philosophers have used symmetry to discuss the ontology and seeming objectivity of the laws of physics. We introduce several notions of symmetry in mathematics and explain how they can also be used in resolving different problems in the philosophy of mathematics. We use symmetry to discuss the objectivity of mathematics, the role of mathematical objects, the unreasonable effectiveness of (...) mathematics and the relationship of mathematics to physics. (shrink)

(No abstract is available for this citation).

I will take it that general intelligence is intelligence of the kind that a typical human being—Fred, say—manifests in his role as a cognitive agent, that is, as an acquirer, receiver and circulator of knowledge in his cognitive economy. Framed in these terms, the word “general” underserves our ends. Hereafter our questions will bear upon the all-purpose intelligence of beings like Fred. Frederika appears as Fred’s AI-counterpart, not as a fully programmed and engineered being, but as a presently unrealized theoretical (...) construct. Our basic question is whether it is in principle possible to equip Frederika to do what Fred does as an all-purpose participant in his own cognitive economy. Can she achieve a sufficiency of relevant similarity to him to allow us to say that she herself can do what Fred can do, perhaps even better? One of the things that Fred can do—or at least could learn from experience to do—is discharge the duties of an Appeals Court judge. As set down in the ancient doctrine of lex non scripta, Fred must be able to detect, understand and correctly apply certain tacit and implicit rules of law which defy express propositional formulation and linguistic articulation. Fred has an even more widespread capacity for the epistemically tacit and implicit, clearly one of his most cost-saving kinds of intelligence. Indeed, most by far of what Fred will ever know he will know tacitly and implicitly. So we must ask: how tightly bound to the peculiarities of Fred’s cognitive enablement conditions is the character of the intelligence that he manifests? And how far down Fred’s causal make-up does intelligence actually go? (shrink)

The idea that justified modal belief can be accounted for in terms of empirically justified, non-modal belief is enjoying increasing popularity in the epistemology of modality. One alleged reason to prefer modal empiricism over more traditional, rationalist modal epistemologies is that empiricism avoids the problem with the integration challenge that arise for rationalism, assuming that we want to be realists about modal metaphysics. In this paper, I argue that given two very reasonable constraints on what it means to meet the (...) integration challenge for modality, empiricism is currently at best on a par with, but potentially worse off than, rationalist alternatives, with respect to the integration challenge. (shrink)

Embodied approaches to cognition see abstract thought and language as grounded in interactions between mind, body, and world. A particularly important challenge for embodied approaches to cognition is mathematics, perhaps the most abstract domain of human knowledge. Conceptual metaphor theory, a branch of cognitive linguistics, describes how abstract mathematical concepts are grounded in concrete physical representations. In this paper, we consider the implications of this research for the metaphysics and epistemology of mathematics. In the case of metaphysics, we argue that (...) embodied mathematics is neutral in the sense of being compatible with all existing accounts of what mathematical entities really are. However, embodied mathematics may be able to revive an older position known as psychologism and overcome the difficulties it faces. In the case of epistemology, we argue that the evidence collected in the embodied mathematics literature is inconclusive: It does not show that abstract mathematical thinking is constituted by metaphor; it may simply show that abstract thinking is facilitated by metaphor. Our arguments suggest that closer interaction between the philosophy and cognitive science of mathematics could yield a more precise, empirically informed account of what mathematics is and how we come to have knowledge of it. (shrink)

It is tempting to analyse causality in terms of just one of the indicators of causal relationships, e.g., mechanisms, probabilistic dependencies or independencies, counterfactual conditionals or agency considerations. While such an analysis will surely shed light on some aspect of our concept of cause, it will fail to capture the whole, rather multifarious, notion. So one might instead plump for pluralism: a different analysis for a different occasion. But we do not seem to have lots of different concepts of cause (...) – just one eclectic notion. The resolution of this conundrum, I think, requires us to accept that our causal beliefs are generated by a wide variety of indicators, but to deny that this variety of indicators yields a variety of concepts of cause. This focus on the relation between evidence and causal beliefs leads to what I call epistemic causality. Under this view, certain causal beliefs are appropriate or rational on the basis of observed evidence; our notion of cause can be understood purely in terms of these rational beliefs. Causality, then, is a feature of our epistemic representation of the world, rather than of the world itself. This yields one, multifaceted notion of cause. (shrink)

This article examines how Quine and Sellars develop informatively contrasting responses to a fundamental tension in Carnap’s semantics ca. 1950. Quine’s philosophy could well be styled ‘Essays in Radical Empiricism’; his assay of radical empiricism is invaluable for what it reveals about the inherent limits of empiricism. Careful examination shows that Quine’s criticism of Carnap’s semantics in ‘Two Dogmas of Empiricism’ fails, that at its core Quine’s semantics is for two key reasons incoherent and that his hallmark Thesis of Extensionalism (...) is untenable. The tension in Carnap’s semantics together with Quine’s exposure of the severe limits of radical empiricism illuminate central features of Sellars’s philosophy: the fully general form of the myth of givenness, together with Sellars’s alternative Kantian characterisation of understanding; the full significance of Carnap’s distinction between conceptual analysis and conceptual explication, and its important methodological implications; the specifically pragmatic character of Sellars’s realism; and Sellars’s methodological reasons for holding that philosophy must be systematic and that systematic philosophy must be deeply historically and textually informed. This paper thus re-examines this recent episode of philosophical history for its philosophical benefits and systematic insights. (shrink)

Many mathematicians, physicists, and philosophers have suggested that the fact that mathematics—an a priori discipline informed substantially by aesthetic considerations—can be applied to natural science is mysterious. This paper sharpens and responds to a challenge to this effect. I argue that the aesthetic considerations used to evaluate and motivate mathematics are much more closely connected with the physical world than one might presume, and (with reference to case-studies within Galois theory and probabilistic number theory) show that they are correlated with (...) generally recognized theoretical virtues, such as explanatory depth, unifying power, fruitfulness, and importance. (shrink)

Theodore Sider’s recent book, “Writing the Book of the World”, employs a primitive notion of metaphysical structure in order to make sense of substantive metaphysics. But Sider and others who employ metaphysical primitives face serious epistemological challenges. In the first section I develop a specific form of this challenge for Sider’s own proposed epistemology for structure; the second section develops a general reliability challenge for Sider’s theory; and the third and final section argues for the rejection of Siderean structure in (...) the course of answering a transcendental argument against such rejection. (shrink)

In “Truth by Convention” W.V. Quine gave an influential argument against logical conventionalism. Even today his argument is often taken to decisively refute logical conventionalism. Here I break Quine’s arguments into two— the super-task argument and the regress argument—and argue that while these arguments together refute implausible explicit versions of conventionalism, they cannot be successfully mounted against a more plausible implicit version of conventionalism. Unlike some of his modern followers, Quine himself recognized this, but argued that implicit conventionalism was explanatorily (...) idle. Against this I show that pace Quine’s claim that implicit conventionalism has no content beyond the claim that logic is firmly accepted, implicit rules of inference can be used to distinguish the firmly accepted from the conventional. As part of my case, I argue that positing syntactic rules of inference as part of our linguistic competence follows from the same methodology that leads contemporary linguists and cognitive scientists to posit rules of phonology, morphology, and grammar. The upshot of my discussion is a diagnosis of the fallacy in Quine’s master critique of logical conventionalism and a re-opening of possibilities for an attractive conventionalist theory of logic. (shrink)

Over the last half century, possible worlds have bled into almost every area of philosophy. In the metaphysics of modality, for example, philosophers have used possible worlds almost exclusively to illuminate discourse about metaphysical necessity and possibility. But recently, some have grown dissatisfied with possible worlds. Why are horses necessarily mammals? Because the property of being a horse bears a special relationship to the property of being a mammal, they say. Not because every horse is a mammal in every possible (...) world. Some have recently begun to use properties to develop rivals to possible worlds semantics which may someday compare in formal power and capture the different systems of modal logic. In this paper, I do two things. I first offer a quick primer on possible worlds semantics. Then I discuss three rivals and the work they have left to do. (shrink)

This paper formulates a general epistemological argument against what I call non-causal realism, generalizing domain specific arguments by Benacerraf, Field, and others. First I lay out the background to the argument, making a number of distinctions that are sometimes missed in discussions of epistemological arguments against realism. Then I define the target of the argument—non-causal realism—and argue that any non-causal realist theory, no matter the subject matter, cannot be given a reasonable epistemology and so should be rejected. Finally I discuss (...) and respond to several possible responses to the argument. In addition to clearing up and avoiding numerous misunderstandings of arguments of this kind that are quite common in the literature, this paper aims to present and endorse a rigorous and fully general epistemological argument against realism. (shrink)

This paper investigates the determinacy of mathematics. We begin by clarifying how we are understanding the notion of determinacy before turning to the questions of whether and how famous independence results bear on issues of determinacy in mathematics. From there, we pose a metasemantic challenge for those who believe that mathematical language is determinate, motivate two important constraints on attempts to meet our challenge, and then use these constraints to develop an argument against determinacy and discuss a particularly popular approach (...) to resolving indeterminacy, before offering some brief closing reflections. We believe our discussion poses a serious challenge for most philosophical theories of mathematics, since it puts considerable pressure on all views that accept a non-trivial amount of determinacy for even basic arithmetic. (shrink)

Modal primitivists hold that some modal truths are primitively true. They thus seem to face a special epistemological problem: how can primitive modal truths be known? The epistemological objection has not been adequately developed in the literature. I undertake to develop the objection, and then to argue that the best formulation of the epistemological objection targets all realists about modality, rather than the primitivist alone. Furthermore, the moves available to reductionists in response to the objection are also available to primitivists. (...) I conclude by suggesting that extant theories of the epistemology of modality are not sensitive to the question of primitivism versus reductionism. (shrink)

Shamik Dasgupta (2016) proposes to tame the Principle of Sufficient Reason (PSR) to apply to only non-autonomous facts, which are facts that are apt for explanation. Call this strategy to tame the PSR the taming strategy. In a recent paper, Della Rocca (2020a) argues that proponents of the taming strategy, in attempting to formulate a restricted version of the PSR, nevertheless find themselves committed to endorsing a form of radical monism, which, in turn, leads right back to an untamed-PSR. Suppose, (...) for the sake of argument, that Della Rocca is right. My question is this: Is there reason to believe the principle of sufficient reason (in its untamed version)? In this paper, I argue that it is impossible for there to be a reason to believe the untamed-PSR. (shrink)

Evolutionary debunking arguments move from a premise about the influence of evolutionary forces on our moral beliefs to a skeptical conclusion about those beliefs. My primary aim is to clarify this empirically grounded epistemological challenge. I begin by distinguishing among importantly different sorts of epistemological attacks. I then demonstrate that instances of each appear in the literature under the ‘evolutionary debunking’ title. Distinguishing them clears up some confusions and helps us better understand the structure and potential of evolutionary debunking arguments.

It is by now well known that Gödel first advocated the philosophy of Leibniz and then, since 1959, that of Husserl. This raises three questions:1.How is this turn to Husserl to be interpreted? Is it a dismissal of the Leibnizian philosophy, or a different way to achieve similar goals?2.Why did Gödel turn specifically to the later Husserl's transcendental idealism?3.Is there any detectable influence from Husserl on Gödel's writings?Regarding the first question, Wang [96, p.165] reports that Gödel ‘[saw] in Husserl's work (...) a method of refining and consolidating Leibniz' monadology’. But what does this mean? In what for Gödel relevant sense is Husserl's work a refinement and consolidation of Leibniz' monadology?The second question is particularly pressing, given that Gödel was, by his own admission, a realist in mathematics since 1925. Wouldn't the uncompromising realism of the early Husserl's Logical investigations have been a more obvious choice for a Platonist like Gödel?The third question can only be approached when an answer to the second has been given, and we want to suggest that the answer to the first question follows from the answer to the second. We begin, therefore, with a closer look at the actual turn towards phenomenology.Some 30 years before his serious study of Husserl began, Gödel was well aware of the existence of phenomenology. Apart from its likely appearance in the philosophy courses that Gödel took, it reached him from various directions. (shrink)

It is often alleged that Cantor’s views about how the set theoretic universe as a whole should be considered are fundamentally unclear. In this article we argue that Cantor’s views on this subject, at least up until around 1896, are relatively clear, coherent, and interesting. We then go on to argue that Cantor’s views about the set theoretic universe as a whole have implications for theology that have hitherto not been sufficiently recognised. However, the theological implications in question, at least (...) as articulated here, would not have satisfied Cantor himself. (shrink)

Recent discussions of externalism about mental content have been dominated by the question whether it undermines the intuitively plausible idea that we have knowledge of the contents of our thoughts. In this article I focus on one main line of reasoning (the so-called 'slow switching argument') for the thesis that externalism and self-knowledge are incompatible. After criticizing a number of influential responses to the argument, I set out to explain why it fails. It will be claimed that the argument trades (...) on an ambiguity, and that only by incorporating certain controversial assumptions does it stand a chance of establishing its conclusion. Finally, drawing on an analogy with Benacerraf's challenge to Platonism, I shall offer some reasons as to why the slow switching argument fails to reveal the real source of tension between externalism and privileged self-knowledge. (shrink)

We often decide whether a state of affairs is possible by trying to mentally depict a scenario where the state in question obtains . These mental acts seem to provide us with an epistemic route to the space of possibilities. The problem this raises is whether conceivability judgments provide justification-conferring grounds for the ensuing possibility-claims . Although the question has a long history, contemporary interest in it was, to a large extent, prompted by Kripke's utilization of modal intuitions in the (...) course of propounding certain influential theses in the philosophy of language and mind. The interest has been given a further boost by the recent two-dimensional approach to the Kripkean framework. In this paper, I begin by providing a detailed examination of a most recent attempt to defend the thesis and argue that it is unsuccessful. This is followed by presenting my own gloss on Kripke's explanation of the illusions of contingency and I close by raising a general problem intended to undermine the prospects for a successful defense of the thesis. (shrink)

sBuilding models as a practical aspect of ecological theory has as a principal purpose the determination of relations in formal language. In this paper, the authors provide a formalization of ecological models based on impure systems theory. Impure systems contain objects and subjects: subjects are human beings. We can distinguish a person as an observer that by definition is the subject himself and part of the system. In this case he acquires the category of object. Objects are significances, which are (...) the consequence of perceptual beliefs on the part of the subject about material or energetic objects with certain characteristics. The impure system approach is as follows: objects are perceptual significances of material or energetic objects. The set of these objects will form an impure set of the first order. The existing relations between these relative objects will be of two classes: transactions of matter and/or energy and inferential relations. Transactions can have alethic modality: necessity, possibility, impossibility and contingency. In this work we define measures which let us choose the more suitable variables to relate both the model with the ecosystem and with different models. In this way we define different comparison indexes. (shrink)

One of the standard views on plural quantification is that its use commits one to the existence of abstract objects–sets. On this view claims like ‘some logicians admire only each other’ involve ineliminable quantification over subsets of a salient domain. The main motivation for this view is that plural quantification has to be given some sort of semantics, and among the two main candidates—substitutional and set-theoretic—only the latter can provide the language of plurals with the desired expressive power (given that (...) the nominalist seems committed to the assumption that there can be at most countably many names). To counter this approach I develop a modal-substitutional semantics of plural quantification (on which plural variables, roughly speaking, range over ways names could be) and argue for its nominalistic acceptability. (shrink)

According to quasi-empiricism, mathematics is very like a branch of natural science. But if mathematics is like a branch of science, and science studies real objects, then mathematics should study real objects. Thus a quasi-empirical account of mathematics must answer the old epistemological question: How is knowledge of abstract objects possible? This paper attempts to show how it is possible.The second section examines the problem as it was posed by Benacerraf in Mathematical Truth and the next section presents a way (...) of looking at abstract objects that purports to demythologize them. In particular, it shows how we can have empirical knowledge of various abstract objects and even how we might causally interact with them. (shrink)

(No abstract is available for this citation).

Norms are standards against which actions, dispositions of mind and character, states of affairs and so forth can be measured. They also govern our behaviour, make claims on us, bind us and provide reasons for action and thought that motivate us. J. L. Mackie argued that the intrinsic prescriptivity, or to-be-pursuedness, of moral norms would make them utterly unlike anything else that we know of. Therefore, we should favour an error theory of morality. Mackie thought that the to-be-pursuedness would have (...) to be built into mind-independent moral reality. One alternative, however, is that the to-be-pursuedness is built into our faculty of moral sensibility. There is a large body of empirical evidence demonstrating that the emotions play a central role in making moral judgments. I shall argue that this helps to explain how normative judgments are reliably and non-accidentally related to motivation. I shall also argue that emotional experience has the right structure and properties to provide us with a defeasible warrant for normative knowledge. The role of the emotions in our moral psychology does not obviously support anti-realism. Rather, emotional experience can be intentional, evaluative, evaluable, and quasi-perceptual. This makes emotional experience a plausible candidate for constituting a non-queer faculty of moral sensibility. (shrink)