Goldberg 2016 is a collection of papers dedicated to Putnam’s (1981) brain in a vat (‘BIV’) scenario. The collection divides into three parts, though the issues are inter-connected. Putnam uses conceptual tools from philosophy of language in order to establish theses in epistemology and metaphysics. Putnam’s BIV is considered a contemporary version of Descartes’s skeptical argument of the Evil Genius, but I argue that deception (the possibility of having massively false belief) is not essential, externalism does all the anti-skeptical work. (...) The largest section in the collection covers Putnam’s model-theoretic argument (MTA) against metaphysical realism (MR) and its connections with the brain in vat argument (BVA). There are two camps—unifiers (there is a deep connection in Putnam’s thoughts on BVA, MTA and MR) and patchwork theorists and I try to provide some support for the second camp. All of the papers in the collection are discussed and the anti-skeptical potential of BVA is critically assessed. (shrink)

Often philosophers have reason to ask fundamental questions about the aims, methods, nature, or value of their own discipline. When philosophers systematically examine such questions, the resulting work is sometimes referred to as “metaphilosophy.” Metaphilosophy, it should be said, is not a well-established, or clearly demarcated, field of philosophical inquiry like epistemology or the philosophy of art. However, in the late 20th and early 21st centuries there has been a great deal of metaphilosophical work on issues concerning the methodology of (...) philosophy in the analytic tradition. This article focuses on that work. (shrink)

Published in 1891, Edmund Husserl’s first book, Philosophie der Arithmetik, aimed to “prepare the scientific foundations for a future construction of that discipline.” His goals should seem reasonable to contemporary philosophers of mathematics: . . . through patient investigation of details, to seek foundations, and to test noteworthy theories through painstaking criticism, separating the correct from the erroneous, in order, thus informed, to set in their place new ones which are, if possible, more adequately secured. [7, p. 5]2 But the (...) ensuing strategy for grounding mathematical knowledge sounds strange to the modern ear. For Husserl cast his work as a sequence of “psychological and logical investigations,” providing a psychological analysis.. (shrink)

 ’ The Significance of Philosophical Scepticism has been widely read and discussed by philosophers who are interested in skepticism about our knowledge of the external world.1 Some of his later writings on the topic (such as Stroud (1989) and (1994)) are considered essential reading too. This does not, however, mean that what Stroud says about skepticism2 has as much impact on the discussion of skepticism as it deserves. It seems that his insights into the nature of skepticism have been (...) largely misunderstood or missed. Although Stroud has never argued for skepticism or claimed that skepticism is true, he has been ” ( 2001 37)  The Significance of Philosophical Scepticism is, as the title says so clearly, that skepticism is philosophically significant and should be considered seriously, but skepticism is still felt by most philosophers. (shrink)

This dissertation makes two primary contributions. The first three chapters develop an interpretation of Carnap's Meta-Philosophical Program which places stress upon his methodological analysis of the sciences over and above the Principle of Tolerance. Most importantly, I suggest, is that Carnap sees philosophy as contiguous with science—as a part of the scientific enterprise—so utilizing the very same methods and subject to the same limitations. I argue that the methodological reforms he suggests for philosophy amount to philosophy as the explication of (...) the concepts of science through the construction and use of suitably robust meta-logical languages. My primary interpretive claim is that Carnap's understanding of logic and mathematics as a set of formal auxiliaries is premised upon this prior analysis of the character of logico-mathematical knowledge, his understanding of its role in the language of science, and the methods used by practicing mathematicians. Thus the Principle of Tolerance, and so Carnap's logical pluralism, is licensed and justified by these methodological insights. This interpretation of Carnap's program contrasts with the popular Deflationary reading as proposed in Goldfarb & Ricketts. The leading idea they attribute to Carnap is a Logocentrism: That philosophical assertions are always made relative to some particular language, and that our choice of syntactical rules for a language are constitutive of its inferential structure and methods of possible justification. Consequently Tolerance is considered the foundation of Carnap's entire program. My third chapter argues that this reading makes Carnap's program philosophically inert, and I present significant evidence that such a reading is misguided. The final chapter attempts to extend the methodological ideals of Carnap's program to the analysis of the ongoing debate between category- and set-theoretic foundations for mathematics. Recent criticism of category theory as a foundation charges that it is neither autonomous from set theory, nor offers a suitable ontological grounding for mathematics. I argue that an analysis of concepts can be foundationally informative without requiring the construction of those concepts from first principles, and that ontological worries can be seen as methodologically unfruitful. (shrink)

A problem with recent work about the relationship between metaphysics and science, especially in the theorizing of those who identify as “naturalized metaphysicians”, is the spotty, metaphorical characterization of what it means for science to “constrain” metaphysics. The most robust account of scientific constraint on metaphysical theorizing is advanced by James Ladyman and Don Ross in their 2007 book Every Thing Must Go. Ladyman & Ross claim that the only legitimate metaphysical hypotheses are those that unify two previously disparate scientific (...) explanations. I will critique Ladyman & Ross’ account of naturalized metaphysics, and offer an alternative view of naturalized metaphysics as a practice of constructing physically possible models of reality. This account yields a different view of science’s constraint on metaphysics, specifically, that models must be physically possible in order to be of methodological and heuristic use to scientists. (shrink)

This note describes Saunders Mac Lane as a philosopher, and indeed as a paragon naturalist philosopher. He approaches philosophy as a mathematician. But, more than that, he learned philosophy from David Hilbert’s lectures on it, and by discussing it with Hermann Weyl, as much as he did by studying it with the mathematically informed Göttingen Philosophy professor Moritz Geiger.

Mathematicians often speak of conjectures, yet unproved, as probable or well-confirmed by evidence. The Riemann Hypothesis, for example, is widely believed to be almost certainly true. There seems no initial reason to distinguish such probability from the same notion in empirical science. Yet it is hard to see how there could be probabilistic relations between the necessary truths of pure mathematics. The existence of such logical relations, short of certainty, is defended using the theory of logical probability (or objective Bayesianism (...) or non-deductive logic), and some detailed examples of its use in mathematics surveyed. Examples of inductive reasoning in experimental mathematics are given and it is argued that the problem of induction is best appreciated in the mathematical case. (shrink)

Opinionated state of the art paper on mathematical explanation. After a general introduction to the subject, the paper is divided into two parts. The first part is dedicated to intra-mathematical explanation and the second is dedicated to extra-mathematical explanation. Each of these parts begins to present a set of diverse problems regarding each type of explanation and, afterwards, it analyses relevant models of the literature. Regarding the intra-mathematical explanation, the models of deformable proofs, mathematical saliences and the demonstrative structure of (...) mathematical induction are addressed. Regarding the extra-mathematical explanation, modal, abstract and deductive models are addressed. (shrink)

Abstract In the new millennium there have been important empirical developments in the philosophy of mathematics. One of these is the so-called “Empirical Philosophy of Mathematics”(EPM) of Buldt, Löwe, Müller and Müller-Hill, which aims to complement the methodology of the philosophy of mathematics with empirical work. Among other things, this includes surveys of mathematicians, which EPM believes to give philosophically important results. In this paper I take a critical look at the sociological part of EPM as a case study of (...) ... (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)

This project investigates naturalized metaphysics as a recent trend in analytic metaphysics originating in the naturalist attitude of James Ladyman and Don Ross in their seminal work Everything must Go: Metaphysics Naturalized (2007). The primary focus, however, will be the more recent article “Neo-Positivist Metaphysics” (2012) by Alyssa Ney that originates in this tradition. The project will conclude that naturalized metaphysics is an unsuccessful attempt at an answer to the question ’how is metaphysics possible’. More precisely, the project will establish (...) that any answer to this question must instruct how to succeed at attempts at assertions about the Kantian thing in itself. This requirement is the result of an argument that no other conception of ’reality’ is robust enough to accommodate an ambitious metaphysics. Subsequently, it will be argued that naturalized metaphysics is conceived by its proponents as an attempt at such an answer, but that naturalized metaphysics does not provide the required instruction. This problem occurs because of Carnap’s challenge to metaphysics. Carnap observes that no assertion can be made outside a linguistic framework which has the consequence that metaphysical assertions must be about the conceptual conventions of the linguistic framework rather than the thing in itself. It is the view of Ney and the other proponents of naturalized metaphysics that metaphysics is possible as a naturalized metaphysics; a metaphysics that appropriately defers or yields to the findings of science. The project argues that this requirement does nothing to ensure that Carnap’s challenge is avoided. The challenge is equally significant to naturalized and non-naturalized metaphysics, so long as both require that successful attempts at metaphysics must be assertions about the thing in itself. -/- The project concludes that until or unless Carnap’s challenge is refuted, naturalized metaphysics remain impossible, just like the metaphysics it is supposed to replace. (shrink)

In this paper I return to the mid-20th-century debate between Quine and Carnap on the status of metaphysics questions with an eye toward advancing contemporary debates about whether naturalists can coherently undertake substantive metaphysical inquiry. Following Huw Price, I take the debate between Quine and Carnap to hinge, in part, on whether human inquiry is functionally unified. However, unlike Price, I suggest that this question is not best understood as a question about the function(s) of descriptive discourse. This goes along (...) with rejecting a “linguistic conception” of the starting point of metaphysical inquiry, which, although shared by Quine and Carnap, Price gives us no good reason to think is mandatory for naturalists. I sketch two reasons naturalists have to reject a particular manifestation of this linguistic conception in Quine’s work—his criterion of ontological commitment. Finally, I show how these reasons can help us identify the grains of truth in some recent critiques of “mainstream metaphysics of mind.”. (shrink)

Tutkin tässä artikkelissa Kurt Gödelin epätäydellisyysteoreemojen tulkintoja filosofiassa. Aihepiiri kattaa valtavan määrän eri tulkintoja tekoälystä fysiikkaan ja runouteen asti. Osoitan, että kriittisesti tarkasteltuna kaikki radikaalit epätäydellisyysteoreemojen sovellukset ovat virheellisiä.

The main task in this paper is to detail and investigate Carnap’s conception of a “linguistic framework”. On this basis, we will see whether Carnap’s dichotomies, such as the analytic-synthetic distinction, are to be construed as absolute/fundamental dichotomies or merely as relative dichotomies. I argue for a novel interpretation of Carnap’s conception of a LF and, on that basis, will show that, according to Carnap, all the dichotomies to be discussed are relative dichotomies; they depend on conventional decisions concerning the (...) logical syntax of LF. Thus, all of the dichotomies directly hinge on the conception of the LF. The LF’s logical structure, in turn, is an immediate consequence of adopting the linguistic doctrine of logical truths. As we will see, no appeal to any of these distinctions is necessary in establishing a LF and all of its components. I will also draw attention to the differences between what Carnap labels a “way of speaking”, “language”, and “artificial language”. Consequently, I will briefly conclude that none of Quine’s major objections address the main points of Carnap’s theory. (shrink)

State of the art paper on the topic realism/anti-realism. The first part of the paper elucidates the notions of existence and independence of the metaphysical characterization of the realism/anti-realism dispute. The second part of the paper presents a critical taxonomy of the most important positions and doctrines in the contemporary literature on the domains of science and mathematics: scientific realism, scientific anti-realism, constructive empiricism, structural realism, mathematical Platonism, mathematical indispensability, mathematical empiricism, intuitionism, mathematical fictionalism and second philosophy.

This paper examines some aspects of Strawson’s conception of descriptive metaphysics, as it is developed in Individuals. Descriptive metaphysics sets out to describe ”the actual structure of our thought about the world”. Three specific problems for this project are discussed. First, isn’t the description of our actual thought about the world mainly an empirical task? Second, how determinate and consistent is the stuff we find, how determinate and consistent is our conceptual scheme? Third, who are “we” here? Answers to these (...) sets of questions are mainly negative in spirit. But all this will probably not mean that there will be no place for metaphysics, descriptive or revisionary, as a subject. The whole enterprise is perhaps more fraught with difficulties than Strawson thought, however. (shrink)

Traditional philosophy has been under attack from several quarters in recent years. The traditional philosopher views philosophy as an armchair discipline relying, for the most part, on reason and reflection. Some philosophers doubt the legitimacy of this type of inquiry. Their arguments usually occur along two dimensions. Some argue that the primary data source for the armchair philosopher--intuition--does not provide evidence for philosophical theories. Others argue that conceptual analysis, which is the preferred method of inquiry for armchair philosophers, can't yield (...) the results the philosopher is looking for, since concepts like 'knowledge' or 'free-will' vary from culture to culture or even between persons within a culture. Finally, some philosophers argue that we should abandon the armchair program because philosophy should be an empirical enterprise continuous with the sciences. I argue that attempts to undermine intuition fail and that one can justify the evidential status of intuition in a non-question begging way. I then argue that attacks on the belief in shared concepts do not succeed because they often conflate the nature of scientific objects with those of interest to the philosopher. However, if concepts do vary from culture to culture, I show that the philosopher need not abandon the armchair. She can still do conceptual analysis but it will be only the entry point into the philosophical dialogue. I apply this approach to epistemology arguing that the central epistemic questions ought to be the existential and the normative. This approach helps to vindicate epistemic internalism. (shrink)

Most science requires applied mathematics. This truism underlies the Quine-Putnam indispensability argument: we cannot be mathematical nominalists without rejecting whole swaths of good science that are seamlessly linked with mathematics. One style of response accepts the challenge head-on and attempts to show how to do science without mathematics. There is some consensus that the response fails because the nominalistic apparatus deployed either is not extendible to all of mathematical physics or is merely a deft reconstrual equivalent to standard mathematics. A (...) second style of response denies that indispensability entails realism: when we mathematize a physical problem we treat its physical content as if it were the mathematical representation; provided the two are sufficiently similar, we can use the mathematics to draw conclusions about the physics; even if we cannot represent physical facts without mathematical tools, as-if-fictionalism is reasonable. In this paper I argue that uses of mathematics in science reach deeper than is appreciated by this second response and, indeed, in the more general literature. More specifically, our confidence that we can use the mathematics to draw conclusions about the physics itself depends on mathematics. If the mathematical premises we employ in concluding that a certain application is trustworthy are false, we may lack a justification for supposing that the application will reliably lead us from correct input to correct output. For example, solutions to many physical problems require the determination of a function satisfying a differential equation. Sometimes the existence of a solution for initial value problems can be established directly; where direct methods fail, the existence of a solution must be established indirectly, generally by constructing a sequence of functions that converges to a limit function that satisfies the initial value problem. Moreover, the solution often cannot be evaluated by analytic methods, and scientists must rely on finite element numerical methods to approximate the solution. Mathematical analysis of errors provides further useful information governing the choice of approximation method and of the step size and number of elements needed for the approximation to reach a desired precision. Mathematical physicists rely on the background mathematical theories presupposed in proving the existence of the solutions and approximating them. It is difficult to see how they could do this while adding the fictionalist disclaimer, “But, you know, I don’t believe any of the mathematics I’m using”. It is difficult to see how a fictionalist pursuing the second strategy can account for the soundness of mathematical reasoning in mathematical physics and elsewhere in the sciences. The paper will fill out this argument by appeal to examples and attempt to make clear how mathematics is indispensable to understanding – and thus underwriting our confidence in – applications that would otherwise be shaky approximations and idealizations and how this role is difficult to square with fictionalism. (shrink)