Putnam rejects having argued in the terms of the argument known in the literature as “the Quine-Putnam indispensability argument”. He considers that mathematics contribution to physics does not have to be interpreted in platonist terms but in his favorite modal variety (Putnam 1975; Putnam 2012). The purpose of this paper is to consider Putnam’s acknowledged argument and philosophical position against contemporary so called in the literature ‘fictionalist’ views about applied mathematics. The conclusion will be that the account of the applicability of mathematics that stems from Putnam‘s acknowledged argument can be assimilated to so-called ‘fictionalist’ views about applied mathematics.

Crucial to Hilary Putnam’s realism in the philosophy of mathematics is to maintain the objectivity of mathematics without the commitment to the existence of mathematical objects. Putnam’s indispensability argument was devised as part of this conception. In this paper, I reconstruct and reassess Putnam’s argument for the indispensability of mathematics, and distinguish it from the more familiar, Quinean version of the argument. Although I argue that Putnam’s approach ultimately fails, I develop an alternative way of implementing his form of realism about mathematics that, by using different resources than those Putnam invokes, avoids the difficulties faced by his view.

The so-called ‘Quine-Putnam Indispensability Argument’, as characterized e.g. by Mark Colyvan (2001), is an argument for mathematical Platonism, the claim that at least some of our mathematical theories (specifically, those that are indispensable to empirical science) are true of a realm of abstract mathematical objects. But Hilary Putnam (2012) complains that his indispensability argument was never intended as an argument for Platonism, but only for a non-ontological form of mathematical realism, where what is defended is mathematical objectivity, but not the existence of mathematical objects. Precisely what does Putnam’s mathematical ‘realism without ontology’ amount to, and is Putnam’s right that his indispensability considerations establish his realism without establishing Platonism?

Bayesianism and likelihoodism are two of the most important frameworks philosophers of science use to analyse scientific methodology. However, both frameworks face a serious objection: much scientific inquiry takes place in highly idealized frameworks where all the hypotheses are known to be false. Yet, both Bayesianism and likelihoodism seem to be based on the assumption that the goal of scientific inquiry is always truth rather than closeness to the truth. Here, I argue in favor of a verisimilitude framework for inductive inference. In the verisimilitude framework, scientific inquiry is conceived of, in part, as a process where inference methods ought to be calibrated to appropriate measures of closeness to the truth. To illustrate the verisimilitude framework, I offer a reconstruction of parsimony evaluations of scientific theories, and I give a reconstruction and extended analysis of the use of parsimony inference in phylogenetics. By recasting phylogenetic inference in the verisimilitude framework, it becomes possible to both raise and address objections to phylogenetic methods that rely on parsimony.

This paper focuses on Putnam’s conception of logical truth as grounded in his picture of mathematical practice and ontology. Putnam’s 1971 book Philosophy of Logic came one year later than Quine’s homonymous volume. In the first section, I compare these two Philosophies of Logic which exemplify realist-nominalist viewpoints in a most conspicuous way. The next section examines Putnam’s views on modality, moving from the modal qualification of his intuitive conception to his official generalized non-modal second-order set-theoretic concept of logical truth. In the third section, I emphasize how Putnam´s “mathematics as modal logic” departs from Quine’s “reluctant Platonism”. I also suggest a complementary view of Platonism and modalism showing them perhaps interchangeable but underlying different stages of research processes that make up a rich and dynamic mathematical practice. The final, more speculative section, argues for the pervasive platonistic conception enhancing the aims of inquiry in the practice of the working mathematician.

This paper discusses Baker’s Enhanced Indispensability Argument (EIA) for mathematical realism on the basis of the indispensable role mathematics plays in scientific explanations of physical facts, along with various responses to it. I argue that there is an analogue of causal explanation for mathematics which, of several basic types of explanation, holds the most promise for use in the EIA. I consider a plausible case where mathematics plays an explanatory role in this sense, but argue that such use still does not support realism about mathematical objects.

Naturalness is an extra-empirical quality that aims to assess plausibility of a theory. Finetuning measures are one way to quantify the task. However, knowing statistical distributions on parameters appears necessary for rigor. Such meta-theories are not known yet. A critical discussion of these issues is presented, including their possible resolutions in fixed points. Skepticism of naturalness’s utility remains credible, as is skepticism to any extra-empirical theory assessment (SEETA) that claims to identify “more correct” theories that are equally empirically adequate. Specifically to naturalness, SEETA implies that one must accept all concordant theory points as a priori equally plausible, with the practical implication that a theory can never have its plausibility status diminished by even a “massive reduction” of its viable parameter space as long as a single theory point still survives. A second implication of SEETA suggests that only falsifiable theories allow their plausibility status to change, but only after discovery or after null experiments with total theory coverage. And a third implication of SEETA is that theory preference then becomes not about what theory is more correct but what theory is practically more advantageous, such as fewer parameters, easier to calculate, or has new experimental signatures to pursue.

In recent years, much discussion has been devoted to the relations between cognition and mathematical practice, thanks to the work of cognitive scientists, philosophers and historians of mathematics dedicated to this topic. Initially, the investigation focused in particular on the question which ‘core’ cognitive systems might ground several mathematical notions and results —especially the number concept. More recently it has moved towards discussion of mathematics as a product of embodied cognition, evaluating the role of conceptual metaphors, bodily experience, and external representations in mathematical practice and mathematical understanding. Some of these proposals claim that mathematics is a unique type of human conceptual system, sustained by specific neural activity and bodily functions, and brought forth via the recruitment of everyday cognitive mechanisms that make human imagination, abstraction, and semiotic processes (work on notations) possible. The question of the nature of mathematics has been addressed as an empirical issue subject to methodological investigations of an interdisciplinary nature, involving hypothesis testing. At the same time, however, such claims have been received with skepticism, be it that they are considered premature or because their actual links with mathematical knowledge, properly speaking, are found wanting.

Two conceptions of the nature of mathematical objects are contrasted: the conception of mathematical objects as preconceived objects (Yablo 2010), and heavy duty platonism (Knowles 2015). It is argued that some theses defended by friends of the indispensability argument are in harmony with heavy duty platonism and in tension with the conception of mathematical objects as preconceived objects.

We are delighted to have the opportunity to respond to Martha Nussbaum’s excellent Creating Capabilities. In that book Nussbaum pays us the great compliment of discussing some aspects of our own book Disadvantage (Wolff and de-Shalit, 2007), both endorsing some of our analysis, yet also entering some criticisms. We would like here to explain the issues and provide our response.

Many philosophers say that the nature of personal identity has to do with narratives: the stories we tell about ourselves. While different narrativists address different questions of personal identity, some propose narrativist accounts of personal identity over time. The paper argues that such accounts have troubling consequences about the beginning and end of our lives, lead to inconsistencies, and involve backwards causation. The problems can be solved, but only by modifying the accounts in ways that deprive them of their appeal.

Richard Swinburne argues that if my cerebral hemispheres were each transplanted into a different head, what would happen to me is not determined by my material parts, and I must therefore have an immaterial part. The paper argues that this argument relies on modal claims that Swinburne has not established. And the means he proposes for establishing such claims cannot succeed.

Modern logic emerged in the period from 1879 to the Second World War. In the post-war period what we know as classical first-order logic largely replaced traditional syllogistic logic in introductory textbooks, but the main development has been simply enormous growth: The publications of the Association for Symbolic Logic, the main professional organization for logicians, became ever thicker. While 1950 saw volume 15 of the Journal of Symbolic Logic, about 300 pages of articles and reviews and a 6-page member list, 2000 saw volume 65 of that journal, over 1900 pages of articles, plus volume 6 of the Bulletin of Symbolic Logic, 570 pages of reviews and a 60-page member list. Of so large a field, the present survey will have to be ruthlessly selective, with no coverage of the history of informal or inductive logic, or of philosophy or historiography of logic, and slight coverage of applications. Remaining are five branches of pure, formal, deductive logic, four being the branches of mathematical logic recognized in Barwise 1977, first of many handbooks put out by academic publishers: set theory, model theory, recursion theory, proof theory. The fifth is philosophical logic, in one sense of that label, otherwise called non-classical logic, including extensions of and alternatives to textbook logic. For each branch, a brief review of pre-war background will be followed by a few highlights of subsequent history. The references will be mix primary and secondary sources, landmark papers and survey articles.

Chance-talk is ubiquitous in science, both in fundamental science and in the special sciences, and no less common in nonscientific contexts. We talk about the chance of winning the lottery, the chance of a defendant being found guilty, the chance of a politician winning reelection, and so on.

The ongoing epistemological debate on scientific thought experiments (TEs) revolves, in part, around the now famous Galileo’s falling bodies TE and how it could justify its conclusions. In this paper, I argue that the TE's function is misrepresented in this a- historical debate. I retrace the history of this TE and show that it constituted the first step in two general “argumentative strategies”, excogitated by Galileo to defend two different theories of free-fall, in 1590’s and then in the 1638. I analyse both argumentative strategies and argue that their function was to eliminate potential causal factors: the TE serving to eliminate absolute weight as a causal factor, while the subsequent arguments served to explore the effect of specific weight, with conflicting conclusions in 1590 and 1638. I will argue thorough the paper that the TE is best grasped when we analyse Galileo’s restriction, in the TE’s scenario and conclusion, to bodies of the same material or specific weight. Finally, I will draw out two implications for the debate on TEs.

Within feminist theory and a wide range of social sciences, intersectionality has been a relevant focus of research. It has been argued that intersectionality allowed an analytic shift from considering gender, race, class or sexuality as separate and added to each other to considering them as interconnected. This has led most authors to assume mutual constitution as the pertinent model, most times without much scrutiny. In this paper we review the main senses of ‘mutual constitution’ in the literature, critically examine them and present what we take to be a problematic assumption: the problem of reification. This is to be understood as the conceptualization of social categories as entities or objects, in a broad sense, and not as properties of them. We then present the property framework, together with the emergent experience view, which conceptualizes categories and social systems in a way that maintains their ontological specificity while allowing for their being deeply affected by each other.

“Nemo judex in causa sua,” we are told: no one should be a judge in their own case. But while this may be a good rule to follow in legal proceedings, its epistemic analogue would be harder to uphold. In fact, we’re often put in a position where we have no choice but to judge our own epistemic performance. We’re put in this sort of position when, for example, we form the opinion that a female candidate’s qualifications are slightly less good than her male competitor’s—while aware of strong evidence that we’re likely to undervalue women’s CVs relative to men’s. Or when we form an opinion about the results of some economic policy that’s tightly connected to our passionate political views—while aware of strong evidence that political passions frequently distort people’s reasoning on this type of matter. A small-plane pilot is put in this position when she’s deciding whether she has enough fuel to make it to an airport a bit further away than her original destination, while aware that her altitude makes it likely that she’s affected by hypoxia, which notoriously affects this sort of judgment while leaving its victims feeling totally clear-headed. A medical resident is put in this positon when he forms an opinion about the appropriate drug dosage for a patient, while aware of strong evidence that he’s been awake so long that his thinking about appropriate dosages is likely to be degraded. And many of us are put in this position when we form an opinion on some controversial issue while aware that others—who share our evidence and who seem as likely as we are to form accurate beliefs on the basis of such evidence—have reached a contrary opinion.

People often encounter evidence which bears directly on the reliability or expected accuracy of their thinking about some topic. This has come to be called “higher-order evidence”. For example, suppose I have some evidence E, and come to have high confidence in hypothesis H on its basis. But then I get some evidence to the effect that I’m likely to do badly at assessing the way E bears on H. Perhaps E bears on H statistically, and I’m given evidence that I’m bad at statistical thinking. Or perhaps E is a set of CVs of male and female candidates, H is the hypothesis that a certain male candidate is a bit better than a certain female candidate, and I get evidence that I’m likely to overrate the CVs of males relative to those of females. Or perhaps E consists of gauge and dial readings in the small plane I’m flying over Alaska, H is the hypothesis that I have enough fuel to reach Sitka, and I realize that my altitude is over 13,000 feet, which I know means that my reasoning from E to H is likely affected by hypoxia. Or finally, perhaps E is a body of meteorological data that seems to me to support rain tomorrow, H is the hypothesis that it’ll rain tomorrow, and I learn that my friend, another reliable meteorologist with the same data E, has predicted that it won’t rain tomorrow.

I return to the material in [1] “Paris-Harrington in an NF context”. Various people had commented that the concept of a relatively large set of natural numbers is unstratified, and in that essay I mused about whether or not the extra strength of PH over finite Ramsey was to do with this failure of stratification. In the present—self-contained— note I shall show that—somewhat to my annoyance—it is not: Paris-Harrington has a stratified formulation.

At around 3.5 to 4 years of age, children in Western and other numerate cultures experience a profound shift in their understanding of numbers: they come to understand how counting works. They can use number words to denote the cardinality of collections of items in a precise fashion by placing each item to be counted into a one-to-one correspondence with elements of a counting list and using the last item to denote the cardinality of the set (see e.g., Sarnecka, in press; Le Corre, 2014). Children’s acquisition of number concepts is often conceptualized in terms of individual discovery and personal reconstruction. For example, Carey (2009, 302) writes that children learn to individuate three items “before figuring out how the numeral list represents natural number”. Davidson, Eng, and Barner (2012, 163) put it this way: “Sometime between the ages of 3-and-a-half and 4, children discover that counting can be used to generate sets of the correct size for any word in their count list” (emphasis added in both).

This paper examines the role of prestige bias in shaping academic philosophy, with a focus on its demographics. I argue that prestige bias exacerbates the structural underrepresentation of minorities in philosophy. It works as a filter against (among others) philosophers of color, women philosophers, and philosophers of low socio- economic status. As a consequence of prestige bias our judgments of philosophical quality become distorted. I outline ways in which prestige bias in philosophy can be mitigated.

The aim of this paper is to cast new light on an important and often overlooked notion of perspectival knowledge arising from Kant. In addition to a traditional notion of perspectival knowledge as “knowledge from a vantage point” (perspectival knowledge1), a second novel notion — “knowledge towards a vantage point” (perspectival knowledge ) —is here introduced. The origin and rationale of perspectival knowledge2 are traced back to Kant’s so-called transcendental illusion (and some of its pre-Critical sources). The legacy of the Kantian notion of perspectival knowledge2 for contemporary discussions on disagreement and the role of metaphysics in scientific knowledge is discussed.

Moral dilemmas, at the very least, involve conflicts between moral requirements. Consider the cases given below.