Logical structuralism and Benacerraf’s problem

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.     

Two approaches to natural kinds

Philosophical treatments of natural kinds are embedded in two distinct projects. I call these the philosophy of science approach and the philosophy of language approach. Each is characterized by its own set of philosophical questions, concerns, and assumptions. The kinds studied in the philosophy of science approach are projectible categories that can ground inductive inferences and scientific explanation. The kinds studied in the philosophy of language approach are the referential objects of a special linguistic category—natural kind terms—thought to refer directly. Philosophers may hope for a unified account addresses both sets of concerns. This paper argues that this cannot be done successfully. No single account can satisfy both the semantic objectives of the philosophy of language approach and the explanatory projects of the philosophy of science approach. After analyzing where the tensions arise, I make recommendations about assumptions and projects that are best abandoned, those that should be retained, and those that should go their separate ways. I also recommend adopting the disambiguating terminology of “scientific kinds” and “natural kinds” for the different notions of kinds developed in these different approaches.

     

An application of Carnapian inductive logic to an argument in the philosophy of statistics

I claim that an argument from the philosophy of statistics can be improved by using Carnapian inductive logic. Gelman and Shalizi [9] criticise a philosophical account of how statisticians ought to choose statistical models which they call ‘the received view of Bayesian inference’ and propose a different account inspired by falsificationist philosophy of science. I introduce another philosophical account inspired by Carnapian inductive logic and argue that it is even better than Gelman and Shalizi's falsificationist account.     

The philosopher and the Fly Bottle

Wittgenstein said that what he does in philosophy is ‘to show the fly out of the fly bottle’ (Philosophical Investigations¶309). He is, himself, both the fly, his alter-ego, and the philosopher who turns the fly around. This is a transformation in his vision of and perspective on those matters which tempted him, through the questions it posed for him, into the bottle, there to be trapped – trapped into a form of scepticism, realism, or one of its many reductionist satellites, for instance. The transformation which releases him into the open takes philosophical work which unearths unspoken assumptions and subjects them to criticism. As for the movement into and out of the bottle, this is the philosophical journey in the course of which the philosopher comes to a new understanding of the matters he questioned in a way that led him into the bottle. To come to such a better understanding, therefore, the philosopher has to have the courage of his temptations and not be afraid to give up what he holds on to. What he learns in coming out of the bottle belongs to the work that frees him from the compelling pictures that held him captive within the space of opposed theories held together by common assumptions. It cannot be acquired or conveyed independently of such work. It is in this sense that philosophy is a struggle with difficulties which each philosopher has to face and work through himself. The difficulties are not in him, but they are his– they are difficulties for him. He has to work on them. That is why, while he can learn from others, he cannot borrow from them, build on or go on from what they have established. In the first section of the paper I put on some flesh on this. But what I provide is still a thumb-nail sketch. The question ‘what is philosophy?’ is itself a philosophical question, like any other, and can only be ‘answered’ like them. It is only that with which we are familiar – in our mastery of the language we speak or in our experience of life –that can raise philosophical questions for us. Thus contrast ‘what is knowledge?’, ‘what is thinking?’ with ‘what is cancer?’, ‘what is osmosis?’. The question ‘what is philosophy?’ similarly can only be asked by a philosopher, someone who has asked and struggled with its questions. Otherwise it is a request for information to which the full answer is: you have to study philosophy if you really want to find out. It follows that what I say about the way philosophical questions are to be answered applies equally to the question about the nature of philosophy. Hence I can do no other than provide a thumb-nail sketch for those who have themselves struggled with philosophical questions. As for what I provide in the following three sections, they are no more than illustrations of a way of working on those sample questions – questions on which hopefully the reader will have thought himself. I am able to offer such illustrations only because I have myself been caught up by these questions and have worked on them and discussed them more fully elsewhere (see Bibliography).     

Philosophy,Addiction and Inquiry

ABSTRACT

This introductory paper raises, partly as a preparation for the other papers in this issue, questions about how philosophy ought to proceed in the light of knowledge we have in surrounding disciplines, with a focus on the case of addiction. It also raises issues about how addiction research might be enlightened by philosophical work. In the background for the paper are two competing approaches to the evidential grounding of philosophical insight. According to a widespread view, philosophical knowledge rests on a set of intuitions. According to another, philosophy has no special evidential grounding. This paper resists the attractions of the first picture, and argues against the separateness of philosophy that it lends support. I try to make plausible that such a picture is harmful both for philosophy and for empirical science. We should replace it with a mild form of unity of science or unity of inquiry, in the spirit of the founder of this journal.     

Using Linguistic Corpora as a Philosophical Tool

The central aims of this paper are to show how linguistic corpora have been used and can be used in philosophy and to argue that linguistic corpora and corpus analysis should be added to the philosopher’s toolkit of ways to address philosophical questions. A linguistic corpus is a curated collection of texts representing language use that can be queried to answer research questions. Among many other uses, linguistic corpora can help answer questions about the meaning of words and the structure of discourse. Through a discussion of examples, the paper shows that there are many philosophical questions that can be addressed by using a linguistic corpus. However, linguistic corpora need not (and often cannot) replace traditional philosophical methods. Lastly, it argues that the special properties of linguistic corpora, including their independence and the current ease and cheapness of access, make them an indispensable resource for philosophers.     

Sex in the Head

Abstract Recent philosophical writing on sexual desire divides broadly into two camps. Reductionists take sexual desire to aim at an essentially physical bodily pleasure, whereas intentionalist accounts take a focus upon the reciprocal interaction of the mental states of the partners to be crucial for understanding the phenomenon. I argue that the apparent plausibility of reductionism rests upon the flawed assumption that sexual pleasure has the same uniform bodily character in all sexual encounters, which rests in turn upon flawed assumptions in the philosophy of mind. Drawing on an Aristotelian understanding of persons as essentially embodied minds, I outline an alternative account of sexual desire, showing how the nature of the sexual pleasure we take in the body of another can be transformed by the significance the person or situation has for us. I proceed to show that my account of sexual desire is able to accommodate the entire range of sexual phenomena, including those that seem to undermine standard intentionalist accounts as well as those that reductionists have difficulty in fully explaining. Finally I make some brief remarks about the implications of my account of sexual desire for sexual morality, suggesting some reasons why it casts doubt on the view that universal participant consent is sufficient for a sexual act to be morally unproblematic.     

Comments on Guyer

Paul Guyer's paper “Naturalistic and Transcendental Moments in Kant's Moral Philosophy” raises a set of issues about how Kantian ethics should be understood in relation to present day “philosophical naturalism” that are very much in need of discussion. The paper itself is challenging, even in some respects iconoclastic, and provides a highly welcome provocation to raise in new ways some basic questions about what Kantian ethics is and what it ought to be. Guyer offers us an admirably informed and complex argument, both historical and philosophical, that tangles with some of the most difficult problems in Kant's moral philosophy. It begins with some ambitious and controversial claims about Kant's moral philosophy prior to the Groundwork of 1785. It then offers an interpretation, and also a fundamental criticism, of the Groundwork's attempt to establish the moral law based on the idea of freedom of the will. And finally, it raises – and expresses some opinions on – the large and vexed questions of the relationship between transcendental philosophy and philosophical naturalism, and whether Kantian ethics can be made consistent with a naturalistic philosophical outlook. In these comments I will have something to say on each of these three topics, without pretending (any more than Guyer does) to have exhausted what might be said about them.     

A partial defense of intuition on naturalist grounds

The debate concerning the role of intuitions in philosophy has been characterized by a fundamental disagreement between two main camps. The first, the autonomists, hold that, due to the use in philosophical investigation of appeals to intuition, most of the central questions of philosophy can in principle be answered by philosophical investigation and argument without relying on the sciences. The second, the naturalists, deny the possibility of a priori knowledge and are skeptical of the role of intuition in providing evidence in philosophical inquiry. In spite of the seemingly stark and deep disagreement between the autonomist and the naturalist, in this paper I will attempt to suggest that there is a way to mount a partial defense of intuition-based philosophical practice on naturalist grounds. As will be seen, doing so will require a number of concessions that will satisfy few autonomists while simultaneously disappointing those naturalists who might have thought that all notions of the a priori had been successfully laid to rest. However, I will argue that the account proposed here will preserve those features of traditional philosophical practice that matter most and better explain the history of successes and failures of that practice, thus answering the worries of the autonomist, and that the rejection of the No A Priori Thesis attendant with the account presented here is indeed demanded by the current theories of our best scientific understanding of the mind, thus pacifying the rabid naturalistic critic of any version of apriorism.     

Intuitions as Evidence,Philosophical Expertise and the Developmental Challenge

Abstract

Appeals to intuitions as evidence in philosophy are challenged by experimental philosophers and other critics. A common response to experimental philosophical criticisms is to hold that only professional philosophers’ intuitions count as evidence in philosophy. This ‘expert intuitions defence’ is inadequate for two reasons. First, recent studies indicate significant variability in professional philosophers’ intuitions. Second, the academic literature on professional intuitions gives us reasons to doubt that professional philosophers develop truth-apt intuitions. The onus falls on those who mount the expert intuitions defence to meet these objections because it is implicitly being claimed that training and practice caused professional philosophers to acquire reliably accurate intuitions and we are owed an account of how this transformation takes place. A possible response to this situation is to attempt to reform philosophical practice to improve the quality of intuitions. Another possible response, advocated here, is to avoid appeals to intuitions as evidence.     

Ernst Cassirer's Neo-Kantian Philosophy of Geometry

One of the most important philosophical topics in the early twentieth century – and a topic that was seminal in the emergence of analytic philosophy – was the relationship between Kantian philosophy and modern geometry. This paper discusses how this question was tackled by the Neo-Kantian trained philosopher Ernst Cassirer. Surprisingly, Cassirer does not affirm the theses that contemporary philosophers often associate with Kantian philosophy of mathematics. He does not defend the necessary truth of Euclidean geometry but instead develops a kind of logicism modeled on Richard Dedekind's foundations of arithmetic. Further, because he shared with other Neo-Kantians an appreciation of the developmental and historical nature of mathematics, Cassirer developed a philosophical account of the unity and methodology of mathematics over time. With its impressive attention to the detail of contemporary mathematics and its exploration of philosophical questions to which other philosophers paid scant attention, Cassirer's philosophy of mathematics surely deserves a place among the classic works of twentieth century philosophy of mathematics. Though focused on Cassirer's philosophy of geometry, this paper also addresses both Cassirer's general philosophical orientation and his reading of Kant.     

Wittgenstein’s ‘Non-Cognitivism’ – Explained and Vindicated

The later Wittgenstein advanced a revolutionary but puzzling conception of how philosophy ought to be practised: Philosophical problems are not to be coped with by establishing substantive claims or devising explanations or theories. Instead, philosophical questions ought to be treated ‘like an illness’. Even though this ‘non-cognitivism’ about philosophy has become a focus of debate, the specifically ‘therapeutic’ aims and ‘non-theoretical’ methods constitutive of it remain ill understood. They are motivated by Wittgenstein’s view that the problems he addresses result from misinterpretation, driven by ‘urges to misunderstand’. The present paper clarifies this neglected concept and analyses how such ‘urges’ give rise to pseudo-problems of one particular, hitherto little understood, kind. This will reveal ‘therapeutic’ aims reasonable and ‘non-theoretical’ methods necessary, in one clearly delineated and important part of philosophy. I.e.: By developing a novel account of nature and genesis of one important class of philosophical problems, the paper explains and vindicates a revolutionary reorientation of philosophical work, at the level of both aims and methods.     

Anti-Naturalism: The Role of Non-Empirical Methods in Philosophy

Some naturalistic conceptions of philosophical methodologies interpret the doctrine that philosophy is continuous with science to mean that philosophical investigations must implement empirical methods and must not depart from the experimental results that the scientific application of those methods reveal. In this paper, I argue that while our answers to philosophical questions are certainly constrained by empirical considerations, this does not imply that the methods by which these questions are correctly settled are wholly captured by empirical methods. Many historical cases of successful answers to philosophical questions involve strategies and methods that allow the divergence from empirically established results. I develop this idea and then illustrate it with Frege's methodology in his Foundations of Arithmetic.     

关于三大神学问题的哲学思考

灵魂是否不灭?上帝是否存在?上帝意志是否具有超必然的自由?这三个问题涉及宗教的根本基础。宗教神学家一直把上述三个问题视为神学的基本问题。一方面把它们奉为神圣的信条,不许信仰者怀疑;另一方面,也不断利用哲学和理性的形式,对之作出各式各样的证明。但是历史上的启蒙哲学家和自然科学家对之发出了公开的挑战,从哲学世界观的高度,从自然科学新成就出发,证明统一的自然界不可能有任何超自然存在。围绕三大神学问题的争论,一直是哲学与神学关系史上的中心问题,它也成了宗教哲学必须解答的重要理论问题。     

Intuitions, evidence and hopefulness

Experimental philosophers have recently conducted surveys of folk judgements about a range of phenomena of interest to philosophy including knowledge, reference, and free will. Some experimental philosophers take these results to undermine the philosophical practice of appealing to intuitions as evidence. I consider several different replies to the suggestion that these results undermine philosophical appeal to intuition, both piecemeal replies which raise concerns about particular surveys, and more general replies. The general replies include the suggestions that the surveys consider the wrong sort of judgement, or the wrong kind of judge, or that the results of the surveys do not generate scepticism about philosophical appeal to intuition in particular, but rather a more problematic and general scepticism. I argue that the last of these general replies is the most promising. To assess its merits, I consider the most developed account of how the survey results are supposed to raise sceptical problems specifically for philosophical appeal to intuition, that presented in Weinberg (Midwest Stud Philos XXXI:318–343, 2007). I argue that there are significant objections to Weinberg’s account. I conclude that, so far, experimental philosophers have failed to show how their survey results raise a sceptical challenge that applies to philosophical appeal to intuition in particular, rather than having a problematic, more general scope.     

On the Domain of Metaphilosophy

This article argues for four interrelated claims: (i) Metaphilosophy is not one sub‐discipline of philosophy, nor is it restricted to questions of methodology. Rather, metaphilosophical inquiry encompasses the general background conditions of philosophical practice. (ii) These background conditions are of various sorts, not only those routinely considered “philosophical” but also those considered biographical, historical, and sociological. Accordingly, we should be wary of the customary distinction between what is proper (internal) and merely contingent (external) to philosophy. (iii) “What is philosophy?” is best understood as a practical question concerning how members of different philosophical sub‐communities identify what is pertinent to their respective activities and self‐conceptions. (iv) Given (i)–(iii), understanding what philosophy is requires us to take more seriously the social‐institutional dimension of contemporary philosophical practice.     

A New Framework for Comparative Study of Philosophy

The aim of this essay is to outline a conceptual framework for a type of philosophy (or approach to philosophy) to be herein called “non-sentential philosophy.” Although I will primarily concern myself with the conceptual coherence of the framework in this essay, illustrations will be provided to show that the notion has rich implications for comparative studies. In particular, I believe this theoretical framework will be of interest to those looking for a way to capture the differences between certain non-Western philosophical traditions—such as Chinese philosophy—and Western philosophy, a tradition in which the sentential approach is dominant.     

Experimental Explication

Two recently popular metaphilosophical movements, formal philosophy and experimental philosophy, promote what seem to be conflicting methodologies. Nonetheless, I argue that the two can be mutually supportive. I propose an experimentally‐informed variation on explication, a powerful formal philosophical tool introduced by Carnap. The resulting method, which I call “experimental explication,” provides the formalist with a means of responding to explication's gravest criticism. Moreover, this method introduces a philosophically salient, positive role for survey‐style experiments while steering clear of several objections that critics of “positive experimental philosophy” raise. Thus, it provides the experimentalist with a more defensible example of how empirical work can have positive philosophical import. For these reasons, experimental explication should appeal to experimental philosophers (at least those working within the positive program) and formal philosophers alike.     

The ethical implications of Sengzhao’s concept of the Sage

This paper is an exploration of the ethical significance of Sengzhao’s concept of the sage as exhibited through a Buddhist practitioner’s expanded understanding and cognition of reality. From a philosophical point of view, I aim to show that the ethical significance of his concept of the sage comprises a shift first from ontology to epistemology, and then from epistemology to ethics. I firstly define Sengzhao’s concept of the sage and present a preliminary account of this concept before elaborating on its philosophical aspects. Next, I attempt to illustrate how ethical implications can be derived from Sengzhao’s ethical shift, and lastly, I shed light on the value and significance of this philosophical standpoint within Buddhist philosophy.