A number of people have recently argued for a structural approach to accounting for the applications of mathematics. Such an approach has been called "the mapping account". According to this view, the applicability of mathematics is fully accounted for by appreciating the relevant structural similarities between the empirical system under study and the mathematics used in the investigation ofthat system. This account of applications requires the truth of applied mathematical assertions, but it does not require the existence of mathematical objects. (...) In this paper, we discuss the shortcomings of this account, and show how these shortcomings can be overcome by a broader view of the application of mathematics: the inferential conception. (shrink)
In this paper we argue that there is a kind of moral disagreement that survives the Rawlsian veil of ignorance. While a veil of ignorance eliminates sources of disagreement stemming from self-interest, it does not do anything to eliminate deeper sources of disagreement. These disagreements not only persist, but transform their structure once behind the veil of ignorance. We consider formal frameworks for exploring these differences in structure between interested and disinterested disagreement, and argue that consensus models offer us a (...) solution concept for disagreements behind the veil of ignorance. (shrink)
The argument from fine tuning is supposed to establish the existence of God from the fact that the evolution of carbon-based life requires the laws of physics and the boundary conditions of the universe to be more or less as they are. We demonstrate that this argument fails. In particular, we focus on problems associated with the role probabilities play in the argument. We show that, even granting the fine tuning of the universe, it does not follow that the universe (...) is improbable, thus no explanation of the fine tuning, theistic or otherwise, is required. (shrink)
Games such as the St. Petersburg game present serious problems for decision theory.1 The St. Petersburg game invokes an unbounded utility function to produce an infinite expectation for playing the game. The problem is usually presented as a clash between decision theory and intuition: most people are not prepared to pay a large finite sum to buy into this game, yet this is precisely what decision theory suggests we ought to do. But there is another problem associated with the St. (...) Petersburg game. The problem is that standard decision theory counsels us to be indifferent between any two actions that have infinite expected utility. So, for example, consider the decision problem of whether to play the St. Petersburg game or a game where every payoff is $1 higher. Let’s call this second game the Petrograd game (it’s the same as St. Petersburg but with a bit of twentieth century inflation). Standard decision theory is indifferent between these two options. Indeed, it might be argued that any intuition that the Petrograd game is better than the St. Petersburg game is a result of misguided and na¨ıve intuitions about infinity.2 But this argument against the intuition in question is misguided. The Petrograd game is clearly better than the St. Petersburg game. And what is more, there is no confusion about infinity involved in thinking this. When the series of coin tosses comes to an end (and it comes to an end with probability 1), no matter how many tails precede the first head, the payoff for the Petrograd game is one dollar higher than the St. Petersburg game. Whatever the outcome, you are better off playing the Petrograd game. Infinity has nothing to do with it. Indeed, a straightforward application of dominance reasoning backs up this line of reasoning.3 Standard decision theory. (shrink)
David Malament argued that Hartry Field's nominalisation program is unlikely to be able to deal with non-space-time theories such as phase-space theories. We give a specific example of such a phase-space theory and argue that this presentation of the theory delivers explanations that are not available in the classical presentation of the theory. This suggests that even if phase-space theories can be nominalised, the resulting theory will not have the explanatory power of the original. Phase-space theories thus raise problems for (...) nominalists that go beyond Malament's initial concerns. Thanks to Mark Steiner, Jens Christian Bjerring, Ben Fraser, John Mathewson, and two anonymous referees for helpful comments on an earlier draft of this paper. CiteULike Connotea Del.icio.us What's this? (shrink)
We discuss a recent attempt by Chris Daly and Simon Langford to do away with mathematical explanations of physical phenomena. Daly and Langford suggest that mathematics merely indexes parts of the physical world, and on this understanding of the role of mathematics in science, there is no need to countenance mathematical explanation of physical facts. We argue that their strategy is at best a sketch and only looks plausible in simple cases. We also draw attention to how frequently Daly and (...) Langford find themselves in conflict with mathematical and scientific practice. (shrink)
Mark Balaguer’s project in this book is extremely ambitious; he sets out to defend both platonism and ﬁctionalism about mathematical entities. Moreover, Balaguer argues that at the end of the day, platonism and ﬁctionalism are on an equal footing. Not content to leave the matter there, however, he advances the anti-metaphysical conclusion that there is no fact of the matter about the existence of mathematical objects.1 Despite the ambitious nature of this project, for the most part Balaguer does not shortchange (...) the reader on rigor; all the main theses advanced are argued for at length and with remarkable clarity and cogency. There are, of course, gaps in the account but these should not be allowed to overshadow the sig-. (shrink)
Standard approaches to counterfactuals in the philosophy of explanation are geared toward causal explanation. We show how to extend the counterfactual theory of explanation to non-causal cases, involving extra-mathematical explanation: the explanation of physical facts by mathematical facts. Using a structural equation framework, we model impossible perturbations to mathematics and the resulting differences made to physical explananda in two important cases of extra-mathematical explanation. We address some objections to our approach.
Philosophical interest in ecology is relatively new. Standard texts in the philosophy of biology pay little or no attention to ecology (though Sterelny and Griffiths 1999 is an exception). This is in part because the science of ecology itself is relatively new, but whatever the reasons for the neglect in the past, the situation must change. A good philosophical understanding of ecology is important for a number of reasons. First, ecology is an important and fascinating branch of biology with distinctive (...) philosophical issues that arise from its study. Second, ecology is only one small step away from urgent political, ethical, and management decisions about how best to live in an apparently increasingly-fragile environment. Third, philosophy of ecology, properly conceived, can contribute directly to both our understanding of ecology and help with its advancement. Philosophy of ecology can thus be seen as part of the emerging discipline of “biohumanities”, where biology and humanities disciplines together advance our understanding and knowledge of biology (Stotz and Griffiths forthcoming). In this paper, we focus primarily on this third role of the philosophy of ecology and consider a number of places where philosophy can play an important role in ecology. In the process, we.. (shrink)
In this paper I present an argument for belief in inconsistent objects. The argument relies on a particular, plausible version of scientific realism, and the fact that often our best scientific theories are inconsistent. It is not clear what to make of this argument. Is it a reductio of the version of scientific realism under consideration? If it is, what are the alternatives? Should we just accept the conclusion? I will argue (rather tentatively and suitably qualified) for a positive answer (...) to the last question: there are times when it is legitimate to believe in inconsistent objects. (shrink)
This paper considers a generalisation of the sorites paradox, in which only topological notions are employed. We argue that by increasing the level of abstraction in this way, we see the sorites paradox in a new, more revealing light—a light that forces attention on cut-off points of vague predicates. The generalised sorites paradox presented here also gives rise to a new, more tractable definition of vagueness.
One of the most intriguing features of mathematics is its applicability to empirical science. Every branch of science draws upon large and often diverse portions of mathematics, from the use of Hilbert spaces in quantum mechanics to the use of differential geometry in general relativity. It's not just the physical sciences that avail themselves of the services of mathematics either. Biology, for instance, makes extensive use of difference equations and statistics. The roles mathematics plays in these theories is also varied. (...) Not only does mathematics help with empirical predictions, it allows elegant and economical statement of many theories. Indeed, so important is the language of mathematics to science, that it is hard to imagine how theories such as quantum mechanics and general relativity could even be stated without employing a substantial amount of mathematics. (shrink)
This paper explores the scope and limits of rational consensus through mutual respect, with the primary focus on the best known formal model of consensus: the Lehrer–Wagner model. We consider various arguments against the rationality of the Lehrer–Wagner model as a model of consensus about factual matters. We conclude that models such as this face problems in achieving rational consensus on disagreements about unknown factual matters, but that they hold considerable promise as models of how to rationally resolve non-factual disagreements.
The Quine-Putnam Indispensability argument is the argument for treating mathematical entities on a par with other theoretical entities of our best scientific theories. This argument is usually taken to be an argument for mathematical realism. In this chapter I will argue that the proper way to understand this argument is as putting pressure on the viability of the marriage of scientific realism and mathematical nominalism. Although such a marriage is a popular option amongst philosophers of science and mathematics, in light (...) of the indispensability argument, the marriage is seen to be very unstable. Unless one is careful about how the Quine-Putnam argument is disarmed, one can be forced to either mathematical realism or, alternatively, scientific instrumentalism. I will explore the various options: (i) finding a way to reconcile the two partners in the marriage by disarming the indispensability argument (Jody Azzouni , Hartry Field [13, 14], Alan Musgrave [18, 19], David Papineau ); (ii) embracing mathematical realism (W.V.O. Quine , Michael Resnik , J.J.C. Smart ); and (iii) embracing some form of scientific instrumentalism (Ot´ avio Bueno [7, 8], Bas van Fraassen ). Elsewhere , I have argued for option (ii) and I won’t repeat those arguments here. Instead, I will consider the difficulties for each of the three options just mentioned, with special attention to option (i). In relation to the latter, I will discuss an argument due to Alan Musgrave  for why option (i) is a plausible and promising approach. From the discussion of Musgrave’s argument, it will emerge that the issue of holist versus separatist theories of confirmation plays a curious role in the realism–antirealism debate in the philosophy of mathematics. I will argue that if you take confirmation to be an holistic matter—it’s whole theories (or significant parts thereof) that are confirmed in any experiment—then there’s an inclination to opt for (ii) in order to resolve the marital tension outlined above.. (shrink)
We argue that standard definitions of ‘vagueness’ prejudice the question of how best to deal with the phenomenon of vagueness. In particular, the usual understanding of ‘vagueness’ in terms of borderline cases, where the latter are thought of as truth-value gaps, begs the question against the subvaluational approach. According to this latter approach, borderline cases are inconsistent (i.e., glutty not gappy). We suggest that a definition of ‘vagueness’ should be general enough to accommodate any genuine contender in the debate over (...) how to best deal with the sorites paradox. Moreover, a definition of ‘vagueness’ must be able to accommodate the variety of forms sorites arguments can take. These include numerical, total-ordered sorites arguments, discrete versions, continuous versions, as well as others without any obvious metric structure at all. After considering the shortcomings of various definitions of ‘vagueness’, we propose a very general non-question-begging definition. (shrink)
The main focus of the book is the presentation of the 'inertial' view of population growth. This view provides a rather simple model for complex population dynamics, and is achieved at the level of the single species without invoking species interactions. An important part of this account is the maternal effect. Investment of mothers in the quality of their daughters makes the rate of reproduction of the current generation depend not only on the current environment, but also on the environment (...) experienced by the previous generation. (shrink)
Evidence-based policy is gaining support in many areas of government and in public affairs more generally. In this paper we outline what evidence—based policy is then discuss its strengths and weaknesses. In particular, we argue that it faces a serious challenge to provide a plausible account of evidence. This account needs to be at least in the spirit of the hierarchy of evidence subscribed to by evidence-based medicine (from which evidence—based policy derives its name and inspiration). Yet evidence-based policy’s hierarchy (...) needs to be tailored to the kinds of evidence relevant and available to the policy arena. The evidence required for policy decisions does not easily lend itself to randomised controlled trials (the "gold standard" in evidence-based medicine), nor, for that matter, being listed in a single all—purpose hierarchy. (shrink)
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The present paper advances an analogy between cases of extra-mathematical explanation and cases of what might be termed ‘extra-logical explanation’: the explanation of a physical fact by a logical fact. A particular case of extra-logical explanation is identified that arises in the philosophical literature on time travel. This instance of extra-logical explanation is subsequently shown to be of a piece with cases of extra-mathematical explanation. Using this analogy, we argue extra-mathematical explanation is part of a broader class of non-causal explanation. (...) This has important implications for extra-mathematical explanation, for time travel and for theories of explanation more generally. (shrink)
“Offsetting” habitat destruction has widespread appeal as an instrument for balancing economic growth with biodiversity conservation. Requiring proponents to pay the nontrivial costs of habitat loss encourages sensitive planning approaches. Offsetting, biobanking, and biodiverse carbon sequestration schemes will play an important role in conserving biodiversity under increasing human pressures. However, untenable assumptions in existing schemes are undermining their beneﬁts. Policies that allow habitat destruction to be offset by the protection of existing habitat are guaranteed to result in further loss of (...) biodiversity. Similarly, schemes that allow trading the immediate loss of existing habitat for restoration projects that promise future habitat will, at best, result in time lags in the availability of habitat that increases extinction risks, or at worst, fail to achieve the offset at all. We detail concerns about existing approaches and describe how offsetting and trading policies can be improved to provide genuine beneﬁts for biodiversity. Due to uncertainties about the way in which restored vegetation matures, we propose that the biodiversity bank should be a savings bank. Accrued biodiversity values should be demonstrated before they can be used to offset biodiversity losses. We provide recommendations about how this could be achieved in practice. (shrink)
The Eleatic Principle or causal criterion is a causal test that entities must pass in order to gain admission to some philosophers’ ontology.1 This principle justifies belief in only those entities to which causal power can be attributed, that is, to those entities which can bring about changes in the world. The idea of such a test is rather important in modern ontology, since it is neither without intuitive appeal nor without influential supporters. Its supporters have included David Armstrong (1978, (...) Vol 2, 5), Brian Ellis (1990, 22) and Hartry Field2 (1989, 68) to name but a few. (shrink)
At various times, mathematicians have been forced to work with inconsistent mathematical theories. Sometimes the inconsistency of the theory in question was apparent (e.g. the early calculus), while at other times it was not (e.g. pre-paradox na¨ıve set theory). The way mathematicians confronted such difficulties is the subject of a great deal of interesting work in the history of mathematics but, apart from the crisis in set theory, there has been very little philosophical work on the topic of inconsistent mathematics. (...) In this paper I will address a couple of philosophical issues arising from the applications of inconsistent mathematics. The first is the issue of whether finding applications for inconsistent mathematics commits us to the existence of inconsistent objects. I then consider what we can learn about a general philosophical account of the applicability of mathematics from successful applications of inconsistent mathematics. (shrink)
Yablo’s paradox is generated by the following (infinite) list of sentences (called the Yablo list): (s1) For all k > 1, sk is not true. (s2) For all k > 2, sk is not true. (s3) For all k > 3, sk is not true. . . . . . . . .
It has been argued in the conservation literature that giving conservation absolute priority over competing interests would best protect the environment. Attributing infinite value to the environment or claiming it is ‘priceless’ are two ways of ensuring this priority (e.g. Hargrove 1989; Bulte and van Kooten 2000; Ackerman and Heinzerling 2002; McCauley 2006; Halsing and Moore 2008). But such proposals would paralyse conservation efforts. We describe the serious problems with these proposals and what they mean for practical applications, and we (...) diagnose and resolve some conceptual confusions permeating the literature on this topic. (shrink)
Environmental ethics concerns itself with ethical issues arising from the relationship between humans and the natural environment. Of particular interest are ethical considerations in relation to human efforts to conserve the natural environment. Some of the key environmental ethics issues are whether environmental value is intrinsic or instrumental, whether biodiversity is valuable in itself or whether it is an indicator of some other value(s), and what the appropriate time scale is for conservation planning. But there is much more to environmental (...) philosophy than environmental ethics. For a start, environmental philosophy covers a whole raft of issues in philosophy of science such as the role of mathematical models in population ecology,1 the relationship between the stability of ecosystems and the complexity of those ecosystems,2 the representation and treatment of uncertainty in ecological and conservation biology applications,3 and whether ecology has laws4. None of these issues has anything to do with ethics. But there is another sense in which environmental philosophy is much broader than environmental ethics: even in relation to topics where there are value or ethical issues, there are other philosophical issues that we would do well to disentangle from the ethics. I will argue that it is a mistake to think of the philosophical issues in question as merely environmental ethics. (shrink)
In this article, I discuss an argument that purports to prove that probability theory is the only sensible means of dealing with uncertainty. I show that this argument can succeed only if some rather controversial assumptions about the nature of uncertainty are accepted. I discuss these assumptions and provide reasons for rejecting them. I also present examples of what I take to..
ON DECEMBER 10, 1991 Charles Shonubi, a Nigerian citizen but a resident of the USA, was arrested at John F. Kennedy International Airport for the importation of heroin into the United States.1 Shonubi's modus operandi was ``balloon swallowing.'' That is, heroin was mixed with another substance to form a paste and this paste was sealed in balloons which were then swallowed. The idea was that once the illegal substance was safely inside the USA, the smuggler would pass the balloons and (...) recover the heroin. On the date of his arrest, Shonubi was found to have swallowed 103 balloons containing a total of 427.4 grams of heroin. There was little doubt about Shonubi's guilt. In fact, there was considerable evidence that he had made at least seven prior heroin-smuggling trips to the USA (although he was not tried for these). In October 1992 Shonubi was convicted in a United States District Court for possessing and importing heroin. Although the conviction was only for crimes associated with Shonubi's arrest date of December 10, 1991, the sentencing judge, Jack B. Weinstein, also made a ®nding that Shonubi had indeed made seven prior drug-smuggling trips to the USA. The interesting part of this case was in the sentencing. According to the federal sentencing guidelines, the sentence in cases such as this should depend on the total quantity of heroin involved. This instruction was interpreted rather broadly.. (shrink)
Time is perceived very differently from different vantage points. A year in the life of a primary-school student, for instance, is a very long time—somewhere between 1/5 and 1/ 12 of a primary-school child’s life. When you tlirow in the massive amount a child learns in any one year, compared with the diminishing returns that conspire against us later in life, a child’s year is more like a decade in adult years. But for a primary-school teacher, a school year is (...) just another ten or so months spent trying to remember names, delivering lessons, writing report cards, and endeavoring to shepherd students through the educational system. And, of course, the classroom is just one part of a teacher’s life. Teachers are juggling other serious and timeconsuming matters such as relationships, mortgages, further study, family and so forth. The best teachers, however, don’t let on about these asymmetries between the child’s world and their own; they conceal the differences in temporal perception and they give no clue that each student is just a small part of their life. Such sleight of hand can’t be easy, yet all my primary school teachers pulled it off to perfection. One, however, deserves special mention: Mr. Williams. In 1969 I turned 11 and was in 6th class at the Armidale Demonstration.. (shrink)
The standard mathematical models in population ecology assume that a population's growth rate is a function of its environment. In this paper we investigate an alternative proposal according to which the rate of change of the growth rate is a function of the environment and of environmental change. We focus on the philosophical issues involved in such a fundamental shift in theoretical assumptions, as well as on the explanations the two theories offer for some of the key data such as (...) cyclic populations. We also discuss the relationship between this move in population ecology and a similar move from first-order to second-order differential equations championed by Galileo and Newton in celestial mechanics. (shrink)
On the face of it, ethics and decision theory give quite different advice about what the best course of action is in a given situation. In this paper we examine this alleged conflict in the realm of environmental decision-making. We focus on a couple of places where ethics and decision theory might be thought to be offering conflicting advice: environmental triage and carbon trading. We argue that the conflict can be seen as conflicts about other things (like appropriate temporal scales (...) for value assignments, idealisations of the decision situation, whether the conservation budget really is fixed and the like). The good news is that there is no conflict between decision theory and environmental ethics. The bad news is that a great deal of environmental decision modelling may be rather simple minded, in that it does not fully incorporate some of these broader issues about temporal scales and the dynamics of many of the decision situations. (shrink)
In many of the special sciences, mathematical models are used to provide information about specified target systems. For instance, population models are used in ecology to make predictions about the abundance of real populations of particular organisms. The status of mathematical models, though, is unclear and their use is hotly contested by some practitioners. A common objection levelled against the use of these models is that they ignore all the known, causally-relevant details of the often complex target systems. Indeed, the (...) objection continues, mathematical models, by their very nature, abstract away from what matters and thus cannot be relied upon to provide any useful information about the systems they are supposed to represent. In this paper, I will examine the role of some typical mathematical models in population ecology and elsewhere. I argue that while, in a sense, these models do ignore the causal details, this move can not only be justified, it is necessary. I will argue that idealising away from complicating causal details often gives a clearer view of what really matters. And often what really matters is not the push and shove of base-level causal processes, but higher-level predictions and (non-causal) explanations. (shrink)
A good philosophical understanding of ecology is important for a number of reasons. First, ecology is an important and fascinating branch of biology, with distinctive philosophical issues. Second, ecology is only one small step away from urgent political, ethical, and management decisions about how best to live in an apparently fragile and increasingly-degraded environment. Third, philosophy of ecology, properly conceived, can contribute directly to both our understanding of ecology and help with its advancement. Philosophy of ecology can thus be seen (...) as part of the emerging discipline of “biohumanities”, where biology and humanities disciplines together advance our understanding and knowledge of biology (Stotz and Griffiths 2008). In this paper, we focus primarily on this third role of the philosophy of ecology and consider a number of places where philosophy can play an important role in ecology. In the process, we survey some of the current research being done in philosophy of ecology, as well as make suggestions about the agenda for future research in this area. We also hope to help clarify what philosophy of ecology is and what it should aspire to be. In what follows, we discuss several topics in the philosophy of ecology and conservation biology, starting with the role and understanding of mathematical models. This is followed by a discussion of a couple of practical problems involving the standard model of hypothesis testing and the use of decision-theoretic methods in environmental science. We then move on to discuss the issue of how we should understand biodiversity, and why this matters for conservation management. Finally, we look at environmental ethics and its relationship with ecology and conservation biology. These four topics were chosen because they are all of contemporary interest in philosophy of ecology circles and are ones where there is much fruitful work still to be done. The topics in question are also useful vehicles for highlighting the variety of issues in ecology and conservation biology where philosophy might prove useful.. (shrink)
JSTOR is a not-for-profit organization founded in 1995 to build trusted digital archives for scholarship. We work with the scholarly community to preserve their work and the materials they rely upon, and to build a common research platform that promotes the discovery and use of these resources. For more information about JSTOR, please contact email@example.com.
We consider several ways in which a good understanding of modern techniques and principles in physics can elucidate ecology. We focus on analogical reasoning between these two branches of science. This style of reasoning requires an understanding of both sciences and an appreciation of the similarities and points of contact between the two. In the current ecological literature on the relationship between ecology and physics, there has been some misunderstanding about the nature of modern physics and its methods. Physics is (...) seen as being much cleaner and tidier than ecology. When ecology is compared to this idealised, fictional version of physics, ecology looks very different, and the prospect of ecology and physics learning from one another is questionable. We argue that physics, once properly appreciated, is more like ecology than ecologists have thus far appreciated. Physicists and ecologists can and do learn from each other, and in this paper we outline how analogical reasoning can facilitate such exchanges. (shrink)
There has been a long history of discussion on the usefulness of formal methods in legal settings.1 Some of the recent debate has focussed on foundational issues in statistics, in particular, how the reference-class problem affects legal decisions based on certain types of statistical evidence.2 Here we examine aspects of this debate, stressing why the reference-class problem presents serious difficulties for the kinds of statistical inferences under consideration and the relevance of this for the use of statistics in the courtroom. (...) We also consider the relevance of foundational statistical issues in the broader context of.. (shrink)
Why do people stay together in monogamous relationships? Love? Fear? Habit? Ethics? Integrity? Desperation? In this paper I will consider a rather surprising answer that comes from mathematics. It turns out that cooperative behaviour, such as mutually-faithful marriages, can be given a firm basis in a mathematical theory known as game theory. I will suggest that faithfulness in relationships is fully accounted for by narrow self interest in the appropriate game theory setting. This is a surprising answer because faithful behaviour (...) is usually thought to involve love, ethics, and caring about the well being of your partner. It seems that the game-theory account of faithfulness has no need for such romantic notions. I will consider the philosophical upshot of the game-theoretic answer and see if it really does deliver what is required. Does the game-theoretic answer miss what is important about faithful relationships or does it help us get to the heart of the matter? Before we start looking at lasting, faithful relationships, though, let’s get a feel for how mathematics might be employed to help in matters of the heart. Let’s first consider how mathematics might shed light on dating to find a suitable partner. (shrink)
The recent publication of a couple of guidebooks to some of the many crags around Armidale (in the New England area of northern New South Wales) has resulted in a bit of interest from outof-towners. (So far guides have been published on Dome Wall and Moonbi, arguably the best two crags in the district.) This article aims to give a bit of inside information on some of the climbs and, hopefully, entice some new blood (and splintered bone) to the area. (...) Fortunately, however, from your point of view as baggees and potential baggees, Armidale is a very good place to be— there are no scary routes and everything is fairly graded (particularly if you are in the back bar of the Wicklow Hotel). This, naturally enough, makes my job as bagger very difficult; however, I’ll do my best. (shrink)
In philosophy of logic and elsewhere, it is generally thought that similar problems should be solved by similar means. This advice is sometimes elevated to the status of a principle: the principle of uniform solution. In this paper I will explore the question of what counts as a similar problem and consider reasons for subscribing to the principle of uniform solution.
In this paper I discuss the kinds of idealisations invoked in normative theories—logic, epistemology, and decision theory. I argue that very often the so-called norms of rationality are in fact mere idealisations invoked to make life easier. As such, these idealisations are not too different from various idealisations employed in scientific modelling. Examples of the latter include: fluids are incompressible (in fluid mechanics), growth rates are constant (in population ecology), and the gravitational influence of distant bodies can be ignored (in (...) celestial mechanics). Thinking of logic, epistemology, and decision theory as normative models employing various idealisations of these kinds, changes the way we approach the justification of the models in question. (shrink)
Recently a fascinating debate has been rekindled over whether vagueness is metaphysical or linguistic. That is, is vagueness an objective feature of reality or is it merely an artifact of our language? Bertrand Russell's contribution to this debate is considered by many to be decisive. Russell suggested that it is a mistake to conclude that the world is vague simply because the language we use to describe it is vague. He argued that to draw such an inference is to commit (...) "the fallacy of verbalism". I argue that this is only a fallacy if we have no reason to believe that the world is as our language says. Since vagueness is apparently not eliminable from our language—a fact that Russell himself acknowledged—an indispensability argument can be launched for metaphysical vagueness. In this paper I outliine such an argument. (shrink)
Mathematics has a great variety ofapplications in the physical sciences.This simple, undeniable fact, however,gives rise to an interestingphilosophical problem:why should physical scientistsfind that they are unable to evenstate their theories without theresources of abstract mathematicaltheories? Moreover, theformulation of physical theories inthe language of mathematicsoften leads to new physical predictionswhich were quite unexpected onpurely physical grounds. It is thought by somethat the puzzles the applications of mathematicspresent are artefacts of out-dated philosophical theories about thenature of mathematics. In this paper I argue (...) that this is not so.I outline two contemporary philosophical accounts of mathematics thatpay a great deal of attention to the applicability of mathematics and showthat even these leave a large part of the puzzles in question unexplained. (shrink)
In this paper I examine Quine''s indispensability argument, with particular emphasis on what is meant by ''indispensable''. I show that confirmation theory plays a crucial role in answering this question and that once indispensability is understood in this light, Quine''s argument is seen to be a serious stumbling block for any scientific realist wishing to maintain an anti-realist position with regard to mathematical entities.