Robust metanormative realists think that there are irreducibly normative, metaphysically heavy normative facts. One might wonder how we could be epistemically justified in believing that such facts exist. In this paper, I offer an answer to this question: one’s belief in the existence of robustly real normative facts is epistemically justified because so believing is indispensable to being a successful inquirer for creatures like us. The argument builds on Enoch's (2007, 2011) deliberative indispensability argument for Robust Realism but avoids (...) relying on an overly pragmatic account of the sources of basic epistemic justification. Instead, I suggest that the sources of basic epistemic justification are those belief-forming methods which are indispensable for zetetically indispensable projects, that is, projects which are constitutive of being a successful inquirer for embodied, agential creatures like ourselves. (shrink)

Many of us care about the existence of ethical facts because they appear crucial to making sense of our practical lives. On one tempting line of thought, this idea can also play a central role in justifying our belief in those facts. David Enoch has developed this thought into a formidable new proposal in moral epistemology: that the deliberative indispensability of ethical facts gives us epistemic justification for believing in such facts. This chapter argues that Enoch’s proposal fails because (...) it conflicts with a central fact about epistemic justification: that the norms of epistemic justification have the content that they do in part because of some positive connection between those norms and the truth of the beliefs that these norms govern. Alternatives to Enoch’s attempt to defend the idea that deliberative indispensability confers epistemic justification fail for parallel reasons. The chapter concludes that deliberative indispensability does not provide epistemic justification. (shrink)

Many of us care about the existence of ethical facts because such facts appear crucial to making sense of our practical lives. On one tempting line of thought, this idea does more than raise the metaethical stakes: it can also play a central role in justifying our belief in those facts. In recent work, David Enoch has developed this tempting thought into a formidable new proposal in moral epistemology, that aims to explain how the deliberative indispensability of ethical facts (...) gives us epistemic justification for believing in such facts. In this paper, we argue that Enoch’s proposal fails because it conflicts with a central fact about epistemic justification: that the norms of epistemic justification have the content that they do in part because of some positive connection between those norms and the truth of the beliefs that these norms govern. We then argue that the most salient alternatives to Enoch’s attempt to defend the idea that deliberative indispensability confers epistemic justification fail for parallel reasons. We conclude that the tempting line of thought should be rejected: deliberative indispensability does not provide epistemic justification. (shrink)

In this note, I discuss David Enoch's influential deliberative indispensability argument for metanormative realism, and contend that the argument fails. In doing so, I uncover an important disanalogy between explanatory indispensability arguments and deliberative indispensability arguments, one that explains how we could accept the former without accepting the latter.

In this paper, I propose a solution to a challenge formulated by Judith Jarvis Thomson: We have to explain why the moral asymmetry between doing and allowing harm is a deep feature of our moral thinking. In a nutshell, my solution is this: It could not be otherwise. Accepting the asymmetry is indispensable for the construction and maintenance of stable moral communities. -/- My argument centrally involves mental resource management. Moral communities depend on their members’ commitment to moral norms. And, (...) I argue, community members can only be committed to these norms in the required ways without overextending their mental resources if morality contains the doing/allowing asymmetry. -/- This has two noteworthy implications. Firstly, we can and should stop discussing the asymmetry in normative ethics and, instead, regard it as “moral axiom” we cannot but accept. Secondly, even consequentialists have to accept the asymmetry but, by doing so, their view loses part of its intuitive appeal. Lastly, I turn to an objection. One might think that my indispensability argument confuses issues in moral psychology with issues in normative ethics. I reject the objection on broadly pragmatist grounds. (shrink)

According to Quine’s indispensability argument, we ought to believe in just those mathematical entities that we quantify over in our best scientific theories. Quine’s criterion of ontological commitment is part of the standard indispensability argument. However, we suggest that a new indispensability argument can be run using Armstrong’s criterion of ontological commitment rather than Quine’s. According to Armstrong’s criterion, ‘to be is to be a truthmaker (or part of one)’. We supplement this criterion with our own brand (...) of metaphysics, 'Aristotelian (...) realism', in order to identify the truthmakers of mathematics. We consider in particular as a case study the indispensability to physics of real analysis (the theory of the real numbers). We conclude that it is possible to run an indispensability argument without Quinean baggage. (shrink)

The literature on the indispensability argument for mathematical realism often refers to the ‘indispensable explanatory role’ of mathematics. I argue that we should examine the notion of explanatory indispensability from the point of view of specific conceptions of scientific explanation. The reason is that explanatory indispensability in and of itself turns out to be insufficient for justifying the ontological conclusions at stake. To show this I introduce a distinction between different kinds of explanatory roles—some ‘thick’ and ontologically (...) committing, others ‘thin’ and ontologically peripheral—and examine this distinction in relation to some notable ‘ontic’ accounts of explanation. I also discuss the issue in the broader context of other ‘explanationist’ realist arguments. (shrink)

There is a way of talking that would appear to involve ascriptions of purpose, goal directed activity, and intentional states to groups. Cases are familiar enough: classmates intend to vacation in Switzerland, the department is searching for a metaphysician, the Democrats want to minimize losses in the upcoming elections, and the US intends to improve relations with such and such country. But is this talk to be understood just in terms of the attitudes and actions of the individuals involved? Is (...) the talk, to take an overly simple proposal as an example, a mere summary of familiar individual attitudes of the group members? Or is the ascription of attitudes and actions to groups to be taken more literally, as suggesting that the group for example believes that P, or intends to A, over and above what the members individually think and do? In short, are there groups with minds of their own? Philip Pettit has deployed the “discursive dilemma” to defend the thesis that there are such group minds. In what follows, I explore the relationship between the group allegedly with a mind of its own and the individuals it comprises, and I consider just how this relationship must be understood in order to give Pettit’s argument for group minds its best chance for success. As I understand it, the discursive dilemma has to be used in conjunction with what might be called an indispensability argument for group minds. It is useful to distinguish two forms of this argument. The explanatory version of the indispensability argument is, very schematically, as follows: there is a compelling explanatory theory T concerning the social, certain indispensable elements of T entail the group mind thesis, so the group mind thesis is true. Several questions immediately arise: What sort of theory is T? In what sense is it indispensable? Are there other forms of indispensability? I don’t have definitive answers to these questions. But how we settle them will have implications for the interaction and support the discursive dilemma provides the indispensability argument. In particular, using the discursive dilemma to defend what I characterize below as a practical version of the indispensability argument commits us to the rationality of individual participants in a way that the explanatory version of the indispensability argument does not. My point in the first part of the paper is that if Pettit wants to avoid the weaknesses of the explanatory indispensability argument and pursue the practical version, then he owes us a story about the rationality of individual participation in groups. Pettit also owes us a story about the agency an individual exercises as part of a group. If it takes the actions of individuals to execute the intentions of the group, how are we to understand those actions in order for the group to count as having a mind of its own? How must group intentions figure in the practical or deliberative perspective of individuals who execute those intentions? I will argue that the proponent of the group mind thesis must proceed with some care here, because some natural ways of answering these questions will undermine the thesis. But in the end, I think that these questions are interesting independently of whether Pettit is right to think that groups do have minds of their own. That’s because investigating Pettit’s arguments might lead to new ideas about how the rationality and agency of individuals can be exercised, and suggests new ways of understanding how individuals can act together, irrespective of whether the groups they compose ever have minds of their own. (shrink)

Recent debates about mathematical ontology are guided by the view that Platonism's prospects depend on mathematics' explanatory role in science. If mathematics plays an explanatory role, and in the right kind of way, this carries ontological commitment to mathematical objects. Conversely, the assumption goes, if mathematics merely plays a representational role then our world-oriented uses of mathematics fail to commit us to mathematical objects. I argue that it is a mistake to think that mathematical representation is necessarily ontologically innocent and (...) that there is an argument from mathematics' representational capacity to Platonism. Given that it is common ground between the Platonist and nominalist that mathematics plays a representational role in science, this representationalist argument is to be preferred over the explanatory, or enhanced, indispensability argument. (shrink)

Pluralist mathematical realism, the view that there exists more than one mathematical universe, has become an influential position in the philosophy of mathematics. I argue that, if mathematical pluralism is true (and we have good reason to believe that it is), then mathematical realism cannot (easily) be justified by arguments from the indispensability of mathematics to science. This is because any justificatory chain of inferences from mathematical applications in science to the total body of mathematical theorems can cover at (...) most one mathematical universe. Indispensability arguments may thus lose their central role in the debate about mathematical ontology. (shrink)

In this paper, I argue against Michael Gorman’s objection to Tim Crane’s view of intentional objects. Gorman (“Talking about Intentional Objects,” 2006), following Searle (Intentionality, 1983), argues that intentional content can be cashed out solely in terms of conditions of satisfaction. For Gorman, we have reason to prefer his more minimal satisfaction-condition approach to Crane’s be- cause we cannot understand Crane’s notion of an intentional object when applied to non-existent objects. I argue that Gorman’s criticism rests on a misunderstanding of (...) Crane’s position. I also discuss the importance of keeping track of the distinction between the intentional objects of intentional states and the referents of such states. I do agree with Gorman that conditions of satisfaction are needed to cash out propositional intentional content, but we cannot get these conditions of satisfaction right if we do not capture how the subject takes the world to be. And we cannot properly capture how the subject takes the world to be without commitment to intentional objects. I argue that Crane’s notion of an intentional object is one that avoids questionable ontological commitments. So, in the end we have a view of intentional objects with a respectable metaphysics and ontology that can properly capture the intentional content of subjects’ intentional states. (shrink)

The “right intention” requirement, in the form of a requirement that the agent must have a justified true belief that the mind-independent conditions of the justification to use force are fulfilled, is not an additional criterion, but one that constrains the interpretation of the other criteria. Without it, the only possible interpretation of the mind-independent criteria is purely objectivist, that is, purely fact-relative. Pure objectivism condemns self-defense and just war theory to irrelevance since it cannot provide proper action guidance: it (...) is impractically demanding. This means that “revisionist” just war theories which base their doctrine of the moral inequality of combatants on the idea that objective justification defeats liability are irrelevant for the real world, where objective justification is virtually inaccessible. Moreover, only the right intention requirement in the form of a knowledge requirement, as opposed to requiring “good intentions” or “acceptable motivations,” can solve this problem. (shrink)

Within the context of the Quine–Putnam indispensability argument, one discussion about the status of mathematics is concerned with the ‘Enhanced Indispensability Argument’, which makes explicit in what way mathematics is supposed to be indispensable in science, namely explanatory. If there are genuine mathematical explanations of empirical phenomena, an argument for mathematical platonism could be extracted by using inference to the best explanation. The best explanation of the primeness of the life cycles of Periodical Cicadas is genuinely mathematical, according (...) to Baker :223–238, 2005; Br J Philos Sci 60:611–633, 2009). Furthermore, the result is then also used to strengthen the platonist position :779–793, 2017a). We pick up the circularity problem brought up by Leng Mathematical reasoning, heuristics and the development of mathematics, King’s College Publications, London, pp 167–189, 2005) and Bangu :13–20, 2008). We will argue that Baker’s attempt to solve this problem fails, if Hume’s Principle is analytic. We will also provide the opponent of the Enhanced Indispensability Argument with the so-called ‘interpretability strategy’, which can be used to come up with alternative explanations in case Hume’s Principle is non-analytic. (shrink)

Most set theorists accept AC, and reject AD, i.e. for them, AC is true in the "world of sets", and AD is false. Applying to set theory the above-mentioned formalistic explanation of the existence of quarks, we could say: if, for a long time in the future, set theorists will continue their believing in AC, then one may think of a unique "world of sets" as existing in the same sense as quarks are believed to exist.

During the first half of the twentieth century, many philosophers of memory opposed the postulation of memory traces based on the claim that a satisfactory account of remembering need not include references to causal processes involved in recollection. However, in 1966, an influential paper by Martin and Deutscher showed that causal claims are indeed necessary for a proper account of remembering. This, however, did not settle the issue, as in 1977 Malcolm argued that even if one were to buy Martin (...) and Deutscher’s argument for causal claims, we still don’t need to postulate the existence of memory traces. This paper reconstructs the dialectic between realists and anti-realists about memory traces, suggesting that ultimately realists’ arguments amount to inferences to the best explanation. I then argue that Malcolm’s anti-realist strategy consists in the suggestion that causal explanations that do not invoke memory traces are at least as good as those that do. But then, Malcolm, I argue that there are a large number of memory phenomena for which explanations that do not postulate the existence of memory traces are definitively worse than explanations that do postulate them. Next, I offer a causal model based on an interventionist framework to illustrate when memory traces can help to explain memory phenomena and proceed to substantiate the model with details coming from extant findings in the neuroscience of memory. (shrink)

While scientific inquiry crucially relies on the extraction of patterns from data, we still have a far from perfect understanding of the metaphysics of patterns—and, in particular, of what makes a pattern real. In this paper we derive a criterion of real-patternhood from the notion of conditional Kolmogorov complexity. The resulting account belongs to the philosophical tradition, initiated by Dennett :27–51, 1991), that links real-patternhood to data compressibility, but is simpler and formally more perspicuous than other proposals previously defended in (...) the literature. It also successfully enforces a non-redundancy principle, suggested by Ladyman and Ross, that aims to exclude from real-patternhood those patterns that can be ignored without loss of information about the target dataset, and which their own account fails to enforce. (shrink)

In this critical review of Robert Hanna's ingenious book (2006), I aim to support Hanna‟s main insightful reading of Kant, namely what he calls “a priori truth with a human face," without appealing to Kant's divide between a priori and a posteriori and analytic and synthetic truths. My suggestion is that transcendental propositions are necessary neither in the usual epistemological sense that analytic propositions are, let alone in the metaphysical sense that some empirical propositions are. Instead, they are necessary in (...) the theoretical domain in the weak alternative sense that they make possible the empirical recognition of appearances as an object as an indispensable condition of our self-consciousness experience, and they are a priori in the practical domain in the sense that their truth is vital for our self-comprehension as human beings. (shrink)

According to modal realism formulated by David Lewis, there exist concrete possible worlds. As he argues the hypothesis is serviceable and that is a sufficient reason to think it is true. On the other side, Lewis does not consider the pragmatic reasons to be conclusive. He admits that the theoretical benefits of modal realism can be illusory or that the acceptance of controversial ontology for the sake of theoretical benefits might be misguided in the first place. In the first part (...) of the paper, I consider the worry and conclude that although the worry is justified, there can be an epistemological justification for his theory. Next, I outline the so-called indispensability argument for the legitimacy of mathematical Platonism. Finally, I argue that the argument, if accepted, can be applied to metaphysics in general, to the arguing for the existence of concrete (im)possibilia in particular. (shrink)

I examine explanations’ realist commitments in relation to dynamical systems theory. First I rebut an ‘explanatory indispensability argument’ for mathematical realism from the explanatory power of phase spaces (Lyon and Colyvan 2007). Then I critically consider a possible way of strengthening the indispensability argument by reference to attractors in dynamical systems theory. The take-home message is that understanding of the modal character of explanations (in dynamical systems theory) can undermine platonist arguments from explanatory indispensability.

The Enhanced Indispensability Argument appeals to the existence of Mathematical Explanations of Physical Phenomena to justify mathematical Platonism, following the principle of Inference to the Best Explanation. In this paper, I examine one example of a MEPP—the explanation of the 13-year and 17-year life cycle of magicicadas—and argue that this case cannot be used defend the EIA. I then generalize my analysis of the cicada case to other MEPPs, and show that these explanations rely on what I will call (...) ‘optimal representations’, which are representations that capture all that is relevant to explain a physical phenomenon at a specified level of description. In the end, because the role of mathematics in MEPPs is ultimately representational, they cannot be used to support mathematical Platonism. I finish the paper by addressing the claim, advanced by many EIA defendants, that quantification over mathematical objects results in explanations that have more theoretical virtues, especially that they are more general and modally stronger than alternative explanations. I will show that the EIA cannot be successfully defended by appealing to these notions. (shrink)

I argue that modal epistemology should pay more attention to questions about the structure and function of modal thought. We can treat these questions from synchronic and diachronic angles. From a synchronic perspective, I consider whether a general argument for the epistemic support of modal though can be made on the basis of modal thoughs’s indispensability for what Enoch and Schechter (2008) call rationally required epistemic projects. After formulating the argument, I defend it from various objections. I also examine (...) the possibility of considering the indispensability of modal thought in terms of its components. Finally, I argue that we also need to approach these issues from a diachronic perspective, and I sketch how to approach this task. (shrink)

Revolutionary violence stems from the conatus of survival, from the appetite for life and joy rather than from the desire to destroy and the hubristic pretension to punish. It is an incursion of one's desire to affirm life and annihilate pain. Following Laruelle's methodology of nonstandard philosophy, I conclude that revolutionary violence is the product of an intensive expansion of life. Pure violence, conceived in non-philosophical terms, is a pre-lingual, presubjective force affected by the “lived,; analogous to Badiou's void and (...) it is radically revolutionary. It is fundamentally different from Benjamin's lawmaking “divine violence; and its appropriations by Žižek. Revolutionary experience is inevitably translated into language. What preserves the revolutionary substance in a post-revolution political discourse is that it is constantly checked by the sense of fidelity to the experience of the revolutionary event. Agamben, Benjamin, Schmidt and Žižek are discussed from an essentially non-philosophical stance, informed by Laruelle's theory that has been supplemented in some aspects by Badiou's concept of the pre-lingual event. (shrink)

Much recent discussion in the philosophy of mathematics has concerned the indispensability argument—an argument which aims to establish the existence of abstract mathematical objects through appealing to the role that mathematics plays in empirical science. The indispensability argument is standardly attributed to W. V. Quine and Hilary Putnam. In this paper, I show that this attribution is mistaken. Quine's argument for the existence of abstract mathematical objects differs from the argument which many philosophers of mathematics ascribe to him. (...) Contrary to appearances, Putnam did not argue for the existence of abstract mathematical objects at all. I close by suggesting that attention to Quine and Putnam's writings reveals some neglected arguments for platonism which may be superior to the indispensability argument. (shrink)

It is an under-appreciated fact that Quine's rejection of the analytic/synthetic distinction, when coupled with some other plausible and related views, implies that there are serious difficulties in demarcating empirical theories from pure mathematical theories within the Quinean framework. This is a serious problem because there seems to be a principled difference between the two disciplines that cannot apparently be captured in the orthodox Quienan framework. For the purpose of simplicity let us call this Quine's problem of demarcation. In this (...) paper this problem will be articulated and it will be shown that the typical sorts of responses to this problem are all unworkable within the Quinean framework. It will then be shown that the lack of resources to solve this problem within the Quinean framework implies that Quine’s version of the indispensability argument cannot get off the ground, for it presupposes the possibility of making such a distinction. (shrink)

In recent years there has been a lot of skepticism about the existence of facts. It seems that one of the last places for their application is in truthmaking theory. In this paper I discuss two approaches to the use of facts in truthmaking. The first, categorial, holds that facts are entities that belong to one of three ontological categories (true propositions, truth of propositions, instantiations of universals).The second, deflationary, holds that a fact is merely a functional concept denoting any (...) entity that performs a truthmaking function. I argue that in the face of significant criticism of categorial facts as truthmakers, a defender of facts may resort to the deflationary concept. Nevertheless, even in this case we can do without facts as truthmakers. (shrink)

Comprehensive resource for indispensability research.

Over the decades, scholarly discourses on sovereignty and globalization have been produced following various theories and numerous debates about the strength and weakness of the sovereign nation-state and globalization. In this paper, the various theories on the discourse of sovereignty and globalization are traced and placed into four categories as: contending paradigm, globalization paradigm, transformation paradigm and complementary paradigm. Both concepts, sovereignty and globalization, are explored by adopting the methodological framework, sources of explanation. The argument is that there is an (...) intricate relationship between these concepts. To determine the relationship between sovereignty and globalization, three world systems were examined and it revealed that, globalization is born of the sovereign nation-state and that globalization can only be assert in the current sovereign world system and not the ones preceding it. The overall conclusion is that globalization emerged as a result of sovereignty and since the discourse of sovereignty and globalization is about the same space and its inhabitants, they are bound to be discursively set against each other if the discourse focusses solely on the phenomena seen as globalization. The forces of globalization and sovereignty need to be further researched into to be able to tell where they are leading us. (shrink)

The aim of the present article is to accomplish two things. The first is to show that given some further plausible assumptions, existing challenges to the indispensability of knowledge in causal explanation of action fail. The second is to elaborate an overlooked and distinct argument in favor of the causal efficacy of knowledge. In short, even if knowledge were dispensable in causal explanation of action, it is still indispensable in causal explanation of other mental attitudes and, in particular, some (...) reactive attitudes and factive emotions. Taking into account this sort of causal efficacy in determining which mental states are genuine mental states opens up new perspectives for defending the view that knowledge is the most general factive and genuine mental state. (shrink)

The predisposition of the Indispensability Argument to objections, rephrasing and versions associated with the various views in philosophy of mathematics grants it a special status of a “blueprint” type rather than a debatable theme in the philosophy of science. From this point of view, it follows that the Argument has more an epistemic character than ontological.

Mereological Nihilism is the thesis that no material object has proper parts; every material object is a simple. Recent developments in plural semantics have made it possible to develop and motivate this position. In particular, some have argued that the tools of plural reference and quantification enable us to systematically paraphrase true statements apparently about composites into statements that only concern simples. Are composites really surplus to philosophical requirements? Given the resources of plural semantics, what must the world be like (...) if composites are to be theoretically indispensable? I will describe and defend the possibility of scenario in which mention of composites cannot be paraphrased. We will therefore come to appreciate one way in which the world would have to be in order for composites to be required and for Nihilism to fail. (shrink)

Some explanations in social science, psychology and biology belong to a higher level than other explanations. And higher explanations possess the virtue of abstracting away from the details of lower explanations, many philosophers argue. As a result, these higher explanations are irreplaceable. And this suggests that there are genuine higher laws or patterns involving social, psychological and biological states. I show that this ‘abstractness argument’ is really an argument schema, not a single argument. This is because the argument uses the (...) ‘is lower than’ relation, and this relation admits of different readings. I then suggest four rigorous definitions of the ‘is lower than’ relation, and show that the abstractness argument’s prospects are much brighter for some of these definitions than for others. To show this, I evaluate the so-called ‘disjunctive threat’ to the abstractness argument. (shrink)

Is the institutionalization of religious freedom through human rights jurisprudence simply a means by which the modern nation-state manufactures and regulates “religion”? Is the discourse of religious freedom principally a technology of state governance? These questions challenge the ways that scholars conceptualize the relation between states, nationalism, human rights, and religious freedom. This article forwards an approach to human rights and methodological nationalism that both counters and explores alternatives to the prevailing conceptions of human rights, nationalism, and state sovereignty in (...) the discourse on the putative impossibility—and, by some accounts, insidiousness—of religious freedom. I first explicate the interpretive and contestatory dimensions of human rights discourse concerning religious freedom. I then explore cross-cutting ambivalences within the nationalisms that states need and cultivate in effort to transmute their monopoly upon coercive force (i.e. power) into legitimated authority. I argue that these provide two dimensions in and through which state sovereignty may be opposed, criticized, held accountable, and subject to change. (shrink)

We demonstrate how real progress can be made in the debate surrounding the enhanced indispensability argument. Drawing on a counterfactual theory of explanation, well-motivated independently of the debate, we provide a novel analysis of ‘explanatory generality’ and how mathematics is involved in its procurement. On our analysis, mathematics’ sole explanatory contribution to the procurement of explanatory generality is to make counterfactual information about physical dependencies easier to grasp and reason with for creatures like us. This gives precise content to (...) key intuitions traded in the debate, regarding mathematics’ procurement of explanatory generality, and adjudicates unambiguously in favour of the nominalist, at least as far as explanatory generality is concerned. (shrink)

The enhanced mathematical indispensability argument, proposed by Alan Baker (2005), argues that we must commit to mathematical entities, because mathematical entities play an indispensable explanatory role in our best scientific theories. This article clarifies the doctrines that support this argument, namely, the doctrines of naturalism and confirmational holism.

Numbers without Science opposes the Quine-Putnam indispensability argument, seeking to undermine the argument and reduce its profound influence. Philosophers rely on indispensability to justify mathematical knowledge using only empiricist epistemology. I argue that we need an independent account of our knowledge of mathematics. The indispensability argument, in broad form, consists of two premises. The major premise alleges that we are committed to mathematical objects if science requires them. The minor premise alleges that science in fact requires mathematical (...) objects. The most common rejection of the argument denies its minor premise by introducing scientific theories which do not refer to mathematical objects. Hartry Field has shown how we can reformulate some physical theories without mathematical commitments. I argue that Field’s preference for intrinsic explanation, which underlies his reformulation, is ill-motivated, and that his resultant fictionalism suffers unacceptable consequences. I attack the major premise instead. I argue that Quine provides a mistaken criterion for ontic commitment. Our uses of mathematics in scientific theory are instrumental and do not commit us to mathematical objects. Furthermore, even if we accept Quine’s criterion for ontic commitment, the indispensability argument justifies only an anemic version of mathematics, and does not yield traditional mathematical objects. The first two chapters of the dissertation develop these results for Quine’s indispensability argument. In the third chapter, I apply my findings to other contemporary indispensabilists, specifically the structuralists Michael Resnik and Stewart Shapiro. In the fourth chapter, I show that indispensability arguments which do not rely on Quine’s holism, like that of Putnam, are even less successful. Also in Chapter 4, I show how Putnam’s work in the philosophy of mathematics is unified around the indispensability argument. In the last chapter of the dissertation, I conclude that we need an account of mathematical knowledge which does not appeal to empirical science and which does not succumb to mysticism and speculation. Briefly, my strategy is to argue that any defensible solution to the demarcation problem of separating good scientific theories from bad ones will find mathematics to be good, if not empirical, science. (shrink)

The aim of this expository paper is to give an informal overview of a plausible naturalistic case for free will. I will describe what I take to be the main naturalistically motivated challenges for free will and respond to them by presenting an indispensability argument for free will. The argument supports the reality of free will as an emergent higher-level phenomenon. I will also explain why the resulting picture of free will does not conflict with the possibility that the (...) fundamental laws of nature are deterministic, and I will address some common objections. (shrink)

The Quine/Putnam indispensability argument is regarded by many as the chief argument for the existence of platonic objects. We argue that this argument cannot establish what its proponents intend. The form of our argument is simple. Suppose indispensability to science is the only good reason for believing in the existence of platonic objects. Either the dispensability of mathematical objects to science can be demonstrated and, hence, there is no good reason for believing in the existence of platonic objects, (...) or their dispensability cannot be demonstrated and, hence, there is no good reason for believing in the existence of mathematical objects which are genuinely platonic. Therefore, indispensability, whether true or false, does not support platonism. (shrink)

It is often argued that the indispensability of continuum models comes from their empirical adequacy despite their decoupling from the microscopic details of the modelled physical system. There is thus a commonly held misconception that temperature varying across a region of space or time can always be accurately represented as a continuous function. We discuss three inter-related cases of temperature modelling — in phase transitions, thermal boundary resistance and slip flows — and show that the continuum view is fallacious (...) on the ground that the microscopic details of a physical system are not necessarily decoupled from continuum models. We show how temperature discontinuities are present in both data (experiments and simulations) and phenomena (theory and models) and how discontinuum models of temperature variation may have greater empirical adequacy and explanatory power. The conclusions of our paper are: a) continuum idealisations are not indispensable to modelling physical phenomena and both continuous and discontinuous representations of phenomena work depending on the context; b) temperature is not necessarily a continuously defined function in our best scientific representations of the world; and c) that its continuity, where applicable, is a contingent matter. We also raise a question as to whether discontinuous representations should be considered truly de-idealised descriptions of physical phenomena. (shrink)

Some scientific explanations appear to turn on pure mathematical claims. The enhanced indispensability argument appeals to these ‘mathematical explanations’ in support of mathematical platonism. I argue that the success of this argument rests on the claim that mathematical explanations locate pure mathematical facts on which their physical explananda depend, and that any account of mathematical explanation that supports this claim fails to provide an adequate understanding of mathematical explanation.

This paper argues that scientific realism commits us to a metaphysical determination relation between the mathematical entities that are indispensible to scientific explanation and the modal structure of the empirical phenomena those entities explain. The argument presupposes that scientific realism commits us to the indispensability argument. The viewpresented here is that the indispensability of mathematics commits us not only to the existence of mathematical structures and entities but to a metaphysical determination relation between those entities and the modal (...) structure of the physical world. The no-miracles argument is the primary motivation for scientific realism. It is a presupposition of this argument that unobservable entities are explanatory only when they determine the empirical phenomena they explain. I argue that mathematical entities should also be seen as explanatory only when they determine the empirical facts they explain, namely, the modal structure of the physical world. Thus, scientific realism commits us to a metaphysical determination relation between mathematics and physical modality that has not been previously recognized. The requirement to account for the metaphysical dependence of modal physical structure on mathematics limits the class of acceptable solutions to the applicability problem that are available to the scientific realist. (shrink)

According to Ian Hacking’s Entity Realism, unobservable entities that scientists carefully manipulate to study other phenomena are real. Although Hacking presents his case in an intuitive, attractive, and persuasive way, his argument remains elusive. I present five possible readings of Hacking’s argument: a no-miracle argument, an indispensability argument, a transcendental argument, a Vichian argument, and a non-argument. I elucidate Hacking’s argument according to each reading, and review their strengths, their weaknesses, and their compatibility with each other.

Indispensablists argue that when our belief system conflicts with our experiences, we can negate a mathematical belief but we do not because if we do, we would have to make an excessive revision of our belief system. Thus, we retain a mathematical belief not because we have good evidence for it but because it is convenient to do so. I call this view ‘ mathematical convenientism.’ I argue that mathematical convenientism commits the consequential fallacy and that it demolishes the Quine-Putnam (...) indispensability argument and Baker’s enhanced indispensability argument. (shrink)

This paper argues that Internet access should be recognised as a human right because it has become practically indispensable for having adequate opportunities to realise our socio-economic human rights. This argument is significant for a philosophically informed public understanding of the Internet and because it provides the basis for creating new duties. For instance, accepting a human right to Internet access minimally requires guaranteeing access for everyone and protecting Internet access and use from certain objectionable interferences (e.g. surveillance, censorship, online (...) abuse). Realising this right thus requires creating an Internet that is crucially different from the one we currently have. The argument thus has wide-ranging implications. (shrink)

In the debate over whether mathematical facts, properties, or entities explain physical events (in what philosophers call “extra-mathematical” explanations), Aidan Lyon’s (2012) affirmative answer stands out for its employment of the program explanation (PE) methodology of Frank Jackson and Philip Pettit (1990). Juha Saatsi (2012; 2016) objects, however, that Lyon’s examples from the indispensabilist literature are (i) unsuitable for PE, (ii) nominalizable into non-mathematical terms, and (iii) mysterious about the explanatory relation alleged to obtain between the PE’s mathematical explanantia and (...) physical explananda. In this paper, I propose a counterexample to Saatsi’s objections. My counterexample is Frank Jackson’s (1998a) program explanation for color experience, which I argue needs recasting as an extra-mathematical PE due to its implicit reliance on reflectance, a property that suffers conceptual regress unless redefined with Fourier harmonics. Pace Saatsi, I argue that this recast example is an authoritative PE, non-nominalizable, and minimally esoteric. Important for the indispensability debate at large, moreover, is that my counterexample reifies Fourier harmonics without the Enhanced Indispensability Argument (an argument to which Lyon applies PE as a premise). Indispensabilists have long overlooked the conditionalization of a limited mathematical realism on property realism, and my counterexample to Saatsi exploits this conditionalization. (shrink)

Unlike other organs that operate continuously, such as the heart and kidneys, many of the operations of the nervous system shut down during sleep. The evolutionarily conserved unconscious state of sleep that puts animals at risk from predators indicates that it is an indispensable integral part of systems operation. A reasonable expectation is that any hypothesis for the mechanism of the nervous system functions should be able to provide an explanation for sleep. In this regard, the semblance hypothesis is examined. (...) Postsynaptic membranes are continuously being depolarized by the quantally released neurotransmitter molecules arriving from their presynaptic terminals. In this context, an incidental lateral activation of the postsynaptic membrane is expected to induce a semblance (cellular hallucination of arrival of activity from its presynaptic terminal, which forms a unit for internal sensation) of the arrival of activity from its presynaptic terminal as a systems property. This restricts induction of semblance to a context of a very high ratio of the duration of the default state of neurotransmitter-induced postsynaptic depolarization to the total duration of incidental lateral activations of the postsynaptic membrane. This requirement spans within a time-bin of a few sleep-wake cycles. Since the duration of quantal release remains maximized, the above requirement can be achieved only by ceiling the total duration of incidental lateral activations of the postsynaptic membrane, which necessitates a state of sleep. (shrink)

“Structuralism, Fictionalism, and the Applicability of Mathematics in Science”. This article has two objectives. The first one is to review some of the most important questions in the contemporary philosophy of mathematics: What is the nature of mathematical objects? How do we acquire knowledge about these objects? Should mathematical statements be interpreted differently than ordinary ones? And, finally, how can we explain the applicability of mathematics in science? The debate that guides these reflections is the one between mathematical realism and (...) anti-realism. On the other hand, the second objective is to discuss the arguments that use the applicability of mathematics in science to justify mathematical realism, and show that none of them reaches its aim. To this end, we will distinguish three aspects of the problem of the applicability of mathematics: the utility of mathematics in science, the unexpected utility of some mathematical theories, and the apparent indispensability of mathematics in our best scientific theories - in particular, in our best scientific explanations. Finally, I argue that none of these aspects constitutes a reason to adopt mathematical realism. (shrink)

Indispensability arguments are used as a way of working out what there is: our best science tells us what things there are. Some philosophers think that indispensability arguments can be used to show that we should be committed to the existence of mathematical objects (numbers, functions, sets). Do indispensability arguments also deliver conclusions about the modal properties of these mathematical entities? Colyvan (in Leng, Paseau, Potter (eds) Mathematical knowledge, OUP, Oxford, 109-122, 2007) and Hartry Field (Realism, mathematics (...) and modality, Blackwell, Oxford, 1989) each suggest that a consequence of the empirical methodology of indispensability arguments is that the resulting mathematical objects can only be said to exist (or not exist) contingently. Kristie Miller has argued that this line of thought doesn’t work (Miller in Erkenntnis, 77 (3), 335-359, 2012). Miller argues that indispensability arguments are in direct tension with contingentism about mathematical objects, and that they cannot tell us about the modal status of mathematical objects. I argue that Miller’s argument is crucially imprecise, and that the best way of making it clearer no longer shows that the indispensability strategy collapses or is unstable if it delivers contingentist conclusions about what there is. (shrink)

Otávio Bueno* * and Steven French.** ** Applying Mathematics: Immersion, Inference, Interpretation. Oxford University Press, 2018. ISBN: 978-0-19-881504-4 978-0-19-185286-2. doi:10.1093/oso/9780198815044. 001.0001. Pp. xvii + 257.

Words are indispensable linguistic tools for beings like us. However, there is not much philosophical work done about what words really are. In this paper, I develop a new ontology for words. I argue that words are abstract artifacts that are created to fulfill various kinds of purposes, and words are abstract in the sense that they are not located in space but they have a beginning and may have an end in time given that certain conditions are met. What (...) follows from this two-fold argument is that words, from an ontological point of view, are more like musical works, fictional characters or computer programs, than numbers or sets. (shrink)