Many explanations in science make use of mathematics. But are there cases where the mathematical component of a scientific explanation is explanatory in its own right? This issue of mathematical explanations in science has been for the most part neglected. I argue that there are genuine mathematical explanations in science, and present in some detail an example of such an explanation, taken from evolutionary biology, involving periodical cicadas. I also indicate how the answer to my title question impacts on broader (...) issues in the philosophy of mathematics; in particular it may help platonists respond to a recent challenge by Joseph Melia concerning the force of the Indispensability Argument. (shrink)

I argue that most counterfactuals are false.

Historians and sociologists chart the consequences of the expansion of knowledge; philosophers of science examine the causes. This book bridges the gap. The focus is on ‘academisation’ — the paradox whereby, as the general public becomes better educated to live and work with knowledge, the ‘academy’ increases its intellectual distance from the public, so that the nature of social and natural reality becomes more rather than less obscure.

A centipede can walk until it thinks about howit does so. Thereafter it stumbles, over thesheer impossibility of the information andcoordination required. Life in the economy islittle different. Those engaged in productionand exchange discover, pragmatically, ways tomake them work. Those observing the processsee, realistically, the immense improbabilitythat it should do so. That most economies workin practice, but must pass such toughteleological tests to succeed in theory,highlights a difference between players' andspectators' outlook which may help to explainwhy the game has repeatedly (...) been thrown wideopen just when conclusive results seemed withinreach.Section 1 of this paper identifies the fourforms of realism which economists have tendedto adopt. Section 2 considers the pragmatism ofeconomic agents, when observed in action bypsychologists and management scholars notoverly steeped in economic theory. Theconcluding section reviews the ways in whicheconomists have tried to blur the distinction,by reclassifying agents as realistic or theirown views as pragmatic, and suggests that amore pragmatic economics might bridge thedivide. (shrink)

Actualists who believe in possible worlds typically regard them as "abstract" objects of some special sort. For example, Alvin Plantinga takes worlds to be maximal possible states-of-affairs, all of which "exist", as actualism requires, but only one of which "obtains". Views like Plantinga's run into difficulty in the interpretation of statements of "iterated" modality, statements about what is "possible" for individuals that "could" exist but that do not actually exist. These statements seem to require the existence of "singular" states-Of-affairs that (...) have nonactual individuals as constituents, a requirement that is incompatible with actualism. One can try to avoid the troublesome singular states-of-affairs by introducing "unexemplified individual essences" and maintaining that these are the true constituents of the required states-of-affairs, rather than the nonactual possibles themselves. However, serious arguments are raised against this employment of individual essences. (shrink)

One foundational question in contemporarybiology is how to `rejoin evolution anddevelopment. The emerging research program(evolutionary developmental biology or`evo-devo) requires a meshing of disciplines,concepts, and explanations that have beendeveloped largely in independence over the pastcentury. In the attempt to comprehend thepresent separation between evolution anddevelopment much attention has been paid to thesplit between genetics and embryology in theearly part of the 20th century with itscodification in the exclusion of embryologyfrom the Modern Synthesis. This encourages acharacterization of evolutionary developmentalbiology as the marriage (...) of evolutionary theoryand embryology via developmental genetics. Butthere remains a largely untold story about thesignificance of morphology and comparativeanatomy (also minimized in the ModernSynthesis). Functional and evolutionarymorphology are critical for understanding thedevelopment of a concept central toevolutionary developmental biology,evolutionary innovation. Highlighting thediscipline of morphology and the concepts ofinnovation and novelty provides an alternativeway of conceptualizing the `evo and the `devoto be synthesized. (shrink)

According to finite frequentism, the probability of an attribute A in a finite reference class B is the relative frequency of actual occurrences of A within B. I present fifteen arguments against this position.

In this paper I examine a dispositional property that has been receiving increased attention in biology, evolvability. First, I identify three compatible but distinct investigative approaches, distinguish two interpretations of evolvability, and treat the difference between dispositions of individuals versus populations. Second, I explore the relevance of philosophical distinctions about dispositions for evolvability, isolating the assumption that dispositions are intrinsically located. I conclude that some instances of evolvability cannot be understood as purely intrinsic to populations and suggest alternative strategies for (...) resolving this difficulty. (shrink)

Confirmation theory is intended to codify the evidential bearing of observations on hypotheses, characterizing relations of inductive “support” and “counter­support” in full generality. The central task is to understand what it means to say that datum E confirms or supports a hypothesis H when E does not logically entail H.

One criticism of David Lewis's account of counterfactuals is that it sometimes assigns the wrong truth-value to a counterfactual when both antecedent and consequent happen to be true. Lewis has suggested a possible remedy to this situation, but commentators have found this to be unsatisfactory. I suggest an alternative solution which involves a modification of Lewis's truth conditions, but which confines itself to the resources already present in his account. This modification involves the device of embedding one counterfactual within another. (...) On the revised set of truth conditions, counterfactuals with true components are sometimes true and sometimes false, in a way that is more in keeping with our intuitive judgments about such statements. (shrink)

One recent trend in the philosophy of mathematics has been to approach the central epistemological and metaphysical issues concerning mathematics from the perspective of the applications of mathematics to describing the world, especially within the context of empirical science. A second area of activity is where philosophy of mathematics intersects with foundational issues in mathematics, including debates over the choice of set-theoretic axioms, and over whether category theory, for example, may provide an alternative foundation for mathematics. My central claim is (...) that these latter issues are of direct relevance to philosophical arguments connected to the applicability of mathematics. In particular, the possibility of there being distinct alternative foundations for mathematics blocks the standard argument from the indispensable role of mathematics in science to the existence of specific mathematical objects. (shrink)

Roger Jones asks what Newtonian realists should be realists about, given that there are four empirically equivalent formulations of Newtonian mechanics which have different ontological commitments and explanatory mechanisms. A realist answer is sketched: Newtonians should be realists about what the best metaphysical considerations dictate, where the best metaphysical considerations are those which have yielded the best physics. Metaphysical considerations are required within physics, just as they are required to eliminate idealist and surrealist theories which are empirically equivalent to realist (...) ones. Realists must reject the positivist assumption that empirically equivalent theories are explanatory and evidential equivalents, too. (shrink)

This essay explores some of the issues raised as regards the relations of philosophy and sociology of science in the work of Rudolf Carnap and Hans Reichenbach. It argues that Hans Reichenbach's distinction between the contexts of discovery and justification should not be seen as erecting a principled normative/descriptive distinction that demarcates philosophy of science from sociology of science. The essay also raises certain issues about the role of volition, decision, and the limits of epistemological concern in the work of (...) Carnap and Reichenbach and in some recent sociology of science. The relations of philosophy of science to sociology of science are seen to be more deeply rooted and more interesting than the Science Warriors would have us believe. (shrink)

Many leading management scientists have advocated ethicalism: the incorporation of social and ethical concerns into traditional "rational" OR-MS techniques and management decisions. In fact, elementary forms of decision analysis can readily be augmented, using ethical theory, in ways that sweep in ethical issues. In addition, alternative conceptual models of Decision-Analysis, Game-Theory and Optimality are now available, all of which have brought OR-MS and Business-Ethics into a closer alignment.

The goal of this paper is to defend open theism vis-à-vis its main competitors within the family of broadly classical theisms, namely, theological determinism and the various forms of non-open free-will theism, such as Molinism and Ockhamism. After isolating two core theses over which open theists and their opponents differ, I argue for the open theist position on both points. Specifically, I argue against theological determinists that there are future contingents. And I argue against non-open free-will theists that future contingency (...) is incompatible with the future’s being epistemically settled for God. This paper is a follow-up to the author’s Rhoda (Religious Studies, 2008) which was delivered during the APA Pacific 2007 Mini-Conference on Models of God. (shrink)

Alan R White; Needs and Wants, Journal of Philosophy of Education, Volume 8, Issue 2, 30 May 2006, Pages 159–180, https://doi.org/10.1111/j.1467-9752.1974.tb004.

Reid said little in his published writings about his contemporary Joseph Priestley, but his unpublished work is largely devoted to the latter. Much of Priestley's philosophical thought- his materialism, his determinism, his Lockean scientific realism- was as antithetical to Reid's as was Hume's philosophy in a very different way. Neither Reid nor Priestley formulated a full response to the other. Priestley's response to Reid came very early in his career, and is marked by haste and immaturity. In his last decade (...) Reid worried much about Priestley's materialism, but that concern never reached publication. I document Reid's unpublished response to Priestley, and also view Reid's response from Priestley's perspective, as deduced from his published works. Both thinkers attempted to base their arguments on Newtonian method. Reid's position is the more puzzling of the two, since he nowhere makes clear how Newtonian method favours mind-body dualism over materialism, which is the central debate between them. (shrink)

The project of naturalising phenomenology is examined within the larger context of the philosophy of science. Transcendental phenomenology, as defended by Husserl, in opposition to the naturalistic enterprise, reflects a particular way of thinking about philosophy and its relationship to the empirical sciences that stands as an obstacle to the project of naturalisation. This paper develops a critique of a basic assumption made in this conception of philosophy, namely that it is possible to ask and answer questions concerning knowledge in (...) the abstract, prior to and independently of the various investigative contexts which are the immediate concern of practicing scientists. To successfully naturalise phenomenology, we need to abandon this conception of philosophy. (shrink)

It is often claimed that epistemological thought divides around the issue of the place of experience in knowledge: While empiricists argue that experience is the only legitimate source of knowledge, rationalists find other such sources. The trouble with such accounts is not that they are wrong, but that they are incomplete. On occasion, epistemological differences run deeper, raising the very notion of experience as an issue for epistemology. This paper looks at two epistemological debates which concerned not simply the place (...) of experience in knowledge but also the appropriate account of experience itself. The first episode is the rise of Marburg Neo-Kantianism in the 1870s – in particular the seminal work of Hermann Cohen in his Kants Theorie der Erfahrung (1871). Cohen's principal point was that Kant's significance as an epistemologist was in providing a new theory of experience, one that tied experience to exact science and led to a new stress on the formal conditions of exact knowledge. The second episode is Carnap's rejection of epistemology in the 1930s in favour of a program of the logic of science. My focus in each case will be the interplay between an epistemology focused on exact science as the locus of knowledge and a concomitant call for logical methods in epistemology. (shrink)

Alan Bailey offers a clear and vigorous exposition and defence of the philosophy of Sextus Empiricus, one of the most influential of ancient thinkers, the father of philosophical scepticism. The subsequent sceptical tradition in philosophy has not done justice to Sextus: his views stand up today as remarkably insightful, offering a fruitful way to approach issues of knowledge, understanding, belief, and rationality. Bailey's refreshing presentation of Sextus to a modern philosophical readership rescues scepticism from the sceptics.

This paper interprets Bernard Williams's claim that all practical reasons must meet the internal reasons constraint. It is argued that this constraint is independent of any substantive Humean claims about reasons and its rationale is a content scepticism about the capacity of pure reason to supply reasons for action. The final sections attempt a positive reconciliation of the internal reasons account with the motivation for external reasons, namely, securing practical objecitivy in the form of a commitment to impartiality. Impartiality is (...) given a contractualist interpretation in the limited sense that socialised agents have a central disposition to hold those reasons that are defensible to reasonable interlocutors, but this is not a substantive constraint on their content. Such a commitment plays a structural role in motivation illustrated by the analogy of the internalisation of a relativised a priori principle. Theorists of moral motivation such as Nagel and Scheffler have uncovered the importance of such structural motivations, but they are best treated as an architectonic feature of a socialised agent's motivational set, not as a principle or motive akin to other principles or motives within that set. This gives us critical leverage on the motivational sets of individuals that goes beyond launching "optimistic internal reasons" statements at them, but it does not violate Williams's constraints on the idea of a practical reason in general. (shrink)

This paper examines recent developments in U.K. utility regulation from a business ethics perspective. The regulatory framework that facilitated privatisation of the utility companies has foundations based upon free market principles involving a transfer from regulation to competitive markets wherever possible. Where competition is not feasible, continuing economic regulation is relied upon, designed to mirror the competitive market to induce, through comparative competition and the price capping mechanism, incentives for greater efficiency. The New Labour Government, having fundamentally reviewed this framework (...) when it came to office, has surprisingly endorsed its basic tenets. However, it wishes to superimpose social responsibility regulations designed to achieve social policy rather than economic objectives. This interventionist approach is in itself in conflict with the free market inspired regulatory framework but additionally, the imposition of social policy objectives creates fundamental ambiguities within the framework for the key stakeholders. The paper concludes that the Government''s policy, by eliciting stakeholder confusion and perverse behaviour, could be counter-productive but that ethical theories and frameworks can contribute to thinking in this vital area of the economy. (shrink)

This is a simple essay. It raises a familiar question about equality, adduces a very small amount of empirical evidence about the social consequences of equality as distinct from prosperity, and broods on the difficulty of providing a really persuasive answer to the question raised. I begin with the view that there simply cannot be anything intrinsically wrong with inequality, move on to the view that there are extrinsic reasons for anxiety, dividing these into conceptual and empirical reasons, though without (...) any great commitment to the clarity of that distinction in this context, and end with some reflections on recent social and political theory. The essay thus begins with what I hope are clear and (what I am sure are) very simple thoughts, before muddying the water pretty thoroughly thereafter. (shrink)

Most contemporary internalists are fallibilists, denying that there need be anything about which we are infallible for us to have knowledge or justified beliefs. At the same time, internalists standardly appeal to ‘internal twins’ in arguing against externalism and motivating internalism---a Cartesian demon can ruin the ‘external’ relations we have to the world, but one is equally well justified in one’s beliefs whether or not one is subject to such deception. Even if one doesn’t motivate one’s internalism by appeal to (...) internal twins, any internalist must agree that internal twins are equally well justified in their beliefs. I argue that the internal twins argument for, or commitment of internalism, commits one to the claim that the conditions in virtue of which one is justified must be ones about which a believer is infallible. The basic argument is that for anything about which one can be mistaken, one has an internal twin who is mistaken, but is equally well justified---and so, not in virtue of that about which one can be mistaken. If the argument can be resisted, this should tell us something useful about how to properly understand both internalism in general, and the idea of internal twins in particular. (shrink)