The anthropocentrism debate, which centers on the place and status of environmental values, has been a core issue for environmental ethics since the field’s beginning in the 1970s. Nonanthropocentrists attribute value to non-human nature directly, while anthropocentrists claim that humans hold a certain priority. While the debate has produced a wide variety of interesting philosophical positions, it has not achieved its implicit goal of cultural reform. This is not because philosophers fail to agree on a tenable position, but because the (...) debate is misconceived. Both sides of the debate assume that agreement on common values, worldviews, and substantive positions is prerequisite to cultural reform. Pragmatic criticism of this assumption, however, displays its underlying faults, while pragmatic inquiry into the field’s development displays how scholars are already generating methods more commensurate with the goal of cultural reform. Philosophers invested in changing public values should transition from debates in axiology to debating method, where axiology is just one method among others and not the one best suited to supporting cultural reform. A historical survey of the field suggests what scholars of environmental ethics are learning about methods that are both publicly engaged and culturally transformative. (shrink)

Jeffrey Stout's recent essay, "Public Reason and Dialectical Pragmatism", argues that theories of public reason in the tradition of Enlightenment rationalism, including its expression in the work of John Rawls, must be made over in an altogether more public fashion.1 That is, these theories must abandon the private machinations of philosophical minds and come to embrace the messy forums of public debate. There, as the rightful inheritance of democratic publics instead of the exclusive province of erudite philosophers, public reasoning—as a (...) progressive process—becomes an indispensable resource for the continual reconstruction of a liberal and deliberative democracy. Democracy, in Stout's view, is perpetually... (shrink)

This essay overcomes the division between “principled” and “strategic” approaches to nonviolence studies by demonstrating that ethical analysis is key to understanding movement strategy. I show how the moral phenomenologies of Martin Luther King Jr. and Emmanuel Lévinas, figures usually treated by scholars of principled nonviolence, possess genuine insight for nonviolent strategists. With reference to each thinker and supporting evidence from the #BlackLivesMatter movement, I argue that nonviolent resistance makes a moral appeal through the medium of the body to the (...) conscience of those bearing witness. Analysis of the way King combined moral reflection and strategic action recovers his legacy for the pragmatic tradition of social thought, while Lévinas's theory of the face offers additional considerations for nonviolent practitioners aiming for moral transformation at the local level. Studies that elucidate the complex moral dynamics by which nonviolent movements either succeed or fail will make the field a greater asset to practitioners. (shrink)

Evidentialism is the thesis that epistemic justification for belief supervenes on evidential support. However, we claim there are cases in which, even though two subjects have the same evidential support for a proposition, only one of them is justified. What make the difference are pragmatic factors, factors having to do with our cares and concerns. Our argument against evidentialism is not based on intuitions about particular cases. Rather, we aim to provide a theoretical basis for rejecting evidentialism by defending a (...) “pragmatic” necessary condition on epistemic justification. We argue for the following necessary condition for justification: S is justified in believing that p only if S is rational to prefer (and, hence, act) as if p. In light of this necessary condition, the price of evidentialism is skepticism, or something close to it. (shrink)

Author Jeremy Waldron has thoroughly revised thirteen of his most recent essays in order to offer a comprehensive critique of the idea of the judicial review of legislation. He argues that a belief in rights is not the same as a commitment to a Bill of Rights. This book presents legislation by a representative assembly as a form of law making which is especially apt for a society whose members disagree with one another about fundamental issues of principle.

Of all the demands that mathematics imposes on its practitioners, one of the most fundamental is that proofs ought to be correct. It has been common since the turn of the twentieth century to take correctness to be underwritten by the existence of formal derivations in a suitable axiomatic foundation, but then it is hard to see how this normative standard can be met, given the differences between informal proofs and formal derivations, and given the inherent fragility and complexity of (...) the latter. This essay describes some of the ways that mathematical practice makes it possible to reliably and robustly meet the formal standard, preserving the standard normative account while doing justice to epistemically important features of informal mathematical justification. (shrink)

In a wide range of fields, the word “modular” is used to describe complex systems that can be decomposed into smaller systems with limited interactions between them. This essay argues that mathematical knowledge can fruitfully be understood as having a modular structure and explores the ways in which modularity in mathematics is epistemically advantageous.

I compare deterministic and stochastic hidden variable models of the Bell experiment, exphasising philosophical distinctions between the various ways of combining conditionals and probabilities. I make four main claims. (1) Under natural assumptions, locality as it occurs in these models is equivalent to causal independence, as analysed (in the spirit of Lewis) in terms of probabilities and conditionals. (2) Stochastic models are indeed more general than deterministic ones. (3) For factorizable stochastic models, relativity's lack of superluminal causation does not favour (...) locality over completeness. (4) If we prohibit all superluminal causation, then the violation of the Bell inequality teaches us a lesson, besides quantum mechanics' familiar ones that quantities can lack precise values and that pairs of quantities can lack joint probabilities: namely, some pairs of events are not screened off by their common past. (shrink)

On a traditional view, the primary role of a mathematical proof is to warrant the truth of the resulting theorem. This view fails to explain why it is very often the case that a new proof of a theorem is deemed important. Three case studies from elementary arithmetic show, informally, that there are many criteria by which ordinary proofs are valued. I argue that at least some of these criteria depend on the methods of inference the proofs employ, and that (...) standard models of formal deduction are not well-equipped to support such evaluations. I discuss a model of proof that is used in the automated deduction community, and show that this model does better in that respect. (shrink)

"Arguing that debates over legitimacy, political violence, freedom, and justice would benefit greatly from cross-tradition theorizing, this book shows how putting analytic and continental political theory in conversation would help us to overcome these intractable problems"--.

This paper provides a new analysis and critique of Rawlsian public reason’s handling of the abortion question. It is often claimed that public reason is indeterminate on abortion, because it cannot say enough about prenatal moral status, or give content to the (allegedly) political value which Rawls calls ‘respect for human life’. I argue that public reason requires much greater argumentative restraint from citizens debating abortion than critics have acknowledged. Beyond the preliminary observation that fetuses do not meet the criteria (...) of political personhood, I contend, public reasoners may say nothing about prenatal moral status. Indeed, respect for human life (as distinct from respect for persons) is not, I show, a genuine political value, whose interpretation lies within public reason’s remit. This fact does not, however, prevent deliberators from drawing determinate conclusions regarding the law of abortion. Instead, I show, public reason has radically permissive implications for the legal regulation of feticide, inclining heavily towards the view that abortion should be allowed with little or no qualification, right until birth. I end by giving grounds for thinking that, even if the argumentative restraint which public reason enjoins over prenatal moral status does not generate indeterminacy, it is nonetheless objectionable. (shrink)

We show that certain model-theoretic forcing arguments involving subsystems of second-order arithmetic can be formalized in the base theory, thereby converting them to effective proof-theoretic arguments. We use this method to sharpen the conservation theorems of Harrington and Brown-Simpson, giving an effective proof that WKL+0 is conservative over RCA0 with no significant increase in the lengths of proofs.

Many psychological studies of categorization and reasoning use undergraduates to make claims about human conceptualization. Generalizability of findings to other populations is often assumed but rarely tested. Even when comparative studies are conducted, it may be challenging to interpret differences. As a partial remedy, in the present studies we adopt a 'triangulation strategy' to evaluate the ways expertise and culturally different belief systems can lead to different ways of conceptualizing the biological world. We use three groups (US bird experts, US (...) undergraduates, and ordinary Itza' Maya) and two sets of birds (North American and Central American). Categorization tasks show considerable similarity among the three groups' taxonomic sorts, but also systematic differences. Notably, US expert categorization is more similar to Itza' than to US novice categorization. The differences are magnified on inductive reasoning tasks where only undergraduates show patterns of judgment that are largely consistent with current models of category-based taxonomic inference. The Maya commonly employ causal and ecological reasoning rather than taxonomic reasoning. Experts use a mixture of strategies (including causal and ecological reasoning), only some of which current models explain. US and Itza' informants differed markedly when reasoning about passerines (songbirds), reflecting the somewhat different role that songbirds play in the two cultures. The results call into question the importance of similarity-based notions of typicality and central tendency in natural categorization and reasoning. These findings also show that relative expertise leads to a convergence of thought that transcends cultural boundaries and shared experiences. (shrink)

The violation of the Bell inequality means that measurement-results in the two wings of the experiment cannot be screened off from one another, in the sense of Reichenbach. But does this mean that there is causation between the results? I argue that it does, according to Lewis's counterfactual analysis of causation and his associated views. The reason lies in his doctrine that chances evolve by conditionalization on intervening history. This doctrine collapses the distinction between the conditional probabilities that are used (...) to state screening off, and the counterfactuals with chance consequents that are used to state lack of causation. I briefly discuss ways to evade my argument. (shrink)

The purpose of this paper is to think about the various methods of attempting to make money in the capital markets (“investing”). I suggest that though running a betting system on a Roulette wheel is silly, running a betting system on the capital markets may be a good idea.

I discuss the idea of relativistic causality, i.e., the requirement that causal processes or signals can propagate only within the light-cone. After briefly locating this requirement in the philosophy of causation, my main aim is to draw philosophers' attention to the fact that it is subtle, indeed problematic, in relativistic quantum physics: there are scenarios in which it seems to fail. I set aside two such scenarios, which are familiar to philosophers of physics: the pilot-wave approach, and the Newton-Wigner representation. (...) I instead stress two unfamiliar scenarios: the Drummond-Hathrell and Scharnhorst effects. These effects also illustrate a general moral in the philosophy of geometry: that the mathematical structures, especially the metric tensor, that represent geometry get their geometric significance by dint of detailed physical arguments. (shrink)

A notion called Herbrand saturation is shown to provide the model-theoretic analogue of a proof-theoretic method, Herbrand analysis, yielding uniform model-theoretic proofs of a number of important conservation theorems. A constructive, algebraic variation of the method is described, providing yet a third approach, which is finitary but retains the semantic flavor of the model-theoretic version.

A number of classical theories are interpreted in analogous theories that are based on intuitionistic logic. The classical theories considered include subsystems of first- and second-order arithmetic, bounded arithmetic, and admissible set theory.

In 1837, Dirichlet proved that there are infinitely many primes in any arithmetic progression in which the terms do not all share a common factor. We survey implicit and explicit uses ofDirichlet characters in presentations of Dirichlet’s proof in the nineteenth and early twentieth centuries, with an eye toward understanding some of the pragmatic pressures that shaped the evolution of modern mathematical method.

This paper offers a new critical evaluation of the Rawlsian model of global public reason (‘GPR’), focusing on its ability to serve as a normative standard for guiding international diplomacy and deliberation in matters of war. My thesis is that, where war is concerned, the model manifests two fatal weaknesses. First, because it demands extensive neutrality over the moral status of persons – and in particular over whether they possess equal basic worth or value – out of respect for the (...) beliefs of inegalitarian yet ‘decent’ societies, or ‘peoples’, Rawlsian GPR renders calculations of proportionality in war impossible. Second, because its content is provided by a conception of global justice (the so-called ‘Law of Peoples’) whose injunctions are addressed exclusively to peoples, as corporate agents, Rawlsian GPR pushes the moral evaluation of the independent wartime choices of individuals off the agenda of the global public forum altogether. (shrink)

Relationism claims that our physical theory does not commit us to spacetime points. I consider how a relationist might rewrite physical theories without referring to spacetime points, by appealing to possible objects and possible configurations of objects. I argue that a number of difficulties confront this project. I also argue that a relationist need not be Machian in the sense of claiming that objects' spatiotemporal relations determine whether any object is accelerating.

is a fragment of first-order aritlimetic so weak that it cannot prove the totality of an iterated exponential fimction. Surprisingly, however, the theory is remarkably robust. I will discuss formal results that show that many theorems of number theory and combinatorics are derivable in elementary arithmetic, and try to place these results in a broader philosophical context.

Paul Cohen’s method of forcing, together with Saul Kripke’s related semantics for modal and intuitionistic logic, has had profound effects on a number of branches of mathematical logic, from set theory and model theory to constructive and categorical logic. Here, I argue that forcing also has a place in traditional Hilbert-style proof theory, where the goal is to formalize portions of ordinary mathematics in restricted axiomatic theories, and study those theories in constructive or syntactic terms. I will discuss the aspects (...) of forcing that are useful in this respect, and some sample applications. The latter include ways of obtaining conservation results for classical and intuitionistic theories, interpreting classical theories in constructive ones, and constructivizing model-theoretic arguments. (shrink)

I argue, contra Dreier, Blackburn, and others, that there are no morally neutral metaethical positions. Every metaethical position commits you to the denial of some moral statement. So, for example, the metaethical position that there are no moral properties commits you to the denial of the moral conjunction of 1) it is right to interfere violently when someone is wrongly causing massive suffering and 2) it is wrong to interfere violently when only non-moral properties are at stake. The argument generalizes (...) to all metaethical positions. (shrink)

The purpose of this paper is to point the way to the money tree. Currently, almost all investment professionals think that outperformance requires an “edge,” that is, the ability to predict the future to some degree. In this paper, I suggest that money can be made in a 0, or even slightly negative, expected value environment by carefully choosing investment/bet sizes. Philosophical considerations are found mainly in Section 4.

We analyze the pointwise convergence of a sequence of computable elements of L1 in terms of algorithmic randomness. We consider two ways of expressing the dominated convergence theorem and show that, over the base theory RCA0, each is equivalent to the assertion that every Gδ subset of Cantor space with positive measure has an element. This last statement is, in turn, equivalent to weak weak Königʼs lemma relativized to the Turing jump of any set. It is also equivalent to the (...) conjunction of the statement asserting the existence of a 2-random relative to any given set and the principle of Σ2 collection. (shrink)

We investigate the entrepreneurial opportunities and ethical dilemmas presented by technological turbulence. More specifically we investigate the line between Baumol’s [J. Polit. Econ. 98 (1990) 893] productive (e.g. innovation), unproductive (e.g. rent seeking) and destructive (e.g. criminal) entrepreneurship through three examples of Internet innovation – spam (destructive), music file sharing (unproductive), and Internet pharmacies (potentially productive). The emergence of accessible Internet technologies, under present norms, has created the potential for all three entrepreneurial activities. Because of the propensity for self-serving biases (...) and for bending the rules, the need for creativity in overcoming obstacles and overall liabilities of newness, entrepreneurs are likely to challenge established industrial morals and laws. Unlike new entrants, incumbents must abide by the currently accepted norms, and thus suffer from “liabilities of oldness”. The challenge for new entrants is to change sociopolitical legitimacy, whereas incumbents need to defend the established norms. We discuss competitive and other issues that result from technological turbulence and innovation. (shrink)

Solovay has shown that if $\cal{O}$ is an open subset of $P(\omega)$ with code $S$ and no infinite set avoids $\cal{O}$ , then there is an infinite set hyperarithmetic in $S$ that lands in $\cal{O}$ . We provide a direct proof of this theorem that is easily formalizable in $ATR_0$.

Extending Gödel's Dialectica interpretation, we provide a functional interpretation of classical theories of positive arithmetic inductive definitions, reducing them to theories of finite-type functionals defined using transfinite recursion on well-founded trees.

Is the mechanism behind presupposition projection and filtering fundamentally asymmetric or symmetric? This is a foundational question for the theory of presupposition which has been at the centre of attention in recent literature :287–316, 2008b. https://doi.org/10.1515/THLI.2008.021, Semant Pragmat 2:1–78, 2009. https://doi.org/10.3765/sp.2.3; Rothschild in Semant Pragmat 4:1–43, 2011/2015. https://doi.org/10.3765/sp.4.3 a.o.). It also bears on broader issues concerning the source of asymmetries observed in natural language: are these simply rooted in superficial asymmetries of language use ; or are they, at least in (...) part, directly encoded in linguistic knowledge and representations? In this paper we aim to make progress on these questions by exploring presupposition projection across conjunction, which has traditionally been taken as a central piece of evidence that presupposition filtering is asymmetric in general. As a number of authors have recently pointed out, however, the evidence which has typically been used to support this conclusion is muddied by independent issues concerning redundancy; additional concerns have to do with the possibility of local accommodation. We report on a series of experiments, building on previous work by Chemla and Schlenker :177–226, 2012. https://doi.org/10.1007/s11050-012-9080-7) and Schwarz Experimental perspectives on presuppositions, Springer, Cham, 2015), using inference and acceptability tasks, which aim to control for both of these potential confounds. In our results, we find strong evidence for left-to-right filtering across conjunctions, but no evidence for right-to-left filtering—even when right-to-left filtering would, if available, rescue an otherwise unacceptable sentence. These results suggest that presupposition filtering across conjunction is asymmetric, contra suggestions in the recent literature :157–212, 2008a. https://doi.org/10.1515/THLI.2008.013, 2009 a.o.), and pave the way for the investigation of further questions about the nature of this asymmetry and presupposition projection more generally. Our results also have broader implications for the study of presupposition: we find important differences in the verdicts of acceptability versus inference tasks in testing for projected content, which has both methodological ramifications for the question of how to distinguish presupposed content, and theoretical repercussions for understanding the nature of projection and presuppositions more generally. (shrink)

A general method of interpreting weak higher-type theories of nonstandard arithmetic in their standard counterparts is presented. In particular, this provides natural nonstandard conservative extensions of primitive recursive arithmetic, elementary recursive arithmetic, and polynomial-time computable arithmetic. A means of formalizing basic real analysis in such theories is sketched.

The purpose of this note is to contrast a Cantorian outlook with a non-Cantorian one and to present a picture that provides support for the latter. In particular, I suggest that: i) infinite hyperreal numbers are the (actual, determined) infinite numbers, ii) ω is merely potentially infinite, and iii) infinitesimals should not be used in the di Finetti lottery. Though most Cantorians will likely maintain a Cantorian outlook, the picture is meant to motivate the obvious nature of the non-Cantorian outlook.

Fogelin’s Wittgensteinian view of deep disagreement as allowing no rational resolution has been criticized from both argumentation theoretic and epistemological perspectives. These criticisms typically do not recognize how his point applies to the very argumentative resources on which they rely. Additionally, more extremely than Fogelin himself argues, the conditions of deep disagreement make each position literally unintelligible to the other, again disallowing rational resolution. In turn, however, this failure of sense is so extreme that it partly cancels its own meaning (...) as a failure of sense. Consequently, it paradoxically opens new possibilities for sense and therefore rationally unexpected resolutions. (shrink)

We describe a model-theoretic approach to ordinal analysis via the finite combinatorial notion of an α-large set of natural numbers. In contrast to syntactic approaches that use cut elimination, this approach involves constructing finite sets of numbers with combinatorial properties that, in nonstandard instances, give rise to models of the theory being analyzed. This method is applied to obtain ordinal analyses of a number of interesting subsystems of first- and second-order arithmetic.

We develop fundamental aspects of the theory of metric, Hilbert, and Banach spaces in the context of subsystems of second-order arithmetic. In particular, we explore issues having to do with distances, closed subsets and subspaces, closures, bases, norms, and projections. We pay close attention to variations that arise when formalizing definitions and theorems, and study the relationships between them.

Although forgiveness is often taken to bear a close connection to the value of reconciliation, there is a good deal of scepticism about its role in situations where there is no consensus on the moral complexion of the past and no admission of guilt on the part of the perpetrator. This scepticism is typically rooted in the claims that forgiveness without perpetrator acknowledgement aggravates the risk of recidivism; yields a substandard and morally compromised form of political accommodation; and comes across (...) as patronizing and offensive to the recipient, thereby causing further alienation. In this article, my aim is to show, firstly, that none of these arguments is decisive and, secondly, that forgiveness is a suitable object of political concern in the absence of cross-community consensus on the rights and wrongs of a conflict. In this way, I aim to demonstrate that forgiveness deserves to be taken seriously as a means to civic reconciliation in a broader range of situations than many have allowed. (shrink)