The “Mysteries” of Qumran: Mystery, Secrecy, and Esotericism in the Dead Sea Scrolls. By Samuel I. Thomas. Early Judaism and Its Literature, vol. 25. Atlanta: Society of Biblical Literature, 2009. Pp. xvii + 311. $39.95.

Multiple Originals: New Approaches to Hebrew Bible Textual Criticism. By Gary D. Martin. SBL Text-Critical Studies, vol. 7. Atlanta: Society of Biblical Literature, 2010. Pp. xiv + 341. $42.95.

The volume brings together a collection of original papers on some of the main tenets of Joseph Raz's legal and political philosophy: Legal positivism and the nature of law, practical reason, authority, the value of equality, incommensurability, harm, group rights, and multiculturalism. James Griffin and Yael Tamir raise questions concerning Raz's notion of group rights and its application to claims of cultural and political autonomy, while Will Kymlicka and Bernhard Peters examine Raz's theory of multicultural society. Lukas Meyer investigates the (...) applicability of the notion of harm in the intergenerational context. Other papers are devoted to fundamental theoretical tenets of Raz's work. Hillel Steiner and Andrei Marmor examine Raz's account of value pluralism and incommensurability in light of what these authors consider to be goods whose equal distribution must be valued for its own sake. Robert Alexy and Timothy Endicott discuss traditional issues of jurisprudence and legal philosphy with special attention to Raz's contribution. Rüdiger Bittner, Bruno Celano, and J. E. Penner discuss and criticize aspects of Raz's theory of practical reason. Jeremy Waldron presents a critique of Raz's interpretation of authority.This volume concludes with a chapter by Joseph Raz in which he responds to arguments in the foregoing essays. (shrink)

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)

I have two main aims. The first is general, and more philosophical. The second is specific, and more closely related to physics. The first aim is to state my general views about laws and causation at different ”levels’. The main task is to understand how the higher levels sustain notions of law and causation that ”ride free’ of reductions to the lower level or levels. I endeavour to relate my views to those of other symposiasts. The second aim is to (...) give a framework for describing dynamics at different levels, emphasizing how the various levels’ dynamics can mesh or fail to mesh. This framework is essentially that of elementary dynamical systems theory. The main idea will be, for simplicity, to work with just two levels, dubbed ”micro’ and ”macro’, which are related by coarse-graining. I use this framework to describe, in part, the first four of Ellis’ five types of top-down causation. (shrink)

We present a formal system, E, which provides a faithful model of the proofs in Euclid's Elements, including the use of diagrammatic reasoning.

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.

In a recent paper, Guy Kahane asks whether God’s existence is something we should want to be true. Expanding on some cryptic remarks from Thomas Nagel, Kahane’s informative and wide-ranging piece eventually addresses whether personal anti-theism is justified, where personal anti-theism is the view that God’s existence would make things worse overall for oneself. In what follows, I develop, defend, but ultimately reject the Meaningful Life Argument, according to which if God’s existence precludes the realization of certain goods that seem (...) to an agent to constitute a meaningful life, it is rational for an agent both to believe that personal anti-theism is true and to prefer that God not exist. (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"--.

divisibility in Physics VI. I had been assuming at that time that Aristotle's elimination of reference to the infinitely large in his account of the potential inf inite--like the elimination of the infinitely small from nineteenth century accounts of limits and continuity--gave us everything that was important in a theory of the infinite. Hilbert's paper showed me that this was not obviously so. Suddenly other certainties about Aristotle's (apparently) judicious toning down of (supposed) Platonic extremisms began to crumble. The upshot (...) of work I had been doing earlier on Plato's 'Third Man Argument' began to look different from the way it had before. I was confronted with a possibility I had not till then so much as entertained. What if the more extreme posi tions of Plato on these issues were the more likely to be correct? The present work is the first instalment of the result ing reassessment of Plato's metaphysics, and especially of his theory of Forms. It has occupied much of my teaching and scholarly time over the past fifteen years and more. The central question wi th which I concern myself is, "How does Plato argue for the existence of his Forms (if he does )7" The idea of making this the central question is that if we know how he argues for the existence of Forms, we may get a better sense of what they are. (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.

The concept of minimal risk has been used to regulate and limit participation by adolescents in clinical trials. It can be understood as setting an absolute standard of what risks are considered minimal or it can be interpreted as relative to the actual risks faced by members of the host community for the trial. While commentators have almost universally opposed a relative interpretation of the environmental risks faced by potential adolescent trial participants, we argue that the ethical concerns against the (...) relative standard may not be as convincing as these commentators believe. Our aim is to present the case for a relative standard of environmental risk in order to open a debate on this subject. We conclude by discussing how a relative standard of environmental risk could be defended in the specific case of an HIV vaccine trial among adolescents in South Africa. (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.

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)

This paper lays out some of the empirical evidence for the importance of neural reuse—the reuse of existing (inherited and/or early-developing) neural circuitry for multiple behavioral purposes—in defining the overall functional structure of the brain. We then discuss in some detail one particular instance of such reuse: the involvement of a local neural circuit in finger awareness, number representation, and other diverse functions. Finally, we consider whether and how the notion of a developmental homology can help us understand the relationships (...) between the cognitive functions that develop out of shared neural supports. (shrink)

Selon Kirk Lougheed, favoriser une version objective de l’argument du sens de la vie établit une sorte d’antithéisme, c’est-à-dire une perspective qui maintient que l’existence d’un Dieu théiste aggraverait les choses et qu’il est donc plus rationnel de préférer que Dieu n’existe pas. Cette version objective est présentée par Lougheed comme une amélioration par rapport à ma version subjective de l’argument du sens de la vie. Je soutiens que la version de Lougheed ne réussit pas mieux que la version subjective (...) que j’ai développée, puis rejetée. (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.

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.

Pro-theism is the view that God’s existence would be good in that God’s existence increases the value of a world. Anti-theism is the view that God’s existence would decrease the value of a world. We develop and defend the morally good agent argument for pro-theism. The basic idea is that morally good agents tend to add value to states of affairs, and God, moral agent par excellence is no exception. Thus, we argue that the existence of God would be, on (...) balance, a good thing and therefore something that one can rationally desire to be true. (shrink)

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)

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.

Despite the importance of Suárez’s defense of the freedom of the will at the threshold of early modern philosophy, his account has received scant recent attention. This paper aims partially to redress that neglect. Suárez’s position can be understood as a balancing act between desiring to attribute libertarian freedom to agents and desiring to maintain the will’s status as a rational appetite. Hence, he rejects an intellectualism that says that choices are necessitated by the intellect’s judgements (since he does not (...) think that the judgements themselves can be directly free), but affirms that only what is judged good can be chosen. (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.

Thanks to Barbeyrac, Pufendorf and others, there is a long-familiar picture of Grotius as offering a groundbreaking account of natural law. By now there is also a familiar observation that there is no agreement what makes Grotius’s account innovative. Sometimes this leads to skepticism about how innovative Grotius’s account of natural law really is. Some scholars suggest that Grotius’s account of natural law resembles Suárez’s account. But others continue to argue that Barbeyrac is right to see Grotius as breaking the (...) ice of previous philosophy and laying the groundwork for a distinctively modern moral philosophy. I plan to contribute to the debate by arguing that, properly understood, Grotius’s position is similar to Suárez’s on a range of fundamental questions, and, furthermore, that seeing Grotius as making a radical break with the past violates his own self-conception. 1. (shrink)

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)

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.

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.

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.