This paper deploys a Cantor-style diagonal argument which indicates that there is more possible mathematical content than there are propositional functions in Russell and Whitehead's Principia Mathematica and similar formal systems. This technical result raises a historical question: "How did Russell, who was himself an expert in diagonal arguments, not see this coming?" It turns out that answering this question requires an appreciation of Russell's understanding of what logic is, and how he construed the relationship between logic and Principia Mathematica.

During the Second World War, the Allies faced a question colloquially known as the “German Tank Problem”: how many tanks will the Axis ever produce? The answer resulted from an elegant probabilistic argument which was used by Allied mathematicians to make successful upper-bound estimates for the total Axis tank production. This paper shows that if two empirical postulates are true of the history of science, a parallel argument can be used to come up with lower-bound estimates for the number of (...) alternative scientific theories that remain undiscovered. The lower bound in question increases proportionally with the number of theories that have already been discovered. So, the problem of underconsideration is a serious problem and it will get worse, not better, as we discover new theories. (shrink)

The first-person authority view (FPA) is the current dominant view about what someone’s gender is. According to FPA the person has authority over her own gender identity; her sincere self-identification trumps the opinions of others. There are two versions of FPA: epistemic and ethical. Both versions try to explain why a person has authority over her own gender identity. But both have problems. Epistemic FPA attributes to the self-identifier an unrealistic degree of doxastic reliability. Ethical FPA implies the existence of (...) an unreasonably strong and unqualified obligation on the part of others not to reject the person’s identification. This essay offers an alternative: the negotiative theory of identity. Unlike epistemic FPA, the negotiative theory doesn’t presume the reliability of self-directed beliefs. Unlike ethical FPA, the negotiative theory doesn’t imply an obligation not to reject. Instead, it contends that an act of rejection is morally permissible if and only if it respects three ethical and epistemic constraints. In doing so, the negotiative theory combines the strengths and avoids the weaknesses of both versions of FPA, and gives us substantive insight into how far first-person authority reaches in terms of grounding rights and obligating others. (shrink)

Universities regulate speech in various ways. How should we assess when such restrictions are justified, if they ever are? Here, we propose an answer to this question. In short, we argue that we should think about speech restrictions as being like acts of war, and so should approach their justification using just war theory. We also make some suggestions about its implications. For instance, one of the jus ad bellum requirements for a just war is that you have a reasonable (...) hope of success; you shouldn’t enter or continue a war unless you’ve got good reason to think that your objectives are achievable. We offer some reasons to think that many speech restrictions fail to pass this test in our current political climate: we are too far from the kind of society that universities hope to create via speech restrictions, and in employing them, they only exacerbate the problems they’re trying to solve. (shrink)

There are two popular ways of explaining why a person has authority over her own gender identity: epistemic FPA and ethical FPA. Both have problems. Epistemic FPA attributes to the self-identifier an unrealistic degree of doxastic reliability. Ethical FPA implies the existence of an unqualified obligation not to reject which is too strong to be plausible. This essay offers a third explanation called “weak FPA” and investigates how far first-person authority reaches in terms of grounding rights and obligating others. Weak (...) FPA doesn’t obligate one not to reject but it implies that when self-identification can be satisfactorily defended against attempted defeaters, the self-identifier has the right to recognition, which entails the respect and all other legal and social rights any other self-identifier receives from her peers. (shrink)

The Gouldian argument for evolutionary contingency found in Wonderful Life can be dissected into three premises: palaeontological, macro-evolutionary, and developmental. Discussions of evolutionary contingency have revolved primarily around the developmental. However, a shift in methodological practice and new palaeontological evidence subsequent to the book’s publication appears to threaten the palaeontological premise that asserts high Cambrian disparity, or, roughly, that morphological differences between the Cambrian species were high. This presents a prima facie problem: Did the Cambrian consist of enough anatomical variety (...) to fuel a different outcome upon a replay of the tape of life? I investigate the role that disparity plays in the Gouldian argument for evolutionary contingency and conclude that the reduced disparity view does not undermine the argument, per se. As for the macro-evolutionary premise, Gould never offers any explicit justification for the idea that species sorting was indiscriminate or ‘lottery-like’ (though he certainly gestures at it). Putting aside the exegetical, I consider certain empirical avenues for underwriting the macro-evolutionary premise and argue that the most plausible route is to appeal to the special status of mass extinctions, a move that is not entirely unfamiliar to macro-evolutionists. That is, mass extinctions can be good sources of contingency due to their being ‘chancy’ in at least three respects. In sum, I update the palaeontological and macro-evolutionary premises as to reconstrue the Gouldian argument for evolutionary contingency in its strongest form. (shrink)

The term “mental illness” implies that persons with such illnesses are more likely to be dangerous to themselves and/or others than are persons without such illnesses. This is the source of the psychiatrist’s traditional social obligation to control “harm to self and/or others,” that is, suicide and crime. The ethical dilemmas of psychiatry cannot be resolved as long as the contradictory functions of healing persons and protecting society are united in a single discipline.Life is full of dangers. Our highly developed (...) consciousness makes us, of all living forms in the universe, the most keenly aware of, and the most adept at protecting ourselves from, dangers. Magic and religion are mankind’s earliest warning systems. Science arrived on the scene only about 400 years ago, and scientific medicine only 200 years ago. Some time ago I suggested that “formerly, when religion was strong and science weak, men mistook magic for medicine; now, when science is strong and religion weak, men mistake medicine for magic”.1We flatter and deceive ourselves if we believe that we have outgrown the apotropaic use of language .Many people derive comfort from magical objects , and virtually everyone finds reassurance in magical words . The classic example of an apotropaic is the word “abracadabra,” which The American Heritage Dictionary of the English Language defines as “a magical charm or incantation having the power to ward off disease or disaster”. In the ancient world, abracadabra was a magic word, the letters of which were arranged in an inverted pyramid and worn as an amulet around the neck to protect the wearer against disease or trouble. One fewer letter appeared in each line of the pyramid, until only the letter “a” remained to form the vertex of the triangle. As …. (shrink)

This “Legal Briefing” column covers recent legal developments involving patient decision aids. This topic has been the subject of recent articles in JCE. It is included in the 2010 Patient Protection and Affordable Care Act. And it has received significant attention in the biomedical literature, including a new book, a thematic issue of Health Affairs, and a recent article in the New England Journal of Medicine. Moreover, physicians and health systems across the United States are increasingly integrating decision aids into (...) their clinical practice. Both federal and state laws play a significant role in promoting this expanded use. On the other hand, concerns about liability could stymie development and implementation. We categorize legal developments concerning patient decision aids into the following five sections:1. Development of decision aids2. Effectiveness of decision aids3. Federal regulation of decision aids4. State regulation of decision aids5. Legal concerns regarding decision aids. (shrink)

En sus Escolios, Nicolás Gómez Dávila hace manifiesta la relación existente entre las antiguas nociones gnósticas y las pretensiones ilustradas de la modernidad. Al determinar los fundamentos del gnosticismo en un conocimiento que se eleva sobre la fe, ubica rasgos análogos en el pensamiento moderno..

The extension of quantum mechanics to a general functional space (“rigged Hilbert space”), which incorporates time-symmetry breaking, is applied to construct extract dynamical models of entropy production and entropy flow. They are illustrated by using a simple conservative Hamiltonian system for multilevel atoms coupled to a time-dependent external force. The external force destroys the monotonicity of the ℋ-function evolution. This leads to a model of the entropy flow that allows a steady nonequilibrium structure of the emitted field around the unstable (...) particles. (shrink)