Fowers et al. recently made a general argument for virtues as the characteristics necessary for individuals to flourish, given inherent human limitations. For example, people can flourish by developing the virtue of friendship as they navigate the inherent human dependency on others. This general argument also illuminates a pathway to flourishing during the COVID-19 pandemic, the risks of which have induced powerful fears, exacerbated injustices, and rendered life and death decisions far more common. Contexts of risk and fear call for (...) the virtue of courage. Courage has emerged more powerfully as a central virtue among medical personnel, first responders, and essential workers. Longstanding inequalities have been highlighted during the pandemic, calling for the virtue of justice. When important personal and public health decisions must be made, the central virtue of practical wisdom comes to the fore. Wise decisions and actions incorporate the recognition of relevant moral concerns and aims, as well as responding in fitting and practical ways to the specifics of the situation. Practicing courage, justice, and practical wisdom illuminates a path to flourishing, even in a pandemic. (shrink)

The relative strengths of first-order theories axiomatized by transfinite induction, for ordinals less-than 0, and formulas restricted in quantifier complexity, is determined. This is done, in part, by describing the provably recursive functions of such theories. Upper bounds for the provably recursive functions are obtained using model-theoretic techniques. A variety of additional results that come as an application of such techniques are mentioned.

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.

Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. This volume, the fifteenth publication in the Lecture Notes in Logic series, collects papers presented at the symposium 'Reflections on the Foundations of Mathematics' held in celebration of Solomon Feferman's 70th birthday (The 'Feferfest') at Stanford University, California in 1988. (...) Feferman has shaped the field of foundational research for nearly half a century. These papers reflect his broad interests as well as his approach to foundational research, which emphasizes the solution of mathematical and philosophical problems. There are four sections, covering proof theoretic analysis, logic and computation, applicative and self-applicative theories, and philosophy of modern mathematical and logic thought. (shrink)

Homology is the similarity between organisms due to common ancestry. Introduced by Richard Owen in 1843 in a paper entitled “Lectures on comparative anatomy and physiology of the invertebrate animals”, the concept of homology predates Darwin's “Origin of Species” and has been very influential throughout the history of evolutionary biology. Although homology is the central concept of all comparative biology and provides a logical basis for it, the definition of the term and the criteria of its application remain controversial. Here, (...) I will discuss homology in the context of the hierarchy of biological organization. I will provide insights gained from an exemplary case study in evolutionary developmental biology that indicates the uncoupling of homology at different levels of biological organization. I argue that continuity and hierarchy are separate but equally important issues of homology. BioEssays 30:653–658, 2008. © 2008 Wiley Periodicals, Inc. (shrink)

We use model-theoretic methods described in [3] to obtain ordinal analyses of a number of theories of first- and second-order arithmetic, whose proof-theoretic ordinals are less than or equal to Γ0.

This textbook emphasises a hands-on, multimethod, interdisciplinary approach to behavioural research. This edition uses particularly strong observational approaches.

To understand how morphological characters change during evolution, we need insight into the evolution of developmental processes. Comparative developmental approaches that make use of our fundamental understanding of development in certain model organisms have been initiated for different animal systems and flowering plants. Nematodes provide a useful experimental system with which to investigate the genetic and molecular alterations underlying evolutionary changes of cell fate specification in development, by comparing different species to the genetic model system Caenorhabditis elegans. In this review, (...) I will first discuss the different types of evolutionary alterations seen at the cellular level by focusing mainly on the analysis of vulva development in different species. The observed alterations involve changes in cell lineage, cell migration and cell death, as well as induction and cell competence. I then describe a genetic approach in the nematode Pristionchus pacificus that might identify those genetic and molecular processes that cause evolutionary changes of cell fate specification. (shrink)

We use model-theoretic methods described in [3] to obtain ordinal analyses of a number of theories of first-and second-order arithmetic, whose proof-theoretic ordinals are less than or equal to $\Gamma_0$.

Nematodes pervade Earth's biosphere and occupy innumerable ecological niches. The role of Caenorhabditis elegans as a model for developmental processes has encouraged us to cultivate a second nematode, Pristionchus pacificus, as a comparative counterpoint to address questions in development, behavior and ecology in nematode evolution. We hope that this endeavor, now more than a decade underway, will allow us to project findings onto other comparative models for biological processes. To this end, our laboratory has made an extensive genetic map and (...) mutant screens to understand changes in developmental programs. Recently, we have been capitalizing on the whole genome sequence of P. pacificus to describe more thoroughly the molecular basis for these changes, as well as to better integrate our molecular knowledge with the biodiversity of Pristionchus species. BioEssays 28: 651–659, 2006. © 2006 Wiley Periodicals, Inc. (shrink)