Nagel's analysis of reduction: Comments in defense as well as critique

Despite all the criticism showered on Nagel's classic account of reduction, it meets a fundamental desideratum in an analysis of reduction that is difficult to question, namely of providing for a proper identification of the reducing theory. This is not clearly accommodated in radically different accounts. However, the same feature leads me to question Nagel's claim that the reducing theory can be separated from the putative bridge laws, and thus to question his notion of heterogeneous reduction. A further corollary to the requirement that all the necessary conditions be incorporated in an adequate formulation of the putative reducing theory is that the standard example of gas temperature is not reducible to average molecular kinetic energy. As originally conceived, Nagel's conception of reduction takes no account of approximate reasoning and this failure has certainly restricted its applicability, perhaps to the point of making it unrealistic as a model of reduction in science. I suggest approximation can be accommodated by weakening the original requirement of deduction without jeopardizing the fundamental desideratum. Finally, I turn to briefly consider the idea sometimes raised of the ontological reducibility of chemistry.     

Embedding semigroups in groups: not as simple as it might seem

We consider the investigation of the embedding of semigroups in groups, a problem which spans the early-twentieth-century development of abstract algebra. Although this is a simple problem to state, it has proved rather harder to solve, and its apparent simplicity caused some of its would-be solvers to go awry. We begin with the analogous problem for rings, as dealt with by Ernst Steinitz, B. L. van der Waerden and Øystein Ore. After disposing of A. K. Sushkevich’s erroneous contribution in this area, we present A. I. Maltsev’s example of a cancellative semigroup which may not be embedded in a group, which showed for the first time that such an embedding is not possible in general. We then look at the various conditions that were derived for such an embedding to take place: the sufficient conditions of Paul Dubreil and others, and the necessary and sufficient conditions obtained by A. I. Maltsev, Vlastimil Pták and Joachim Lambek. We conclude with some comments on the place of this problem within the theory of semigroups, and also within abstract algebra more generally.     

Brains as analog-model computers

Computational neuroscientists not only employ computer models and simulations in studying brain functions. They also view the modeled nervous system itself as computing. What does it mean to say that the brain computes? And what is the utility of the ‘brain-as-computer’ assumption in studying brain functions? In previous work, I have argued that a structural conception of computation is not adequate to address these questions. Here I outline an alternative conception of computation, which I call the analog-model. The term ‘analog-model’ does not mean continuous, non-discrete or non-digital. It means that the functional performance of the system simulates mathematical relations in some other system, between what is being represented. The brain-as-computer view is invoked to demonstrate that the internal cellular activity is appropriate for the pertinent information-processing (often cognitive) task.     

Phytotoxins as potential herbicides

Phytotoxins are produced in various culture media by many fungi that are pathogenic to weeds. These phytotoxins belong to a wide array of chemical substances including sesquiterpenoids, sesterterpenoids, diketopiperazines, peptides, spirocyclic lactams, isocoumarins, and polyketides. In most cases, the phytotoxin belongs to a family of related compounds produced by the fungus. These related compounds may or may not be phytotoxins. Phytotoxin production, in some cases, is optimized by the addition of a host extract to the culture medium. Biological activity is usually observed in a range of concentrations from 10^–3 to 10^–6 M. The concept of using these molecules, derivatives thereof, or related compounds as herbicides should be explored.     

Neurotransmitter receptors as glycoproteins

Summary Incubation of calf brain membrane preparations with the plant lectins, concanavalin A and wheat germ agglutinin did not inhibit neurotransmitter receptor binding sites directly. Plant lectins did however protect these sites against subsequent trypsin digestion suggesting that neurotransmitter binding sites may be associated with glycoprotein structures.     

Neurotransmitter receptors as glycoproteins

Incubation of calf brain membrane preparations with the plant lectins, concanavalin A and wheat germ agglutinin did not inhibit neurotransmitter receptor binding sites directly. Plant lectins did however protect these sites against subsequent trypsin digestion suggesting that neurotransmitter binding sites may be associated with glycoprotein structures.     

Novobiocin as uncoupling agent

Résumé Les auteurs démontrent que la novobiocine provoque un découplement de l'oxydation phosphorylante dans un homogénat de foic de rat déjà à une concentration 1,575·10^–4 M. Les rapports entre l'activité antibactérienne et l'action biochimique de l'antibiotique sont discutés.     

Hsp70 in parasites: as an inducible protective protein and as an antigen

The heat shock (HS) response is a general homeostatic mechanism that protects cells and the entire organism from the deleterious effects of environmental stresses. It has been demonstrated that heat shock proteins (HSP) play major roles in many cellular processes, and have a unique role in several areas of cell biology, from chronic degenerative diseases to immunology, from cancer research to interaction between host and parasites. This review deals with thehsp70 gene family and with its protein product, hsp70, as an antigen when pathogens infect humans. Members of HSP have been shown to be major antigens of many pathogenic organisms when they experience a major temperature shift upwards at the onset of infection and become targets for host B and T cells.     

Carbon nanotubes as anti-bacterial agents

Multidrug-resistant bacterial infections that have evolved via natural selection have increased alarmingly at a global level. Thus, there is a strong need for the development of novel antibiotics for the treatment of these infections. Functionalized carbon nanotubes through their unique properties hold great promise in the fight against multidrug-resistant bacterial infections. This new family of nanovectors for therapeutic delivery proved to be innovative and efficient for the transport and cellular translocation of therapeutic molecules. The current review examines the latest progress in the antibacterial activity of carbon nanotubes and their composites.     

Scientific progress as increasing verisimilitude

According to the foundationalist picture, shared by many rationalists and positivist empiricists, science makes cognitive progress by accumulating justified truths. Fallibilists, who point out that complete certainty cannot be achieved in empirical science, can still argue that even successions of false theories may progress toward the truth. This proposal was supported by Karl Popper with his notion of truthlikeness or verisimilitude. Popper’s own technical definition failed, but the idea that scientific progress means increasing truthlikeness can be expressed by defining degrees of truthlikeness in terms of similarities between states of affairs. This paper defends the verisimilitude approach against Alexander Bird who argues that the “semantic” definition (in terms of truth or truthlikeness alone) is not sufficient to define progress, but the “epistemic” definition referring to justification and knowledge is more adequate. Here Bird ignores the crucial distinction between real progress and estimated progress, explicated by the difference between absolute (and usually unknown) degrees of truthlikeness and their evidence-relative expected values. Further, it is argued that Bird’s idea of returning to the cumulative model of growth requires an implausible trick of transforming past false theories into true ones.     

6-Methoxymellein as a phytoalexin

Résumé Le dihydroisocoumarin (I) était considéré comme un « phytoalexin » produit par des carottes infectées deCeratocystis fimbriata. Mais l'isocoumarin (II), de structure apparentée ayant été dégagé d'une culture de ce champignon sur bouillon synthétique, on peut douter que (I) tire son origine des carottes.     

Tryptophane as a tuberculostatic agent

Résumé L'étude d'un précurseur probable dans la production de l'acide nicotinique par leMycobacterium tuberculosis hominis, révéla que les acides aminiques hétérocycliques, qui sont indispensables à plusieurs organismes, comme le tryptophan et l'histidine, sont bactériostatiques à l'organisme. Cet organisme se développait dans une solution synthétique de Proskauer & Beck (Vorwald's modification). Les acides aminiques tels que l'ornithine et l'arginine aidèrent à sa croissance et favorisèrent la production d'acide nicotinique, ressemblant sur ce point à l'asparagine. Des études préliminaires faites sur des cobayes infectés par l'organisme tuberculeux confirmèrent l'effet bactériostatique du tryptophanein vitro. Du tryptophane fut administré, de fa?on sous-cutanée, à raison de 125 mg par jour pour 10 jours consécutifs, immédiatement après l'infection, à un groupe d'animaux. Un second groupe subit le même traitement, mais à deux semaines du jour de l'infection. Un troisième groupe fut infecté, mais laissé sans traitement. Tous ces animaux furent observés pendant 9 semaines. Après examen bactériologique, microscopipue et macroscopique, l'effet bactériostatique du tryptophanein vivo put être démontré.      

Duality as a category-theoretic concept

In a paper published in 1939, Ernest Nagel described the role that projective duality had played in the reformulation of mathematical understanding through the turn of the nineteenth century, claiming that the discovery of the principle of duality had freed mathematicians from the belief that their task was to describe intuitive elements. While instances of duality in mathematics have increased enormously through the twentieth century, philosophers since Nagel have paid little attention to the phenomenon. In this paper I will argue that a reassessment is overdue. Something beyond doubt is that category theory has an enormous amount to say on the subject, for example, in terms of arrow reversal, dualising objects and adjunctions. These developments have coincided with changes in our understanding of identity and structure within mathematics. While it transpires that physicists have employed the term ‘duality’ in ways which do not always coincide with those of mathematicians, analysis of the latter should still prove very useful to philosophers of physics. Consequently, category theory presents itself as an extremely important language for the philosophy of physics.