Several problems that pertain to certain arithmetically well-behaved countable subsemirings of Λ, the semiring of isols, are discussed. This is relevant to the present volume memorializing the late John Myhill, in that Myhill was an early co-developer of the theory of Λ.

Hirschfeld and Wheeler proved in 1975 that ∑1 ultrapowers (= “simple models”) are rigid; i.e., they admit no non-trivial automorphisms. We later noted, essentially mimicking their technique, that the same is true of Δ1 ultrapowers (= “Nerode semirings”), a class of models of Π2 Arithmetic that overlaps, but is mutually non-inclusive with, the class of Σ1 ultrapowers. Hirschfeld and Wheeler left as open the question whether some Σ1 ultrapowers might admit proper isomorphic self-injections. We do not answer that question; but (...) we do answer the corresponding question, in the negative, for the Δ1 case. (shrink)

Problems of the history of philosophy, no matter what aspect of that science they deal with, are always very important. Today, when idealist philosophy seeks to give an exaggerated picture of the importance of the major spiritual values created by the peoples of the West, these problems are acquiring particular significance. In the postwar period, the number of works published abroad on the history of philosophy has increased sharply. The most popular of the older works are being revised and reissued. (...) A great number of writings on methodology have appeared. The influence of philosophy is spreading to other fields of knowledge and to their history. Specifically, historians of culture, science, technology and art are striving, influenced by the materialist concept of history, to shed the light of philosophy upon the problems that inevitably arise in these fields when their history is studied, but which cannot be resolved by the cognitive resources of the special sciences. This circumstance renders problems of the methodology of the history of philosophy particularly important and places greater responsibility upon researchers in this field. (shrink)

Well prior to the invention of the term ‘biology’ in the early 1800s by Lamarck and Treviranus (and lesser-known figures in the decades prior), and also prior to the appearance of terms such as ‘organism’ under the pen of Leibniz and Stahl in the early 1700s, the question of ‘Life’, that is, the status of living organisms within the broader physico-mechanical universe, agitated different corners of the European intellectual scene. From modern Epicureanism to medical Newtonianism, from Stahlian animism to the (...) discourse on the ‘animal economy’ in vitalist medicine, models of living being were constructed in opposition to ‘merely anatomical’, structural, mechanical models. It is therefore striking that the classic narratives of the Scientific Revolution conspicuously avoid any consideration of what status to grant living beings in a newly physicalized universe (I discuss this in Wolfe 2011, 2019 chapt. 1). Neither Harvey, nor Boyle, nor Locke (to name some likely candidates, the latter having studied with Willis and collaborated with Sydenham) ever ask what makes organisms unique, or conversely, what does not. In this chapter I seek to establish how something we might call ‘the knowledge of Life’, to use an expression of Georges Canguilhem’s, emerged as part of early modernity without being part of the mainstream history of life science. This leads to the question, can one can correlate early modern “knowledge of life” with the emergence of a science called ‘biology’? (see Zammito 2018, Wolfe 2019, Bognon-Küss and Wolfe eds. 2019). It was once fashionable to speak of, e.g. ‘precursors of Darwin’, and then Canguilhem and Foucault famously did away with the category of precursor. But how then do we account for the phase that precedes the constitution of a science? With the case of biology, how do we account for the increasing fascination with the ontology of Life during the decades prior to the ‘naming of biology’, as McLaughlin has called it, at the end of the eighteenth century? This increased focus on Life and the ontology of Life sits awkwardly, both with mainstream narratives of the Scientific Revolution and of the history of biology. In seeking to address this increased focus (in which vitalism plays a role but was by no means the only conceptual actor: Wolfe 2020), I critically examine Foucault’s notorious claim (Foucault 1966) that there was no such thing as ‘Life’ in the eighteenth century and thus no such thing as biology. (shrink)