Considered by many to be Abraham Robinson's magnum opus, this book offers an explanation of the development and applications of non-standard analysis by the mathematician who founded the subject. Non-standard analysis grew out of Robinson's attempt to resolve the contradictions posed by infinitesimals within calculus. He introduced this new subject in a seminar at Princeton in 1960, and it remains as controversial today as it was then. This paperback reprint of the 1974 revised edition is indispensable reading for anyone interested (...) in non-standard analysis. It treats in rich detail many areas of application, including topology, functions of a real variable, functions of a complex variable, and normed linear spaces, together with problems of boundary layer flow of viscous fluids and rederivations of Saint-Venant's hypothesis concerning the distribution of stresses in an elastic body. (shrink)

A shared narrative in the literature on the evolution of cooperation maintains that social _learning_ evolves early to allow for the transmission of cumulative culture. Social _norms_, whilst present at the outset, only rise to prominence later on, mainly to stabilise cooperation against the threat of defection. In contrast, I argue that once we consider insights from social epistemology, an expansion of this narrative presents itself: An interesting kind of social norm — an epistemic coordination norm — was operative in (...) early and important instances of specialised social learning. I show how there’s a need for such norms in two key social learning strategies and explain how this need is constituted. In assessor-teaching (e.g. Castro et al., 2019b, 2021), epistemic coordination norms allow agents to coordinate around the _content_ of social learning, i.e., what is to be known and how this is to be done. These norms also allow agents to coordinate around the form of cultural learning in what’s sometimes called strategic social learning (Laland, 2004; Hoppitt & Laland, 2013; Heyes, 2018, Chap. 5) and elsewhere. Broadly speaking, this concerns how cultural learning is organised within the social group. The upshot is that the evolution of social learning and social norms are intertwined in important and underappreciated ways from early on. The above matters as it informs our views about the evolution of social norms more generally. Truly _social_ norms emerged to coordinate a plurality of complex behaviours and interactions, amongst them specialised social learning. I substantiate this view by contrasting it with Jonathan Birch’s views on the evolution of norms. What results is a general but cohesive narrative on the early evolution of social norms. (shrink)

Historians and philosophers of science have interpreted the taxonomic theory of Carl Linnaeus as an ‘essentialist’, ‘Aristotelian’, or even ‘scholastic’ one. This interpretation is flatly contradicted by what Linnaeus himself had to say about taxonomy in Systema naturae , Fundamenta botanica and Genera plantarum . This paper straightens out some of the more basic misinterpretations by showing that: Linnaeus’s species concept took account of reproductive relations among organisms and was therefore not metaphysical, but biological; Linnaeus did not favour classification by (...) logical division, but criticized it for necessarily failing to represent what he called ‘natural’ genera; Linnaeus’s definitions of ‘natural’ genera and species were not essentialist, but descriptive and polytypic; Linnaeus’s method in establishing ‘natural’ definitions was not deductive, but consisted in an inductive, bottom-up procedure of comparing concrete specimens. The conclusion will discuss the fragmentary and provisional nature of Linnaeus’s ‘natural method’. I will argue in particular that Linnaeus opted for inductive strategies not on abstract epistemological grounds, but in order to confer stability and continuity to the explorative practices of contemporary natural history. (shrink)

Cumulative cultural knowledge [CCK], the knowledge we acquire via social learning and has been refined by previous generations, is of central importance to our species’ flourishing. Considering its importance, we should expect that our best epistemological theories can account for how this happens. Perhaps surprisingly, CCK and how we acquire it via cultural learning has only received little attention from social epistemologists. Here, I focus on how we should epistemically evaluate how agents acquire CCK. After sampling some reasons why extant (...) theories cannot account for CCK, I suggest that things aren’t as bleak as they might look. I explain how agents deserve epistemic credit for how CCK is transmitted in cultural learning by promoting a central need of their social group: The efficient and safe transmission of CCK. A good initial fit exists between this observation and Greco’s knowledge-economy framework. Ultimately, however, Greco’s account doesn’t straightforwardly account for CCK because of its strict focus on testimony. I point out two issues in the framework due to this focus. The resulting view advocates giving epistemic credit to agents when they act to promote their communities’ epistemic needs in the right way and highlights the various ways in which agents come to do this. (shrink)

In the six decades since the publication of Julian Huxley's Evolution: The Modern Synthesis, spectacular empirical advances in the biological sciences have been accompanied by equally significant developments within the core theoretical framework of the discipline. As a result, evolutionary theory today includes concepts and even entire new fields that were not part of the foundational structure of the Modern Synthesis. In this volume, sixteen leading evolutionary biologists and philosophers of science survey the conceptual changes that have emerged since Huxley's (...) landmark publication, not only in such traditional domains of evolutionary biology as quantitative genetics and paleontology but also in such new fields of research as genomics and EvoDevo. Most of the contributors to Evolution—The Extended Synthesis accept many of the tenets of the classical framework but want to relax some of its assumptions and introduce significant conceptual augmentations of the basic Modern Synthesis structure—just as the architects of the Modern Synthesis themselves expanded and modulated previous versions of Darwinism. This continuing revision of a theoretical edifice the foundations of which were laid in the middle of the nineteenth century—the reexamination of old ideas, proposals of new ones, and the synthesis of the most suitable—shows us how science works, and how scientists have painstakingly built a solid set of explanations for what Darwin called the "grandeur" of life. (shrink)

Prompted by recent recognitions of the omnipresence of horizontal gene transfer among microbial species and the associated emphasis on exchange, rather than isolation, as the driving force of evolution, this essay will reflect on hybridization as one of the central concerns of nineteenth-century biology. I will argue that an emphasis on horizontal exchange was already endorsed by ‘biology’ when it came into being around 1800 and was brought to full fruition with the emergence of genetics in 1900. The true revolution (...) in nineteenth-century life sciences, I maintain, consisted in a fundamental shift in ontology, which eroded the boundaries between individual and species, and allowed biologists to move up and down the scale of organic complexity. Life became a property extending both ‘downwards’, to the parts that organisms were composed of, as well as ‘upwards’, to the collective entities constituted by the relations of exchange and interaction that organisms engage in to reproduce. This mode of thinking was crystallized by Gregor Mendel and consolidated in the late nineteenth-century conjunction of biochemistry, microbiology and breeding in agro-industrial settings. This conjunction and its implications are especially exemplified by Wilhelm Johannsen’s and Martinus Beijerinck’s work on pure lines and cultures. An understanding of the subsequent constraints imposed by the evolutionary synthesis of the twentieth century on models of genetic systems may require us to rethink the history of biology and displace Darwin’s theory of natural selection from that history’s centre. (shrink)

Since the validity of Bell's inequalities implies the existence of joint probabilities for non-commuting observables, there is no universal consensus as to what the violation of these inequalities signifies. While the majority view is that the violation teaches us an important lesson about the possibility of explanations, if not about metaphysical issues, there is also a minimalist position claiming that the violation is to be expected from simple facts about probability theory. This minimalist position is backed by theorems due to (...) A. Fine and I. Pitowsky.Our paper shows that the minimalist position cannot be sustained. To this end,we give a formally rigorous interpretation of joint probabilities in thecombined modal and spatiotemporal framework of `stochastic outcomes inbranching space-time' (SOBST) (Kowalski and Placek, 1999; Placek, 2000). We show in this framework that the claim that there can be no joint probabilities fornon-commuting observables is incorrect. The lesson from Fine's theorem is notthat Bell's inequalities will be violated anyhow, but that an adequate modelfor the Bell/aspect experiment must not define global joint probabilities. Thus we investigate the class of stochastic hidden variable models, whichprima facie do not define such joint probabilities. The reasonwhy these models fail supports the majority view: Bell's inequalities are notjust a mathematical artifact. (shrink)

This paper presents and discusses a series of hybridization experiments carried out by Nils Herman Nilsson-Ehle between 1900 and 1907 at a plant breeding station in Svalöf, Sweden. Since the late 1880s, the Svalöf station had been renowned for its ‘scientific’ breeding methods, which basically consisted of an elaborate system of record-keeping through which the offspring of individual plants were traced over generations while being meticulously described. This record system corresponded to a certain breeding technique and certain theoretical convictions . (...) Inspired by Tschermack’s translation of Mendel’s Pisum-paper, Nilsson-Ehle began his experiments in 1900 and published a first, major synthesis of his findings in 1908. If one compares these experiments as documented in the breeding records, with their representations in print, one encounters discrepancies in terms of procedure and presentation of data. This can be explained by the fact that Nilsson-Ehle was obliged to follow the recording and breeding procedures institutionalised at Svalöf, and these procedures, grounded in a taxonomic discourse, left little room for Mendelian hybridisation experiments. The twists and turns that this story takes are analysed in terms of Bachelardian philosophy of science, where the ‘epistemological obstacle’ functions as a central, analytic category. In contrast to Bachelard, however, I will characterise these obstacles as being of an institutional, rather than mental, nature. Thus characterized, moreover, they turn out to have been prerequisites as much as barriers to scientific progress. (shrink)

Using Sneed's metatheory an attempt is made to reconstruct Hodgkin and Huxley's theory of excitation of cell membranes. The structure of this theory is uncovered by defining set-theoretical predicates for the partial potential models, potential models, and models of the theory. The function of permeability is said to be the only theoretical function with respect to this theory. The main underlying assumptions of the theory are briefly outlined.

May lethal autonomous weapons systems—‘killer robots ’—be used in war? The majority of writers argue against their use, and those who have argued in favour have done so on a consequentialist basis. We defend the moral permissibility of killer robots, but on the basis of the non-aggregative structure of right assumed by Just War theory. This is necessary because the most important argument against killer robots, the responsibility trilemma proposed by Rob Sparrow, makes the same assumptions. We show that the (...) crucial moral question is not one of responsibility. Rather, it is whether the technology can satisfy the requirements of fairness in the re-distribution of risk. Not only is this possible in principle, but some killer robots will actually satisfy these requirements. An implication of our argument is that there is a public responsibility to regulate killer robots ’ design and manufacture. (shrink)

This volume develops a fundamentally different categorical framework for conceptualizing time and reality. The actual taking place of reality is conceived as a “constellatory self-unfolding” characterized by strong self-referentiality and occurring in the primordial form of time, the not yet sequentially structured “time-space of the present.” Concomitantly, both the sequentially ordered aspect of time and the factual aspect of reality appear as emergent phenomena that come into being only after reality has actually taken place. In this new framework, time functions (...) as an ontophainetic [H1] platform, i.e., as the stage on which reality can first occur. Events are merely the “tracks” that the actual taking place of reality leaves behind on the co-emergent “canvas’’ of local spacetime. -/- The view of time proposed here is particularly relevant to the recent debate over the “ER=EPR” conjecture targeting the relation between quantum physics and general relativity theory. The novelty of this radically different framework is that it allows quantum reduction and singularities to be addressed as inverse transitions into and out of the factual layer of reality: In quantum physical state reduction, reality “gains” the chrono-ontological format of facticity, and the sequential aspect of time becomes applicable. In singularities, by contrast, the opposite happens: Reality loses its local spacetime formation and reverts back to its primordial, pre-local shape – making the use of causality relations, Boolean logic and the dichotomization of subject and object obsolete in the process. -/- For our understanding of the relation between quantum and relativistic physics, this new view opens up fundamentally new perspectives: Both are legitimate views of time and reality; they simply address very different chrono-ontological portraits, and thus should not lead us to erroneously prefer one view over the other. -/- The task of the book is to provide a formal framework in which this radically different view of time and reality can be suitably addressed. The mathematical approach is based on the logical and topological features of the Borromean Rings, and draws upon concepts and methods from algebraic and geometric topology – especially the theory of sheaves and links, group theory, logic and information theory in relation to the standard constructions employed in quantum mechanics and general relativity, shedding new light on the problems of their compatibility. The intended audience includes physicists, mathematicians and philosophers with an interest in the conceptual and mathematical foundations of modern physics. (shrink)

Can we make machines that think and act like humans or other natural intelligent agents? The answer to this question depends on how we see ourselves and how we see the machines in question. Classical AI and cognitive science had claimed that cognition is computation, and can thus be reproduced on other computing machines, possibly surpassing the abilities of human intelligence. This consensus has now come under threat and the agenda for the philosophy and theory of AI must be set (...) anew, re-defining the relation between AI and Cognitive Science. We can re-claim the original vision of general AI from the technical AI disciplines; we can reject classical cognitive science and replace it with a new theory ; or we can try to find new ways to approach AI, for example from neuroscience or from systems theory. To do this, we must go back to the basic questions on computing, cognition and ethics for AI. The 30 papers in this volume provide cutting-edge work from leading researchers that define where we stand and where we should go from here. (shrink)