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The chapter sheds fresh light on Aristotle’s account of perception by providing a novel analysis of the puzzles that he articulates within his discussion of the predecessors’ views, especially in An. 1. I argue that Aristotle takes the key insight of the traditional view that like is perceived by like to be expressed in the idea that the perceiver is like the perceptual object by which she is being affected. This idea seems inconsistent with the widely shared assumption that only unlike things can act upon each other. Aristotle’s predecessors were unable to resolve this tension (the notion of a generic likeness is of no help), but he believes that precisely this tension must be resolved by any successful account of what perception is. The only predecessor who at least hinted towards a resolution is Anaxagoras with his account of impassive nous (understood by Aristotle as a general account of cognition). But Anaxagoras failed to account for the causal aspects of cognition as a way of being affected by its object. Aristotle’s own account can be seen as an attempt to incorporate the true insights of both the view that in perception like is affected by like and the view that what perceives must be impassive.
The chapter provides a novel detailed analysis of one of the most discussed chapters in the Aristotelian corpus, namely An. 2.5. The central claim is that in An. 2.5 Aristotle lays down his programmatic definition of perception as a complete passive activity. He does so by classing the perceptive capacity with capacities that are already fulfilments (entelekheiai) of their subjects and by showing how this classification is compatible with perception being passive (i.e. a kind of being affected). By working out the concept of complete passive activity Aristotle fills in a conceptual gap left open elsewhere in the corpus (most strikingly in Metaphysics Θ.6), where both completeness and passivity are taken for granted but without showing how the two features can cohere. In An. 2.5, Aristotle, thus, succeeds in capturing how perception differs not only from manifestations of non-passive complete capacities (such as the art of house-building), but also from passive processes (as exhibited in the inexhaustibility of the perceptive capacity and the object-directedness of perception). His definition is programmatic in the sense that it analyses the explananda without, however, yet providing any explanantia.
In this chapter, we showed the broader application of Polyhedral Graphic statistics in other fields of science and briefly introduced research directions and topics that go beyond the polyhedral limitations of this method. Particularly, we show a research project in which graphical methods were used to analyze the structural pattern of a dragonfly wing. The result was then combined with machine learning methods to generate the structure of a wing of an airplane with enhanced out-of-plane performance. We also visited applications in the design of strut-and-tie structures for referenced concrete and its further application in designing multi-material structural components where the direction of the deposition of material is adjusted with respect to the internal force flow to maximize mechanical performance. The application of Polyhedral Graphic Statics was shown in the design of cellular solids and briefly discussed how particular subdividing of the force diagram can control the stress distribution in the system and the overall behavior of the structure from bending dominant to stretching dominant system. We also showed the application of the structures designed using Polyhedral Graphic Statics in self-healing structural components and 3D-printed structural systems with maximized surface area and minimized mass. Another important topic was the extension of the methods of Polyhedral Graphic Statics to non-polyhedral systems using disjointed force polyhedra. In the end, advanced topics related to completeness, being, and kinematics in Polyhedral Graphic Statics were discussed, which opened the door to many further research directions in this field.
Classical logic – which studies the structural features of purported claims of fact – and modal logic – which studies relations of necessity and possibility – are different but complementary areas of logical thought. In this lively and accessible textbook, Adam Bjorndahl provides a comprehensive and unified introduction to the two subjects, treating them with the same level of rigour and detail and showing how they fit together. The core material appears in the main text, with hundreds of supplemental examples, comments, clarifications, and connections presented throughout in easy-to-read sidenotes, giving the book a distinct conversational feel. A detailed, multi-part appendix covers important background mathematical material that some students may lack, such as induction or the concept of countable infinity. A fully self-contained learning resource, this book will be ideal for a semester-long upper-level university course on either or both of the topics.
“Militant Neoclassicism” argues that W. E. B. Du Bois marshaled post-Kantian aesthetics against the anthropological categories posited by Enlightenment theorists. The chapter departs from the traditional interpretation of Du Bois as a champion of integration, which relies heavily on The Souls of Black Folk at the expense of Du Bois’s later Marxism. This interpretation downplays his controversial advocacy for the self-segregation of African-American communities, which sought to capitalize on intra-group solidarity in order to rectify class conflict. The chapter argues that these collectives, spheres of free action carved out from predominately white social structures, evince the aesthetic autonomy theorized by Friedrich Schiller, whom Du Bois admired and quotes in Souls. Attending to aesthetic autonomy also reveals new connections between Du Bois and cultural anthropology, especially the work of Ruth Benedict, who advanced aesthetic arguments about anthropological communities that distinguished themselves from a dominant social milieu.
Agents are classically considered rational in economics if their preferences satisfy the completeness and transitivity axioms. But no matter how preferences are defined, an agent can always violate these axioms without making decisions that leave the agent worse off. If preferences are defined by an agent’s welfare judgments, those judgments can be incomplete, while if preferences are defined by an agent’s choices then sequences of those choices can be intransitive. In both cases, agents can shield themselves from harm simply by maintaining the status quo unless offered an unambiguously superior option. Agents will then display several of the anomalies discovered by behavioral economists, including the endowment effect, loss aversion, and the willingness-to-accept/willingness-to-pay disparity. These behaviors are therefore consequences rather than violations of rationality. Moreover, a single set of preference judgments can explain all of the choices an agent makes through time; the theory therefore wields predictive power. Behavioral economics in contrast courts unfalsifiability by positing a separate preference for an agent at every decision-making juncture.
The Q-matrix of a cognitively diagnostic test is said to be complete if it allows for the identification of all possible proficiency classes among examinees. Completeness of the Q-matrix is therefore a key requirement for any cognitively diagnostic test. However, completeness of the Q-matrix is often difficult to establish, especially, for tests with a large number of items involving multiple attributes. As an additional complication, completeness is not an intrinsic property of the Q-matrix, but can only be assessed in reference to a specific cognitive diagnosis model (CDM) supposed to underly the data—that is, the Q-matrix of a given test can be complete for one model but incomplete for another. In this article, a method is presented for assessing whether a given Q-matrix is complete for a given CDM. The proposed procedure relies on the theoretical framework of general CDMs and is therefore legitimate for CDMs that can be reparameterized as a general CDM.
This is the first ever English translation of Heisenberg’s unpublished response to the EPR paper. In this chapter, Heisenberg uses his famous cut argument to argue against the possibility of hidden variables.
Schrödinger’s reaction to the EPR paper is less widely known than, say, Bohr’s, and yet our analysis shows that it fits rather nicely with contemporary concerns in foundations of quantum mechanics. Taking the lead both from the EPR paper and from Pauli’s remarks in their correspondence, Schrödinger shows that EPR’s locality considerations lead to the assignment of values to all quantum mechanical observables, but that under apparently mild assumptions this then leads to contradictions of the von Neumann type. This dilemma (as he explicitly calls it) is thus similar to more recent debates between nonlocality on the one hand and no-go results on the other (whether through violation of the Bell inequalities, the Kochen–Specker theorem, or what you will). We shall first look at Schrödinger’s fundamental worries in the years leading up to 1935. The chapter then discusses in detail the direct reaction by Schrödinger to EPR. It will, however, not exhaust our discussion of Schrödinger, who is a recurring character in the book, having poked and prodded his peers on EPR during the whole summer and autumn of 1935.
This is a reprinting of Bohr’s response to the EPR paper, wherein Bohr relies on his principle of complementarity to demonstrate an ambiguity in the criterion of reality as described by EPR and to argue that quantum mechanics is in fact a complete description of reality given the bounds of complementarity.
This is a reprinting from Jammer (1974) of Podolsky’s unpublished response to Kemble’s criticisms of the EPR paper. Podolsky rightly criticises Kemble for missing the point of EPR’s argument and adds a few comments agreeing with Kemble that a statistical interpretation of quantum mechanics is best – yet Podolsky maintains such an interpretation is incomplete.
This is a reprinting of Flint’s response to EPR, originally signed only as ‘H.T.F.’ Flint begins with a fairly accurate outline of the argument in the EPR paper – with which he agrees – but then he expresses doubts as to the validity of the reality criterion. Without describing the nature of these doubts, he concludes by further agreeing with EPR in desiring a more direct description of reality than the one currently provided by quantum mechanics.
This chapter presents a collection of letters between the main protagonists in the EPR debate as analysed in the present volume. Among many other letters, it includes the first ever complete English translation of the correspondence Schrödinger held concerning the EPR paper with, e.g., Einstein, Bohr, Pauli, Born and Teller. He kept these letters in a special folder labelled ‘The Einstein Paradox’, only a small portion of which has previously been discussed in the foundations literature. These historical documents, many of which are published here for the first time, form the basis of our analysis in the beginning chapters of this book.
This chapter introduces in more comprehensive fashion than elsewhere in the literature the interesting role of Heisenberg in the EPR debate. Although we have already published an analysis of Heisenberg’s posthumously published draft response to EPR, only now are we able to situate this excellent primary source in its fullest context, by contributing a chapter describing, for example, Heisenberg’s thinking prior to EPR about interacting systems and hidden variables, the crucial role of Grete Hermann for Heisenberg’s thinking about separability, completeness and observational context, and describing the correspondence between Heisenberg and Bohr discussing Heisenberg’s manuscript.
This is a reprinting of Bohr’s note to Nature advertising his forthcoming response to the EPR paper. It is very brief but contains in essence the argumentative tack Bohr would in fact employ in his full response to EPR.
This is a reprinting of Furry’s response to EPR. Although his response misses the mark, his discussion of an example is intriguing for other aspects of the foundations of quantum mechanics.
This chapter provides a complete list and brief analyses of published and unpublished responses to EPR in 1935 (virtually all of which are reprinted as later chapters in this book). We invite a renewed consideration of certain contributors not much discussed elsewhere in the literature. These include going beyond Kemble’s short criticism of EPR to his ensuing disagreement with Margenau about the viability of an ensemble interpretation of the wavefunction, and also a response to Kemble’s note on EPR by Podolsky himself. We also examine the correspondence between Margenau and Einstein in the wake of EPR, discussing the role of the collapse postulate, and finally we discuss two papers by Furry, which although not entirely satisfactory qua a response to EPR’s arguments, are nevertheless of great potential interest for the foundations literature more generally.
This is a translation of the excerpts published in Naturwissenschaften of Grete Hermann’s 1935 essay on philosophy of quantum mechanics, recently translated into English. Her main thesis, in line with her natural-philosophical training and neo-Kantian commitments, is to argue that quantum mechanics does not refute the principle of causality. Quantum mechanics cannot be completed by, hidden variables, because it is already causally complete (albeit retroductively). In establishing this provocative thesis, she makes important use of Bohr’s principles of correspondence and complementarity and of Weizsäcker's version of the gamma-ray microscope, arguing that the lesson of quantum mechanics is the impossibility of an absolute description of nature independent of the context of observation.
This is a reprinting of the famous May 1935 paper in Physical Review by Einstein, Podolsky and Rosen. In this paper, the authors argued that the wavefunction fails to provide a complete description of reality unleashing the debate analysed in this volume.
This chapter details not only the prehistory of EPR but also examines the structure and logic of the EPR paper – including Einstein’s own preferred version of the argument for incompleteness. We here attempt a seamless interweaving of the excellent extant literature with additional details that have emerged from our work and the recent work of others. Some examples of new aspects in this prehistory of EPR include evidence of a ‘proto’ photon-box thought experiment Einstein had developed in connection with his ill-starred collaboration with Emil Rupp in 1926. We also describe the potential importance to this prehistory of Einstein’s paper with Tolman and Podolsky and of Einstein’s seminar and discussions with Schrödinger in Berlin in the early 1930s.