L. R. Reinhardt; III—Dualism and Categories, Proceedings of the Aristotelian Society, Volume 66, Issue 1, 1 June 1966, Pages 71–92, https://doi.org/10.1093/aris.

After summarizing my own views of 'I' and the first-person perspective, I consider a well-known autistic, Temple Grandin, who claims that she thinks only in pictures, not in language. I argue, to the contrary, that Grandin's mental life as she describes it in fact requires language, which, as a writer, she undoubtedly has. Finally, I turn to the question of whether thought as Temple Grandin describes it is independent of language.

We show that the first order theory of the lattice $\mathscr{L}^{ (S) of finite dimensional closed subsets of any nontrivial infinite dimensional Steinitz Exhange System S has logical complexity at least that of first order number theory and that the first order theory of the lattice L(S ∞ ) of computably enumerable closed subsets of any nontrivial infinite dimensional computable Steinitz Exchange System S ∞ has logical complexity exactly that of first order number theory. Thus, for example, the lattice of (...) finite dimensional subspaces of a standard copy of $\bigoplus_\omega$ Q interprets first order arithmetic and is therefore as complicated as possible. In particular, our results show that the first order theories of the lattice L(V ∞ ) of c.e. subspaces of a fully effective ℵ 0 -dimensional vector space V∞ and the lattice of c.e. algebraically closed subfields of a fully effective algebraically closed field F ∞ of countably infinite transcendence degree each have logical complexity that of first order number theory. (shrink)

Within the framework of Neurological Positivism this article describes how brain algorithms are translated into mathematics in ontogeny and in culture. The purpose is to address seemingly contradictory research findings that suggest that while mathematical axioms are innate, they are not the direct result of processes of selection. It is proposed that self-referencing feedback processes of maximum-power evolution guide the construction of algorithmic isomorphies between preadapted brain algorithms and mathematics. It is concluded that maximum-power evolution as described in NP offers (...) mechanisms that make sense of findings that suggest that mathematical axioms are innate, yet not directly the result of selection as traditionally understood. It is concluded also that these mechanisms provide insight into the often intuitive nature of mathematical discovery. (shrink)

Whether any apology is possible for the form of this paper is doubtful; but perhaps a few words are allowable. The miscellaneous notes, of which it consists, are fairly well described by the title: at all events, the proposals contained in them—with, I fear, many others—have been pencilled at one time or another in one margin or another. Their age varies widely: two or three must go back to days when my only complete Euripides was Kirchhoff's editio minor and my (...) only Sophocles a copy of Tournier; the most date from middle age or ‘quidquid est illud inter iuvenem et senem medium in utriusque confinio positum’; but, whenever they were made, they were not made by a student of the Greek dramatists commanding the equipment that such a student ought to have. The equipment, in any case, was out of my reach; but, though I have read the plays often, I have read them only because the ancients have a way of enabling one to forget the moderns—as I was informed in my youth by an excellent scholar who has now forgotten both. I hope, therefore, that anyone who may happen to read the paper will overlook some errors and ignorances of the amateur; and, above all, if I may borrow a sentence from Markland's preface to his emendations on Lysias, ‘si quando dictatoria ista, Lege, vel Scribe, occurrent, scito me nihil aliud velle quam Forte legendum vel scribendum’. (shrink)

Open peer commentary on the target article “Who Conceives of Society?” by Ernst von Glasersfeld. Excerpt: In the light of the almost brilliant equilibrium of the author, who manages to compose a resourceful explanation, switching between the notional conditionality and the expected contextual understanding, I intend to focus on the interdisciplinary potential of some suggestions that offer new perspectives on conceiving society, which are driven by a non-analytical and holistic vision.

Philosophers of experiment have acknowledged that experiments are often more than mere hypothesis-tests, once thought to be an experiment's exclusive calling. Drawing on examples from contemporary biology, I make an additional amendment to our understanding of experiment by examining the way that `wide' instrumentation can, for reasons of efficiency, lead scientists away from traditional hypothesis-directed methods of experimentation and towards exploratory methods.

Electrophysiology deals with apparatus applied in a stimulus response situation. This technique is partly concerned with physical problems, partly with biological ones. The failure to appreciate differences in these problems leads to assumptions which require critical examination. Assumptions stating the constancy of objective stimuli, the meaning of inter and intra-individual variation, and the stability of the so-called “resting level” are examined.Some experiments are cited which reveal complications by the apperception of the patient and which have a significant influence on electrophysiological (...) data. The evocation of stress reactions by routine laboratory procedures is discussed and a suggestion is made of the way in which the validity of electro-physiological measurements may be improved.Dans la science de l'électro-physiologie on se sert des instruments pour mesurer des processus de réaction d'une objet stimulée.La méthodique dans cette science est dérivée partiellement de la science biologique et partiellement de la science physicale.Une des difficultées est d'apprécier justement des differences dans les problèmes de mesure dans les deux terraines scientifiques, ce que mène à des assumptions douteuses, qui a besoin d'une examination scrupuleuze.Des assumptions concernant la constance de stimulations objectives, la significance des variations inter- et intra-individuelles et la stabilité du niveau, dit „resting level”, sont examinés.Quelques experiments, révelant des complexités dans l'apperception des patients ayant une influence importante sur les données électro-physiologiques, sont cités.L'évocation des réactions de tension, par des procedures routinières en laboratoire sont discutés et une suggestion afin d'améliorer la validité des données de mesure électrophysiologique est donnée.In der Elektrophysiologie ist man beschäftigt mit Instrumentarium, waraus die Zusammenhang zwischen Reiz und Reaktion untersucht wird. In diesen Untersuchungen werden Methoden angewandt, welche teils aus der biologischen, teils aus der physikalischen Wissenschaft stammen. Es kommt vor, dass Unterschiede in Messungsprobleme innerhalb jedem Fachgebiet nicht richtig gewertet werden, was zu Annahmen führt, welche eine kritische Analyse bedürfen.Annahmen was betrifft, die Konstanz von objective Reize, die Bedeutung von inter- und intra-individuellen Variationen und die Konstanz des sogenannten „resting level”, wurden einer Analyse unterzogen.Einige Experimenten sind zitiert, die eine erhebliche Komplexität in der Wahrnehmungsempfindung des Patienten nachweisen und die eine bedeutungsvolle Einfluss haben auf den elektro-physiologischen Angaben. Das Hervorrufen Spannungsreaktionen durch Routine-vorgänge im Laboratorium wurde diskutiert und eine Weise um mit möglicherweise zuverlassigem Erfolg elektro-physiologischen Messungen aus zu führen wurde vorgeschlagen. (shrink)

In computer science, an algorithm is an unambiguous specification of how to solve a class of problems. Algorithms can perform calculation, data processing and automated reasoning tasks. As an effective method, an algorithm can be expressed within a finite amount of space and time and in a well-defined formal language for calculating a function. Starting from an initial state and initial input (perhaps empty), the instructions describe a computation that, when executed, proceeds through a finite number of well-defined successive states, (...) eventually producing "output" and terminating at a final ending state. The transition from one state to the next is not necessarily deterministic; some algorithms, known as randomized algorithms, incorporate random input. This book introduces a set of concepts in solving problems computationally such as Growth of Functions; Backtracking; Divide and Conquer; Greedy Algorithms; Dynamic Programming; Elementary Graph Algorithms; Minimal Spanning Tree; Single-Source Shortest Paths; All Pairs Shortest Paths; Flow Networks; Polynomial Multiplication, to ways of solving NP-Complete Problems, supported with comprehensive, and detailed problems and solutions, making it an ideal resource to those studying computer science, computer engineering and information technology. (shrink)