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  1. From symbols to icons: the return of resemblance in the cognitive neuroscience revolution.Daniel Williams & Lincoln Colling - 2018 - Synthese 195 (5):1941-1967.
    We argue that one important aspect of the “cognitive neuroscience revolution” identified by Boone and Piccinini :1509–1534. doi: 10.1007/s11229-015-0783-4, 2015) is a dramatic shift away from thinking of cognitive representations as arbitrary symbols towards thinking of them as icons that replicate structural characteristics of their targets. We argue that this shift has been driven both “from below” and “from above”—that is, from a greater appreciation of what mechanistic explanation of information-processing systems involves, and from a greater appreciation of the problems (...)
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  • What is Experimental Philosophy of Mathematics?Kazuhisa Todayama - 2015 - Annals of the Japan Association for Philosophy of Science 23:53-58.
    If we take "experimental philosophy" in a wider sense, it is almost the same as methodological naturalism in philosophy. Experiments of this kind would be available and also fruitful in the philosophy of mathematics. They surely will have a substantial contribution to epistemology of mathematics. At present, however, the phrase "experimental philosophy" is used in a much narrower sense. It refers exclusively to a branch of naturalized philosophy that uses the data gathered through questionnaire surveys to investigate the intuitions of (...)
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  • Universality, Invariance, and the Foundations of Computational Complexity in the light of the Quantum Computer.Michael Cuffaro - 2018 - In Hansson Sven Ove (ed.), Technology and Mathematics: Philosophical and Historical Investigations. Cham, Switzerland: Springer Verlag. pp. 253-282.
    Computational complexity theory is a branch of computer science dedicated to classifying computational problems in terms of their difficulty. While computability theory tells us what we can compute in principle, complexity theory informs us regarding our practical limits. In this chapter I argue that the science of \emph{quantum computing} illuminates complexity theory by emphasising that its fundamental concepts are not model-independent, but that this does not, as some suggest, force us to radically revise the foundations of the theory. For model-independence (...)
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  • Turing's Fallacies.Timm Lampert - 2017
    This paper reveals two fallacies in Turing's undecidability proof of first-order logic (FOL), namely, (i) an 'extensional fallacy': from the fact that a sentence is an instance of a provable FOL formula, it is inferred that a meaningful sentence is proven, and (ii) a 'fallacy of substitution': from the fact that a sentence is an instance of a provable FOL formula, it is inferred that a true sentence is proven. The first fallacy erroneously suggests that Turing's proof of the non-existence (...)
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  • Heuristics, Concepts, and Cognitive Architecture: Toward Understanding How The Mind Works.Sheldon J. Chow - unknown
    Heuristics are often invoked in the philosophical, psychological, and cognitive science literatures to describe or explain methodological techniques or "shortcut" mental operations that help in inference, decision-making, and problem-solving. Yet there has been surprisingly little philosophical work done on the nature of heuristics and heuristic reasoning, and a close inspection of the way(s) in which "heuristic" is used throughout the literature reveals a vagueness and uncertainty with respect to what heuristics are and their role in cognition. This dissertation seeks to (...)
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  • Computing with Numbers and Other Non-syntactic Things: De re Knowledge of Abstract Objects.Stewart Shapiro - 2017 - Philosophia Mathematica 25 (2):268-281.
    ABSTRACT Michael Rescorla has argued that it makes sense to compute directly with numbers, and he faulted Turing for not giving an analysis of number-theoretic computability. However, in line with a later paper of his, it only makes sense to compute directly with syntactic entities, such as strings on a given alphabet. Computing with numbers goes via notation. This raises broader issues involving de re propositional attitudes towards numbers and other non-syntactic abstract entities.
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  • Computable and Continuous Partial Homomorphisms on Metric Partial Algebras.Viggo Stoltenberg-Hansen & John V. Tucker - 2003 - Bulletin of Symbolic Logic 9 (3):299-334.
    We analyse the connection between the computability and continuity of functions in the case of homomorphisms between topological algebraic structures. Inspired by the Pour-El and Richards equivalence theorem between computability and boundedness for closed linear operators on Banach spaces, we study the rather general situation of partial homomorphisms between metric partial universal algebras. First, we develop a set of basic notions and results that reveal some of the delicate algebraic, topological and effective properties of partial algebras. Our main computability concepts (...)
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  • Hypercomputation and the Physical Church‐Turing Thesis.Paolo Cotogno - 2003 - British Journal for the Philosophy of Science 54 (2):181-223.
    A version of the Church-Turing Thesis states that every effectively realizable physical system can be simulated by Turing Machines (‘Thesis P’). In this formulation the Thesis appears to be an empirical hypothesis, subject to physical falsification. We review the main approaches to computation beyond Turing definability (‘hypercomputation’): supertask, non-well-founded, analog, quantum, and retrocausal computation. The conclusions are that these models reduce to supertasks, i.e. infinite computation, and that even supertasks are no solution for recursive incomputability. This yields that the realization (...)
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  • Deviant encodings and Turing’s analysis of computability.B. Jack Copeland & Diane Proudfoot - 2010 - Studies in History and Philosophy of Science Part A 41 (3):247-252.
    Turing’s analysis of computability has recently been challenged; it is claimed that it is circular to analyse the intuitive concept of numerical computability in terms of the Turing machine. This claim threatens the view, canonical in mathematics and cognitive science, that the concept of a systematic procedure or algorithm is to be explicated by reference to the capacities of Turing machines. We defend Turing’s analysis against the challenge of ‘deviant encodings’.Keywords: Systematic procedure; Turing machine; Church–Turing thesis; Deviant encoding; Acceptable encoding; (...)
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  • Computation vs. information processing: why their difference matters to cognitive science.Gualtiero Piccinini & Andrea Scarantino - 2010 - Studies in History and Philosophy of Science Part A 41 (3):237-246.
    Since the cognitive revolution, it has become commonplace that cognition involves both computation and information processing. Is this one claim or two? Is computation the same as information processing? The two terms are often used interchangeably, but this usage masks important differences. In this paper, we distinguish information processing from computation and examine some of their mutual relations, shedding light on the role each can play in a theory of cognition. We recommend that theorists of cognition be explicit and careful (...)
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  • Copeland and Proudfoot on computability.Michael Rescorla - 2012 - Studies in History and Philosophy of Science Part A 43 (1):199-202.
    Many philosophers contend that Turing’s work provides a conceptual analysis of numerical computability. In (Rescorla, 2007), I dissented. I argued that the problem of deviant notations stymies existing attempts at conceptual analysis. Copeland and Proudfoot respond to my critique. I argue that their putative solution does not succeed. We are still awaiting a genuine conceptual analysis.
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  • Mitä uutta modernissa logiikassa?Panu Raatikainen - 2004 - In Raatikainen Panu (ed.), Filosofisia tutkielmia – Philosophical Studies in honorem Leila Haaparanta. Tampere University Press.
    logiikka on lopullinen ja täydellinen logiikka. Sittemmin logiikka on kuitenkin kokenut melkoisen mullistuksen. Käsitykset siitä, mikä tässä muutoksessa oli olennaista ja milloin se todella tapahtui, vaihtelevat.
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  • Chains of Life: Turing, Lebensform, and the Emergence of Wittgenstein’s Later Style.Juliet Floyd - 2016 - Nordic Wittgenstein Review 5 (2):7-89.
    This essay accounts for the notion of _Lebensform_ by assigning it a _logical _role in Wittgenstein’s later philosophy. Wittgenstein’s additions of the notion to his manuscripts of the _PI_ occurred during the initial drafting of the book 1936-7, after he abandoned his effort to revise _The Brown Book_. It is argued that this constituted a substantive step forward in his attitude toward the notion of simplicity as it figures within the notion of logical analysis. Next, a reconstruction of his later (...)
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  • How to Make a Meaningful Comparison of Models: The Church–Turing Thesis Over the Reals.Maël Pégny - 2016 - Minds and Machines 26 (4):359-388.
    It is commonly believed that there is no equivalent of the Church–Turing thesis for computation over the reals. In particular, computational models on this domain do not exhibit the convergence of formalisms that supports this thesis in the case of integer computation. In the light of recent philosophical developments on the different meanings of the Church–Turing thesis, and recent technical results on analog computation, I will show that this current belief confounds two distinct issues, namely the extension of the notion (...)
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  • Generating, solving and the mathematics of Homo Sapiens. Emil Post's views on computation.Liesbeth de Mol - unknown
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  • Quantum Deep Learning Triuniverse.Angus McCoss - 2016 - Journal of Quantum Information Science 6 (4).
    An original quantum foundations concept of a deep learning computational Universe is introduced. The fundamental information of the Universe (or Triuniverse)is postulated to evolve about itself in a Red, Green and Blue (RGB) tricoloured stable self-mutuality in three information processing loops. The colour is a non-optical information label. The information processing loops form a feedback-reinforced deep learning macrocycle with trefoil knot topology. Fundamental information processing is driven by ψ-Epistemic Drive, the Natural appetite for information selected for advantageous knowledge. From its (...)
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  • Simplicity, Inference and Modelling: Keeping It Sophisticatedly Simple.Arnold Zellner, Hugo A. Keuzenkamp & Michael McAleer (eds.) - 2001 - New York: Cambridge University Press.
    The idea that simplicity matters in science is as old as science itself, with the much cited example of Ockham's Razor, 'entia non sunt multiplicanda praeter necessitatem': entities are not to be multiplied beyond necessity. A problem with Ockham's razor is that nearly everybody seems to accept it, but few are able to define its exact meaning and to make it operational in a non-arbitrary way. Using a multidisciplinary perspective including philosophers, mathematicians, econometricians and economists, this 2002 monograph examines simplicity (...)
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  • ¿Qué es un algoritmo? Una respuesta desde la obra de Wittgenstein.Sergio Mota - 2015 - Endoxa 36:317.
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  • The Philosophy of Cognitive Science.Margaret A. Boden - 2001 - Royal Institute of Philosophy Supplement 48:209-226.
    If the Trade Descriptions Act were applied to academic labels, cognitive scientists would be in trouble. For what they do is much wider than the name suggests—and wider, too, than most philosophers assume. They give you more for your money than you may have expected.
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  • For a dynamical approach to human computation.Marco Giunti & Simone Pinna - 2016 - Logic Journal of the IGPL 24 (4).
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  • Computably Isometric Spaces.Alexander G. Melnikov - 2013 - Journal of Symbolic Logic 78 (4):1055-1085.
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  • On Optimal Inverters.Yijia Chen & Jörg Flum - 2014 - Bulletin of Symbolic Logic 20 (1):1-23.
    Leonid Levin showed that every algorithm computing a function has an optimal inverter. Recently, we applied his result in various contexts: existence of optimal acceptors, existence of hard sequences for algorithms and proof systems, proofs of Gödel’s incompleteness theorems, analysis of the complexity of the clique problem assuming the nonuniform Exponential Time Hypothesis. We present all these applications here. Even though a simple diagonalization yields Levin’s result, we believe that it is worthwhile to be aware of the explicit result. The (...)
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  • Computation, hypercomputation, and physical science.Konstantine Arkoudas - 2008 - Journal of Applied Logic 6 (4):461-475.
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  • Computational creativity.Ramon López de Mántaras Badia - 2013 - Arbor 189 (764):a082.
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  • Alan Turing and the origins of complexity.Miguel Angel Martin-Delgado - 2013 - Arbor 189 (764):a083.
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  • Alan Turing: person of the XXth century?José M. Sánchez Ron - 2013 - Arbor 189 (764):a085.
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  • Computability of validity and satisfiability in probability logics over finite and countable models.Greg Yang - 2015 - Journal of Applied Non-Classical Logics 25 (4):324-372.
    The -logic of Terwijn is a variant of first-order logic with the same syntax in which the models are equipped with probability measures and the quantifier is interpreted as ‘there exists a set A of a measure such that for each,...’. Previously, Kuyper and Terwijn proved that the general satisfiability and validity problems for this logic are, i) for rational, respectively -complete and -hard, and ii) for, respectively decidable and -complete. The adjective ‘general’ here means ‘uniformly over all languages’. We (...)
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  • The breadth of semantics: reply to critics.Ernie Lepore & Matthew Stone - 2016 - Inquiry: An Interdisciplinary Journal of Philosophy 59 (2):195-206.
    In our 2015 book Imagination and Convention, we explore the scope and limits of linguistic knowledge in semantics and pragmatics for natural language. We draw heavily on the notion of coordination from David Lewis' book on conventions. To the extent that the account we develop is right, general principles like Grice's cooperative principle and the maxims of conversation have little to say about about interpretation. Three commentators—Anne Bezuidenhout, Laurence Horn, and Zoltan Gendler Szabo—discuss and evaluate our program in three essays (...)
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  • Wie Maschinen denken.Thomas Hainscho - 2016 - In Maja Soboleva (ed.), Das Denken des Denkens: Ein Philosophischer Überblick. Bielefeld: Transcript Verlag. pp. 197-220.
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  • Brains-in-vats, giant brains and world brains: the brain as metaphor in digital culture.Charlie Gere - 2004 - Studies in History and Philosophy of Science Part C: Studies in History and Philosophy of Biological and Biomedical Sciences 35 (2):351-366.
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  • Turing's O-machines, Searle, Penrose and the brain.B. J. Copeland - 1998 - Analysis 58 (2):128-138.
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  • From Alan Turing to modern AI: practical solutions and an implicit epistemic stance.George F. Luger & Chayan Chakrabarti - 2017 - AI and Society 32 (3):321-338.
    It has been just over 100 years since the birth of Alan Turing and more than 65 years since he published in Mind his seminal paper, Computing Machinery and Intelligence. In the Mind paper, Turing asked a number of questions, including whether computers could ever be said to have the power of “thinking”. Turing also set up a number of criteria—including his imitation game—under which a human could judge whether a computer could be said to be “intelligent”. Turing’s paper, as (...)
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  • Comprehension of Simple Quantifiers: Empirical Evaluation of a Computational Model.Jakub Szymanik & Marcin Zajenkowski - 2010 - Cognitive Science 34 (3):521-532.
    We examine the verification of simple quantifiers in natural language from a computational model perspective. We refer to previous neuropsychological investigations of the same problem and suggest extending their experimental setting. Moreover, we give some direct empirical evidence linking computational complexity predictions with cognitive reality.<br>In the empirical study we compare time needed for understanding different types of quantifiers. We show that the computational distinction between quantifiers recognized by finite-automata and push-down automata is psychologically relevant. Our research improves upon hypothesis and (...)
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  • The Physical Church–Turing Thesis: Modest or Bold?Gualtiero Piccinini - 2011 - British Journal for the Philosophy of Science 62 (4):733-769.
    This article defends a modest version of the Physical Church-Turing thesis (CT). Following an established recent trend, I distinguish between what I call Mathematical CT—the thesis supported by the original arguments for CT—and Physical CT. I then distinguish between bold formulations of Physical CT, according to which any physical process—anything doable by a physical system—is computable by a Turing machine, and modest formulations, according to which any function that is computable by a physical system is computable by a Turing machine. (...)
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  • When Logic Meets Engineering: Introduction to Logical Issues in the History and Philosophy of Computer Science.Liesbeth De Mol & Giuseppe Primiero - 2015 - History and Philosophy of Logic 36 (3):195-204.
    The birth, growth, stabilization and subsequent understanding of a new field of practical and theoretical enquiry is always a conceptual process including several typologies of events, phenomena an...
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  • A Vindication of Program Verification.Selmer Bringsjord - 2015 - History and Philosophy of Logic 36 (3):262-277.
    Fetzer famously claims that program verification is not even a theoretical possibility, and offers a certain argument for this far-reaching claim. Unfortunately for Fetzer, and like-minded thinkers, this position-argument pair, while based on a seminal insight that program verification, despite its Platonic proof-theoretic airs, is plagued by the inevitable unreliability of messy, real-world causation, is demonstrably self-refuting. As I soon show, Fetzer is like the person who claims: ‘My sole claim is that every claim expressed by an English sentence and (...)
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  • Three forms of physical measurement and their computability.Edwin Beggs, José Félix Costa & John V. Tucker - 2014 - Review of Symbolic Logic 7 (4):618-646.
    We have begun a theory of measurement in which an experimenter and his or her experimental procedure are modeled by algorithms that interact with physical equipment through a simple abstract interface. The theory is based upon using models of physical equipment as oracles to Turing machines. This allows us to investigate the computability and computational complexity of measurement processes. We examine eight different experiments that make measurements and, by introducing the idea of an observable indicator, we identify three distinct forms (...)
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  • Objective Computation Versus Subjective Computation.Nir Fresco - 2015 - Erkenntnis 80 (5):1031-1053.
    The question ‘What is computation?’ might seem a trivial one to many, but this is far from being in consensus in philosophy of mind, cognitive science and even in physics. The lack of consensus leads to some interesting, yet contentious, claims, such as that cognition or even the universe is computational. Some have argued, though, that computation is a subjective phenomenon: whether or not a physical system is computational, and if so, which computation it performs, is entirely a matter of (...)
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  • The machine as data: a computational view of emergence and definability.S. Barry Cooper - 2015 - Synthese 192 (7):1955-1988.
    Turing’s paper on computable numbers has played its role in underpinning different perspectives on the world of information. On the one hand, it encourages a digital ontology, with a perceived flatness of computational structure comprehensively hosting causality at the physical level and beyond. On the other, it can give an insight into the way in which higher order information arises and leads to loss of computational control—while demonstrating how the control can be re-established, in special circumstances, via suitable type reductions. (...)
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  • What is the extension of the extended mind?Hajo Greif - 2017 - Synthese 194 (11):4311-4336.
    Two aspects of cognitive coupling, as brought forward in the Extended Mind Hypothesis, are discussed in this paper: how shall the functional coupling between the organism and some entity in his environment be spelled out in detail? What are the paradigmatic external entities to enter into that coupling? These two related questions are best answered in the light of an aetiological variety of functionalist argument that adds historical depth to the “active externalism” promoted by Clark and Chalmers and helps to (...)
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  • Rational Use of Cognitive Resources: Levels of Analysis Between the Computational and the Algorithmic.Thomas L. Griffiths, Falk Lieder & Noah D. Goodman - 2015 - Topics in Cognitive Science 7 (2):217-229.
    Marr's levels of analysis—computational, algorithmic, and implementation—have served cognitive science well over the last 30 years. But the recent increase in the popularity of the computational level raises a new challenge: How do we begin to relate models at different levels of analysis? We propose that it is possible to define levels of analysis that lie between the computational and the algorithmic, providing a way to build a bridge between computational- and algorithmic-level models. The key idea is to push the (...)
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  • Behavioural Explanation in the Realm of Non-mental Computing Agents.Bernardo Aguilera - 2015 - Minds and Machines 25 (1):37-56.
    Recently, many philosophers have been inclined to ascribe mentality to animals on the main grounds that they possess certain complex computational abilities. In this paper I contend that this view is misleading, since it wrongly assumes that those computational abilities demand a psychological explanation. On the contrary, they can be just characterised from a computational level of explanation, which picks up a domain of computation and information processing that is common to many computing systems but is autonomous from the domain (...)
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  • Recursive Functions and Metamathematics: Problems of Completeness and Decidability, Gödel's Theorems.Rod J. L. Adams & Roman Murawski - 1999 - Dordrecht, Netherland: Springer Verlag.
    Traces the development of recursive functions from their origins in the late nineteenth century to the mid-1930s, with particular emphasis on the work and influence of Kurt Gödel.
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  • The Ricean Objection: An Analogue of Rice's Theorem for First-order Theories.Igor Oliveira & Walter Carnielli - 2008 - Logic Journal of the IGPL 16 (6):585-590.
    We propose here an extension of Rice's Theorem to first-order logic, proven by totally elementary means. If P is any property defined over the collection of all first-order theories and P is non-trivial over the set of finitely axiomatizable theories , then P is undecidable. This not only means that the problem of deciding properties of first-order theories is as hard as the problem of deciding properties about languages accepted by Turing machines, but also offers a general setting for proving (...)
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  • Non-standard numbers: a semantic obstacle for modelling arithmetical reasoning.Anderson De Araújo & Walter Carnielli - 2012 - Logic Journal of the IGPL 20 (2):477-485.
    The existence of non-standard numbers in first-order arithmetics is a semantic obstacle for modelling our arithmetical skills. This article argues that so far there is no adequate approach to overcome such a semantic obstacle, because we can also find out, and deal with, non-standard elements in Turing machines.
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  • On What There is—Infinitesimals and the Nature of Numbers.Jens Erik Fenstad - 2015 - Inquiry: An Interdisciplinary Journal of Philosophy 58 (1):57-79.
    This essay will be divided into three parts. In the first part, we discuss the case of infintesimals seen as a bridge between the discrete and the continuous. This leads in the second part to a discussion of the nature of numbers. In the last part, we follow up with some observations on the obvious applicability of mathematics.
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  • What Does ‘Depth’ Mean in Mathematics?John Stillwell - 2015 - Philosophia Mathematica 23 (2):215-232.
    This paper explores different interpretations of the word ‘deep’ as it is used by mathematicians, with a large number of examples illustrating various criteria for depth. Most of the examples are theorems with ‘historical depth’, in the sense that many generations of mathematicians contributed to their proof. Some also have ‘foundational depth’, in the sense that they support large mathematical theories. Finally, concepts from mathematical logic suggest that it may be possible to order certain theorems or problems according to ‘logical (...)
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  • Effective Computation by Humans and Machines.Shagrir Oron - 2002 - Minds and Machines 12 (2):221-240.
    There is an intensive discussion nowadays about the meaning of effective computability, with implications to the status and provability of the Church–Turing Thesis (CTT). I begin by reviewing what has become the dominant account of the way Turing and Church viewed, in 1936, effective computability. According to this account, to which I refer as the Gandy–Sieg account, Turing and Church aimed to characterize the functions that can be computed by a human computer. In addition, Turing provided a highly convincing argument (...)
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  • Ein Blick zurück auf das 20. Jahrhundert.Peter Schreiber - 2002 - NTM Zeitschrift für Geschichte der Wissenschaften, Technik und Medizin 10 (1-3):40-48.
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  • Beyond the universal Turing machine.B. Jack Copeland & Richard Sylvan - 1999 - Australasian Journal of Philosophy 77 (1):46-66.
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