Search results for 'Recursively defined function' (try it on Scholar)

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  1.  14
    Laureano Luna (2010). Ungrounded Causal Chains and Beginningless Time. Logic and Logical Philosophy 18 (3-4):297-307.
    We use two logical resources, namely, the notion of recursively defined function and the Benardete-Yablo paradox, together with some inherent features of causality and time, as usually conceived, to derive two results: that no ungrounded causal chain exists and that time has a beginning.
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  2.  84
    Laureano Luna (2014). No Successfull Infinite Regress. Logic and Logical Philosophy 23 (2):189-201.
    We model infinite regress structures -not arguments- by means of ungrounded recursively defined functions in order to show that no such structure can perform the task of providing determination to the items composing it, that is, that no determination process containing an infinite regress structure is successful.
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  3.  18
    Laureano Luna (2014). No Successful Infinite Regress. Logic and Logical Philosophy 23 (2):189-201.
    We model infinite regress structures — not arguments — by means of ungrounded recursively defined functions in order to show that no such structure can perform the task of providing determination to the items composing it, that is, that no determination process containing an infinite regress structure is successful.
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  4.  2
    Damian Rössler (2013). Infinitely $P$-Divisible Points on Abelian Varieties Defined Over Function Fields of Characteristic $Pgt 0$. Notre Dame Journal of Formal Logic 54 (3-4):579-589.
    In this article we consider some questions raised by F. Benoist, E. Bouscaren, and A. Pillay. We prove that infinitely $p$-divisible points on abelian varieties defined over function fields of transcendence degree one over a finite field are necessarily torsion points. We also prove that when the endomorphism ring of the abelian variety is $\mathbb{Z}$, then there are no infinitely $p$-divisible points of order a power of $p$.
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  5.  5
    Jesse B. Wright (1972). Characterization of Recursively Enumerable Sets. Journal of Symbolic Logic 37 (3):507-511.
    Let N, O and S denote the set of nonnegative integers, the graph of the constant 0 function and the graph of the successor function respectively. For sets $P, Q, R \subseteq N^2$ operations of transposition, composition, and bracketing are defined as follows: $P^\cup = \{\langle x, y\rangle | \langle y, x\rangle \epsilon P\}, PQ = \{\langle x, z\rangle| \exists y\langle x, y\rangle \epsilon P & \langle y, z\rangle \epsilon Q\}$ , and [ P, Q, R] = (...)
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  6.  1
    Mary Jane Dinardo & Thomas C. Toppino (1984). Formation of Ill-Defined Concepts as a Function of Category Size and Category Exposure. Bulletin of the Psychonomic Society 22 (4):317-320.
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  7. Efrain C. Azmitia & Particia M. Whitaker-Azmitia (1986). Searching for an Ill-Defined Brain Function Results in an Uneasy Reconciliation. Behavioral and Brain Sciences 9 (2):335.
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  8. F. Bagemihl (1971). A Property of the Function Ψ(Α) Defined by 2ℵα = ℵα+Ψ(Α). Mathematical Logic Quarterly 17 (1):23-24.
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  9. F. Bagemihl (1971). A Property of the Function Ψ Defined by 2ℵα = ℵα+Ψ. Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 17 (1):23-24.
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  10.  3
    Xizhong Zheng, Vasco Brattka & Klaus Weihrauch (1999). Approaches to Effective Semi‐Continuity of Real Functions. Mathematical Logic Quarterly 45 (4):481-496.
    For semi-continuous real functions we study different computability concepts defined via computability of epigraphs and hypographs. We call a real function f lower semi-computable of type one, if its open hypograph hypo is recursively enumerably open in dom × ℝ; we call f lower semi-computable of type two, if its closed epigraph Epi is recursively enumerably closed in dom × ℝ; we call f lower semi-computable of type three, if Epi is recursively closed in dom (...)
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  11.  26
    Vincent W. J. Van Gerven Oei (2012). Cumposition: Theses on Philosophy's Etymology. Continent 2 (1).
    continent. 2.1 (2012): 44–55. Philosophers are sperm, poetry erupts sperm and dribbles, philosopher recodes term, to terminate, —A. Staley Groves 1 There is, in the relation of human languages to that of things, something that can be approximately described as “overnaming”—the deepest linguistic reason for all melancholy and (from the point of view of the thing) for all deliberate muteness. Overnaming as the linguistic being of melancholy points to another curious relation of language: the overprecision that obtains in the tragic (...)
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  12.  1
    Farzad Didehvar (1999). On a Class of Recursively Enumerable Sets. Mathematical Logic Quarterly 45 (4):467-470.
    We define a class of so-called ∑-sets as a natural closure of recursively enumerable sets Wn under the relation “∈” and study its properties.
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  13.  30
    Richard Beigel, William Gasarch, Martin Kummer, Georgia Martin, Timothy McNicholl & Frank Stephan (2000). The Complexity of Oddan. Journal of Symbolic Logic 65 (1):1 - 18.
    For a fixed set A, the number of queries to A needed in order to decide a set S is a measure of S's complexity. We consider the complexity of certain sets defined in terms of A: $ODD^A_n = \{(x_1, \dots ,x_n): {\tt\#}^A_n(x_1, \dots, x_n) \text{is odd}\}$ and, for m ≥ 2, $\text{MOD}m^A_n = \{(x_1, \dots ,x_n):{\tt\#}^A_n(x_1, \dots ,x_n) \not\equiv 0 (\text{mod} m)\},$ where ${\tt\#}^A_n(x_1, \dots ,x_n) = A(x_1)+\cdots+A(x_n)$ . (We identify A(x) with χ A (x), where χ A (...)
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  14.  3
    Charles Morgan, Local Connectedness and Distance Functions.
    Local connectedness functions for (κ, 1)-simplified morasses, localisations of the coupling function c studied in [M96, §1], are defined and their elementary properties discussed. Several different, useful, canonical ways of arriving at the functions are examined. This analysis is then used to give explicit formulae for generalisations of the local distance functions which were defined recursively in [K00], leading to simple proofs of the principal properties of those functions. It is then extended to the properties of (...)
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  15.  2
    J. C. E. Dekker (1990). An Isolic Generalization of Cauchy's Theorem for Finite Groups. Archive for Mathematical Logic 29 (4):231-236.
    In his note [5] Hausner states a simple combinatorial principle, namely: $$(H)\left\{ {\begin{array}{*{20}c} {if f is a function a non - empty finite set \sigma into itself, p a} \\ {prime, f^p = i_\sigma and \sigma _0 the set of fixed points of f, then } \\ {\left| \sigma \right| \equiv \left| {\sigma _0 } \right|(mod p).} \\\end{array}} \right.$$ .He then shows how this principle can be used to prove:Fermat's little theorem,Cauchy's theorem for finite groups,Lucas' theorem for binomial numbers.Letε=(0,1, (...)
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  16. Valery Plisko (2001). Arithmetic Complexity of the Predicate Logics of Certain Complete Arithmetic Theories. Annals of Pure and Applied Logic 113 (1-3):243-259.
    It is proved in this paper that the predicate logic of each complete constructive arithmetic theory T having the existential property is Π1T-complete. In this connection, the techniques of a uniform partial truth definition for intuitionistic arithmetic theories is used. The main theorem is applied to the characterization of the predicate logic corresponding to certain variant of the notion of realizable predicate formula. Namely, it is shown that the set of irrefutable predicate formulas is recursively isomorphic to the complement (...)
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  17. Bence Nanay (2010). A Modal Theory of Function. Journal of Philosophy 107 (8):412-431.
    The function of a trait token is usually defined in terms of some properties of other (past, present, future) tokens of the same trait type. I argue that this strategy is problematic, as trait types are (at least partly) individuated by their functional properties, which would lead to circularity. In order to avoid this problem, I suggest a way to define the function of a trait token in terms of the properties of the very same trait token. (...)
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  18.  97
    Ron Amundson & George V. Lauder (1994). Function Without Purpose. Biology and Philosophy 9 (4):443-469.
    Philosophers of evolutionary biology favor the so-called etiological concept of function according to which the function of a trait is its evolutionary purpose, defined as the effect for which that trait was favored by natural selection. We term this the selected effect (SE) analysis of function. An alternative account of function was introduced by Robert Cummins in a non-evolutionary and non-purposive context. Cummins''s account has received attention but little support from philosophers of biology. This paper (...)
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  19.  85
    M. Revzen (2006). The Wigner Function as Distribution Function. Foundations of Physics 36 (4):546-562.
    Some entangled states have nonnegative Wigner representative function. The latter allow being viewed as a distribution function of local hidden variables. It is argued herewith that the interpretation of expectation values using such distribution functions as local hidden variable theory requires restrictions pertaining to the observables under study. The reasoning lead to support the view that violation of Bell’s inequalities that is always possible for entangled states hinges not only on the states involved but also whether the (...)
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  20.  13
    Véronique Izard, Pierre Pica, Elizabeth S. Spelke & Stanislas Dehaene (2008). Exact Equality and Successor Function: Two Key Concepts on the Path Towards Understanding Exact Numbers. Philosophical Psychology 21 (4):491 – 505.
    Humans possess two nonverbal systems capable of representing numbers, both limited in their representational power: the first one represents numbers in an approximate fashion, and the second one conveys information about small numbers only. Conception of exact large numbers has therefore been thought to arise from the manipulation of exact numerical symbols. Here, we focus on two fundamental properties of the exact numbers as prerequisites to the concept of EXACT NUMBERS : the fact that all numbers can be generated by (...)
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  21.  6
    Dingmar van Eck (2015). Validating Function-Based Design Methods: An Explanationist Perspective. Philosophy and Technology 28 (4):511-531.
    Analysis of the adequacy of engineering design methods, as well as analysis of the utility of concepts of function often invoked in these methods, is a neglected topic in both philosophy of technology and in engineering proper. In this paper, I present an approach—dubbed an explanationist perspective—for assessing the adequacy of function-based design methods. Engineering design is often intertwined with explanation, for instance, in reverse engineering and subsequent redesign, knowledge base-assisted designing, and diagnostic reasoning. I (...)
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  22.  43
    Shan Gao, The Wave Function and Particle Ontology.
    In quantum mechanics, the wave function of a N-body system is a mathematical function defined in a 3N-dimensional configuration space. We argue that wave function realism implies particle ontology when assuming: (1) the wave function of a N-body system describes N physical entities; (2) each triple of the 3N coordinates of a point in configuration space that relates to one physical entity represents a point in ordinary three-dimensional space. Moreover, the motion of particles is random (...)
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  23.  24
    Richard Martin Pagni (2009). The Origin and Development of the Acidity Function. Foundations of Chemistry 11 (1):43-50.
    The acidity function is a thermodynamic quantitative measure of acid strength for non-aqueous and concentrated aqueous Brønsted acids, with acid strength being defined as the extent to which the acid protonates a base of known basicity. The acidity function, which was developed, both theoretically and experimentally, by Louis P. Hammett of Columbia University during the 1930s, has proven useful in the area of physical organic chemistry where it has been used to correlate rates of acid-catalyzed reactions (...)
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  24. M. B. Thuraisingham (1993). System Function Languages. Mathematical Logic Quarterly 39 (1):357-366.
    In this paper we define the concept of a system function language which is a language generated by a system function. We identify system function languages with recursively enumerable sets which are non-simple and co-infinite. We then define restricted system function languages and identify them with recursive sets which are co-infinite. Finally we state and prove some independence and dependence relationships between system function languages and some of the more well-known decision problems. MSC: 03D05, (...)
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  25. Frances Egan (forthcoming). Function-Theoretic Explanation and the Search for Neural Mechanisms. In David M. Kaplan (ed.), Integrating Mind and Brain Science: Mechanistic Perspectives and Beyond. Oxford University Press
    A common kind of explanation in cognitive neuroscience might be called function-theoretic: with some target cognitive capacity in view, the theorist hypothesizes that the system computes a well-defined function (in the mathematical sense) and explains how computing this function contributes to the exercise of the cognitive capacity. Recently, proponents of the so-called ‘new mechanist’ approach in philosophy of science have argued that a model of a cognitive capacity is explanatory only to the extent that it reveals (...)
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  26.  40
    Frances Egan (forthcoming). Function-Theoretic Explanation and Neural Mechanisms. In David M. Kaplan (ed.), Integrating Mind and Brain Science: Mechanistic Perspectives and Beyond.
    A common kind of explanation in cognitive neuroscience might be called function-theoretic: with some target cognitive capacity in view, the theorist hypothesizes that the system computes a well-defined function (in the mathematical sense) and explains how computing this function constitutes (in the system’s normal environment) the exercise of the cognitive capacity. Recently, proponents of the so-called ‘new mechanist’ approach in philosophy of science have argued that a model of a cognitive capacity is explanatory only to the (...)
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  27.  8
    Richard Beigel, Harry Buhrman, Peter Fejer, Lance Fortnow, Piotr Grabowski, Luc Longpré, Andrej Muchnik, Frank Stephan & Leen Torenvliet (2006). Enumerations of the Kolmogorov Function. Journal of Symbolic Logic 71 (2):501 - 528.
    A recursive enumerator for a function h is an algorithm f which enumerates for an input x finitely many elements including h(x), f is a k(n)-enumerator if for every input x of length n, h(x) is among the first k(n) elements enumerated by f. If there is a k(n)-enumerator for h then h is called k(n)-enumerable. We also consider enumerators which are only A-recursive for some oracle A. We determine exactly how hard it is to enumerate the Kolmogorov (...), which assigns to each string x its Kolmogorov complexity: • For every underlying universal machine U, there is a constant a such that C is k(n)-enumerable only if k(n) ≥ n/a for almost all n. • For any given constant k, the Kolmogorov function is k-enumerable relative to an oracle A if and only if A is at least as hard as the halting problem. • There exists an r.e., Turing-incomplete set A such for every non-decreasing and unbounded recursive function k, the Kolmogorov function is k(n)-enumerable relative to A. The last result is obtained by using a relativizable construction for a nonrecursive set A relative to which the prefix-free Kolmogorov complexity differs only by a constant from the unrelativized prefix-free Kolmogorov complexity. Although every 2-enumerator for C is Turing hard for K, we show that reductions must depend on the specific choice of the 2-enumerator and there is no bound on the quantity of their queries. We show our negative results even for strong 2-enumerators as an oracle where the querying machine for any x gets directly an explicit list of all hypotheses of the enumerator for this input. The limitations are very general and we show them for any recursively bounded function g: • For every Turing reduction M and every non-recursive set B, there is a strong 2-enumerator f for g such that M does not Turing reduce B to f. • For every non-recursive set B, there is a strong 2-enumerator f for g such that B is not wtt-reducible to f. Furthermore, we deal with the resource-bounded case and give characterizations for the class ${\rm S}_{2}^{{\rm P}}$ introduced by Canetti and independently Russell and Sundaram and the classes PSPACE, EXP. • ${\rm S}_{2}^{{\rm P}}$ is the class of all sets A for which there is a polynomially bounded function g such that there is a polynomial time tt-reduction which reduces A to every strong 2-enumerator for g. • PSPACE is the class of all sets A for which there is a polynomially bounded function g such that there is a polynomial time Turing reduction which reduces A to every strong 2-enumerator for g. Interestingly, g can be taken to be the Kolmogorov function for the conditional space bounded Kolmogorov complexity. • EXP is the class of all sets A for which there is a polynomially bounded function g and a machine M which witnesses A ∈ PSPACEf for all strong 2-enumerators f for g. Finally, we show that any strong O(log n)-enumerator for the conditional space bounded Kolmogorov function must be PSPACE-hard if P = NP. (shrink)
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  28. Richard Heersmink (2013). A Taxonomy of Cognitive Artifacts: Function, Information, and Categories. Review of Philosophy and Psychology 4 (3):1-17.
    The goal of this paper is to develop a systematic taxonomy of cognitive artifacts, i.e., human-made, physical objects that functionally contribute to performing a cognitive task. First, I identify the target domain by conceptualizing the category of cognitive artifacts as a functional kind: a kind of artifact that is defined purely by its function. Next, on the basis of their informational properties, I develop a set of related subcategories in which cognitive artifacts with similar properties can be grouped. (...)
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  29.  55
    Paul E. Griffiths (2006). Function, Homology, and Character Individuation. Philosophy of Science 73 (1):1-25.
    I defend the view that many biological categories are defined by homology against a series of arguments designed to show that all biological categories are defined, at least in part, by selected function. I show that categories of homology are `abnormality inclusive'—something often alleged to be unique to selected function categories. I show that classifications by selected function are logically dependent on classifications by homology, but not vice-versa. Finally, I reject the view that biologists must (...)
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  30.  16
    P. D. Magnus (2014). What Scientists Know Is Not a Function of What Scientists Know. Philosophy of Science 80 (5):840-849.
    There are two senses of ‘what scientists know’: An individual sense (the separate opinions of individual scientists) and a collective sense (the state of the discipline). The latter is what matters for policy and planning, but it is not something that can be directly observed or reported. A function can be defined to map individual judgments onto an aggregate judgment. I argue that such a function cannot effectively capture community opinion, especially in cases that matter to us.
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  31.  86
    Marshall Abrams (2009). Fitness “Kinematics”: Biological Function, Altruism, and Organism–Environment Development. Biology and Philosophy 24 (4):487-504.
    It’s recently been argued that biological fitness can’t change over the course of an organism’s life as a result of organisms’ behaviors. However, some characterizations of biological function and biological altruism tacitly or explicitly assume that an effect of a trait can change an organism’s fitness. In the first part of the paper, I explain that the core idea of changing fitness can be understood in terms of conditional probabilities defined over sequences of events in an organism’s life. (...)
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  32.  3
    Michael Rathjen (1994). Collapsing Functions Based on Recursively Large Ordinals: A Well-Ordering Proof for KPM. [REVIEW] Archive for Mathematical Logic 33 (1):35-55.
    It is shown how the strong ordinal notation systems that figure in proof theory and have been previously defined by employing large cardinals, can be developed directly on the basis of their recursively large counterparts. Thereby we provide a completely new approach to well-ordering proofs as will be exemplified by determining the proof-theoretic ordinal of the systemKPM of [R91].
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  33.  2
    Naama Hirsch & Ramon Y. Birnbaum (2016). Dual Function of DNA Sequences: Protein-Coding Sequences Function as Transcriptional Enhancers. Perspectives in Biology and Medicine 58 (2):182-195.
    The human genome consists of more than 3 billion base pairs built from four different nucleotides that hold the genetic information for the entire organism. The genome is commonly divided into coding and noncoding DNA sequences, with coding DNA sequences defined as those that can be transcribed into mRNA and translated into proteins, or genes. The genetic code determines the impact of a nucleotide change in a gene on the protein sequence and function, and it is essential to (...)
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  34.  41
    Nigel Cutland (1980). Computability, an Introduction to Recursive Function Theory. Cambridge University Press.
    What can computers do in principle? What are their inherent theoretical limitations? These are questions to which computer scientists must address themselves. The theoretical framework which enables such questions to be answered has been developed over the last fifty years from the idea of a computable function: intuitively a function whose values can be calculated in an effective or automatic way. This book is an introduction to computability theory (or recursion theory as it is traditionally known to mathematicians). (...)
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  35.  34
    Justin Garson, Broken Mechanisms: Function, Pathology, and Natural Selection.
    The following describes one distinct sense of ‘mechanism’ which is prevalent in biology and biomedicine and which has important epistemic benefits. According to this sense, mechanisms are defined by the functions they facilitate. This construal has two important implications. Firstly, mechanisms that facilitate functions are capable of breaking. Secondly, on this construal, there are rigid constraints on the sorts of phenomena ‘for which’ there can be a mechanism. In this sense, there are no ‘mechanisms for’ pathology, and natural selection (...)
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  36.  44
    Hugh Lehman (1966). R. K. Merton's Concepts of Function and Functionalism. Inquiry 9 (1-4):274 – 283.
    In this paper an attempt is made to provide an analysis of the meaning of the term function and related terms as they are used by R. K. Merton in the first chapter of his book Social Theory and Social Structure. Several problems are suggested which must be solved if statements about functions are to be considered scientifically adequate. Secondly the term functionalism is defined and several of Merton's functionalist explanations of social phenomena are stated and criticized.
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  37.  9
    Francoise Longy (2006). Function and Probability. Techne 10 (1):66-78.
    The existence of dysfunctions precludes the possibility of identifying the function to do F with the capacity to do F. Nevertheless, we continuously infer capacities from functions. For this and other reasons stated in the first part of this article, I propose a new theory of functions (of the etiological sort), applying to organisms as well as to artefacts, in which to have some determinate probability P to do F (i.e. a probabilistic capacity to do F) is a necessary (...)
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  38.  11
    Richard J. Hall (1990). Does Representational Content Arise From Biological Function? PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1990:193 - 199.
    In virtue of what does a representational state have the content it does? Several philosophers have recently proposed that a representational state gets its content from its biological function. After explaining the sense of biological function used in these views, I criticise the proposal. I argue that biological function only determines representational content up to extensional equivalence. I maintain that this holds even if biological function is defined in terms of an intensional notion like Sober's (...)
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  39. Gerd Sommerhoff (2000). Understanding Consciousness: Its Function and Brain Processes. Sage Publications.
    “This is surely the ultimate expression of the top-down approach to consciousness, written with Sommerhoff's characteristic clarity and precision. It says far more than other books four times the size of this admirably concise volume. This book is destined to become a pillar of the subject.” —Rodney Cotterill, Technical University of Denmark The problem of consciousness has been described as a mystery about which we are still in a terrible muddle and in Understanding Consciousness: Its Function and Brain Processes, (...)
     
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  40.  6
    Samuel Mickey (2008). On the Function of the Epoche in Phenomenological Interpretations of Religion. Phaenex 3 (1):56-81.
    This essay presents an inquiry into the phenomenological epoche , specifically with a view to the function of the epoche in efforts to interpret sacred or religious meaning. Reflecting on contributions from phenomenology, hermeneutics, and deconstruction, with particular attention to the phenomenology of religion developed by Gerardus Van der Leeuw, I argue that the epoche can be defined in terms of hospitable restraint. By holding the presuppositions of one’s unique historical horizon in abeyance (e.g., presuppositions regarding the historical (...)
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  41.  1
    Krishna Del Toso (2015). The Function of Saññā in the Perceptual Process According to the Sutta-Piṭaka: An Assessment. Philosophy East and West 65 (3):690-716.
    This article deals with the meaning and function of saññā in perception according to the Suttapiṭaka. As regards its meaning, the discussion stresses the fact that the renderings “perception” and “apperception” seem to overinterpret the actual function/activity of saññā. Also the translations “idea” and “ideation” should be used cautiously, in order to avoid misunderstandings, since these terms are fraught with very specific philosophical and psychological implications in the Western context. Moreover, though “cognition” could be a good rendering, “recognition” (...)
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  42.  2
    James Bradley (2002). The Speculative Generalization of the Function: A Key to Whitehead. Tijdschrift Voor Filosofie 64 (2):253 - 271.
    In Process and Reality (1929) and subsequent writings, A.N. Whitehead builds on the success of the Frege-Russell generalization of the mathematical function and develops his philosophy on that basis. He holds that the proper generalization of the meaning of the function shows that it is primarily to be defined in terms of many-to-one mapping activity, which he terms 'creativity'. This allows him to generalize the range of the function, so that it constitutes a universal ontology of (...)
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  43.  6
    Andreas Weiermann (1994). A Functorial Property of the Aczel-Buchholz-Feferman Function. Journal of Symbolic Logic 59 (3):945-955.
    Let Ω be the least uncountable ordinal. Let K(Ω) be the category where the objects are the countable ordinals and where the morphisms are the strictly monotonic increasing functions. A dilator is a functor on K(Ω) which preserves direct limits and pullbacks. Let $\tau \Omega: \xi = \omega^\xi\}$ . Then τ has a unique "term"-representation in Ω. λξη.ω ξ + η and countable ordinals called the constituents of τ. Let $\delta and K(τ) be the set of the constituents of τ. (...)
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  44.  9
    H. Jerome Keisler (1978). The Stability Function of a Theory. Journal of Symbolic Logic 43 (3):481-486.
    Let T be a complete theory with infinite models in a countable language. The stability function g T (κ) is defined as the supremum of the number of types over models of T of power κ. It is proved that there are only six possible stability functions, namely $\kappa, \kappa + 2^\omega, \kappa^\omega, \operatorname{ded} \kappa, (\operatorname{ded} \kappa)^\omega, 2^\kappa$.
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  45.  1
    Olga Xirotiri (2006). There is No Safe Pairing Function Over an Arbitrary Structure. Mathematical Logic Quarterly 52 (4):362-366.
    In [1] the class of safe recursive functions over an arbitrary structure is defined. We prove that in this class, one cannot define a total pairing function independently of the structure.
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  46. Milton Friedman (2008). Theory of the Consumption Function. Princeton University Press.
    What is the exact nature of the consumption function? Can this term be defined so that it will be consistent with empirical evidence and a valid instrument in the hands of future economic researchers and policy makers? In this volume a distinguished American economist presents a new theory of the consumption function, tests it against extensive statistical J material and suggests some of its significant implications.Central to the new theory is its sharp distinction between two concepts of (...)
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  47. Ricardo Karam (2015). Interactions Between Mathematics and Physics: The History of the Concept of Function—Teaching with and About Nature of Mathematics. Science and Education 24 (5 - 6):543-559.
    In this paper, we discuss the history of the concept of function and emphasize in particular how problems in physics have led to essential changes in its definition and application in mathematical practices. Euler defined a function as an analytic expression, whereas Dirichlet defined it as a variable that depends in an arbitrary manner on another variable. The change was required when mathematicians discovered that analytic expressions were not sufficient to represent physical phenomena such as (...)
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  48.  3
    László Á Kóczy (2007). A Recursive Core for Partition Function Form Games. Theory and Decision 63 (1):41-51.
    We present a well-defined generalisation of the core to coalitional games with externalities, where the value of a deviation is given by an endogenous response, the solution (if nonempty: the core) of the residual game.
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  49.  2
    Cristian Calude, Gabriel Istrate & Marius Zimand (1992). Recursive Baire Classification and Speedable Functions. Mathematical Logic Quarterly 38 (1):169-178.
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  50. Qing Zhou (1996). Computable Real‐Valued Functions on Recursive Open and Closed Subsets of Euclidean Space. Mathematical Logic Quarterly 42 (1):379-409.
    In this paper we study intrinsic notions of “computability” for open and closed subsets of Euclidean space. Here we combine together the two concepts, computability on abstract metric spaces and computability for continuous functions, and delineate the basic properties of computable open and closed sets. The paper concludes with a comprehensive examination of the Effective Riemann Mapping Theorem and related questions.
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