Search results for 'Mathematical analysis' (try it on Scholar)

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  1.  9
    Kajsa Bråting (2012). Ambiguities of Fundamental Concepts in Mathematical Analysis During the Mid-Nineteenth Century. Foundations of Science 17 (4):301-320.
    In this paper we consider the major development of mathematical analysis during the mid-nineteenth century. On the basis of Jahnke’s (Hist Math 20(3):265–284, 1993 ) distinction between considering mathematics as an empirical science based on time and space and considering mathematics as a purely conceptual science we discuss the Swedish nineteenth century mathematician E.G. Björling’s general view of real- and complexvalued functions. We argue that Björling had a tendency to sometimes consider mathematical objects in a naturalistic way. (...)
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  2.  7
    David S. G. Stirling (2009). Mathematical Analysis and Proof. Horwood Pub..
    This fundamental and straightforward text addresses a weakness observed among present-day students, namely a lack of familiarity with formal proof. Beginning with the idea of mathematical proof and the need for it, associated technical and logical skills are developed with care and then brought to bear on the core material of analysis in such a lucid presentation that the development reads naturally and in a straightforward progression. Retaining the core text, the second edition has additional worked examples which (...)
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  3. George Boole (1847). The Mathematical Analysis of Logic Being an Essay Towards a Calculus of Deductive Reasoning. Macmillan, Barclay & Macmillan.
     
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  4. Nicolas Fillion & Robert M. Corless (2014). On the Epistemological Analysis of Modeling and Computational Error in the Mathematical Sciences. Synthese 191 (7):1451-1467.
    Interest in the computational aspects of modeling has been steadily growing in philosophy of science. This paper aims to advance the discussion by articulating the way in which modeling and computational errors are related and by explaining the significance of error management strategies for the rational reconstruction of scientific practice. To this end, we first characterize the role and nature of modeling error in relation to a recipe for model construction known as Euler’s recipe. We then describe a general model (...)
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  5.  4
    G. C. Smith (1983). Boole's Annotations on 'the Mathematical Analysis of Logic'. History and Philosophy of Logic 4 (1-2):27-39.
    George Boole collected ideas for the improvement of his Mathematical analysis of logic(1847) on interleaved copies of that work. Some of the notes on the interleaves are merely minor changes in explanation. Others amount to considerable extension of method in his mathematical approach to logic. In particular, he developed his technique in solving simultaneous elective equations and handling hypotheticals and elective functions. These notes and extensions provided a source for his later book Laws of thought(1854).
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  6.  1
    N. A. Shanin (2001). On a Finitary Version of Mathematical Analysis. Annals of Pure and Applied Logic 113 (1-3):261-295.
    An approach to constructing counterparts of some fields of mathematical analysis in the frames of Pilbert's “finitary standpoint” is sketched in this paper. This approach is based on certain results of functional spaces theory development in classical mathematics.
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  7. Thomas Mormann, Mathematical Aspects of Similarity and Quasi-Analysis - Order, Topology, and Sheaves.
    The concept of similarity has had a rather mixed reputation in philosophy and the sciences. On the one hand, philosophers such as Goodman and Quine emphasized the „logically repugnant“ and „insidious“ character of the concept of similarity that allegedly renders it inaccessible for a proper logical analysis. On the other hand, a philosopher such as Carnap assigned a central role to similarity in his constitutional theory. Moreover, the importance and perhaps even indispensibility of the concept of similarity for many (...)
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  8.  2
    D. L. Herr (1938). A Mathematical Analysis of the Experiments in Extra-Sensory Perception. Journal of Experimental Psychology 22 (5):491.
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  9. R. Schouwenaars (2014). Some Basic Results in the Mathematical Analysis of Dislocation Storage and Annihilation in Stage II and Stage III Strain Hardening. Philosophical Magazine 94 (27):3120-3136.
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  10.  59
    Geoffrey Hellman (2006). Mathematical Pluralism: The Case of Smooth Infinitesimal Analysis. [REVIEW] Journal of Philosophical Logic 35 (6):621 - 651.
    A remarkable development in twentieth-century mathematics is smooth infinitesimal analysis ('SIA'), introducing nilsquare and nilpotent infinitesimals, recovering the bulk of scientifically applicable classical analysis ('CA') without resort to the method of limits. Formally, however, unlike Robinsonian 'nonstandard analysis', SIA conflicts with CA, deriving, e.g., 'not every quantity is either = 0 or not = 0.' Internally, consistency is maintained by using intuitionistic logic (without the law of excluded middle). This paper examines problems of interpretation resulting from this (...)
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  11.  27
    C. P. Bhunu, W. Garira & G. Magombedze (2009). Mathematical Analysis of a Two Strain Hiv/Aids Model with Antiretroviral Treatment. Acta Biotheoretica 57 (3):361-381.
    A two strain HIV/AIDS model with treatment which allows AIDS patients with sensitive HIV-strain to undergo amelioration is presented as a system of non-linear ordinary differential equations. The disease-free equilibrium is shown to be globally asymptotically stable when the associated epidemic threshold known as the basic reproduction number for the model is less than unity. The centre manifold theory is used to show that the sensitive HIV-strain only and resistant HIV-strain only endemic equilibria are locally asymptotically stable when the associated (...)
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  12.  1
    G. Samanta (2015). Mathematical Analysis of a Chlamydia Epidemic Model with Pulse Vaccination Strategy. Acta Biotheoretica 63 (1):1-21.
    In this paper, we have considered a dynamical model of Chlamydia disease with varying total population size, bilinear incidence rate and pulse vaccination strategy. We have defined two positive numbers $$R_{0}$$ R 0 and $$R_{1}$$ R 1. It is proved that there exists an infection-free periodic solution which is globally attractive if $$R_{0} 1.$$ R 1 > 1. The important mathematical findings for the dynamical behaviour of the Chlamydia disease model are also numerically verified using MATLAB. Finally epidemiological implications (...)
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  13.  7
    William M. O'Fallon, Richard I. Walker & H. Robert Van Der Vaart (1971). The Study of Granulocyte Kinetics by Mathematical Analysis of DNA Labelling. Acta Biotheoretica 20 (3-4):95-124.
    A commonly used experimental procedure for the study of granulocyte kinetics involves the labelling and subsequent tracing of granulocyte DNA. Following the introduction of a label into the system, observations are made periodically on the concentration of label in the DNA of granulocytes taken from the circulating blood. A mathematical model for the expected value of this concentration has been derived, studied, and related to experimental observations from studies using P32 as a label. Insofar as the derivation of the (...)
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  14. G. F. Roach, I. G. Stratis & A. N. Yannacopoulos (2012). Mathematical Analysis of Deterministic and Stochastic Problems in Complex Media Electromagnetics. Princeton University Press.
    But a body of rigorous mathematical theory has also gradually developed, and this is the first book to present that theory.
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  15.  1
    George Boole (1948). The Mathematical Analysis of Logic. Philosophical Library.
  16.  22
    Alonzo Church (1948). Review: George Boole, The Mathematical Analysis of Logic, Being an Essay Towards a Calculus of Deductive Reasoning. [REVIEW] Journal of Symbolic Logic 13 (4):216-216.
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  17.  17
    Wiebke Petersen (2004). A Mathematical Analysis of Pānini's Śivasūtras. Journal of Logic, Language and Information 13 (4):471-489.
    In Pninis grammar of Sanskrit one finds the ivastras, a table which defines the natural classes of phonological segments in Sanskrit by intervals. We present a formal argument which shows that, using his representation method, Pninis way of ordering the phonological segments to represent the natural classes is optimal. The argument is based on a strictly set-theoretical point of view depending only on the set of natural classes and does not explicitly take into account the phonological features of the segments, (...)
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  18.  4
    Risto Vilkko (2004). George Boole. The Mathematical Analysis of Logic. Being an Essay Towards a Calculus of Deductive Reasoning by George Boole—Die Mathematische Analyse der Logik. Der Versuch Eines Kalküls des Deduktiven Schließens von George Boole, Schriftenreihe Zur Geistes-Und Kulturgeschichte: Texte Und Dokumente. Hallescher Verlag, Halle, Saale, 2001, 195 Pp. [REVIEW] Bulletin of Symbolic Logic 10 (1):108-109.
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  19.  4
    Eliahu Shamir (1968). Review: Joachim Lambek, The Mathematics of Sentence Structure; Joachim Lambek, Contributions to a Mathematical Analysis of the English Verb-Phrase; Joachim Lambek, Structure of Languages and its Mathematical Aspects. [REVIEW] Journal of Symbolic Logic 33 (4):627-628.
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  20.  9
    P. F. Strawson (1950). The Mathematical Analysis of Logic. By George Boole. Pp. 82. (Oxford: Basil Black Well. 1948. Price 7s. 6d.). Philosophy 25 (95):350-.
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  21.  1
    Ibrahim Seini, Oluwole Makinde & Baba Seidu (2015). Mathematical Analysis of the Effects of HIV-Malaria Co-Infection on Workplace Productivity. Acta Biotheoretica 63 (2):151-182.
    In this paper, a nonlinear dynamical system is proposed and qualitatively analyzed to study the dynamics and effects of HIV-malaria co-infection in the workplace. Basic reproduction numbers of sub-models are derived and are shown to have LAS disease-free equilibria when their respective basic reproduction numbers are less than unity. Conditions for existence of endemic equilibria of sub-models are also derived. Unlike the HIV-only model, the malaria-only model is shown to exhibit a backward bifurcation under certain conditions. Conditions for optimal control (...)
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  22.  3
    C. West Churchman (1949). Book Review:The Mathematical Analysis of Logic George Boole. [REVIEW] Philosophy of Science 16 (1):88-.
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  23. Michael Bernkopf (1971). The Development of the Foundations of Mathematical Analysis From Euler to RiemannIvor Grattan-Guinness. Isis 62 (4):532-533.
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  24. George Boole (2004). The Mathematical Analysis of Logic. Being an Essay Towards a Calculus of Deductive Reasoning by George Boole - Die Mathematische Analyse der Logik. Der Versuch Eines Kalküls des Deduktiven Schlieβens von George Boole. Bulletin of Symbolic Logic 10 (1):108-109.
     
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  25. Alonzo Church (1948). Boole George. The Mathematical Analysis of Logic, Being an Essay Towards a Calculus of Deductive*Easoning. Basil Blackwell, Oxford 1948, Title Pages + 82 Pp. [REVIEW] Journal of Symbolic Logic 13 (4):216.
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  26. J. M. Dubbey (1972). Mathematics The Development of the Foundations of Mathematical Analysis From Euler to Riemann. By Ivor Grattan-Guinness. Cambridge, Mass., and London: M.I.T. Press, 1970. Pp. Xiii + 186. £4.65. [REVIEW] British Journal for the History of Science 6 (1):88.
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  27. Michael Dummett (1959). Reviews. A. E. Heath. Preface. Studies in Logic and Probability, by George Boole, Watts & Co., London 1952, and the Open Court Publishing Company, LaSalle, Illinois, 1952, Pp. 7–8. R. Rhees. Note in Editing. Studies in Logic and Probability, by George Boole, Watts & Co., London 1952, and the Open Court Publishing Company, LaSalle, Illinois, 1952, Pp. 9–43. George Boole. The Mathematical Analysis of Logic, Being an Essay Towards a Calculus of Deductive Reasoning. A Reprint of 191. Studies in Logic and Probability, by George Boole, Watts & Co., London 1952, and the Open Court Publishing Company, LaSalle, Illinois, 1952, Pp. 45–119. George Boole. Later Notes . Studies in Logic and Probability, by George Boole, Watts & Co., London 1952, and the Open Court Publishing Company, LaSalle, Illinois, 1952, Pp. 119–124. George Boole. The Calculus of Logic. A Reprint of 192. Studies in Logic and Probability, by George Boole, Watts & Co., London 1952, and the Open Court Publishing Company, LaSalle,. [REVIEW] Journal of Symbolic Logic 24 (3):203-209.
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  28. V. H. Dyson (1970). Robinson Julia. On the Decision Problem for Algebraic Rings. Studies in Mathematical Analysis and Related Topics, Essays in Honor of George Pólya, Edited by Szegö Gabor, Loewner Charles, Bergman Stefan, Schiffer Menahem Max, Neyman Jerzy, Gilbarg David, and Solomon Herbert, Stanford University Press, Stanford, California, 1962, Pp. 297–304. [REVIEW] Journal of Symbolic Logic 35 (3):475-476.
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  29. James R. Hofmann (1992). Naissance d'Un Nouveau Pouvoir: Sciences Et Savants En France Nicole Dhombres Jean DhombresConvolutions in French Mathematics, 1800-1840: From the Calculus and Mechanics to Mathematical Analysis and Mathematical PhysicsIvor Grattan-Guinness. [REVIEW] Isis 83 (2):291-297.
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  30. J. Houska (1981). The Principles of Mathematical-Analysis in Bolzanos Work in Reference to the Scientific Development of His Time. Filosoficky Casopis 29 (6):933-941.
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  31. C. A. Jimenez (forthcoming). Mathematical Analysis and Analytical Science. Boston Studies in the Philosophy of Science.
     
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  32. A. Moretto (1991). The'theorie Des Fonctions Analytiques'of Lagrange and the Problem of Being Rigorous in Demonstrations of Mathematical-Analysis. Verifiche: Rivista Trimestrale di Scienze Umane 20 (1-2):83-122.
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  33. Marc Oliver Rieger & Mei Wang (2008). What is Behind the Priority Heuristic? A Mathematical Analysis and Comment on Brandstätter, Gigerenzer, and Hertwig. Psychological Review 115 (1):274-280.
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  34. Eliahu Shamir (1969). Lamber Joachim. The Mathematics of Sentence Structure. American Mathematical Monthly, Vol. 65 No. 3 , Pp. 154–170.Lambek Joachim. Contributions to a Mathematical Analysis of the English Verb-Phrase. Journal of the Canadian Linguistic Association, Vol. 5 , Pp. 83–89.Lambek Joachim. On the Calculus of Syntactic Types. Structure of Language and its Mathematical Aspects, Proceedings of Symposia in Applied Mathematics, Vol. 12, American Mathematical Society, Providence 1961, Pp. 166–178.Court L. M., Lambek J., Hiż H.. Comments. Structure of Language and its Mathematical Aspects, Proceedings of Symposia in Applied Mathematics, Vol. 12, American Mathematical Society, Providence 1961, Pp. 264–265.Cohen Joel M.. The Equivalence of Two Concepts of Categorial Grammar. Information and Control, Vol. 10 , Pp. 475–484. [REVIEW] Journal of Symbolic Logic 33 (4):627-628.
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  35. Risto Vilkko (2004). The Mathematical Analysis of Logic. [REVIEW] Bulletin of Symbolic Logic 10 (1):108-109.
     
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  36.  59
    Ting-Chao Chou (2008). A New Look at the Ancient Asian Philosophy Through Modern Mathematical and Topological Scientific Analysis. Proceedings of the Xxii World Congress of Philosophy 2:21-39.
    The unified theory of dose and effect, as indicated by the median-effect equation for single and multiple entities and for the first and higher order kinetic/dynamic, has been established by T.C. Chou and it is based on the physical/chemical principle of the massaction law (J. Theor. Biol. 59: 253-276, 1976 (質量作用中效定理) and Pharmacological Rev. 58: 621-681, 2006) (普世中效指數定理). The theory was developed by the principle of mathematical induction and deduction (數學演繹歸納法). Rearrangements of the median-effect equation lead to Michaelis-Menten, Hill, (...)
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  37.  28
    Marvin R. G. Schiller (2013). Granularity Analysis for Mathematical Proofs. Topics in Cognitive Science 5 (2):251-269.
    Mathematical proofs generally allow for various levels of detail and conciseness, such that they can be adapted for a particular audience or purpose. Using automated reasoning approaches for teaching proof construction in mathematics presupposes that the step size of proofs in such a system is appropriate within the teaching context. This work proposes a framework that supports the granularity analysis of mathematical proofs, to be used in the automated assessment of students' proof attempts and for the presentation (...)
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  38.  26
    Reinhard Kahle (2002). Mathematical Proof Theory in the Light of Ordinal Analysis. Synthese 133 (1/2):237 - 255.
    We give an overview of recent results in ordinal analysis. Therefore, we discuss the different frameworks used in mathematical proof-theory, namely "subsystem of analysis" including "reverse mathematics", "Kripke-Platek set theory", "explicit mathematics", "theories of inductive definitions", "constructive set theory", and "Martin-Löf's type theory".
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  39.  3
    V. V. Cifarelli & V. Sevim (2014). Examining the Role of Re-Presentation in Mathematical Problem Solving: An Application of Ernst von Glasersfeld's Conceptual Analysis. Constructivist Foundations 9 (3):360-369.
    Context: The paper utilizes a conceptual analysis to examine the development of abstract conceptual structures in mathematical problem solving. In so doing, we address two questions: 1. How have the ideas of RC influenced our own educational theory? and 2. How has our application of the ideas of RC helped to improve our understanding of the connection between teaching practice and students’ learning processes? Problem: The paper documents how Ernst von Glasersfeld’s view of mental representation can be illustrated (...)
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  40.  2
    D. Wade Hands (2016). Derivational Robustness, Credible Substitute Systems and Mathematical Economic Models: The Case of Stability Analysis in Walrasian General Equilibrium Theory. European Journal for Philosophy of Science 6 (1):31-53.
    This paper supports the literature which argues that derivational robustness can have epistemic import in highly idealized economic models. The defense is based on a particular example from mathematical economic theory, the dynamic Walrasian general equilibrium model. It is argued that derivational robustness first increased and later decreased the credibility of the Walrasian model. The example demonstrates that derivational robustness correctly describes the practices of a particular group of influential economic theorists and provides support for the arguments of philosophers (...)
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  41.  71
    Jaakko Hintikka (2011). Method of Analysis: A Paradigm of Mathematical Reasoning? History and Philosophy of Logic 33 (1):49 - 67.
    The ancient Greek method of analysis has a rational reconstruction in the form of the tableau method of logical proof. This reconstruction shows that the format of analysis was largely determined by the requirement that proofs could be formulated by reference to geometrical figures. In problematic analysis, it has to be assumed not only that the theorem to be proved is true, but also that it is known. This means using epistemic logic, where instantiations of variables are (...)
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  42.  1
    Hiroki Hoshino (2011). Traveling Wave Analysis for a Mathematical Model of Malignant Tumor Invasion. Analysis 31 (3):237-248.
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  43.  17
    Andrés Rivadulla (1991). Mathematical Statistics and Metastatistical Analysis. Erkenntnis 34 (2):211 - 236.
    This paper deals with meta-statistical questions concerning frequentist statistics. In Sections 2 to 4 I analyse the dispute between Fisher and Neyman on the so called logic of statistical inference, a polemic that has been concomitant of the development of mathematical statistics. My conclusion is that, whenever mathematical statistics makes it possible to draw inferences, it only uses deductive reasoning. Therefore I reject Fisher's inductive approach to the statistical estimation theory and adhere to Neyman's deductive one. On the (...)
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  44. Marvin R. G. Schiller (2011). Granularity Analysis for Tutoring Mathematical Proofs. Aka Verlag.
     
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  45.  71
    Michel J. Blais (1989). A Pragmatic Analysis of Mathematical Realism and Intuitionism. Philosophia Mathematica (1):61-85.
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  46. Niccolò Guicciardini (2002). Analysis and Synthesis in Newton's Mathematical Work. In I. Bernard Cohen & George E. Smith (eds.), The Cambridge Companion to Newton. Cambridge University Press
     
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  47.  10
    Saunders Mac Lane (1935). A Logical Analysis of Mathematical Structure. The Monist 45 (1):118 - 130.
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  48.  1
    Joseph S. Ullian (1968). Chomsky Noam and Miller George A.. Introduction to the Formal Analysis of Natural Languages. Handbook of Mathematical Psychology, Volume II, Edited by Duncan Luce R., Bush Robert R., and Galanter Eugene, John Wiley and Sons, Inc., New York and London 1963, Pp. 269–321.Chomsky Noam. Formal Properties of Grammars. Handbook of Mathematical Psychology, Volume II, Edited by Duncan Luce R., Bush Robert R., and Galanter Eugene, John Wiley and Sons, Inc., New York and London 1963, Pp. 323–418.Miller George A. And Chomsky Noam. Finitary Models of Language Users. Handbook of Mathematical Psychology, Volume II, Edited by Duncan Luce R., Bush Robert R., and Galanter Eugene, John Wiley and Sons, Inc., New York and London 1963, Pp. 419–491. [REVIEW] Journal of Symbolic Logic 33 (2):299-300.
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  49.  11
    Saunders MacLane (1935). A Logical Analysis of Mathematical Structure. The Monist 45 (1):118-130.
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  50.  18
    Joseph W. Dauben (2003). Mathematics, Ideology, and the Politics of Infinitesimals: Mathematical Logic and Nonstandard Analysis in Modern China. History and Philosophy of Logic 24 (4):327-363.
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