Yıl: 2011 Cilt: 0 Sayı: 19 Sayfa Aralığı: 283 - 314 Metin Dili: Türkçe İndeks Tarihi: 29-07-2022

George Boole ve mantık cebiri

Öz:
Mantık tarihinin modern kesitindeki en ilgi çekici konulardan birisi, mantık ile matematik arasındaki izdivacın mahiyetiyle ilgilidir. Bu izdivacın neden meydana geldiği ve hangi aşamalardan geçtiği gibi tarihsel sorular bir yana, bazılarına göre matematik mantık (MM), aslında matematiktir; bazıları onun geleneksel mantığın (GM) yeni bir biçimi olduğu hususunda ısrarlıdır; bazıları onun matematik ile mantığın ortak temellerine dayanmakla birlikte ne GM ne de matematik olduğunu düşünürken, bazılarına göre o hiçbir şey değildir. Bu çalışmada, çağdaş mantık tarihinde olduğu kadar matematikte de önemli bir yeri bulunan İngiliz filozofu George Boole'nin (1815-1864) GM ile matematiği sentezleme teşebbüsü olarak bilinen mantık cebiri (MC) konusundaki görüşleri ana hatlarıyla tasvir edilmeye çalışılacaktır. Çalışmanın, MMm gelişiminde çok önemli bir aşamayı teşkil edeıı MCnin ne olduğu tartışmasının yanı sıra GM, MC ve cebir arasındaki yöntem farklılıklarına da ışık tutacağını umuyoruz.
Anahtar Kelime:

Konular: Tarih Matematik Beşeri Bilimler Mantık Felsefe

George Boole and the algebra of logic

Öz:
One of the most interesting topics in the modern part of the history of logic is concerned with the essence of the relationship between logic and mathematics. Putting aside the questions such as what has caused this relationship and which stages it has passed through, according to some the mathematical logic (ML) is mathematics in fact, some insists that it is a new form of the traditional logic (TL), some thinks it is neither TL nor mathematics even though it depends on the common grounds of mathematics and logic, and yet according to some it is nothing. In this study, it will be attempted to outline the views of the English philosopher George Boole (1815-1864) who has a significant place in the contemporary history of logic and mathematics as well. His views are known as an endeavor of synthesis between TL and mathematics, i.e. the algebra of logic (AL). I hope that the study will give light on what is the AL which forms a very significant stage in the progress of the ML, and on the methodical variations between TL, AL, and algebra as well.
Anahtar Kelime:

Konular: Tarih Matematik Beşeri Bilimler Mantık Felsefe
Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Bibliyografik
  • Boole, George 1847. The Mathematical Analysis of Logic Being an Essay towards a Calculus of Deductive Reasoning, Cambridge - Londra: Macmillan, Barclay & Macmillan - George Bell.
  • Boole, George 1854. An Investigation of the Laws of Thought on which are Found the Mathematical Theories of Logic and Probabilities, Cambridge - Londra: Macmillan & Co. - Walton and Maberley.
  • Burtt, Edwin Arthur 1925. The Metaphysical Foundations of Modern Physical Science: A Historical and Critical Essay, London - New York: Kegan Paul, Trench, Trumbner and Co. - Hardcourt, Brace & Co.
  • Church, Alanzo 1951. An Introduction to Mathematical Logic, Princeton, Princeton University Press.
  • Corcoran, John 2003. "Aristotle's Prior Analytics and Boole's Laws of Thought", History f;. and Philosophy of Logic, 24, s. 261-288.
  • Couturat, Louis 1914. The Algebra of Logic, çev. L.G. Robinson, Chicago - Londra, The F Open Court Publishing Co.
  • Croce, Benedetto 1917. Logic as the Science of the Pure Concept, çev. D. Ainslie, Londra, p MacMillan and Co.
  • Cudworth, Ralph 1845. A Treatise Concerning Eternal and Immutable Morality, The True i Intellectual System of the Universe, 3 c, Londra, Thomas Tegg.
  • Davis, Ellery W. 1890. An Introducton to the Logic of Algebra with Illustrative Exercises, fe ,.New York: John Wiley & Sons.
  • De Morgan, Augustus 1847. Formal Logic or the Calculus of Inference Necessary and |L, Probable, Londra, Taylor Walton.
  • De Morgan,1914. Essays on the Life and Work of Newton, ed. P.E.B. Jourdain, Chicago - Londra: The Open Court Publishing Co.
  • Descartes, Rene i 927. A Discourse on Method, çev. J. Veitch, Londra - Toronto New fcj York, J.M. Dent & Sons - E.P. Dutton and Co.
  • Euler, Leonard 1822. Elements of Algebra, 3. bsk, çev. F. Horiıer, Londra, Longman Rees Orme and Co.
  • Hobbes, Thomas 1963. Computation or Logic, The Metaphysical System of Hobbes, ed. I' M.W. Chalkins, 2. bsk, La Salle - Illinois, The Open Court Publishing Co.
  • Jevons, W. Stanley 1869. The Substitution of Similars: The True Principles of Reasoning Derivedfrom a Modification of Aristotle's Dictum, Londra, Macmillan and Co.
  • Jevons, W.1874. A Treatise on Logic and Scientific Method, 2 c, Londra, MacMillan and Co.
  • Jevons, W. 1884. Studies in Deductive Logic: A Manuel for Students, 2. bsk, Londra, Macmillan and Co.
  • Kant, Immanuel 1819. Logic, çev. J. Richardson, London, W. Simpkin and R. Marshall.
  • Kant, Immanuel.1881. Immanuel Kant's Critique of Pure Reason: In Commemoration of the Centenary of its First Publication, sunuş ve çev. Ludwig Noire, F. Max Müller, 2 c,Londra, MacMillan and Co.
  • Keynes, John Neville 1906. Studies and Exircises in Formal Logic Including A Generalization of Logical Processes in Their Application to Complex Inferences, 4. bsk, Londra - New York, MacMillan and Co. - The MacMillan Co.
  • Kneale, W. 1956. "Boole and the Algebra of Logic", Notes and Records of the Royal fe Society of London, 12/1, s. 53-63.
  • Ladd, Christine 1883, "On the Algebra of Logic", Studies in Logic, Boston, Little, Brown, and Co, s. 17-71.
  • Latham, R.G. 1878. Outlines of General or Developmental Philology: Inflection, London,Longmans, Green, and Co.
  • Leibniz, W.G. 1908. "Animadversions on Descartes' Principles of Philosophy 1692", The Philosophical Works of Leibniz, çev. G.M. Duncan, 2. bsk, New Haven, Tuttle,Morehouse & Taylor, s. 47-65.
  • Lewis, C.I. 1918. A Survey of Symbolic Logic, Berkeley, University of California Press.
  • Macfarlane, Alexander 1916. Lectures on Ten British Mathematicians of the 19th Century, Mathematical Monographs 17, ed. M. Merriman, R.S. Woodward, 1. bsk, New York -Londra, John Wiley & Sons - Chapman and Hall.
  • McColl, Hugh 1906. Symbolic Logic and Its Applications, New York - Londra, Longmans, Green, and Co.
  • Mercier, Charles 1912. A New Logic, Londra, William Heinemann.
  • Pascal, Blaise 1890. The Thoughts, Letters, and Opuscules of Blaise Pascal, transl. 0."ty Wight, Boston - Cambridge, Houghton, Mifflin and Co. - The Riverside Press.
  • Peacock, George 1842. A Treatise on Algebra, 2 c., Cambridge - Londra, J. & j j Deighton - G.F. & J. Rivington, and Whittaker.
  • Peckhaus, Volker 1999. "19th Century Logic between Philosophy and Mathematics", The Bulletin of Symbolic Logic, 5/4, s. 433-450.
  • Quine, Willard Van Orman 1961. Mathematical Logic, Revised Ed., Cambridge, Harvard University Press.
  • Reichenbach, Hans 1939. Lojistik, çev. H.V. Eralp, İstanbul, İstanbul Üniversitesi Yay.
  • Schoroeder, Michael 1997. "A Brief History of the Notation of Boole's Algebra", Nordic Journal of Philosophical Logic, 2/1, s. 41-62.
  • Shearman, A.T. 1906. The Development of Symbolic Logic: A Critical-Historical Study of the Logical Calculus, Londra, Williams and Norgate.
  • Smith, Norman Kemp 1918. A Commentary to Kant's 'Critique of Pure Reason', Londra, MacMillan and Co.
  • Tarski, Alfred 1944. "Semantic Conception of Truth and the Foundations of Semantics", Philosophy and Phenomenological Research, 4/3, pp. 341-376.
  • Türker, Sadık 2002. Aristoteles, Gazzâlî ile Leibniz'de Yargı Mantığı, 1. bsk, İstanbul^ Degah Yay.
  • Türker, Sadık 2007. "Anlam, Kavram ile Kelime/Sembol Üzerine", Felsefe Arkivi, 31, s. 63-86.
  • Ural, Şafak 1995. Temel Mantık, 2. bsk, İstanbul, Çantay Kitabevi.
  • Venn, John 1876. "Boole's Logical System", Mind, 1/4, s. 479-491.
  • Venn, John,1881. Symbolic Logic, Londra: Macmillan and Co.
  • Whitehead, Alfred North 1898. A Treatise on Universal Algebra with Applications, Cambridge, Cambridge University Press.
APA TÜRKER S (2011). George Boole ve mantık cebiri. , 283 - 314.
Chicago TÜRKER Sadık George Boole ve mantık cebiri. (2011): 283 - 314.
MLA TÜRKER Sadık George Boole ve mantık cebiri. , 2011, ss.283 - 314.
AMA TÜRKER S George Boole ve mantık cebiri. . 2011; 283 - 314.
Vancouver TÜRKER S George Boole ve mantık cebiri. . 2011; 283 - 314.
IEEE TÜRKER S "George Boole ve mantık cebiri." , ss.283 - 314, 2011.
ISNAD TÜRKER, Sadık. "George Boole ve mantık cebiri". (2011), 283-314.
APA TÜRKER S (2011). George Boole ve mantık cebiri. Kutadgubilig: Felsefe Bilim Araştırmaları, 0(19), 283 - 314.
Chicago TÜRKER Sadık George Boole ve mantık cebiri. Kutadgubilig: Felsefe Bilim Araştırmaları 0, no.19 (2011): 283 - 314.
MLA TÜRKER Sadık George Boole ve mantık cebiri. Kutadgubilig: Felsefe Bilim Araştırmaları, vol.0, no.19, 2011, ss.283 - 314.
AMA TÜRKER S George Boole ve mantık cebiri. Kutadgubilig: Felsefe Bilim Araştırmaları. 2011; 0(19): 283 - 314.
Vancouver TÜRKER S George Boole ve mantık cebiri. Kutadgubilig: Felsefe Bilim Araştırmaları. 2011; 0(19): 283 - 314.
IEEE TÜRKER S "George Boole ve mantık cebiri." Kutadgubilig: Felsefe Bilim Araştırmaları, 0, ss.283 - 314, 2011.
ISNAD TÜRKER, Sadık. "George Boole ve mantık cebiri". Kutadgubilig: Felsefe Bilim Araştırmaları 19 (2011), 283-314.