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History of logic - The advent of modern logic | | History of logic - The advent of modern logic: Encyclopedia II - History of logic - The advent of modern logic | | Historically, Descartes, may have been the first philosopher to have had the idea of using algebra, especially its techniques for solving for unknown quantities in equations, as a vehicle for scientific exploration. The idea of a calculus of reasoning was also cultivated by Gottfried Wilhelm Leibniz. Leibniz was the first to formulate the notion of a broadly applicable system of mathematical logic. However, the relevant documents were not published until 1901 or remain unpublished to the present day, and the current understanding of the power of Leibniz's discoveries did not emerge un ...
See also:History of logic, History of logic - Logic in China, History of logic - Logic in India, History of logic - Logic in Greece, History of logic - Logic in Islamic philosophy, History of logic - Medieval Logic, History of logic - Traditional Logic, History of logic - The advent of modern logic | | | History of logic, History of logic - Logic in China, History of logic - Logic in Greece, History of logic - Logic in India, History of logic - Logic in Islamic philosophy, History of logic - Medieval Logic, History of logic - The advent of modern logic, History of logic - Traditional Logic, Term Logic, Ernst Schröder, Charles Peirce | | |
| | | History of logic: Encyclopedia II - History of logic - The advent of modern logic
History of logic - The advent of modern logic
Historically, Descartes, may have been the first philosopher to have had the idea of using algebra, especially its techniques for solving for unknown quantities in equations, as a vehicle for scientific exploration. The idea of a calculus of reasoning was also cultivated by Gottfried Wilhelm Leibniz. Leibniz was the first to formulate the notion of a broadly applicable system of mathematical logic. However, the relevant documents were not published until 1901 or remain unpublished to the present day, and the current understanding of the power of Leibniz's discoveries did not emerge until the 1980s. See Lenzen's chapter in Gabbay and Woods (2004).
Gottlob Frege in his 1879 Begriffsschrift extended formal logic beyond propositional logic to include constructors such as "all", "some". He showed how to introduce variables and quantifiers to reveal the logical structure of sentences, which may have been obscured by their grammatical structure. For instance, "All humans are mortal" becomes "All things x are such that, if x is a human then x is mortal." Frege's peculiar two dimensional notation led to his work being ignored for many years.
In a masterly 1885 article read by Peano, Ernst Schröder, and others, Charles Peirce introduced the term "second-order logic" and provided us with much of our modern logical notation, including prefixed symbols for universal and existential quantification. Logicians in the late 19th and early 20th centuries were thus more familiar with the Peirce-Schröder system of logic, although Frege is generally recognized today as being the "Father of modern logic".
In 1889 Giuseppe Peano published the first version of the logical axiomatization of arithmetic. Five of the nine axioms he came up with are now known as the Peano axioms. One of these axioms was a formalized statement of the principle of mathematical induction.
Other related archives1879, 1889, 19th, 20th centuries, 4th century BC, Aksapada Gautama, Al-Ghazali, Antoine Arnauld, Aristotelian logic, Aristotle, Asharite, Averroes, Begriffsschrift, Buddhist philosophy, Buddhists, Charles Peirce, China, Confucius, Descartes, Dharmakirti, Dignaga, Ernst Schröder, Euclid of Megara, Giuseppe Peano, Gottfried Wilhelm Leibniz, Gottlob Frege, Greece, Hindu, India, Indian logic, Isaac Watts, Islamic philosophers, John Stuart Mill, Kalam, Legalism, Logic in China, Logic in Islamic philosophy, Logicians, Madhyamika, Medieval European, Mohism, Mozi, Muhammed, Mutazilite, Nagarjuna, Nineteenth Century, Nyaya, Nyaya Sutras, Organon, Peano, Peano axioms, Peripatetic, Peter of Spain, Port-Royal Logic, Qin Dynasty, Richard Whately, Socrates, Stoic, Term Logic, Vaisheshika, William of Ockham, formal logic, idealist, induction, inference, logic, materialist, mathematical, propositional logic, propositions, realist, second-order logic, syllogism
 Adapted from the Wikipedia article "The advent of modern logic", under the G.N U Free Docmentation License. Please also see http://en.wikipedia.org/wiki |
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