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The philosophy of mathematics is the branch of philosophy that studies the assumptions, foundations, and implications of mathematics. It aims to understand the nature and methods of mathematics, and find out the place of mathematics in people's lives. The logical and structural nature of mathematics makes this branch of philosophy broad and unique.
Reductionism is any of several related philosophical ideas regarding the associations between phenomena which can be described in terms of other simpler or more fundamental phenomena. It is also described as an intellectual and philosophical position that interprets a complex system as the sum of its parts.
Abductive reasoning is a form of logical inference that seeks the simplest and most likely conclusion from a set of observations. It was formulated and advanced by American philosopher Charles Sanders Peirce beginning in the last third of the 19th century.
Pragmatism is a philosophical tradition that views language and thought as tools for prediction, problem solving, and action, rather than describing, representing, or mirroring reality. Pragmatists contend that most philosophical topics—such as the nature of knowledge, language, concepts, meaning, belief, and science—are all best viewed in terms of their practical uses and successes.
Luitzen Egbertus Jan Brouwer, usually cited as L. E. J. Brouwer but known to his friends as Bertus, was a Dutch mathematician and philosopher who worked in topology, set theory, measure theory and complex analysis. Regarded as one of the greatest mathematicians of the 20th century, he is known as the founder of modern topology, particularly for establishing his fixed-point theorem and the topological invariance of dimension.
In logic, a three-valued logic is any of several many-valued logic systems in which there are three truth values indicating true, false and some third value. This is contrasted with the more commonly known bivalent logics which provide only for true and false.
In logic, temporal logic is any system of rules and symbolism for representing, and reasoning about, propositions qualified in terms of time. It is sometimes also used to refer to tense logic, a modal logic-based system of temporal logic introduced by Arthur Prior in the late 1950s, with important contributions by Hans Kamp. It has been further developed by computer scientists, notably Amir Pnueli, and logicians.
Clarence Irving Lewis, usually cited as C. I. Lewis, was an American academic philosopher. He is considered the progenitor of modern modal logic and the founder of conceptual pragmatism. First a noted logician, he later branched into epistemology, and during the last 20 years of his life, he wrote much on ethics. The New York Times memorialized him as "a leading authority on symbolic logic and on the philosophic concepts of knowledge and value." He was the first to coin the term "Qualia" as it is used today in philosophy, linguistics, and cognitive sciences.
In logic, anti-psychologism is a theory about the nature of logical truth, that it does not depend upon the contents of human ideas but exists independent of human ideas.
The unity of science is a thesis in philosophy of science that says that all the sciences form a unified whole. The variants of the thesis can be classified as ontological and/or as epistemic/pragmatic. There are also philosophers who emphasize the disunity of science, which does not necessarily imply that there could be no unity in some sense but does emphasize pluralism in the ontology and/or practice of science.
An existential graph is a type of diagrammatic or visual notation for logical expressions, proposed by Charles Sanders Peirce, who wrote on graphical logic as early as 1882, and continued to develop the method until his death in 1914.
Originally, fallibilism is the philosophical principle that propositions can be accepted even though they cannot be conclusively proven or justified, or that neither knowledge nor belief is certain. The term was coined in the late nineteenth century by the American philosopher Charles Sanders Peirce, as a response to foundationalism. Theorists, following Austrian-British philosopher Karl Popper, may also refer to fallibilism as the notion that knowledge might turn out to be false. Furthermore, fallibilism is said to imply corrigibilism, the principle that propositions are open to revision. Fallibilism is often juxtaposed with infallibilism.
This Charles Sanders Peirce bibliography consolidates numerous references to the writings of Charles Sanders Peirce, including letters, manuscripts, publications, and Nachlass. For an extensive chronological list of Peirce's works, see the Chronologische Übersicht on the Schriften (Writings) page for Charles Sanders Peirce.
The propensity theory of probability is a probability interpretation in which the probability is thought of as a physical propensity, disposition, or tendency of a given type of situation to yield an outcome of a certain kind, or to yield a long-run relative frequency of such an outcome.
Charles Sanders Peirce began writing on semiotics, which he also called semeiotics, meaning the philosophical study of signs, in the 1860s, around the time that he devised his system of three categories. During the 20th century, the term "semiotics" was adopted to cover all tendencies of sign researches, including Ferdinand de Saussure's semiology, which began in linguistics as a completely separate tradition.
On May 14, 1867, the 27–year-old Charles Sanders Peirce, who eventually founded pragmatism, presented a paper entitled "On a New List of Categories" to the American Academy of Arts and Sciences. Among other things, this paper outlined a theory of predication involving three universal categories that Peirce continued to apply in philosophy and elsewhere for the rest of his life. The categories demonstrate and concentrate the pattern seen in "How to Make Our Ideas Clear", and other three-way distinctions in Peirce's work.
Pragmatic ethics is a theory of normative philosophical ethics and meta-ethics. Ethical pragmatists such as John Dewey believe that some societies have progressed morally in much the way they have attained progress in science. Scientists can pursue inquiry into the truth of a hypothesis and accept the hypothesis, in the sense that they act as though the hypothesis were true; nonetheless, they think that future generations can advance science, and thus future generations can refine or replace their accepted hypotheses. Similarly, ethical pragmatists think that norms, principles, and moral criteria are likely to be improved as a result of inquiry.
Kenneth Laine Ketner is an American philosopher. He is Paul Whitfield Horn Professor, Charles Sanders Peirce Interdisciplinary Professor and Director of Institute for Studies in Pragmaticism, Texas Tech University.
Irving H. Anellis was a historian of philosophy.
References
- ↑ Dau, Frithjof; Correia, Joachim Hereth (2006). "Two Instances of Peirce's Reduction Thesis". Formal Concept Analysis. Springer: 105–118. doi:10.1007/11671404_7.
- ↑ Anellis, Irving H. (October 1993). "Review of A Peircean Reduction Thesis: The Foundations of Topological Logic by Robert W. Burch". Modern Logic. 3 (4): 401–406. ISSN 1047-5982.
- ↑ Hereth, Joachim; Pöschel, Reinhard (1 August 2011). "Peircean Algebraic Logic and Peirce's Reduction Thesis". Semiotica. 2011 (186): 141–167. doi:10.1515/semi.2011.050. ISSN 1613-3692.
