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Ludwig Wittgenstein's Philosophy Of Mathematics
Ludwig Wittgenstein considered his chief contribution to be in the philosophy of mathematics, a topic to which he devoted much of his work between 1929 and 1944.Roydich V''Wittgenstein's Philosophy of Mathematics'' The Stanford Encyclopedia of Philosophy As with his philosophy of language, Wittgenstein's views on mathematics evolved from the period of the Tractatus Logico-Philosophicus: with him changing from logicism (which was endorsed by his mentor Bertrand Russell) towards a general anti-foundationalism and constructivism that was not readily accepted by the mathematical community. The success of Wittgenstein's general philosophy has tended to displace the real debates on more technical issues. His ''Remarks on the Foundations of Mathematics'' contains his compiled views, notably a controversial repudiation of Gödel's incompleteness theorems. Tractatus Wittgenstein's initial conception of mathematics was logicist and even formalist. The ''Tractatus'' described the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ludwig Wittgenstein
Ludwig Josef Johann Wittgenstein ( ; ; 26 April 1889 – 29 April 1951) was an Austrian- British philosopher who worked primarily in logic, the philosophy of mathematics, the philosophy of mind, and the philosophy of language. He is considered by some to be the greatest philosopher of the 20th century. From 1929 to 1947, Wittgenstein taught at the University of Cambridge. In spite of his position, during his entire life only one book of his philosophy was published, the 75-page ''Logisch-Philosophische Abhandlung'' (''Logical-Philosophical Treatise'', 1921), which appeared, together with an English translation, in 1922 under the Latin title '' Tractatus Logico-Philosophicus''. His only other published works were an article, " Some Remarks on Logical Form" (1929); a book review; and a children's dictionary. His voluminous manuscripts were edited and published posthumously. The first and best-known of this posthumous series is the 1953 book '' Philosophical Investigations' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Elementary Propositions
In logic and analytic philosophy, an atomic sentence is a type of declarative sentence which is either true or false (may also be referred to as a proposition, statement or truthbearer) and which cannot be broken down into other simpler sentences. For example, "The dog ran" is an atomic sentence in natural language, whereas "The dog ran and the cat hid" is a molecular sentence in natural language. From a logical analysis point of view, the truth or falsity of sentences in general is determined by only two things: the logical form of the sentence and the truth or falsity of its simple sentences. This is to say, for example, that the truth of the sentence "John is Greek and John is happy" is a function of the meaning of " and", and the truth values of the atomic sentences "John is Greek" and "John is happy". However, the truth or falsity of an atomic sentence is not a matter that is within the scope of logic itself, but rather whatever art or science the content of the atomic sentenc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Crispin Wright
Crispin James Garth Wright (; born 21 December 1942) is a British philosopher, who has written on neo-Fregean (neo-logicist) philosophy of mathematics, Wittgenstein's later philosophy, and on issues related to truth, realism, cognitivism, skepticism, knowledge, and objectivity. He is Professor of Philosophy at New York University and Professor of Philosophical Research at the University of Stirling, and taught previously at the University of St Andrews, University of Aberdeen, Princeton University and University of Michigan. Life and career Wright was born in Surrey and was educated at Birkenhead School (1950–61) and at Trinity College, Cambridge, graduating in Moral Sciences in 1964 and taking a PhD in 1968. He took an Oxford BPhil in 1969 and was elected Prize Fellow and then Research Fellow at All Souls College, Oxford, where he worked until 1978. He then moved to the University of St. Andrews, where he was appointed Professor of Logic and Metaphysics and then ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cora Diamond
Cora Diamond (born 1937) is an American philosopher who works on Ludwig Wittgenstein, Gottlob Frege, moral philosophy, animal ethics, political philosophy, philosophy of language, and philosophy and literature. Diamond is the Kenan Professor of Philosophy Emerita at the University of Virginia. Education and career Diamond received her Bachelor of Arts degree from Swarthmore College in 1957 and her Bachelor of Philosophy degree from St Hugh's College, Oxford (where her tutor was Paul Grice), in 1961. Philosophical work One of Diamond's most famous articles, "What Nonsense Might Be", criticizes the way that the logical positivists think about nonsense on Fregean grounds (see category mistake). Another well-known article, "Eating Meat and Eating People", examines the rhetorical and philosophical nature of contemporary attitudes towards animal rights. Diamond's writings on both "early" ('' Tractatus Logico-Philosophicus'' era) and "late" ('' Philosophical Investigations'' e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Correspondence Theory Of Truth
In metaphysics and philosophy of language, the correspondence theory of truth states that the truth or falsity of a statement is determined only by how it relates to the world and whether it accurately describes (i.e., corresponds with) that world.Hanna and Harrison (2004), ch. 1, p. 21, quotation: "The assessment of truth and falsity is made possible by the existence of semantically mediated correlations between the members of some class of linguistic entities possessing assertoric force (in some versions of the Correspondence Theory propositions, in others sentences, or bodies of sentences), and the members of some class of extralinguistic entities: “states of affairs,” or “facts,” or bodies of truth-conditions, or of assertion-warranting circumstances." Correspondence theories claim that true beliefs and true statements correspond to the actual state of affairs. This type of theory attempts to posit a relationship between thoughts or statements on one hand, and thi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ideal Language Philosophy
Ideal language philosophy is contrasted with ordinary language philosophy. From about 1910 to 1930, analytic philosophers like Bertrand Russell and Ludwig Wittgenstein emphasized creating an ideal language for philosophical analysis, which would be free from the ambiguities of natural language that, in their opinion, often made for philosophical error. During this phase, Russell and Wittgenstein sought to understand language (and hence philosophical problems) by using formal logic to formalize the way in which philosophical statements are made. Wittgenstein developed a comprehensive system of logical atomism in his ''Tractatus Logico-Philosophicus'' ( de , Logisch-Philosophische Abhandlung, 1921). He thereby argued that the universe is the totality of facts and not things: actual states of affairs and that these states of affairs can be expressed by the language of first-order predicate logic. Thus a ''picture'' of the universe can be construed by means of expressing atomic facts i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Some Remarks On Logical Form
"Some Remarks on Logical Form" (1929) was the only academic paper ever published by Ludwig Wittgenstein, and contained Wittgenstein's thinking on logic and the philosophy of mathematics immediately before the rupture that divided the early Wittgenstein of the ''Tractatus Logico-Philosophicus'' from the late Wittgenstein. The approach to logical form in the paper reflected Frank P. Ramsey's critique of Wittgenstein's account of color in the Tractatus, and has been analyzed by G. E. M. Anscombe and Jaakko Hintikka Kaarlo Jaakko Juhani Hintikka (12 January 1929 – 12 August 2015) was a Finnish philosopher and logician. Life and career Hintikka was born in Helsingin maalaiskunta (now Vantaa). In 1953, he received his doctorate from the University of Hels ..., among others. References Ludwig Wittgenstein Books by Ludwig Wittgenstein Philosophy of mathematics literature Logic literature {{science-philo-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Frank P
Frank or Franks may refer to: People * Frank (given name) * Frank (surname) * Franks (surname) * Franks, a medieval Germanic people * Frank, a term in the Muslim world for all western Europeans, particularly during the Crusades - see Farang Currency * Liechtenstein franc or frank, the currency of Liechtenstein since 1920 * Swiss franc or frank, the currency of Switzerland since 1850 * Westphalian frank, currency of the Kingdom of Westphalia between 1808 and 1813 * The currencies of the German-speaking cantons of Switzerland (1803–1814): ** Appenzell frank ** Argovia frank ** Basel frank ** Berne frank ** Fribourg frank ** Glarus frank ** Graubünden frank ** Luzern frank ** Schaffhausen frank ** Schwyz frank ** Solothurn frank ** St. Gallen frank ** Thurgau frank ** Unterwalden frank ** Uri frank ** Zürich frank Places * Frank, Alberta, Canada, an urban community, formerly a village * Franks, Illinois, United States, an unincorporated community * Franks, Missou ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Logical Truth
Logical truth is one of the most fundamental concepts in logic. Broadly speaking, a logical truth is a statement which is true regardless of the truth or falsity of its constituent propositions. In other words, a logical truth is a statement which is not only true, but one which is true under all interpretations of its logical components (other than its logical constants). Thus, logical truths such as "if p, then p" can be considered tautologies. Logical truths are thought to be the simplest case of statements which are analytically true (or in other words, true by definition). All of philosophical logic can be thought of as providing accounts of the nature of logical truth, as well as logical consequence. Logical truths are generally considered to be ''necessarily true''. This is to say that they are such that no situation could arise in which they could fail to be true. The view that logical statements are necessarily true is sometimes treated as equivalent to saying that ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Intuitionism
In the philosophy of mathematics, intuitionism, or neointuitionism (opposed to preintuitionism), is an approach where mathematics is considered to be purely the result of the constructive mental activity of humans rather than the discovery of fundamental principles claimed to exist in an objective reality. That is, logic and mathematics are not considered analytic activities wherein deep properties of objective reality are revealed and applied, but are instead considered the application of internally consistent methods used to realize more complex mental constructs, regardless of their possible independent existence in an objective reality. Truth and proof The fundamental distinguishing characteristic of intuitionism is its interpretation of what it means for a mathematical statement to be true. In Brouwer's original intuitionism, the truth of a mathematical statement is a subjective claim: a mathematical statement corresponds to a mental construction, and a mathematician c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
States Of Affairs
In philosophy, a state of affairs (german: Sachverhalt), also known as a situation, is a way the actual world must be in order to make some given ''proposition'' about the actual world true; in other words, a state of affairs is a ''truth-maker'', whereas a proposition is a ''truth-bearer''. Whereas states of affairs either ''obtain'' or ''fail-to-obtain'', propositions are either ''true'' or ''false''. Some philosophers understand the term "states of affairs" in a more restricted sense as a synonym for " fact". In this sense, there are no states of affairs that do not obtain. David Malet Armstrong is well known for his defence of a factualism, a position according to which the world is a world of facts and not a world of things. Overview States of affairs are complex entities: they are built up from or constituted by other entities. Atomic states of affairs are constituted by one particular and one property exemplified by this particular. For example, the state of affairs that So ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Picture Theory Of Language
The picture theory of language, also known as the picture theory of meaning, is a theory of linguistic reference and meaning articulated by Ludwig Wittgenstein in the ''Tractatus Logico-Philosophicus''. Wittgenstein suggested that a meaningful proposition pictured a state of affairs or atomic fact. Wittgenstein compared the concept of logical pictures (german: Bilder) with spatial pictures. The picture theory of language is considered a correspondence theory of truth. Wittgenstein claims there is an unbridgeable gap between what can be expressed in language and what can only be expressed in non-verbal ways. The picture theory of meaning states that statements are meaningful if, and only if, they can be defined or pictured in the real world. Wittgenstein's later investigations laid out in the First Part of ''Philosophical Investigations'' refuted and replaced his earlier picture-based theory with a use theory of meaning. However, the second psychology-focused Part of ''Philosophic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
