Information: - Imre Lakatos (; November 9, 1922 February 2, 1974) was a Hungarian philosopher of mathematics and science, known for his thesis of the fallibility of mathematics and its 'methodology of proofs and refutations' in its pre-axiomatic stages of development, and also for introducing the concept of the 'research programme' in his methodology of scientific research programmes. - Methodology is the systematic, theoretical analysis of the methods applied to a field of study. It comprises the theoretical analysis of the body of methods and principles associated with a branch of knowledge. Typically, it encompasses concepts such as paradigm, theoretical model, phases and quantitative or qualitative techniques. - Philosophy (from Greek , "philosophia", literally "love of wisdom") is the study of general and fundamental problems concerning matters such as existence, knowledge, values, reason, mind, and language. The term was probably coined by Pythagoras (c. 570 c. 495 BC). Philosophical methods include questioning, critical discussion, rational argument and systematic presentation. Classic philosophical questions include: Is it possible to know anything and to prove it? What is most real? However, philosophers might also pose more practical and concrete questions such as: Is there a best way to live? Is it better to be just or unjust (if one can get away with it)? Do humans have free will? - Broadly speaking, Fallibilism (from Medieval Latin: "fallibilis", "liable to err") is the philosophical claim that no belief can have justification which guarantees the truth of the belief. However, not all fallibilists believe that fallibilism extends to all domains of knowledge. - A philosopher is someone who practices philosophy, which involves rational inquiry into areas that are outside of either theology or science. The term "philosopher" comes from the Ancient Greek ("philosophos") meaning "lover of wisdom". The coining of the term has been attributed to the Greek thinker Pythagoras (6th century BC). - 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. From 1929 to 1947, Wittgenstein taught at the University of Cambridge. During his lifetime he published just one slim book, the 75-page "Tractatus Logico-Philosophicus" (1921), one article, one book review and a children's dictionary. His voluminous manuscripts were edited and published posthumously. "Philosophical Investigations" appeared as a book in 1953, and has since come to be recognised as one of the most important works of philosophy in the twentieth century. His teacher Bertrand Russell described Wittgenstein as "the most perfect example I have ever known of genius as traditionally conceived; passionate, profound, intense, and dominating." - Paul Ernest is a contributor to the social constructivist ( see social constructivism ) philosophy of mathematics . Ernest 's philosophical sources are the later works of Ludwig Wittgenstein and the fallibilism of Imre Lakatos . This social constructivist philosophy claims that both the theorems and truths of mathematics , and the objects of mathematics , are cultural products created by humans . Furthermore the theorems and truths of mathematics always remain corrigible , revisible , and indeed fallible -- in principle at least . This does not mean that mathematical knowledge is flawed or at risk . However , the claim is that the belief that mathematical knowledge is infallible can not be demonstrated , it is an article of faith , even if the warrants for mathematical knowledge are the strongest warrants available to humankind for any knowledge claims . Ernest illustrates this position in his discussion of the issue of whether mathematics is discovered or invented . His fullest exposition of the social constructivist position is given in the 1998 reference , although an earlier version is given in the 1991 reference . Ernest 's version of social constructivism is controversial and has led to strong criticism . The principal criticism is that mathematical theorems are truths and truths by their nature are infallible . In his account of social constructivism Ernest links the worlds of research mathematics and that of school and college mathematics . This link is achieved though the role of experts who as teachers communicate mathematical knowledge to learners and warrant their personal knowledge by means of testing and assessment . As researchers experts both create new mathematical knowledge and warrant the productions of others . Through this linkage the personal knowledge of the experts is developed and itself warranted . Both explicit mathematical knowledge representations and personal mathematical knowledge circulate between the worlds of education and research , which are not themselves wholly disjoint .... - Philosophy of language seeks to understand the relationship between language and reality. Major topics in philosophy of language are the nature of meaning, intentionality, reference, the constitution of sentences, learning, and thought. - Philosophical Investigations is a work by the philosopher Ludwig Wittgenstein, first published, posthumously, in 1953, in which Wittgenstein discusses numerous problems and puzzles in the fields of semantics, logic, philosophy of mathematics, philosophy of psychology, philosophy of action, and philosophy of mind. He puts forth the view that conceptual confusions surrounding language use are at the root of most philosophical problems, contradicting or discarding much of what he argued in his earlier work, the "Tractatus Logico-Philosophicus" (1921). - The Tractatus Logico-Philosophicus (TLP) (Latin for "Logico-Philosophical Treatise") is the only book-length philosophical work published by the Austrian philosopher Ludwig Wittgenstein in his lifetime. The project had a broad aimto identify the relationship between language and reality and to define the limits of scienceand is recognized as a significant philosophical work of the twentieth century. G. E. Moore originally suggested the work's Latin title as homage to the "Tractatus Theologico-Politicus" by Baruch Spinoza. - The philosophy of mathematics is the branch of philosophy that studies the philosophical assumptions, foundations, and implications of mathematics. The aim of the philosophy of mathematics is to provide an account of the nature and methodology of mathematics and to understand the place of mathematics in people's lives. The logical and structural nature of mathematics itself makes this study both broad and unique among its philosophical counterparts. - Bertrand Arthur William Russell, 3rd Earl Russell, (18 May 1872 2 February 1970) was a British philosopher, logician, mathematician, historian, writer, social critic, political activist and Nobel laureate. At various points in his life he considered himself a liberal, a socialist, and a pacifist, but he also admitted that he had "never been any of these things, in any profound sense". He was born in Monmouthshire into one of the most prominent aristocratic families in the United Kingdom. - Medieval Latin was the form of Latin used in the Middle Ages, primarily: as a medium of scholarly exchange; as the liturgical language of Chalcedonian Christianity and the Roman Catholic Church; and as a language of science, literature, law, and administration. Despite the clerical origin of many of its authors, medieval Latin should not be confused with Ecclesiastical Latin. There is no real consensus on the exact boundary where Late Latin ends and medieval Latin begins. Some scholarly surveys begin with the rise of early Ecclesiastical Latin in the middle of the 4th century, others around 500, and still others with the replacement of written Late Latin by written Romance languages starting around the year 900. After reading the paragraphs above, we are interested in knowing the entity with which 'paul ernest' exhibits the relationship of 'occupation'. Find the answer from the choices below. Choices: - book - general - logician - major - mathematician - model - page - philosopher - political activist - research - science - socialist - teacher - united kingdom
mathematician