is sometimes used to denote an arbitrary tautology, with the dual symbol (falsum) representing an arbitrary contradiction. Tautologies are a key concept in propositional logic, where a tautology is defined as a propositional formula that is true under any possible Boolean valuation of its propositional variables. In 1800, Immanuel Kant wrote in his book Logic: "The identity of concepts in analytical judgments can be either explicit (explicita) or non-explicit (implicita). Here analytic proposition refers to an analytic truth, a statement in natural language that is true solely because of the terms involved. In 1884, Gottlob Frege proposed in his Grundlagen that a truth is analytic exactly if it can be derived using logic. In 1921, in his Tractatus Logico-Philosophicus, Ludwig Wittgenstein proposed that statements that can be deduced by logical deduction are tautological (empty of meaning) as well as being analytic truths. and representing negation, the following formula can be obtained:: .
Russell's paradoxIn the foundations of mathematics, Russell's paradox (also known as Russell's antinomy), discovered by Bertrand Russell in 1901, showed that the naive set theory created by Georg Cantor leads to a contradiction. The same paradox had been discovered a year before by Ernst Zermelo but he did not publish the idea, which remained known only to Hilbert, Husserl and other members of the University of Göttingen. In 1908, two ways of avoiding the paradox were proposed, Russell's type theory and the Zermelo set theory, the first constructed axiomatic set theory. Zermelo's axioms went well beyond Frege's axioms of extensionality and unlimited set abstraction, and evolved into the now-canonical Zermelo–Fraenkel set theory (ZF). Informal presentation Now we consider the set of all normal sets, R. Formal presentation and the following axiom schema of unrestricted comprehension: for any formula P with only the variable x free. for . a contradiction. Set-theoretic responses or "elect"
Tautology (rhetoric)Rhetorical tautologies state the same thing twice, while appearing to state two or more different things, while logical tautologies state the same thing twice and must do so by logical necessity. The inherent meanings and subsequent conclusions in rhetorical and logical tautologies or logical necessities are very different. Logical tautologies are neither refutable nor verifiable under any condition by axiomatic necessity. All world views contain circularity in terms of the Münchhausen_trilemma or Bootstrapping trilemma. In both the phrases "raising the question" and "begging the question" the same term 'question' is used as a dissimilar reference to premise and conclusion respectively. Figures of Speech: Tautology
Reflective EquilibriumFirst published Mon Apr 28, 2003; substantive revision Wed Jan 12, 2011 Many of us, perhaps all of us, have examined our moral judgments about a particular issue by looking for their coherence with our beliefs about similar cases and our beliefs about a broader range of moral and factual issues. In this everyday practice, we have sought “reflective equilibrium” among these various beliefs as a way of clarifying for ourselves just what we ought to do. In addition, we may also have been persuading ourselves that our conclusions were justifiable and ultimately acceptable to us by seeking coherence among them. Even though it is part of our everyday practice, is this approach to deliberating about what is right and finding justification for our views defensible? Viewed most generally, a “reflective equilibrium” is the end-point of a deliberative process in which we reflect on and revise our beliefs about an area of inquiry, moral or non-moral. 1. 2. 2.1 Origins in justification of logic 3.
Vetmeduni Vienna : Press release 02-25-2014 - The importance of (experimental) design02-25-2014 - One of the hottest debates in evolutionary biology concerns the origin of behaviour: is it genetically encoded or do animals and birds copy their parents or other individuals? A classic experiment published in 2000 seemed to provide overwhelming evidence that a particular behavioural choice (whether individuals of a species of swallow breed in a small colony or a large one) is largely genetically determined. Together with colleagues in France, Richard Wagner of the University of Veterinary Medicine, Vienna has re-examined the data and shown that the findings could be explained by random choice. The design of the original experiment – which represents a blueprint for a vast range of studies of heritability of behaviour – contains two pitfalls that combine to undermine the conclusions. There are clear advantages to living in cities: safety, ready availability of infrastructure, plenty of company etc. It's all in the genes Or is it? A question of design
Rudolf CarnapRudolf Carnap (May 18, 1891 – September 14, 1970) was a German-born philosopher who was active in Europe before 1935 and in the United States thereafter. He was a major member of the Vienna Circle and an advocate of logical positivism. Life and work Carnap's Birthplace in Wuppertal Carnap's father had risen from the status of a poor ribbon-weaver to become the owner of a ribbon-making factory. His mother came from academic stock; her father was an educational reformer and her oldest brother was the archaeologist Wilhelm Dörpfeld. In 1928, Carnap published two important books: The Logical Structure of the World (German: "Der logische Aufbau der Welt"), in which he developed a rigorous formal version of empiricism, defining all scientific terms in phenomenalistic terms. In February 1930 Tarski lectured in Vienna, and during November 1930 Carnap visited Warsaw. Carnap taught himself Esperanto when he was 14 years of age, and remained sympathetic to it (Carnap 1963). Logical syntax
TautologyFrom Wikipedia, the free encyclopedia Tautology may refer to:NasreddinA 17th century miniature of Nasreddin, currently in the Topkapi Palace Museum Library. Nasreddin (Turkish: Nasreddin Hoca, Ottoman Turkish: نصر الدين خواجه, Persian: خواجه نصرالدین, Pashto: ملا نصرالدین, Arabic: نصرالدین جحا / ALA-LC: Naṣraddīn Juḥā, Urdu: ملا نصر الدین / ALA-LC: Mullā Naṣru l-dīn, Uzbek: Nosiriddin Xo'ja, Nasreddīn Hodja, Bosnian: Nasrudin Hodža, Albanian: Nastradin Hoxha, Nastradini) was a Seljuq satirical Sufi, believed to have lived and died during the 13th century in Akşehir, near Konya, a capital of the Seljuk Sultanate of Rum, in today's Turkey. He is considered a populist philosopher and wise man, remembered for his funny stories and anecdotes. He appears in thousands of stories, sometimes witty, sometimes wise, but often, too, a fool or the butt of a joke. A Nasreddin story usually has a subtle humour and a pedagogic nature. The International Nasreddin Hodja fest is celebrated between 5 and 10 July in his hometown every year. According to Prof.
Systems thinkingImpression of systems thinking about society A system is composed of interrelated parts or components (structures) that cooperate in processes (behavior). Natural systems include biological entities, ocean currents, the climate, the solar system and ecosystems. Designed systems include airplanes, software systems, technologies and machines of all kinds, government agencies and business systems. Systems Thinking has at least some roots in the General System Theory that was advanced by Ludwig von Bertalanffy in the 1940s and furthered by Ross Ashby in the 1950s. Systems thinking has been applied to problem solving, by viewing "problems" as parts of an overall system, rather than reacting to specific parts, outcomes or events and potentially contributing to further development of unintended consequences. Systems science thinking attempts to illustrate how small catalytic events that are separated by distance and time can be the cause of significant changes in complex systems.