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Hannes Leitgeb
Hannes Leitgeb (born June 26, 1972, Salzburg) is an Austrian philosopher and mathematician. He is Professor of Philosophy at the Ludwig Maximilian University of Munich and has received a Humboldt Professorship in 2010. His areas of research include logic (theories of truth and modality, paradox, conditionals, nonmonotonic reasoning, dynamic doxastic logic), epistemology (belief, inference, belief revision, foundations of probability, Bayesianism), philosophy of mathematics (structuralism, informal provability, abstraction, criteria of identity), philosophy of language (indeterminacy of translation, compositionality), cognitive science (symbolic representation and neural networks, metacognition), philosophy of science (empirical content, measurement theory), and history of philosophy (logical positivism, Carnap, Quine). Leitgeb studied mathematics at the University of Salzburg and graduated with a Master's degree in 1997. After his PhDs in mathematics (1998) and philosophy (2 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hannes Leitgeb
Hannes Leitgeb (born June 26, 1972, Salzburg) is an Austrian philosopher and mathematician. He is Professor of Philosophy at the Ludwig Maximilian University of Munich and has received a Humboldt Professorship in 2010. His areas of research include logic (theories of truth and modality, paradox, conditionals, nonmonotonic reasoning, dynamic doxastic logic), epistemology (belief, inference, belief revision, foundations of probability, Bayesianism), philosophy of mathematics (structuralism, informal provability, abstraction, criteria of identity), philosophy of language (indeterminacy of translation, compositionality), cognitive science (symbolic representation and neural networks, metacognition), philosophy of science (empirical content, measurement theory), and history of philosophy (logical positivism, Carnap, Quine). Leitgeb studied mathematics at the University of Salzburg and graduated with a Master's degree in 1997. After his PhDs in mathematics (1998) and philosophy (2 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Structuralism (mathematics)
Structuralism is a theory in the philosophy of mathematics that holds that mathematical theories describe structures of mathematical objects. Mathematical objects are exhaustively defined by their place in such structures. Consequently, structuralism maintains that mathematical objects do not possess any intrinsic properties but are defined by their external relations in a system. For instance, structuralism holds that the number 1 is exhaustively defined by being the successor of 0 in the structure of the theory of natural numbers. By generalization of this example, any natural number is defined by its respective place in that theory. Other examples of mathematical objects might include lines and planes in geometry, or elements and operations in abstract algebra. Structuralism is an epistemologically realistic view in that it holds that mathematical statements have an objective truth value. However, its central claim only relates to what ''kind'' of entity a mathematical obje ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
21st-century Austrian Philosophers
The 1st century was the century spanning AD 1 ( I) through AD 100 ( C) according to the Julian calendar. It is often written as the or to distinguish it from the 1st century BC (or BCE) which preceded it. The 1st century is considered part of the Classical era, epoch, or historical period. The 1st century also saw the appearance of Christianity. During this period, Europe, North Africa and the Near East fell under increasing domination by the Roman Empire, which continued expanding, most notably conquering Britain under the emperor Claudius (AD 43). The reforms introduced by Augustus during his long reign stabilized the empire after the turmoil of the previous century's civil wars. Later in the century the Julio-Claudian dynasty, which had been founded by Augustus, came to an end with the suicide of Nero in AD 68. There followed the famous Year of Four Emperors, a brief period of civil war and instability, which was finally brought to an end by Vespasian, ninth Roman emperor, a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
German Academy Of Sciences Leopoldina
The German National Academy of Sciences Leopoldina (german: Deutsche Akademie der Naturforscher Leopoldina – Nationale Akademie der Wissenschaften), short Leopoldina, is the national academy of Germany, and is located in Halle (Saale). Founded on January 1, 1652, based on academic models in Italy, it was originally named the ''Academia Naturae Curiosorum'' until 1687 when Emperor Leopold I raised it to an academy and named it after himself. It was since known under the German name ''Deutsche Akademie der Naturforscher Leopoldina'' until 2007, when it was declared to be Germany's National Academy of Sciences. History ' The Leopoldina was founded in the imperial city of Schweinfurt on 1 January 1652 under the Latin name sometimes translated into English as "Academy of the Curious as to Nature." It was founded by four local physicians- Johann Laurentius Bausch, the first president of the society, Johann Michael Fehr, Georg Balthasar Metzger, and Georg Balthasar Wohlfarth; and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Willard Van Orman Quine
Willard Van Orman Quine (; known to his friends as "Van"; June 25, 1908 – December 25, 2000) was an American philosopher and logician in the analytic tradition, recognized as "one of the most influential philosophers of the twentieth century". From 1930 until his death 70 years later, Quine was continually affiliated with Harvard University in one way or another, first as a student, then as a professor. He filled the Edgar Pierce Chair of Philosophy at Harvard from 1956 to 1978. Quine was a teacher of logic and set theory. Quine was famous for his position that first order logic is the only kind worthy of the name, and developed his own system of mathematics and set theory, known as New Foundations. In philosophy of mathematics, he and his Harvard colleague Hilary Putnam developed the Quine–Putnam indispensability argument, an argument for the reality of mathematical entities.Colyvan, Mark"Indispensability Arguments in the Philosophy of Mathematics" The Stanford Encyclopedi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Carnap
Rudolf Carnap (; ; 18 May 1891 – 14 September 1970) was a German-language 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. He is considered "one of the giants among twentieth-century philosophers." Biography Carnap's father had risen from being a poor ribbon-weaver to be the owner of a ribbon-making factory. His mother came from an academic family; her father was an educational reformer and her oldest brother was the archaeologist Wilhelm Dörpfeld. As a ten-year-old, Carnap accompanied Wilhelm Dörpfeld on an expedition to Greece. Carnap was raised in a profoundly religious Protestant family, but later became an atheist. He began his formal education at the Barmen Gymnasium and the Gymnasium in Jena. From 1910 to 1914, he attended the University of Jena, intending to write a thesis in physics. He also intently studied Immanuel Kant's '' Critique of Pur ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Logical Positivism
Logical positivism, later called logical empiricism, and both of which together are also known as neopositivism, is a movement in Western philosophy whose central thesis was the verification principle (also known as the verifiability criterion of meaning). This theory of knowledge asserted that only statements verifiable through direct observation or logical proof are meaningful in terms of conveying truth value, information or factual content. Starting in the late 1920s, groups of philosophers, scientists, and mathematicians formed the Berlin Circle and the Vienna Circle, which, in these two cities, would propound the ideas of logical positivism. Flourishing in several European centres through the 1930s, the movement sought to prevent confusion rooted in unclear language and unverifiable claims by converting philosophy into "scientific philosophy", which, according to the logical positivists, ought to share the bases and structures of empirical sciences' best examples, such as ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
History Of Philosophy
Philosophy (from , ) is the systematized study of general and fundamental questions, such as those about existence, reason, knowledge, values, mind, and language. Such questions are often posed as problems to be studied or resolved. Some sources claim the term was coined by Pythagoras ( BCE), although this theory is disputed by some. Philosophical methods include questioning, critical discussion, rational argument, and systematic presentation. in . Historically, ''philosophy'' encompassed all bodies of knowledge and a practitioner was known as a ''philosopher''."The English word "philosophy" is first attested to , meaning "knowledge, body of knowledge." "natural philosophy," which began as a discipline in ancient India and Ancient Greece, encompasses astronomy, medicine, and physics. For example, Newton's 1687 ''Mathematical Principles of Natural Philosophy'' later became classified as a book of physics. In the 19th century, the growth of modern research universiti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Philosophy Of Science
Philosophy of science is a branch of philosophy concerned with the foundations, methods, and implications of science. The central questions of this study concern what qualifies as science, the reliability of scientific theories, and the ultimate purpose of science. This discipline overlaps with metaphysics, ontology, and epistemology, for example, when it explores the relationship between science and truth. Philosophy of science focuses on metaphysical, epistemic and semantic aspects of science. Ethical issues such as bioethics and scientific misconduct are often considered ethics or science studies rather than the philosophy of science. There is no consensus among philosophers about many of the central problems concerned with the philosophy of science, including whether science can reveal the truth about unobservable things and whether scientific reasoning can be justified at all. In addition to these general questions about science as a whole, philosophers of science consi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Neural Networks
A neural network is a network or circuit of biological neurons, or, in a modern sense, an artificial neural network, composed of artificial neurons or nodes. Thus, a neural network is either a biological neural network, made up of biological neurons, or an artificial neural network, used for solving artificial intelligence (AI) problems. The connections of the biological neuron are modeled in artificial neural networks as weights between nodes. A positive weight reflects an excitatory connection, while negative values mean inhibitory connections. All inputs are modified by a weight and summed. This activity is referred to as a linear combination. Finally, an activation function controls the amplitude of the output. For example, an acceptable range of output is usually between 0 and 1, or it could be −1 and 1. These artificial networks may be used for predictive modeling, adaptive control and applications where they can be trained via a dataset. Self-learning resulting from e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Compositionality
In semantics, mathematical logic and related disciplines, the principle of compositionality is the principle that the meaning of a complex expression is determined by the meanings of its constituent expressions and the rules used to combine them. This principle is also called Frege's principle, because Gottlob Frege is widely credited for the first modern formulation of it. The principle was never explicitly stated by Frege, and it was arguably already assumed by George Boole decades before Frege's work. The principle of compositionality is highly debated in linguistics, and among its most challenging problems there are the issues of contextuality, the non-compositionality of idiomatic expressions, and the non-compositionality of quotations. History Discussion of compositionality started to appear at the beginning of the 19th century, during which it was debated whether what was most fundamental in language was compositionality or contextuality, and compositionality was usuall ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
