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Emil Post
Emil Leon Post (; February 11, 1897 – April 21, 1954) was an American mathematician and logician. He is best known for his work in the field that eventually became known as computability theory. Life Post was born in Augustów, Suwałki Governorate, Congress Poland, Russian Empire (now Poland) into a Polish-Jewish family that immigrated to New York City in May 1904. His parents were Arnold and Pearl Post. Post had been interested in astronomy, but at the age of twelve lost his left arm in a car accident. This loss was a significant obstacle to being a professional astronomer, leading to his decision to pursue mathematics rather than astronomy. Post attended the Townsend Harris High School and continued on to graduate from City College of New York in 1917 with a B.S. in Mathematics. After completing his Ph.D. in mathematics in 1920 at Columbia University, supervised by Cassius Jackson Keyser, he did a post-doctorate at Princeton University in the 1920–1921 academic year ...
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Augustów
Augustów (; lt, Augustavas, formerly known in English as ''Augustovo'' or ''Augustowo'')" is a city in north-eastern Poland with 29,729 inhabitants as of December 2021. It lies on the Netta River and the Augustów Canal. It is situated in the Podlaskie Voivodeship (since 1999), having previously been in Suwałki Voivodeship (1975–1998). It is the seat of Augustów County and of Gmina Augustów. In 1970, Augustów became officially recognized as a health and relaxation resort. In 1973, surrounding settlements were named a part of it, forming a popular resort town. History A settlement in the area was first mentioned in 1496. Augustów was established around 1540 by Bona Sforza and granted Magdeburg rights in 1557 by Sigismund II Augustus, after whom it was also named. It was laid out in a very regular manner, with a spacious market-place. Until 1569 Augustów belonged to the Grand Duchy of Lithuania. In 1569 it became part of the Crown of the Kingdom of Poland, wh ...
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Logician
Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the science of deductively valid inferences or of logical truths. It is a formal science investigating how conclusions follow from premises in a topic-neutral way. When used as a countable noun, the term "a logic" refers to a logical formal system that articulates a proof system. Formal logic contrasts with informal logic, which is associated with informal fallacies, critical thinking, and argumentation theory. While there is no general agreement on how formal and informal logic are to be distinguished, one prominent approach associates their difference with whether the studied arguments are expressed in formal or informal languages. Logic plays a central role in multiple fields, such as philosophy, mathematics, computer science, and linguistics. Logic studies arguments, which consist of a set of premises together with a conclusion. Premises and conclusions are usually und ...
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Charles Sanders Peirce
Charles Sanders Peirce ( ; September 10, 1839 – April 19, 1914) was an American philosopher, logician, mathematician and scientist who is sometimes known as "the father of pragmatism". Educated as a chemist and employed as a scientist for thirty years, Peirce made major contributions to logic, a subject that, for him, encompassed much of what is now called epistemology and the philosophy of science. He saw logic as the formal branch of semiotics, of which he is a founder, which foreshadowed the debate among logical positivists and proponents of philosophy of language that dominated 20th-century Western philosophy. Additionally, he defined the concept of abductive reasoning, as well as rigorously formulated mathematical induction and deductive reasoning. As early as 1886, he saw that logic gate, logical operations could be carried out by electrical switching circuits. The same idea was used decades later to produce digital computers. See Also In 1934, the philosopher Paul W ...
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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 ...
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Truth Table
A truth table is a mathematical table used in logic—specifically in connection with Boolean algebra, boolean functions, and propositional calculus—which sets out the functional values of logical expressions on each of their functional arguments, that is, for each combination of values taken by their logical variables. In particular, truth tables can be used to show whether a propositional expression is true for all legitimate input values, that is, logically valid. A truth table has one column for each input variable (for example, P and Q), and one final column showing all of the possible results of the logical operation that the table represents (for example, P XOR Q). Each row of the truth table contains one possible configuration of the input variables (for instance, P=true Q=false), and the result of the operation for those values. See the examples below for further clarification. Ludwig Wittgenstein is generally credited with inventing and popularizing the truth table ...
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Modus Ponens
In propositional logic, ''modus ponens'' (; MP), also known as ''modus ponendo ponens'' (Latin for "method of putting by placing") or implication elimination or affirming the antecedent, is a deductive argument form and rule of inference. It can be summarized as "''P implies Q.'' ''P'' is true. Therefore ''Q'' must also be true." ''Modus ponens'' is closely related to another valid form of argument, '' modus tollens''. Both have apparently similar but invalid forms such as affirming the consequent, denying the antecedent, and evidence of absence. Constructive dilemma is the disjunctive version of ''modus ponens''. Hypothetical syllogism is closely related to ''modus ponens'' and sometimes thought of as "double ''modus ponens''." The history of ''modus ponens'' goes back to antiquity. The first to explicitly describe the argument form ''modus ponens'' was Theophrastus. It, along with '' modus tollens'', is one of the standard patterns of inference that can be appl ...
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Theorem
In mathematics, a theorem is a statement that has been proved, or can be proved. The ''proof'' of a theorem is a logical argument that uses the inference rules of a deductive system to establish that the theorem is a logical consequence of the axioms and previously proved theorems. In the mainstream of mathematics, the axioms and the inference rules are commonly left implicit, and, in this case, they are almost always those of Zermelo–Fraenkel set theory with the axiom of choice, or of a less powerful theory, such as Peano arithmetic. A notable exception is Wiles's proof of Fermat's Last Theorem, which involves the Grothendieck universes whose existence requires the addition of a new axiom to the set theory. Generally, an assertion that is explicitly called a theorem is a proved result that is not an immediate consequence of other known theorems. Moreover, many authors qualify as ''theorems'' only the most important results, and use the terms ''lemma'', ''proposition'' ...
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Tautology (logic)
In mathematical logic, a tautology (from el, ταυτολογία) is a formula or assertion that is true in every possible interpretation. An example is "x=y or x≠y". Similarly, "either the ball is green, or the ball is not green" is always true, regardless of the colour of the ball. The philosopher Ludwig Wittgenstein first applied the term to redundancies of propositional logic in 1921, borrowing from rhetoric, where a tautology is a repetitive statement. In logic, a formula is satisfiable if it is true under at least one interpretation, and thus a tautology is a formula whose negation is unsatisfiable. In other words, it cannot be false. It cannot be untrue. Unsatisfiable statements, both through negation and affirmation, are known formally as contradictions. A formula that is neither a tautology nor a contradiction is said to be logically contingent. Such a formula can be made either true or false based on the values assigned to its propositional variables. The dou ...
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Depression (mood)
Depression is a mental state of low mood and aversion to activity, which affects more than 280 million people of all ages (about 3.5% of the global population). Classified medically as a mental and behavioral disorder, the experience of depression affects a person's thoughts, behavior, motivation, feelings, and sense of well-being. The core symptom of depression is said to be anhedonia, which refers to loss of interest or a loss of feeling of pleasure in certain activities that usually bring joy to people. Depressed mood is a symptom of some mood disorders such as major depressive disorder and dysthymia; it is a normal temporary reaction to life events, such as the loss of a loved one; and it is also a symptom of some physical diseases and a side effect of some drugs and medical treatments. It may feature sadness, difficulty in thinking and concentration and a significant increase or decrease in appetite and time spent sleeping. People experiencing depression may ha ...
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Electroconvulsive Therapy
Electroconvulsive therapy (ECT) is a psychiatric treatment where a generalized seizure (without muscular convulsions) is electrically induced to manage refractory mental disorders.Rudorfer, MV, Henry, ME, Sackeim, HA (2003)"Electroconvulsive therapy". In A Tasman, J Kay, JA Lieberman (eds) ''Psychiatry, Second Edition''. Chichester: John Wiley & Sons Ltd, 1865–1901. Typically, 70 to 120 volts are applied externally to the patient's head, resulting in approximately 800 milliamperes of direct current passing between the electrodes, for a duration of 100 milliseconds to 6 seconds, either from temple to temple (bilateral ECT) or from front to back of one side of the head (unilateral ECT). However, only about 1% of the electrical current crosses the bony skull into the brain because skull impedance is about 100 times higher than skin impedance. The ECT procedure was first conducted in 1938 by Italian psychiatrist Ugo Cerletti and rapidly replaced less safe and effective forms of ...
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Myocardial Infarction
A myocardial infarction (MI), commonly known as a heart attack, occurs when blood flow decreases or stops to the coronary artery of the heart, causing damage to the heart muscle. The most common symptom is chest pain or discomfort which may travel into the shoulder, arm, back, neck or jaw. Often it occurs in the center or left side of the chest and lasts for more than a few minutes. The discomfort may occasionally feel like heartburn. Other symptoms may include shortness of breath, nausea, feeling faint, a cold sweat or feeling tired. About 30% of people have atypical symptoms. Women more often present without chest pain and instead have neck pain, arm pain or feel tired. Among those over 75 years old, about 5% have had an MI with little or no history of symptoms. An MI may cause heart failure, an irregular heartbeat, cardiogenic shock or cardiac arrest. Most MIs occur due to coronary artery disease. Risk factors include high blood pressure, smoking, diabetes, ...
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Doctor Of Philosophy
A Doctor of Philosophy (PhD, Ph.D., or DPhil; Latin: or ') is the most common degree at the highest academic level awarded following a course of study. PhDs are awarded for programs across the whole breadth of academic fields. Because it is an earned research degree, those studying for a PhD are required to produce original research that expands the boundaries of knowledge, normally in the form of a dissertation, and defend their work before a panel of other experts in the field. The completion of a PhD is often a requirement for employment as a university professor, researcher, or scientist in many fields. Individuals who have earned a Doctor of Philosophy degree may, in many jurisdictions, use the title ''Doctor'' (often abbreviated "Dr" or "Dr.") with their name, although the proper etiquette associated with this usage may also be subject to the professional ethics of their own scholarly field, culture, or society. Those who teach at universities or work in academic, edu ...
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