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Bernard Bolzano
Bernard Bolzano (, ; ; ; born Bernardus Placidus Johann Nepomuk Bolzano; 5 October 1781 – 18 December 1848) was a Bohemian mathematician, logician, philosopher, theologian and Catholic priest of Italian extraction, also known for his liberal views. Bolzano wrote in German, his native language. For the most part, his work came to prominence posthumously. Family Bolzano was the son of two pious Catholics. His father, Bernard Pompeius Bolzano, was an Italian who had moved to Prague, where he married Maria Cecilia Maurer who came from Prague's German-speaking family Maurer. Only two of their twelve children lived to adulthood. Career When he was ten years old, Bolzano entered the Gymnasium of the Piarists in Prague, which he attended from 1791 to 1796. Bolzano entered the University of Prague in 1796 and studied mathematics, philosophy and physics. Starting in 1800, he also began studying theology, becoming a Catholic priest in 1804. He was appointed to the new chair of p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Western Philosophy
Western philosophy refers to the Philosophy, philosophical thought, traditions and works of the Western world. Historically, the term refers to the philosophical thinking of Western culture, beginning with the ancient Greek philosophy of the Pre-Socratic philosophy, pre-Socratics. The word ''philosophy'' itself originated from the Ancient Greek (φιλοσοφία), literally, "the love of wisdom" , "to love" and σοφία ''Sophia (wisdom), sophía'', "wisdom". History Ancient The scope of ancient Western philosophy included the problems of philosophy as they are understood today; but it also included many other disciplines, such as pure mathematics and natural sciences such as physics, astronomy, and biology (Aristotle, for example, wrote on all of these topics). Pre-Socratics The pre-Socratic philosophers were interested in cosmology (the nature and origin of the universe), while rejecting unargued fables in place for argued theory, i.e., dogma superseded reason, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Analytic Proof
{{Short description, Fundamental theory of logical analysis In mathematics, an analytic proof is a proof of a theorem in analysis that only makes use of methods from analysis, and that does not predominantly make use of algebraic or geometrical methods. The term was first used by Bernard Bolzano, who first provided a non-analytic proof of his intermediate value theorem and then, several years later provided a proof of the theorem that was free from intuitions concerning lines crossing each other at a point, and so he felt happy calling it analytic (Bolzano 1817). Bolzano's philosophical work encouraged a more abstract reading of when a demonstration could be regarded as analytic, where a proof is analytic if it does not go beyond its subject matter (Sebastik 2007). In proof theory, an analytic proof has come to mean a proof whose structure is simple in a special way, due to conditions on the kind of inferences that ensure none of them go beyond what is contained in the assumptions ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
German Language
German (, ) is a West Germanic language in the Indo-European language family, mainly spoken in Western Europe, Western and Central Europe. It is the majority and Official language, official (or co-official) language in Germany, Austria, Switzerland, and Liechtenstein. It is also an official language of Luxembourg, German-speaking Community of Belgium, Belgium and the Italian autonomous province of South Tyrol, as well as a recognized national language in Namibia. There are also notable German-speaking communities in other parts of Europe, including: Poland (Upper Silesia), the Czech Republic (North Bohemia), Denmark (South Jutland County, North Schleswig), Slovakia (Krahule), Germans of Romania, Romania, Hungary (Sopron), and France (European Collectivity of Alsace, Alsace). Overseas, sizeable communities of German-speakers are found in the Americas. German is one of the global language system, major languages of the world, with nearly 80 million native speakers and over 130 mi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Catholic Priest
The priesthood is the office of the ministers of religion, who have been commissioned ("ordained") with the holy orders of the Catholic Church. Technically, bishops are a priestly order as well; however, in common English usage ''priest'' refers only to presbyters and pastors (parish priests). The church's doctrine also sometimes refers to all baptised members (inclusive of the laity) as the " common priesthood", which can be confused with the ministerial priesthood of the ordained clergy. The church has different rules for priests in the Latin Church–the largest Catholic particular church–and in the 23 Eastern Catholic Churches. Notably, priests in the Latin Church must take a vow of celibacy, whereas most Eastern Catholic Churches permit married men to be ordained. Deacons are male and usually belong to the diocesan clergy, but, unlike almost all Latin Church (Western Catholic) priests and all bishops from Eastern or Western Catholicism, they may marry as laymen before ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Philosopher
Philosophy ('love of wisdom' in Ancient Greek) is a systematic study of general and fundamental questions concerning topics like existence, reason, knowledge, Value (ethics and social sciences), value, mind, and language. It is a rational and critical inquiry that reflects on its methods and assumptions. Historically, many of the individual sciences, such as physics and psychology, formed part of philosophy. However, they are considered separate academic disciplines in the modern sense of the term. Influential traditions in the history of philosophy include Western philosophy, Western, Islamic philosophy, Arabic–Persian, Indian philosophy, Indian, and Chinese philosophy. Western philosophy originated in Ancient Greece and covers a wide area of philosophical subfields. A central topic in Arabic–Persian philosophy is the relation between reason and revelation. Indian philosophy combines the Spirituality, spiritual problem of how to reach Enlightenment in Buddhism, enlighten ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Logician
Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the study of deductively valid inferences or logical truths. It examines how conclusions follow from premises based on the structure of arguments alone, independent of their topic and content. Informal logic is associated with informal fallacies, critical thinking, and argumentation theory. Informal logic examines arguments expressed in natural language whereas formal logic uses formal language. When used as a countable noun, the term "a logic" refers to a specific logical formal system that articulates a proof system. Logic plays a central role in many fields, such as philosophy, mathematics, computer science, and linguistics. Logic studies arguments, which consist of a set of premises that leads to a conclusion. An example is the argument from the premises "it's Sunday" and "if it's Sunday then I don't have to work" leading to the conclusion "I don't have to work." Premise ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematical model, models, and mathematics#Calculus and analysis, change. History One of the earliest known mathematicians was Thales of Miletus (); he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed. He is credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales's theorem. The number of known mathematicians grew when Pythagoras of Samos () established the Pythagorean school, whose doctrine it was that mathematics ruled the universe and whose motto was "All is number". It was the Pythagoreans who coined the term "mathematics", and with whom the study of mathematics for its own sake begins. The first woman math ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Catholic Church
The Catholic Church (), also known as the Roman Catholic Church, is the List of Christian denominations by number of members, largest Christian church, with 1.27 to 1.41 billion baptized Catholics Catholic Church by country, worldwide as of 2025. It is among the world's oldest and largest international institutions and has played a prominent role in the history and development of Western civilization.Gerald O'Collins, O'Collins, p. v (preface). The church consists of 24 Catholic particular churches and liturgical rites#Churches, ''sui iuris'' (autonomous) churches, including the Latin Church and 23 Eastern Catholic Churches, which comprise almost 3,500 dioceses and Eparchy, eparchies List of Catholic dioceses (structured view), around the world, each overseen by one or more Bishops in the Catholic Church, bishops. The pope, who is the bishop of Rome, is the Papal supremacy, chief pastor of the church. The core beliefs of Catholicism are found in the Nicene Creed. The ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Christianity
Christianity is an Abrahamic monotheistic religion, which states that Jesus in Christianity, Jesus is the Son of God (Christianity), Son of God and Resurrection of Jesus, rose from the dead after his Crucifixion of Jesus, crucifixion, whose coming as the Messiah#Christianity, messiah (Christ (title), Christ) was Old Testament messianic prophecies quoted in the New Testament, prophesied in the Old Testament and chronicled in the New Testament. It is the Major religious groups, world's largest and most widespread religion with over 2.3 billion followers, comprising around 28.8% of the world population. Its adherents, known as Christians, are estimated to make up a majority of the population in Christianity by country, 157 countries and territories. Christianity remains Christian culture, culturally diverse in its Western Christianity, Western and Eastern Christianity, Eastern branches, and doctrinally diverse concerning Justification (theology), justification and the natur ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Robert Von Zimmermann
Robert von Zimmermann or Robert Zimmermann (2 November 1824, Prague – 1 September 1898, Prague) was an Austrian-Czech philosopher. The mathematician and philosopher, Bernard Bolzano, entrusted his unfinished work, ''Grössenlehre'' ("Theory of Quantity", a philosophical foundation for mathematics), which had not been completed at the time of his death in 1848, to von Zimmermann who was 24 years old. Zimmermann had been a student of Bolzano's. Since Zimmermann's interests were more in the area of philosophy as he had been appointed to the chair of philosophy at the University of Prague in 1852, he didn't do much with Bolzano's papers. Most of the remaining manuscripts stayed in Zimmermann's possession until 1882 when he gave them to the Austrian Academy of Sciences (Kaiserliche Akademie der Wissenschaften in Wien). Robert von Zimmermann taught at the University of Vienna from 1861. [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Franz Josef Gerstner
Franz Josef Gerstner (from 1810 Franz Josef Ritter von Gerstner; ; 23 February 1756 – 25 July 1832) was a German-Bohemian physicist, astronomer and engineer. Life Gerstner was born in Komotau in Bohemia then part of the Habsburg Empire (present-day Chomutov in the Czech Republic). He was the son of Florian Gerstner (1730–1783) and Maria Elisabeth, born Englert. He studied at the Jesuits gymnasium in Komotau. After that he studied mathematics and astronomy at the Faculty of Philosophy at the Charles-Ferdinand University in Prague between 1772 and 1777. In 1781 he started to study medicine at the University of Vienna, but later decided to quit his studies. Instead, he worked as an assistant at the astronomical observatory in Vienna under supervision of Maximilian Hell. In 1784 he returned to Prague, where he got a position at the Klementinum astronomical observatory in Prague. In 1789 he became professor of higher mathematics, mechanics and hydraulics at the University in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Least-upper-bound Property
In mathematics, the least-upper-bound property (sometimes called completeness, supremum property or l.u.b. property) is a fundamental property of the real numbers. More generally, a partially ordered set has the least-upper-bound property if every non-empty subset of with an upper bound has a ''least'' upper bound (supremum) in . Not every (partially) ordered set has the least upper bound property. For example, the set \mathbb of all rational numbers with its natural order does ''not'' have the least upper bound property. The least-upper-bound property is one form of the completeness axiom for the real numbers, and is sometimes referred to as Dedekind completeness.Willard says that an ordered space "X is Dedekind complete if every subset of X having an upper bound has a least upper bound." (pp. 124-5, Problem 17E.) It can be used to prove many of the fundamental results of real analysis, such as the intermediate value theorem, the Bolzano–Weierstrass theorem, the extreme valu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
