Ludwig Wittgenstein in the context of Verifiability (science)

German philosophy, meaning philosophy in the German language or philosophy by German people, in its diversity, is fundamental for both the analytic and continental traditions. It covers figures such as Gottfried Wilhelm Leibniz, Immanuel Kant, Georg Wilhelm Friedrich Hegel, Karl Marx, Friedrich Nietzsche, Martin Heidegger, Ludwig Wittgenstein, the Vienna Circle, and the Frankfurt School, who now count among the most famous and studied philosophers of all time. They are central to major philosophical movements such as rationalism, German idealism, Romanticism, dialectical materialism, existentialism, phenomenology, hermeneutics, logical positivism, and critical theory. The Danish philosopher Søren Kierkegaard is often also included in surveys of German philosophy due to his extensive engagement with German thinkers.

In philosophy, an action is something an agent does. Actions contrast with events which merely happen to someone and are typically performed for a purpose and guided by an intention. The first question in the philosophy of action is to determine how actions differ from other forms of behavior, like involuntary reflexes. According to Ludwig Wittgenstein, it involves discovering "What is left over if I subtract the fact that my arm goes up from the fact that I raise my arm". A common response to this question focuses on the agent's intentions. So driving a car is an action since the agent intends to do so, but sneezing is a mere behavior since it happens independent of the agent's intention. The dominant theory of the relation between the intention and the behavior is causalism: driving the car is an action because it is caused by the agent's intention to do so. On this view, actions are distinguished from other events by their causal history. Causalist theories include Donald Davidson's account, which defines actions as bodily movements caused by intentions in the right way, and volitionalist theories, according to which volitions form a core aspect of actions. Non-causalist theories, on the other hand, often see intentions not as the action's cause but as a constituent of it.

An important distinction among actions is between non-basic actions, which are done by doing something else, and basic actions, for which this is not the case. Most philosophical discussions of actions focus on physical actions in the form of bodily movements. But many philosophers consider mental actions to be a distinct type of action that has characteristics quite different from physical actions. Deliberations and decisions are processes that often precede and lead to actions. Actions can be rational or irrational depending on the reason for which they are performed. The problem of responsibility is closely related to the philosophy of actions since people are usually held responsible by others for what they do.

In philosophy, a state of affairs (German: Sachverhalt), also known as a situation, is a way the actual world must be in order to make some given proposition about the actual world true; in other words, a state of affairs is a truth-maker, whereas a proposition is a truth-bearer. Whereas states of affairs either obtain or fail-to-obtain, propositions are either true or false. Some philosophers understand the term "states of affairs" in a more restricted sense as a synonym for "fact". In this sense, there are no states of affairs that do not obtain.

The early Ludwig Wittgenstein and David Malet Armstrong are well known for their defence of a factualism, a position according to which the world is a world of facts and not a world of things.

Bertrand Arthur William Russell, 3rd Earl Russell (18 May 1872 – 2 February 1970), was a British philosopher, logician, mathematician, and public intellectual. He influenced mathematics, logic, set theory, and various areas of analytic philosophy.

He was one of the early 20th century's prominent logicians and a founder of analytic philosophy, along with his predecessor Gottlob Frege, his friend and colleague G. E. Moore, and his student and protégé Ludwig Wittgenstein. Russell with Moore led the British "revolt against idealism". Together with his former teacher Alfred North Whitehead, Russell wrote Principia Mathematica, a milestone in the development of classical logic and a major attempt to reduce the whole of mathematics to logic (see logicism). Russell's article "On Denoting" has been considered a "paradigm of philosophy".

Philosophy of language is the philosophical study of the nature of language. It investigates the relationship between language, language users, and the world. Investigations may include inquiry into the nature of meaning, intentionality, reference, the constitution of sentences, concepts, learning, and thought.

Gottlob Frege and Bertrand Russell were pivotal figures in analytic philosophy's "linguistic turn". These writers were followed by Ludwig Wittgenstein (Tractatus Logico-Philosophicus), the Vienna Circle, logical positivists, and Willard Van Orman Quine.

Analytic philosophy is a broad movement and methodology within contemporary Western philosophy, especially anglophone philosophy, focused on: analysis as a philosophical method; clarity of prose; rigor in arguments; and making use of formal logic, mathematics, and to a lesser degree the natural sciences. It is further characterized by the linguistic turn, or a concern with language and meaning. Analytic philosophy has developed several new branches of philosophy and logic, notably philosophy of language, philosophy of mathematics, philosophy of science, modern predicate logic and mathematical logic.

The proliferation of analysis in philosophy began around the turn of the 20th century and has been dominant since the latter half of the 20th century. Central figures in its historical development are Gottlob Frege, Bertrand Russell, G. E. Moore, and Ludwig Wittgenstein. Other important figures in its history include Franz Brentano, the logical positivists (especially Rudolf Carnap), the ordinary language philosophers, W. V. O. Quine, and Karl Popper. After the decline of logical positivism, Saul Kripke, David Lewis, and others led a revival in metaphysics.

In mathematical logic, a tautology (from Ancient Greek: ταυτολογία) is a formula that is true regardless of the interpretation of its component terms, with only the logical constants having a fixed meaning. It is a logical truth. For example, a formula that states "the ball is green or the ball is not green" is always true, regardless of what a ball is and regardless of its colour. Tautology is usually, though not always, used to refer to valid formulas of propositional logic.

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.

Verificationism, also known as the verification principle or the verifiability criterion of meaning, is a doctrine in philosophy and the philosophy of language which holds that a declarative sentence is cognitively meaningful only if it is either analytic or tautological (true or false in virtue of its logical form and definitions) or at least in principle verifiable by experience. On this view, many traditional statements of metaphysics, theology, and some of ethics and aesthetics are said to lack truth value or factual content, even though they may still function as expressions of emotions or attitudes rather than as genuine assertions. Verificationism was typically formulated as an empiricist criterion of cognitive significance: a proposed test for distinguishing meaningful, truth-apt sentences from "nonsense".

As a self-conscious movement, verificationism was a central thesis of logical positivism (or logical empiricism), developed in the 1920s and 1930s by members of the Vienna Circle and their allies in early analytic philosophy. Drawing on earlier empiricism and positivism (especially David Hume, Auguste Comte and Ernst Mach), on pragmatism (notably C. S. Peirce and William James), and on the logical and semantic innovations of Gottlob Frege and the early Wittgenstein, these philosophers sought a "scientific" conception of philosophy in which meaningful discourse would either consist in empirical claims ultimately testable by observation or in analytic truths of logic and mathematics. The verification principle was intended to explain why many traditional metaphysical disputes seemed irresolvable, to demarcate science from pseudo-science and speculative metaphysics, and to vindicate the special status of the natural sciences by taking empirical testability as the paradigm of serious inquiry.

The Vienna Circle (German: Wiener Kreis) of logical empiricism was a group of elite philosophers and scientists drawn from the natural and social sciences, logic and mathematics who met regularly from 1924 to 1936 at the University of Vienna, chaired by Moritz Schlick. The Vienna Circle had a profound influence on 20th-century philosophy, especially philosophy of science and analytic philosophy.

The philosophical position of the Vienna Circle was called logical empiricism (German: logischer Empirismus), logical positivism or neopositivism. It was influenced by Ernst Mach, David Hilbert, French conventionalism (Henri Poincaré and Pierre Duhem), Gottlob Frege, Bertrand Russell, Ludwig Wittgenstein and Albert Einstein. The Vienna Circle was pluralistic and committed to the ideals of the Enlightenment. It was unified by the aim of making philosophy scientific with the help of modern logic. Main topics were foundational debates in the natural and social sciences, logic and mathematics; the modernization of empiricism by modern logic; the search for an empiricist criterion of meaning; the critique of metaphysics and the unification of the sciences in the unity of science.

Georg Ferdinand Ludwig Philipp Cantor (/ˈkæntɔːr/ KAN-tor; German: [ˈɡeːɔʁk ˈfɛʁdinant ˈluːtvɪç ˈfiːlɪp ˈkantoːɐ̯]; 3 March [O.S. 19 February] 1845 – 6 January 1918) was a mathematician who played a pivotal role in the creation of set theory, which has become a fundamental theory in mathematics. Cantor established the importance of one-to-one correspondence between the members of two sets, defined infinite and well-ordered sets, and proved that the real numbers are more numerous than the natural numbers. Cantor's method of proof of this theorem implies the existence of an infinity of infinities. He defined the cardinal and ordinal numbers and their arithmetic. Cantor's work is of great philosophical interest, a fact he was well aware of.

Originally, Cantor's theory of transfinite numbers was regarded as counter-intuitive – even shocking. This caused it to encounter resistance from mathematical contemporaries such as Leopold Kronecker and Henri Poincaré and later from Hermann Weyl and L. E. J. Brouwer, while Ludwig Wittgenstein raised philosophical objections; see Controversy over Cantor's theory. Cantor, a devout Lutheran Christian, believed the theory had been communicated to him by God. Some Christian theologians (particularly neo-Scholastics) saw Cantor's work as a challenge to the uniqueness of the absolute infinity in the nature of God – on one occasion equating the theory of transfinite numbers with pantheism – a proposition that Cantor vigorously rejected. Not all theologians were against Cantor's theory; prominent neo-scholastic philosopher Konstantin Gutberlet [de; it] was in favor of it and Cardinal Johann Baptist Franzelin accepted it as a valid theory (after Cantor made some important clarifications).

Friedrich Ludwig Gottlob Frege (/ˈfreɪɡə/; German: [ˈɡɔtloːp ˈfreːɡə]; 8 November 1848 – 26 July 1925) was a German philosopher, logician, and mathematician. He was a mathematics professor at the University of Jena, and is understood by many to be the father of analytic philosophy, concentrating on the philosophy of language, logic, and mathematics. Though he was largely ignored during his lifetime, Giuseppe Peano (1858–1932), Bertrand Russell (1872–1970), and, to some extent, Ludwig Wittgenstein (1889–1951) introduced his work to later generations of philosophers. Frege is widely considered to be one of the greatest logicians since Aristotle, and one of the most profound philosophers of mathematics ever.

His contributions include the development of modern logic in the Begriffsschrift and work in the foundations of mathematics. His book the Foundations of Arithmetic is the seminal text of the logicist project, and is cited by Michael Dummett as where to pinpoint the linguistic turn. His philosophical papers "On Sense and Reference" and "The Thought" are also widely cited. The former argues for two different types of meaning and descriptivism. In Foundations and "The Thought", Frege argues for Platonism against psychologism or formalism, concerning numbers and propositions respectively.

George Edward Moore OM FBA (4 November 1873 – 24 October 1958) was an English philosopher, who with Bertrand Russell, Ludwig Wittgenstein and earlier Gottlob Frege was among the initiators of analytic philosophy. He and Russell began de-emphasising the idealism which was then prevalent among British philosophers and became known for advocating common-sense concepts and contributing to ethics, epistemology and metaphysics. He was said to have had an "exceptional personality and moral character". Ray Monk dubbed him "the most revered philosopher of his era".

As Professor of Philosophy at the University of Cambridge, he influenced but abstained from the Bloomsbury Group, an informal set of intellectuals. He edited the journal Mind. He was a member of the Cambridge Apostles from 1894 to 1901, a fellow of the British Academy from 1918, and was chairman of the Cambridge University Moral Sciences Club in 1912–1944. A humanist, he presided over the British Ethical Union (now Humanists UK) in 1935–1936.

Gertrude Elizabeth Margaret Anscombe FBA (/ˈænskəm/; 18 March 1919 – 5 January 2001), usually cited as G. E. M. Anscombe or Elizabeth Anscombe, was a British analytic philosopher. She wrote on the philosophy of mind, philosophy of action, philosophical logic, philosophy of language, and ethics. She was a prominent figure of analytical Thomism, a fellow of Somerville College, Oxford, and a professor of philosophy at the University of Cambridge.

Anscombe was a student of Ludwig Wittgenstein and became an authority on his work and edited and translated many books drawn from his writings, above all his Philosophical Investigations. Anscombe's 1958 article "Modern Moral Philosophy" introduced the term consequentialism into the language of analytic philosophy, and had a seminal influence on contemporary virtue ethics. Her monograph Intention (1957) was described by Donald Davidson as "the most important treatment of action since Aristotle". It is "widely considered a foundational text in contemporary philosophy of action" and has also had influence in the philosophy of practical reason."

Trinity College is a constituent college of the University of Cambridge. Founded in 1546 by King Henry VIII, Trinity is one of the largest Cambridge colleges, with the largest financial endowment of any college at Oxford or Cambridge. Trinity has some of the most distinctive architecture in Cambridge with its Great Court said to be the largest enclosed courtyard in Europe. Academically, Trinity performs exceptionally as measured by the Tompkins Table (the annual unofficial league table of Cambridge colleges), coming top from 2011 to 2017, and regaining the position in 2024.

Members of Trinity have been awarded 34 Nobel Prizes out of the 121 received by members of the University of Cambridge (more than any other Oxford or Cambridge college). Members of the college have received four Fields Medals, one Turing Award and one Abel Prize. Trinity alumni include Francis Bacon, six British prime ministers (the highest number of any Cambridge college), physicists Isaac Newton, James Clerk Maxwell, Ernest Rutherford and Niels Bohr, mathematicians Srinivasa Ramanujan and Charles Babbage, poets Lord Byron and Lord Tennyson, English jurist Edward Coke, writers Vladimir Nabokov and A. A. Milne, historians Lord Macaulay and G. M. Trevelyan, and philosophers Ludwig Wittgenstein and Bertrand Russell (who the college expelled before reaccepting). Two members of the British royal family have studied at Trinity and been awarded degrees: Prince William of Gloucester and Edinburgh, who gained an MA in 1790, and King Charles III, who was awarded a lower second class BA in 1970.

The Tractatus Logico-Philosophicus (widely abbreviated and cited as TLP) is the only book-length philosophical work by the Austrian philosopher Ludwig Wittgenstein that was published during his lifetime. The project had a broad goal: to identify the relationship between language and reality, and to define the limits of science. Wittgenstein wrote the notes for the Tractatus while he was a soldier during World War I and completed it during a military leave in the summer of 1918. It was originally published in German in 1921 as Logisch-Philosophische Abhandlung (Logical-Philosophical Treatise). In 1922 it was published together with an English translation and a Latin title, which was suggested by G. E. Moore as homage to Baruch Spinoza's Tractatus Theologico-Politicus (1670).

The Tractatus is written in an austere and succinct literary style, containing almost no arguments as such, but consists of 525 declarative statements altogether, which are hierarchically numbered.

Ordinary language philosophy (OLP, sometimes called linguistic philosophy) is a methodological approach within analytic philosophy which treats many traditional philosophical problems as the result of misunderstandings of how words are ordinarily used. Rather than proposing ideal or artificial languages, ordinary language philosophers investigate the actual use of expressions in everyday contexts, and often argue that once such uses are described carefully, many philosophical "problems" dissolve or change their shape.

In the twentieth century OLP was primarily associated with the later work of Ludwig Wittgenstein, early to mid-century philosophers at the University of Cambridge such as G. E. Moore and John Wisdom, and mid-century philosophers at the University of Oxford, including Gilbert Ryle, J. L. Austin, P. F. Strawson, H. L. A. Hart, and Paul Grice. Because a number of its most prominent practitioners taught at Oxford, OLP is sometimes informally referred to as "Oxford philosophy".