Logical positivism in the context of "Quantitative 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.

Theodor W. Adorno (/əˈdɔːrnoʊ/ ə-DOR-noh; German: [ˈteːodoːɐ̯ aˈdɔʁno] ; born Theodor Ludwig Wiesengrund; 11 September 1903 – 6 August 1969) was a German philosopher, musicologist, and social theorist. He was a leading member of the Frankfurt School of critical theory, whose work has come to be associated with thinkers such as Ernst Bloch, Walter Benjamin, Max Horkheimer, Erich Fromm, and Herbert Marcuse, for whom the works of Sigmund Freud, Karl Marx, and G. W. F. Hegel were essential to a critique of modern society. As a critic of both fascism and what he called the culture industry, his writings—such as Dialectic of Enlightenment (1947), Minima Moralia (1951), and Negative Dialectics (1966)—strongly influenced the European New Left.

In an intellectual climate shaped by existentialism and logical positivism, Adorno developed a dialectical conception of history and philosophy that challenged the foundations of both, anticipating the divide that would later emerge between the analytic and continental traditions. As a classically trained musician, Adorno studied composition with Alban Berg of the Second Viennese School, influenced by his early admiration for the music of Arnold Schoenberg. Adorno's commitment to avant-garde music formed the backdrop of his subsequent writings and led to his collaboration with Thomas Mann on the latter's novel Doctor Faustus (1947), while the two men lived in California as exiles during the Second World War. Working at the newly relocated Institute for Social Research, Adorno collaborated on influential studies of authoritarianism, antisemitism, and propaganda that would later serve as models for sociological studies the institute carried out in post-war Germany.

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.

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.

Falsifiability is a standard of evaluation of scientific theories and hypotheses. A hypothesis is falsifiable if it belongs to a language or logical structure capable of describing an empirical observation that contradicts it. It was introduced by the philosopher of science Karl Popper in his book The Logic of Scientific Discovery (1934). Popper emphasized that the contradiction is to be found in the logical structure alone, without having to worry about methodological considerations external to this structure. He proposed falsifiability as the cornerstone solution to both the problem of induction and the problem of demarcation.

Popper also emphasized the related asymmetry created by the relation of a universal law with basic observation statements and contrasted falsifiability with the intuitively similar concept of verifiability that was then current in the philosophical discipline of logical positivism. He argued that the only way to verify a claim such as "All swans are white" would be if one could empirically observe all swans, which is not possible. On the other hand, the observation of a single black swan is enough to refute this claim.