A posteriori

David Hume (/hjuːm/; born David Home; 7 May 1711 – 25 August 1776) was a Scottish philosopher, historian, economist and essayist who is known for his highly influential system of empiricism, philosophical scepticism and metaphysical naturalism. Beginning with A Treatise of Human Nature (1739–40), Hume strove to create a naturalistic science of man that examined the psychological basis of human nature. Hume followed John Locke in rejecting the existence of innate ideas, concluding that all human knowledge derives solely from experience; this places him amongst such empiricists as Francis Bacon, Thomas Hobbes, John Locke, and George Berkeley.

Hume argued that inductive reasoning and belief in causality cannot be justified rationally; instead, they result from custom and mental habit. People never actually perceive that one event causes another but only experience the "constant conjunction" of events. This problem of induction means that to draw any causal inferences from past experience, it is necessary to presuppose that the future will resemble the past; this metaphysical presupposition cannot itself be grounded in prior experience.

Positivism is a philosophical school that holds that all genuine knowledge is either true by definition or positive – meaning a posteriori facts derived by reason and logic from sensory experience. Other ways of knowing, such as intuition, introspection, or religious faith, are rejected or considered meaningless.

Although the positivist approach has been a recurrent theme in the history of Western thought, modern positivism was first articulated in the early 19th century by Auguste Comte. His school of sociological positivism holds that society, like the physical world, operates according to scientific laws. After Comte, positivist schools arose in logic, psychology, economics, historiography, and other fields of thought. Generally, positivists attempted to introduce scientific methods to their respective fields. Since the turn of the 20th century, positivism, although still popular, has declined under criticism within the social sciences by antipositivists and critical theorists, among others, for its alleged scientism, reductionism, overgeneralizations, and methodological limitations. Positivism also exerted an unusual influence on Kardecism.

The Critique of Pure Reason (German: Kritik der reinen Vernunft; 1781; second edition 1787) is a book by the German philosopher Immanuel Kant, in which the author seeks to determine the limits and scope of metaphysics. Also referred to as Kant's "First Critique", it was followed by his Critique of Practical Reason (1788) and Critique of Judgment (1790). In the preface to the first edition, Kant explains that by a "critique of pure reason" he means a critique "of the faculty of reason in general, in respect of all knowledge after which it may strive independently of all experience" and that he aims to decide on "the possibility or impossibility of metaphysics".

Kant builds on the work of empiricist philosophers such as John Locke and David Hume, as well as rationalist philosophers such as René Descartes, Gottfried Wilhelm Leibniz and Christian Wolff. He expounds new ideas on the nature of space and time, and tries to provide solutions to the skepticism of Hume regarding knowledge of the relation of cause and effect and that of René Descartes regarding knowledge of the external world. This is argued through the transcendental idealism of objects (as appearance) and their form of appearance. Kant regards the former "as mere representations and not as things in themselves", and the latter as "only sensible forms of our intuition, but not determinations given for themselves or conditions of objects as things in themselves". This grants the possibility of a priori knowledge, since objects as appearance "must conform to our cognition...which is to establish something about objects before they are given to us." Knowledge independent of experience Kant calls "a priori" knowledge, while knowledge obtained through experience is termed "a posteriori". According to Kant, a proposition is a priori if it is necessary and universal. A proposition is necessary if it is not false in any case and so cannot be rejected; rejection is contradiction. A proposition is universal if it is true in all cases, and so does not admit of any exceptions. Knowledge gained a posteriori through the senses, Kant argues, never imparts absolute necessity and universality, because it is possible that we might encounter an exception.