A priori and a posteriori

a prioria posterioriA priori'' and ''a posterioria priori knowledgea priori proofa priori'' knowledgea-prioriapriorismaprioritya posteriori'' knowledge
The Latin phrases a priori ('from the earlier') and a posteriori ('from the later') are philosophical terms popularized by Immanuel Kant's Critique of Pure Reason (first published in 1781, second edition in 1787), one of the most influential works in the history of philosophy.wikipedia
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Immanuel Kant

KantKantianKant, Immanuel
The Latin phrases a priori ('from the earlier') and a posteriori ('from the later') are philosophical terms popularized by Immanuel Kant's Critique of Pure Reason (first published in 1781, second edition in 1787), one of the most influential works in the history of philosophy. The 18th-century German philosopher Immanuel Kant (1781) advocated a blend of rationalist and empiricist theories.
He drew a parallel to the Copernican revolution in his proposition that worldly objects can be intuited a priori ('beforehand'), and that intuition is therefore independent from objective reality.

Epistemology

epistemologicalepistemictheory of knowledge
However, most philosophers at least seem to agree that while the various distinctions may overlap, the notions are clearly not identical: the a priori/a posteriori distinction is epistemological, the analytic/synthetic distinction is linguistic, and the necessary/contingent distinction is metaphysical.

Ontological argument

ontological proofontologicalOntological argument for the existence of God
More specifically, ontological arguments tend to start with a priori theory about the organization of the universe.

Empirical evidence

empiricala posterioriempirical data
After Immanuel Kant, in philosophy, it is common to call the knowledge gained a posteriori knowledge (in contrast to a priori knowledge).

Philosophy

philosophicalphilosopherhistory of philosophy
The Latin phrases a priori ('from the earlier') and a posteriori ('from the later') are philosophical terms popularized by Immanuel Kant's Critique of Pure Reason (first published in 1781, second edition in 1787), one of the most influential works in the history of philosophy.
It is associated with a priori knowledge, which is independent of experience, such as math and logical deduction.

Analytic–synthetic distinction

Analytic-synthetic distinctionsyntheticanalytic
See also the related distinctions: deductive/inductive, analytic/synthetic, necessary/contingent.
Analytic truth defined as a truth confirmed no matter what, however, is closer to one of the traditional accounts of a priori.

Saul Kripke

KripkeKripke, SaulSaul Aaron Kripke
The American philosopher Saul Kripke (1972), for example, provided strong arguments against this position.
Another of his most important contributions is his argument that necessity is a "metaphysical" notion that should be separated from the epistemic notion of a priori, and that there are necessary truths that are a posteriori truths, such as that water is H 2 O. He has also contributed an original reading of Wittgenstein, referred to as "Kripkenstein."

Metaphysics

metaphysicalmetaphysicianmetaphysic
However, most philosophers at least seem to agree that while the various distinctions may overlap, the notions are clearly not identical: the a priori/a posteriori distinction is epistemological, the analytic/synthetic distinction is linguistic, and the necessary/contingent distinction is metaphysical.
Metaphysical study is conducted using deduction from that which is known a priori.

Science

scientificsciencesscientific knowledge
The formal sciences are therefore a priori disciplines and because of this, there is disagreement on whether they actually constitute a science.

Logical positivism

logical positivistslogical empiricismlogical positivist
One theory, popular among the logical positivists of the early 20th century, is what Boghossian calls the "analytic explanation of the a priori."
Concerning knowledge, the a priori is knowable before or without, whereas the a posteriori is knowable only after or through, relevant experience.

Empiricism

empiricistempiricalempirically
The 18th-century German philosopher Immanuel Kant (1781) advocated a blend of rationalist and empiricist theories.
It is a fundamental part of the scientific method that all hypotheses and theories must be tested against observations of the natural world rather than resting solely on a priori reasoning, intuition, or revelation.

Aaron Sloman

Sloman
Aaron Sloman presented a brief defence of Kant's three distinctions (analytic/synthetic, apriori/empirical and necessary/contingent) in.
In Oxford, he became interested in philosophy after a brief period studying mathematical logic supervised by Hao Wang, eventually writing a DPhil in philosophy, defending the ideas of Immanuel Kant about the nature of mathematical knowledge as non-empirical and non-analytic ('Knowing and Understanding', 1962, now online at http://www.cs.bham.ac.uk/research/projects/cogaff/sloman-1962/).

Hilary Putnam

PutnamInternal realismPutnam, Hilary
Following such considerations of Kripke and others (such as Hilary Putnam), philosophers tend to distinguish the notion of aprioricity more clearly from that of necessity and analyticity.
This argument is sometimes referred to as an "a priori argument".

Critique of Pure Reason

The Critique of Pure ReasonTranscendental AestheticEmpirical realism
The Latin phrases a priori ('from the earlier') and a posteriori ('from the later') are philosophical terms popularized by Immanuel Kant's Critique of Pure Reason (first published in 1781, second edition in 1787), one of the most influential works in the history of philosophy. The claim is more formally known as Kant's transcendental deduction and it is the central argument of his major work, the Critique of Pure Reason.
Knowledge independent of experience Kant calls "a priori" knowledge, while knowledge obtained through experience is termed "a posteriori".

Space

spatialphysical spacereal space
Space, time and causality are considered pure a priori intuitions.
Kant referred to the experience of "space" in his Critique of Pure Reason as being a subjective "pure a priori form of intuition".

Innatism

innate ideasinnate ideainnate knowledge
An early philosophical use of what might be considered a notion of a priori knowledge (though not called by that name) is Plato's theory of recollection, related in the dialogue Meno (380 BC), according to which something like a priori knowledge is knowledge inherent, intrinsic in the human mind.
Other philosophers, most notably the empiricists, were critical of the theory and denied the existence of any innate ideas, saying all human knowledge was founded on experience, rather than a priori reasoning.

Rationalism

rationalistrationalistsrationalistic
The 18th-century German philosopher Immanuel Kant (1781) advocated a blend of rationalist and empiricist theories.
Taken to extremes, the empiricist view holds that all ideas come to us a posteriori, that is to say, through experience; either through the external senses or through such inner sensations as pain and gratification.

Transcendence (philosophy)

transcendencetranscendentaltranscendent
Kant says, "Although all our cognition begins with experience, it does not follow that it arises [is caused by] from experience" According to Kant, a priori cognition is transcendental, or based on the form of all possible experience, while a posteriori cognition is empirical, based on the content of experience.
For him transcendental meant knowledge about our cognitive faculty with regard to how objects are possible a priori.

German idealism

post-Kantian philosophyGerman idealistpost-Kantian
After Kant's death, a number of philosophers saw themselves as correcting and expanding his philosophy, leading to the various forms of German Idealism.
Immanuel Kant's work purported to bridge the two dominant philosophical schools in the 18th century: 1) rationalism, which held that knowledge could be attained by reason alone a priori (prior to experience), and 2) empiricism, which held that knowledge could be arrived at only through the senses a posteriori (after experience), as expressed by philosopher David Hume, whom Kant sought to rebut.

Transcendental idealism

transcendentaltranscendentTranscendental idealist
The claim is more formally known as Kant's transcendental deduction and it is the central argument of his major work, the Critique of Pure Reason.
That section is devoted to inquiry into the a priori conditions of human sensibility, i.e. the faculty by which humans intuit objects.

Time

temporaldurationsequence of events
Space, time and causality are considered pure a priori intuitions.
Immanuel Kant, in the Critique of Pure Reason, described time as an a priori intuition that allows us (together with the other a priori intuition, space) to comprehend sense experience.

A priori probability

a prioria priori probabilitiesA priori'' probability
Similar to the distinction in philosophy between a priori and a posteriori, in Bayesian inference a priori denotes general knowledge about the data distribution before making an inference, while a posteriori denotes knowledge that incorporates the results of making an inference.

Condition of possibility

conditions of possibility condition of their possibilitycondition of their possibility
And unlike the rationalists, Kant thinks that a priori cognition, in its pure form, that is without the admixture of any empirical content, is limited to the deduction of the conditions of possible experience.
Immanuel Kant does just this in the Transcendental Aesthetic, when he examines the necessary conditions for the synthetic a priori cognition of mathematics.

Phenomenology (philosophy)

phenomenologyphenomenologicalphenomenologist
Modern scholarship also recognizes the existence of the following varieties: late Heidegger's transcendental hermeneutic phenomenology (see transcendental philosophy and a priori), Maurice Merleau-Ponty's embodied phenomenology (see embodied cognition), Michel Henry's material phenomenology (also based on embodied cognition), analytic phenomenology (see analytic philosophy), J. L. Austin's linguistic phenomenology (see ordinary language philosophy), and post-analytic phenomenology (see postanalytic philosophy).