A priori and a posteriori

The Latin phrases a priori (lit. "from the earlier") and a posteriori (lit. "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.[1] However, in their Latin forms they appear in Latin translations of Euclid's Elements, of about 300 BCE, a work widely considered during the early European modern period as the model for precise thinking.

These terms are used with respect to reasoning (epistemology) to distinguish "necessary conclusions from first premises" (i.e., what must come before sense observation) from "conclusions based on sense observation" which must follow it. Thus, the two kinds of knowledge, justification, or argument, may be glossed:

There are many points of view on these two types of knowledge, and their relationship gives rise to one of the oldest problems in modern philosophy.

The terms a priori and a posteriori are primarily used as adjectives to modify the noun "knowledge" (for example, "a priori knowledge"). However, "a priori" is sometimes used to modify other nouns, such as "truth". Philosophers also may use "apriority" and "aprioricity" as nouns to refer (approximately) to the quality of being "a priori".[4]

Although definitions and use of the terms have varied in the history of philosophy, they have consistently labeled two separate epistemological notions. See also the related distinctions: deductive/inductive, analytic/synthetic, necessary/contingent.


The intuitive distinction between a priori and a posteriori knowledge (or justification) is best seen via examples, as below:

A priori
Consider the proposition, "If George V reigned at least four days, then he reigned more than three days." This is something that one knows a priori, because it expresses a statement that one can derive by reason alone.
A posteriori
Compare this with the proposition expressed by the sentence, "George V reigned from 1910 to 1936." This is something that (if true) one must come to know a posteriori, because it expresses an empirical fact unknowable by reason alone.

Analyticity and necessity

Relation to the analytic-synthetic

Several philosophers reacting to Kant sought to explain a priori knowledge without appealing to, as Paul Boghossian (MD) explains, "a special faculty ... that has never been described in satisfactory terms."[5] One theory, popular among the logical positivists of the early 20th century, is what Boghossian calls the "analytic explanation of the a priori."[5] The distinction between analytic and synthetic propositions was first introduced by Kant. While Kant's original distinction was primarily drawn in terms of conceptual containment, the contemporary version of the distinction primarily involves, as the American philosopher W. V. O. Quine put it, the notions of "true by virtue of meanings and independently of fact."[6] Analytic propositions are thought to be true in virtue of their meaning alone, while a posteriori analytic propositions are thought to be true in virtue of their meaning and certain facts about the world. According to the analytic explanation of the a priori, all a priori knowledge is analytic; so a priori knowledge need not require a special faculty of pure intuition, since it can be accounted for simply by one's ability to understand the meaning of the proposition in question. In short, proponents of this explanation claimed to have reduced a dubious metaphysical faculty of pure reason to a legitimate linguistic notion of analyticity.

However, the analytic explanation of a priori knowledge has undergone several criticisms. Most notably, Quine argued that the analytic–synthetic distinction is illegitimate. Quine states: "But for all its a priori reasonableness, a boundary between analytic and synthetic statements simply has not been drawn. That there is such a distinction to be drawn at all is an unempirical dogma of empiricists, a metaphysical article of faith."[7] While the soundness of Quine's critique is highly disputed, it had a powerful effect on the project of explaining the a priori in terms of the analytic.

Relation to the necessary and contingent

The metaphysical distinction between necessary and contingent truths has also been related to a priori and a posteriori knowledge. A proposition that is necessarily true is one whose negation is self-contradictory (thus, it is said to be true in every possible world). Consider the proposition that all bachelors are unmarried. Its negation, the proposition that some bachelors are married, is incoherent, because the concept of being unmarried (or the meaning of the word "unmarried") is part of the concept of being a bachelor (or part of the definition of the word "bachelor"). To the extent that contradictions are impossible, self-contradictory propositions are necessarily false, because it is impossible for them to be true. Thus, the negation of a self-contradictory proposition is supposed to be necessarily true. By contrast, a proposition that is contingently true is one whose negation is not self-contradictory (thus, it is said that it is not true in every possible world). As Jason Baehr states, it seems plausible that all necessary propositions are known a priori, because "[s]ense experience can tell us only about the actual world and hence about what is the case; it can say nothing about what must or must not be the case."[8]

Following Kant, some philosophers have considered the relationship between aprioricity, analyticity, and necessity to be extremely close. According to Jerry Fodor, "Positivism, in particular, took it for granted that a priori truths must be necessary...."[9] However, since Kant, the distinction between analytic and synthetic propositions had slightly changed. Analytic propositions were largely taken to be "true by virtue of meanings and independently of fact",[6] while synthetic propositions were not—one must conduct some sort of empirical investigation, looking to the world, to determine the truth-value of synthetic propositions.

Aprioricity, analyticity, and necessity have since been more clearly separated from each other. The American philosopher Saul Kripke (1972), for example, provided strong arguments against this position. Kripke argued that there are necessary a posteriori truths, such as the proposition that water is H2O (if it is true). According to Kripke, this statement is necessarily true (since water and H2O are the same thing, they are identical in every possible world, and truths of identity are logically necessary) and a posteriori (since it is known only through empirical investigation). Following such considerations of Kripke and others (such as Hilary Putnam), philosophers tend to distinguish more clearly the notion of aprioricity from that of necessity and analyticity.

Kripke's definitions of these terms, however, diverge in subtle ways from those of Kant. Taking these differences into account, Kripke's controversial analysis of naming as contingent and a priori would, according to Stephen Palmquist, best fit into Kant's epistemological framework by calling it "analytic a posteriori".[nb 1] Aaron Sloman presented a brief defence of Kant's three distinctions (analytic/synthetic, apriori/empirical and necessary/contingent) in [11]. It did not assume "possible world semantics" for the third distinction, merely that some part of this world might have been different.

Thus, the relationship between aprioricity, necessity, and analyticity is not easy to discern. 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.[12]


Early uses

The phrases "a priori" and "a posteriori" are Latin for "from what comes before" and "from what comes later" (or, less literally, "from first principles, before experience" and "after experience"). They appear in Latin translations of Euclid's Elements, of about 300 bc, a work widely considered during the early European modern period as the model for precise thinking.

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.

Albert of Saxony, a 14th-century logician, wrote on both a priori and a posteriori.[13]

G. W. Leibniz introduced a distinction between a priori and a posteriori criteria for the possibility of a notion in his (1684) short treatise "Meditations on Knowledge, Truth, and Ideas".[14] A priori and a posteriori arguments for the existence of God appear in his Monadology (1714).[14]

George Berkeley outlined the distinction in his 1710 work A Treatise Concerning the Principles of Human Knowledge (para. XXI).

Immanuel Kant

The 18th-century German philosopher Immanuel Kant (1781) advocated a blend of rationalist and empiricist theories. Kant says, "Although all our cognition begins with experience, it does not follow that it arises [is caused by] from experience"[15] 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. Kant states, "[…] it is quite possible that our empirical knowledge is a compound of that which we receive through impressions, and that which the faculty of cognition supplies from itself sensuous impressions [sense data] giving merely the occasion [opportunity for a cause to produce its effect]."[15] Contrary to contemporary usages of the term, Kant thinks that a priori knowledge is not entirely independent of the content of experience. 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. These a priori, or transcendental conditions, are seated in one's cognitive faculties, and are not provided by experience in general or any experience in particular (although an argument exists that a priori intuitions can be "triggered" by experience).

Kant nominated and explored the possibility of a transcendental logic with which to consider the deduction of the a priori in its pure form. Space, time and causality are considered pure a priori intuitions. Kant reasoned that the pure a priori intuitions are established via his transcendental aesthetic and transcendental logic. He claimed that the human subject would not have the kind of experience that it has were these a priori forms not in some way constitutive of him as a human subject. For instance, a person would not experience the world as an orderly, rule-governed place unless time, space and causality were determinant functions in the form of perceptual faculties, i. e., there can be no experience in general without space, time or causality as particular determinants thereon. 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. The transcendental deduction argues that time, space and causality are ideal as much as real. In consideration of a possible logic of the a priori, this most famous of Kant's deductions has made the successful attempt in the case for the fact of subjectivity, what constitutes subjectivity and what relation it holds with objectivity and the empirical.

Johann Fichte

After Kant's death, a number of philosophers saw themselves as correcting and expanding his philosophy, leading to the various forms of German Idealism. One of these philosophers was Johann Fichte. His student (and critic), Arthur Schopenhauer, accused him of rejecting the distinction between a priori and a posteriori knowledge:

... Fichte who, because the thing-in-itself had just been discredited, at once prepared a system without any thing-in-itself. Consequently, he rejected the assumption of anything that was not through and through merely our representation, and therefore let the knowing subject be all in all or at any rate produce everything from its own resources. For this purpose, he at once did away with the essential and most meritorious part of the Kantian doctrine, the distinction between a priori and a posteriori and thus that between the phenomenon and the thing-in-itself. For he declared everything to be a priori, naturally without any evidence for such a monstrous assertion; instead of these, he gave sophisms and even crazy sham demonstrations whose absurdity was concealed under the mask of profundity and of the incomprehensibility ostensibly arising therefrom. Moreover, he appealed boldly and openly to intellectual intuition, that is, really to inspiration.

— Schopenhauer, Parerga and Paralipomena, Vol. I, §13

See also


  1. ^ In this pair of articles, Stephen Palmquist demonstrates that the context often determines how a particular proposition should be classified. A proposition that is synthetic a posteriori in one context might be analytic a priori in another.[10]


  1. ^ Graham Bird (1995). Ted Honderich, ed. The Oxford Companion to Philosophy. Oxford: Oxford University Press. p. 439. ISBN 0-19-866132-0.
  2. ^ Sommers 2003
  3. ^ Galen Strawson has stated that an a priori argument is one in which "you can see that it is true just lying on your couch. You don't have to get up off your couch and go outside and examine the way things are in the physical world. You don't have to do any science."[2]
  4. ^ Kitcher 2001
  5. ^ a b Boghossian 2003, p. 363
  6. ^ a b Quine 1951, p. 21
  7. ^ Quine 1951, p. 34
  8. ^ Baehr 2006, §3
  9. ^ Fodor 1998, p. 86
  10. ^ Palmquist 1987, pp. 269, 273
  11. ^ Sloman, A. (1965-10-01). "'Necessary', 'a priori' and 'analytic'". Analysis. 26 (1): 12–16. doi:10.1093/analys/26.1.12.
  12. ^ Baehr 2006, §2-3
  13. ^ Hoiberg 2010, p. 1
  14. ^ a b Gottfried Wilhelm Leibniz (Stanford Encyclopedia of Philosophy)
  15. ^ a b Kant 1781, p. 1


  • Baehr, Jason S. (2006). "A Priori and A Posteriori". Internet Encyclopedia of Philosophy.
  • Boghossian, Paul Artin (2003) [1997]. "14: Analyticity". In Hale, Bob; Wright, Crispin. A Companion to the Philosophy of Language. Blackwell Companions to Philosophy. Malden, MA: Blackwell Publishing. ISBN 978-0631213260.
  • Fodor, Jerry (1998). Concepts: Where Cognitive Science Went Wrong. New York, NY: Oxford University Press. ISBN 978-0198236368.
  • Hoiberg, Dale H., ed. (2010). "a priori knowledge". Encyclopædia Britannica. I: A-Ak - Bayes (15th ed.). Chicago, Illinois: Encyclopædia Britannica, Inc. ISBN 978-1-59339-837-8.
  • Kant, Immanuel (1781). Kritik der reinen Vernunft [Critique of Pure Reason]. Im Insel-Verlag.
  • Kitcher, Philip (2001). "A Priori Knowledge Revisited". In Boghossian, Paul; Peacocke, Christopher. New Essays on the A Priori. Oxford, UK: Oxford University Press. ISBN 978-0199241279.
  • Palmquist, Stephen (December 1987). "A Priori Knowledge in Perspective: (II) Naming, Necessity and the Analytic A Posteriori". The Review of Metaphysics. 41 (2): 255–282.
  • Quine, Willard Van Orman (1951). "Two Dogmas of Empiricism". The Philosophical Review. 60: 20–43. doi:10.2307/2181906.
  • Sommers, Tamler (March 2003). Jarman, Casey, ed. "Galen Strawson (interview)". Believer Magazine. San Francisco, CA: McSweeney's McMullens. 1 (1). Retrieved 10 July 2013.

Further reading

External links

A posteriori (disambiguation)

A posteriori may refer to:

A posteriori knowledge, that is justified by empirical evidence

A posteriori (languages), a type of constructed language

A Posteriori, a 2006 music album created by the musical project Enigma

A priori

A priori may refer to:

A priori and a posteriori

A priori and a posteriori languages

A priori estimate, a type of estimate for the size of a solution of a differential equation

A priori probability, a type of probability derived by deductive reasoning, with application in statistical mechanics

Apriori algorithm, an algorithm used with databases

A priori probability

An a priori probability is a probability that is derived purely by deductive reasoning. One way of deriving a priori probabilities is the principle of indifference, which has the character of saying that, if there are N mutually exclusive and collectively exhaustive events and if they are equally likely, then the probability of a given event occurring is 1/N. Similarly the probability of one of a given collection of K events is K / N.

One disadvantage of defining probabilities in the above way is that it applies only to finite collections of events.

In Bayesian inference, "uninformative priors" or "objective priors" are particular choices of a priori probabilities.

Note that "prior probability" is a broader concept.

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.

Always already

Always already is a philosophical term regarding the perception of phenomena by the mind of an observer. The features of a phenomenon that seem to precede any perception of it are said to be "always already" present.

Analytic apriori

Analytic apriori may refer to:

A priori and a posteriori

Analytic–synthetic distinction

Analytic truth

Armchair theorizing

Armchair theorizing, armchair philosophizing, or armchair scholarship is an approach to providing new developments in a field that does not involve the collection of new information but, rather, a careful analysis or synthesis of existent scholarship, especially frivolously or superficially so.

Bolak language

Bolak is a constructed language that was invented by Léon Bollack. The name of the language means both "blue language" and "ingenious creation" in the language itself.

Constructed language

A constructed language (sometimes called a conlang) is a language whose phonology, grammar, and vocabulary are, instead of having developed naturally, consciously devised for communication between intelligent beings, most commonly for use by humanoids. Constructed languages may also be referred to as artificial, planned or invented languages and in some cases fictional languages. There are many possible reasons to create a constructed language, such as to ease human communication (see international auxiliary language and code), to give fiction or an associated constructed setting an added layer of realism, for experimentation in the fields of linguistics, cognitive science, and machine learning, for artistic creation, and for language games.

The expression planned language is sometimes used to indicate international auxiliary languages and other languages designed for actual use in human communication. Some prefer it to the adjective artificial, as this term may be perceived as pejorative. Outside Esperanto culture, the term language planning means the prescriptions given to a natural language to standardize it; in this regard, even a "natural language" may be artificial in some respects, meaning some of its words have been crafted by conscious decision. Prescriptive grammars, which date to ancient times for classical languages such as Latin and Sanskrit, are rule-based codifications of natural languages, such codifications being a middle ground between naïve natural selection and development of language and its explicit construction. The term glossopoeia is also used to mean language construction, particularly construction of artistic languages.Conlang speakers are rare. For example, the Hungarian census of 2001 found 4570 speakers of Esperanto, 10 of Romanid, two each of Interlingua and Ido and one each of Idiom Neutral and Mundolinco. The Russian census of 2010 found 992 speakers of Esperanto, nine of Ido, one of Edo and no speakers of Slovio or Interlingua.

Critical philosophy

Attributed to Immanuel Kant, the critical philosophy (German: kritische Philosophie) movement sees the primary task of philosophy as criticism rather than justification of knowledge; criticism, for Kant, meant judging as to the possibilities of knowledge before advancing to knowledge itself (from the Greek kritike (techne), or "art of judgment"). The basic task of philosophers, according to this view, is not to establish and demonstrate theories about reality, but rather to subject all theories—including those about philosophy itself—to critical review, and measure their validity by how well they withstand criticism.

"Critical philosophy" is also used as another name for Kant's philosophy itself. Kant said that philosophy's proper enquiry is not about what is out there in reality, but rather about the character and foundations of experience itself. We must first judge how human reason works, and within what limits, so that we can afterwards correctly apply it to sense experience and determine whether it can be applied at all to metaphysical objects.

Distinction (philosophy)

Distinction, the fundamental philosophical abstraction, involves the recognition of difference.In classical philosophy, there were various ways in which things could be distinguished. The merely logical or virtual distinction, such as the difference between concavity and convexity, involves the mental apprehension of two definitions, but which cannot be realized outside the mind, as any concave line would be a convex line considered from another perspective. A real distinction involves a level of ontological separation, as when squirrels are distinguished from llamas (for no squirrel is a llama, and no llama is a squirrel). A real distinction is thus different than a merely conceptual one, in that in a real distinction, one of the terms can be realized in reality without the other being realized.

Later developments include Duns Scotus's formal distinction, which developed in part out of the recognition in previous authors that there need to be an intermediary between logical and real distinctions.Some relevant distinctions to the history of Western philosophy include:

Necessity and Contingency

Inductive and Deductive

Empirical evidence

Empirical evidence is the information received by means of the senses, particularly by observation and documentation of patterns and behavior through experimentation. The term comes from the Greek word for experience, ἐμπειρία (empeiría).

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


Endurantism or endurance theory is a philosophical theory of persistence and identity. According to the endurantist view, material objects are persisting three-dimensional individuals wholly present at every moment of their existence, which goes with an A-theory of time. This conception of an individual as always present is opposed to perdurantism or four dimensionalism, which maintains that an object is a series of temporal parts or stages, requiring a B-theory of time. The use of "endure" and "perdure" to distinguish two ways in which an object can be thought to persist can be traced to David Lewis.


Epistemology ( (listen); from Greek, Modern ἐπιστήμη, epistēmē, meaning 'knowledge', and λόγος, logos, meaning 'logical discourse') is the branch of philosophy concerned with the theory of knowledge.Epistemology is the study of the nature of knowledge, justification, and the rationality of belief. Much debate in epistemology centers on four areas: (1) the philosophical analysis of the nature of knowledge and how it relates to such concepts as truth, belief, and justification, (2) various problems of skepticism, (3) the sources and scope of knowledge and justified belief, and (4) the criteria for knowledge and justification. Epistemology addresses such questions as: "What makes justified beliefs justified?", "What does it mean to say that we know something?", and fundamentally "How do we know that we know?".

Hypothetical imperative

A hypothetical imperative (German: hypothetischer Imperativ) is originally introduced in the philosophical writings of Immanuel Kant. This sort of imperative is contrasted with a categorical imperative.

Jumping after Wirkola

Jumping after Wirkola, idiom of Norwegian origin (hoppe etter Wirkola), signifying the prospect of and the difficulties associated with embarking on a task where one's immediate predecessor has accomplished an unusually good job. Its nearest English equivalent is a hard act to follow. The difficulties alluded to may be both practical and psychological in nature, and are sometimes related to the aspect of the situation that no one really cares how you are doing, as the surroundings might have spent all their attention forces and enthusiasm admiring and applauding your predecessor. The etymology of this eponymous idiom relates to the Norwegian ski jumper Bjørn Wirkola. Since Wirkola would be the a priori and

a posteriori

star of any event he participated in, spectator attention and excitement levels were building up in the minutes leading up to any of his ski jumps, with appropriate crescendo and forte fortissimo culmination during his flying through the air – inadvertently causing the next participant, regardless of fame, nationality or ability, to jump in and into the vacuum of tired spectator silence.

Kingdom of Ends

The Kingdom of Ends (German: Reich der Zwecke) is a thought experiment centered on the moral philosophy of Immanuel Kant. Kant introduced the concept in his Groundwork of the Metaphysic of Morals (4:439). The thought experiment proposes a world in which all human beings are treated as ends (meaning treated as if they and their well-being are the goal), not as mere means to an end for other people.

Metaphysical necessity

In philosophy, metaphysical necessity, sometimes called broad logical necessity, is one of many different kinds of necessity, which sits between logical necessity and nomological (or physical) necessity, in the sense that logical necessity entails metaphysical necessity, but not vice versa, and metaphysical necessity entails physical necessity, but not vice versa. A proposition is said to be necessary if it could not have failed to be the case. Nomological necessity is necessity according to the laws of physics and logical necessity is necessity according to the laws of logic, while metaphysical necessities are necessary in the sense that the world could not possibly have been otherwise. What facts are metaphysically necessary, and on what basis we might view certain facts as metaphysically but not logically necessary are subjects of substantial discussion in contemporary philosophy.

The concept of a metaphysically necessary being plays an important role in certain arguments for the existence of God, especially the ontological argument, but metaphysical necessity is also one of the central concepts in late 20th century analytic philosophy. Metaphysical necessity has proved a controversial concept, and criticized by David Hume, Immanuel Kant, J. L. Mackie, and Richard Swinburne, among others.

Metaphysical necessity is contrasted with other types of necessity. For example, the philosophers of religion John Hick and William L. Rowe distinguished the following three:

factual necessity (existential necessity): a factually necessary being is not causally dependent on any other being, while any other being is causally dependent on it.

causal necessity (subsumed by Hicks under the former type): a causally necessary being is such that it is logically impossible for it to be causally dependent on any other being, and it is logically impossible for any other being to be causally independent of it.

logical necessity: a logically necessary being is a being whose non-existence is a logical impossibility, and which therefore exists either timeless or eternally in all possible worlds.While many theologians (e.g. Anselm of Canterbury, René Descartes, and Gottfried Leibniz) considered God to be a logically or metaphysically necessary being, Richard Swinburne argued for factual necessity, and Alvin Plantinga argues that God is a causally necessary being. Because a factually or causally necessary being does not exist by logical necessity, it does not exist in all logically possible worlds. Therefore, Swinburne used the term "ultimate brute fact" for the existence of God.

The Metaphysics of Morals

The Metaphysics of Morals (German: Die Metaphysik der Sitten) is a 1797 work of political and moral philosophy by Immanuel Kant.


The thing-in-itself (German: Ding an sich) is a concept introduced by Immanuel Kant. Things-in-themselves would be objects as they are, independent of observation. The concept led to much controversy among philosophers.

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