A priori and a posteriori

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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 BC, a work widely considered during the early European modern period as the model for precise thinking.

Latin Indo-European language of the Italic family

Latin is a classical language belonging to the Italic branch of the Indo-European languages. The Latin alphabet is derived from the Etruscan and Greek alphabets and ultimately from the Phoenician alphabet.

Philosophy Study of general and fundamental questions

Philosophy is the study of general and fundamental questions about existence, knowledge, values, reason, mind, and language. Such questions are often posed as problems to be studied or resolved. The term was probably coined by Pythagoras. Philosophical methods include questioning, critical discussion, rational argument, and systematic presentation. Classic philosophical questions include: Is it possible to know anything and to prove it? What is most real? Philosophers also pose more practical and concrete questions such as: Is there a best way to live? Is it better to be just or unjust? Do humans have free will?

Immanuel Kant Prussian philosopher

Immanuel Kant was an influential German philosopher in the Age of Enlightenment. In his doctrine of transcendental idealism, he argued that space, time, and causation are mere sensibilities; "things-in-themselves" exist, but their nature is unknowable. In his view, the mind shapes and structures experience, with all human experience sharing certain structural features. 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. Kant believed that reason is the source of morality, and that aesthetics arise from a faculty of disinterested judgment. Kant's views continue to have a major influence on contemporary philosophy, especially the fields of epistemology, ethics, political theory, and post-modern aesthetics.


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:

Epistemology A branch of philosophy concerned with the nature and scope of knowledge

Epistemology is the branch of philosophy concerned with the theory of knowledge.

Knowledge is a familiarity, awareness, or understanding of someone or something, such as facts, information, descriptions, or skills, which is acquired through experience or education by perceiving, discovering, or learning.

In logic and philosophy, an argument is a series of statements, called the premises or premisses, intended to determine the degree of truth of another statement, the conclusion. The logical form of an argument in a natural language can be represented in a symbolic formal language, and independently of natural language formally defined "arguments" can be made in math and computer science.

Experience is the knowledge or mastery of an event or subject gained through involvement in or exposure to it. Terms in philosophy such as "empirical knowledge" or "a posteriori knowledge" are used to refer to knowledge based on experience. A person with considerable experience in a specific field can gain a reputation as an expert. The concept of experience generally refers to know-how or procedural knowledge, rather than propositional knowledge: on-the-job training rather than book-learning.

Mathematics Field of study concerning quantity, patterns and change

Mathematics includes the study of such topics as quantity, structure (algebra), space (geometry), and change. It has no generally accepted definition.

In logic, a tautology is a formula or assertion that is true in every possible interpretation. An example of a tautology is "(x equals y) or ". A less abstract example is "The ball is green or the ball is not green". It is either one or the other—it cannot be both and there are no other possibilities.

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.

Modern philosophy

Modern philosophy is philosophy developed in the modern era and associated with modernity. It is not a specific doctrine or school, although there are certain assumptions common to much of it, which helps to distinguish it from earlier 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". [3] [ failed verification ]

Adjective part of speech that describes a noun or pronoun

In linguistics, an adjective is word whose main syntactic role is to modify a noun or noun phrase. Its semantic role is to change information given by the noun.

Noun part of speech in grammar denoting a figurative or real thing or person

A noun is a word that functions as the name of some specific thing or set of things, such as living creatures, objects, places, actions, qualities, states of existence, or ideas. However, noun is not a semantic category, so that it cannot be characterized in terms of its meaning. Thus, actions and states of existence can also be expressed by verbs, qualities by adjectives, and places by adverbs. Linguistically, a noun is a member of a large, open part of speech whose members can occur as the main word in the subject of a clause, the object of a verb, or the object of a preposition.

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.

Deductive reasoning, also deductive logic, is the process of reasoning from one or more statements (premises) to reach a logically certain conclusion.

Inductive reasoning is a method of reasoning in which the premises are viewed as supplying some evidence for the truth of the conclusion; this is in contrast to deductive reasoning. While the conclusion of a deductive argument is certain, the truth of the conclusion of an inductive argument may be probable, based upon the evidence given. Many dictionaries define inductive reasoning as the derivation of general principles from specific observations, though there are many inductive arguments that do not have that form.

In philosophy and logic, contingency is the status of propositions that are neither true under every possible valuation nor false under every possible valuation. A contingent proposition is neither necessarily true nor necessarily false. Propositions that are contingent may be so because they contain logical connectives which, along with the truth value of any of its atomic parts, determine the truth value of the proposition. This is to say that the truth value of the proposition is contingent upon the truth values of the sentences which comprise it. Contingent propositions depend on the facts, whereas analytic propositions are true without regard to any facts about which they speak.


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." [4] One theory, popular among the logical positivists of the early 20th century, is what Boghossian calls the "analytic explanation of the a priori." [4] 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." [5] Analytic propositions are thought to be true in virtue of their meaning alone, while a posteriori 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." [6] 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 truths and contingent truths

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). Considering the proposition "all bachelors are unmarried" as an example: its negation (the proposition that some bachelors are married) is incoherent due to the concept of being unmarried (or the meaning of the word "unmarried") being tied to 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 as it is impossible for them to be true. The negation of a self-contradictory proposition is thus 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." [7]

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...." [8] 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", [5] 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

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 the notion of aprioricity more clearly 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". [note 2] Aaron Sloman presented a brief defence of Kant's three distinctions (analytic/synthetic, apriori/empirical and necessary/contingent) in. [10] It did not assume "possible world semantics" for the third distinction, merely that some part of this world might have been different.

The relationship between aprioricity, necessity, and analyticity is not found to be 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. [11]


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. [12]

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". [13] A priori and a posteriori arguments for the existence of God appear in his Monadology (1714). [13]

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" [14] 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]." [14] 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. 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]
  2. 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. [9]

Related Research Articles

Logical positivism, later called logical empiricism, and both of which together are also known as neopositivism, was a movement in Western philosophy whose central thesis was the verification principle. Also called verificationism, this would-be theory of knowledge asserted that only statements verifiable through direct observation or logical proof are meaningful. Starting in the late 1920s, groups of philosophers, scientists, and mathematicians formed the Berlin Circle and the Vienna Circle, which, in these two cities, would propound the ideas of logical positivism.

Philosophical analysis is the techniques typically used by philosophers in the analytic tradition that involve "breaking down" philosophical issues. Arguably the most prominent of these techniques is the analysis of concepts.

In metaphysics, the noumenon is a posited object or event that exists independently of human sense and/or perception. The term noumenon is generally used when contrasted with, or in relation to, the term phenomenon, which refers to anything that can be apprehended by or is an object of the senses. Modern philosophy has generally been skeptical of the possibility of knowledge independent of the senses, and Immanuel Kant gave this point of view its canonical expression: that the noumenal world may exist, but it is completely unknowable through human sensation. In Kantian philosophy, the unknowable noumenon is often linked to the unknowable "thing-in-itself", although how to characterize the nature of the relationship is a question still open to some controversy.

<i>Critique of Pure Reason</i> 1781 book by Immanuel Kant

The Critique of Pure Reason 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 the Critique of Practical Reason (1788) and the 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 reach a decision about "the possibility or impossibility of metaphysics".

Hume's fork is an explanation, developed by later philosophers, of David Hume's 1730s division of "relations of ideas" from "matters of fact and real existence". A distinction is made between necessary versus contingent, a priori versus a posteriori, and analytic versus synthetic. Relations of abstract ideas align on one side, whereas concrete truths align on the other.

Transcendental idealism epistemology, proposed by Kant, in which space and time are merely formal features of how we perceive objects, not things in themselves that exist independently of us

Transcendental idealism is a doctrine founded by German philosopher Immanuel Kant in the 18th century. Kant's doctrine maintains that human experience of things is similar to the way they appear to us—implying a fundamentally subject-based component, rather than being an activity that directly comprehends the things as they are in themselves. The doctrine is most commonly presented as the idea that time and space are just human perceptions; they are not necessarily real concepts, just a medium through which humans internalize the universe.

In philosophy, metaphysical necessity, sometimes called broad logical necessity, is one of many different kinds of necessity, which sits between logical necessity and nomological 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.

In philosophy, transcendence conveys the basic ground concept from the word's literal meaning, of climbing or going beyond, albeit with varying connotations in its different historical and cultural stages. It includes philosophies, systems, and approaches that describe the fundamental structures of being, not as an ontology, but as the framework of emergence and validation of knowledge of being. "Transcendental" is a word derived from the scholastic, designating the extra-categorical attributes of beings.

<i>Prolegomena to Any Future Metaphysics</i> 1783 book by Immanuel Kant

Prolegomena to Any Future Metaphysics That Will Be Able to Present Itself as a Science is a book by the German philosopher Immanuel Kant, published in 1783, two years after the first edition of his Critique of Pure Reason. One of Kant's shorter works, it contains a summary of the Critique‘s main conclusions, sometimes by arguments Kant had not used in the Critique. Kant characterizes his more accessible approach here as an "analytic" one, as opposed to the Critique‘s "synthetic" examination of successive faculties of the mind and their principles.

"Critique of the Kantian philosophy" is a criticism Arthur Schopenhauer appended to the first volume of his The World as Will and Representation (1818). He wanted to show Immanuel Kant's errors so that Kant's merits would be appreciated and his achievements furthered.

<i>Language, Truth, and Logic</i> philosophical book by A. J. Ayer

Language, Truth, and Logic is a 1936 work of philosophy by Alfred Jules Ayer. It brought some of the ideas of the Vienna Circle and the logical empiricists to the attention of the English-speaking world.

Distinction, the fundamental philosophical abstraction, involves the recognition of difference.

Schema (Kant) Kantian term referring to how perceptions are matched to concepts

In Kantian philosophy, a transcendental schema is the procedural rule by which a category or pure, non-empirical concept is associated with a sense impression. A private, subjective intuition is thereby discursively thought to be a representation of an external object. Transcendental schemata are supposedly produced by the imagination in relation to time.

Analytical reasoning refers to the ability to look at information, be it qualitative or quantitative in nature, and discern patterns within the information. Analytical reasoning involves deductive reasoning with no specialised knowledge, such as: comprehending the basic structure of a set of relationships; recognizing logically equivalent statements; and inferring what could be true or must be true from given facts and rules. Analytical reasoning is axiomatic in that its truth is self-evident. In contrast, synthetic reasoning requires that we include empirical observations, which are always open to doubt. The specific terms “analytic” and “synthetic” themselves were introduced by Kant (1781) at the beginning of his Critique of Pure Reason.

The analytic–synthetic distinction is a semantic distinction, used primarily in philosophy to distinguish propositions into two types: analytic propositions and synthetic propositions. Analytic propositions are true by virtue of their meaning, while synthetic propositions are true by how their meaning relates to the world. However, philosophers have used the terms in very different ways. Furthermore, philosophers have debated whether there is a legitimate distinction.

Schopenhauer's criticism of Kant's schemata is part of Schopenhauer's criticism of the Kantian philosophy which was published in 1819. In the appendix to the first volume of his main work, Arthur Schopenhauer attempted to assign the psychological cause of Kant's doctrines of the categories and their schemata. Schopenhauer's analysis holds that Kant misused argument by analogy to connect abstract reasoning to empirical perception; Schopenhauer argues that this comparison is baseless, and that its conclusions are thus invalid.

Two-dimensionalism is an approach to semantics in analytic philosophy. It is a theory of how to determine the sense and reference of a word and the truth-value of a sentence. It is intended to resolve the puzzle: How is it possible to discover empirically that a necessary truth is true? Two-dimensionalism provides an analysis of the semantics of words and sentences that makes sense of this possibility. The theory was first developed by Robert Stalnaker, but it has been advocated by numerous philosophers since, including David Chalmers.

A posteriori necessity is a thesis in metaphysics and the philosophy of language, that some statements of which we must acquire knowledge a posteriori are also necessarily true. It challenges previously widespread belief that only a priori knowledge can be necessary. It draws on a number of philosophical concepts such as necessity, the causal theory of reference, rigidity, and the a priori a posteriori distinction.



  1. Bird, Graham (1995). Honderich, Ted (ed.). The Oxford Companion to Philosophy. Oxford: Oxford University Press. p.  439. ISBN   0-19-866132-0.
  2. Sommers 2003
  3. Kitcher 2001
  4. 1 2 Boghossian 2003 , p. 363
  5. 1 2 Quine 1951 , p. 21
  6. Quine 1951 , p. 34
  7. Baehr 2006, §3
  8. Fodor 1998 , p. 86
  9. Palmquist 1987, pp. 269, 273
  10. Sloman, A. (1 October 1965). "'Necessary', 'a priori' and 'analytic'". Analysis. 26 (1): 12–16. doi:10.1093/analys/26.1.12.
  11. Baehr 2006, §2-3
  12. Hoiberg 2010 , p. 1
  13. 1 2 Gottfried Wilhelm Leibniz (Stanford Encyclopedia of Philosophy)
  14. 1 2 Kant 1781 , p. 1


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  • Quine, Willard Van Orman (1951). "Two Dogmas of Empiricism". The Philosophical Review. 60: 20–43. doi:10.2307/2181906.
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Further reading