A priori and a posteriori

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Latin Indo-European language of the Italic family


Philosophy Study of general and fundamental questions


Immanuel Kant Prussian philosopher




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



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.


Mathematics Field of study concerning quantity, patterns and change


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.


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.


Adjective part of speech that describes a noun or pronoun


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



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.




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



Relation to the necessary truths and contingent truths


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.


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


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.



Early uses






Immanuel Kant



Johann Fichte



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

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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.



  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
  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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