The terms "analytic" and "synthetic" are philosophical terms, used by philosophers to divide propositions into two types: "analytic propositions" and "synthetic propositions." Different philosophers (e.g. Immanuel Kant, the logical positivists) have used the terms in different ways. All, however, believed that the terms marked a distinction that was important to both epistemology and the possibility of metaphysics. Immanuel Kant (22 April 1724 – 12 February 1804), was a German philosopher from Königsberg (now Kaliningrad) in East Prussia. ... Epistemology is the branch of philosophy which studies the nature, origin, and scope of knowledge. ... Plato and Aristotle, by Raphael (Sistine Chapel, Rome). ...

Kant's definitions

The philosopher Immanuel Kant was the first to use the terms "analytic" and "synthetic" to divide propositions into types. Kant introduces the analytic/synthetic distinction in the Introduction to the Critique of Pure Reason (A6-7/B10-11). There, he restricts his attention to affirmative subject-predicate judgments, and defines "analytic proposition" and "synthetic proposition" as follows: Immanuel Kant (22 April 1724 – 12 February 1804), was a German philosopher from Königsberg (now Kaliningrad) in East Prussia. ... This article or section is incomplete and may require cleanup and/or expansion. ...

• analytic proposition: a proposition whose predicate concept is contained in its subject concept

• synthetic proposition: a proposition whose predicate concept is not contained in its subject concept

Examples of analytic propositions, on Kant's definition, include:

• "All bachelors are unmarried."
• "All triangles have three sides."

Kant's own example is:

• "All bodies are extended," i.e. take up space. (A7/B11)

Each of these is an affirmative subject-predicate judgment, and in each, the predicate concept is contained with the subject concept. The concept "bachelor" contains the concepts "unmarried"; the concept "unmarried" is part of the definition of the concept "bachelor." Likewise for "triangle" and "has three sides," and so on.

Examples of synthetic propositions, on Kant's definition, include:

• "All bachelors are happy."
• "All creatures with hearts have kidneys."

Kant's own example is:

• "All bodies are heavy," i.e. have mass. (A7/B11)

As with the examples of analytic propositions, each of these is an affirmative subject-predicate judgment. However, in none of these cases does the subject concept contain the predicate concept. The concept "bachelor" does not contain the concept "happy"; "happy" is not a part of the definition of "bachelor." The same is true for "creatures with hearts" and "have kidneys" - even if every creature with a heart also has kidneys, the concept "creature with a heart" does not contain the concept "has kidneys."

Common criticisms of Kant's definitions

Kant's definitions have been subsequently criticized by several philosophers, including most famously, W. V. Quine. W. V. Quine Willard Van Orman Quine (June 25, 1908 - December 25, 2000) was one of the most influential American philosophers and logicians of the 20th century. ...

One common criticism is that Kant's definitions do not divide ALL propositions into two types. The judgment "Either it is raining or it is not raining" is not an affirmative subject-predicate judgment; thus by Kant's definitions it is neither analytic nor synthetic.

Another common criticism is that Kant's definitions rely upon the notion of "conceptual containment," an idea which many philosophers have found unclear.

Kant's analytic/synthetic distinction and the a priori/a posteriori distinction

In the Introduction to the Critique of Pure Reason, Kant combines his distinction between analytic and synthetic propositions without another distinction, the distinction between a priori and a posteriori propositions. He defines these terms as follows: This article or section is incomplete and may require cleanup and/or expansion. ... A priori is a Latin phrase meaning from the former or less literally before experience. In much of the modern Western tradition, the term a priori is considered to mean propositional knowledge that can be had without, or prior to, experience. ... Empirical or a posteriori knowledge is propositional knowledge obtained by experience. ...

• a priori proposition: a proposition whose justification does not rely upon experience

• a posteriori proposition: a proposition whose justification does rely upon experience

Examples of a priori propositions include:

• "All bachelors are unmarried."
• "7 + 5 =12."

The justification of these propositions does not depend upon experience: one does not need to consult experience in order to determine whether all bachelors or unmarried, or whether 7 + 5 = 12. (Of course, as Kant would have granted, experience is required in order to obtain the concepts "bachelor," "unmarried," "7," "+," and so forth. However, the a priori / a posteriori distinction as employed by Kant here does not refer to the origins of the concepts, but to the justification of the propositions. Once we have the concepts, experience is no longer necessary.)

Examples of a posteriori propositions, on the other hand, include:

• "All bachelors are happy."
• "Tables exist."

Both of these propositions are a posteriori: any justification of them would require one to rely upon one's experience.

The analytic/synthetic distinction and the a priori/a posteriori distinction together yield four types of propositions:

1. analytic a priori

2. synthetic a priori

3. analytic a posteriori

4. synthetic a posteriori

The ease of knowing analytic propositions

Part of Kant's argument in the Introduction to the Critique of Pure Reason involves arguing that there is no problem figuring out how knowledge of analytic propositions is possible. To know an analytic proposition, Kant argued, one need not consult experience. Instead, one need merely "extract from it, in accordance with the principle of contradiction, the required predicate..." (A7/B12) In analytic propositions, the predicate concept is contained in the subject concept. Thus in order to know that an analytic proposition is true, one need merely examine the concept of the subject. If one finds the predicate contained in the subject, the judgment is true. This article or section is incomplete and may require cleanup and/or expansion. ...

Thus, for example, one need not consult experience in order to determine whether "All bachelors are unmarried" is true. One need merely examine the subject concept ("bachelors") and see if the predicate concept "unmarried" is contained in it. And in fact, it is: "unmarried" is part of the definition of "bachelor," and so is contained within it. Thus the proposition "All bachelors are unmarried" can be known to be true without consulting experience.

It follows from this, Kant argued, first: all analytic propositions are a priori; there are no a posteriori analytic propositions. It follows, second: there is no problem understanding how we can know analytic propositions. We can know them because we just need to consult our concepts in order to determine that they are true.

Kant's analytic/synthetic distinction and the possibility of metaphysics

After ruling out the possibility of analytic a posteriori propositions, and explaining how we can obtain knowledge of analytic a posteriori propositions, Kant also explains how we can obtain knowledge of synthetic a posteriori propositions. That leaves only the question of how knowledge of synthetic a priori propositions is possible. This question is exceedingly important, Kant maintains, as all important metaphysical knowledge is of synthetic a priori propositions. If it is impossible to determine which synthetic a priori propositions are true, he argues, then metaphysics as a discipline is impossible. The remainder of the Critique of Pure Reason is devoted to examining whether and how knowledge of synthetic a priori propositions is possible. This article or section is incomplete and may require cleanup and/or expansion. ...

The origin of the logical positivists' definitions

Over a hundred years later, a group of philosophers took interest in Kant and his distinction between analytic and synthetic propositions: the logical positivists.

Part of Kant's examination of the possibility of synthetic a priori knowledge involved the examination of mathematical propositions, such as

• "7 + 5 = 12" (B15-16)
• "The shortest distance between two points is a straight line." (B16-17)

Kant maintained that mathematical propositions such as these were synthetic a priori propositions, and that we knew them. That they were synthetic, he thought, was obvious: the concept "12" is not contained within the concept "5," or the concept "7," or the concept "+." And the concept "straight line" is not contained with the concept "the shortest distance between two points." (B15-17) From this, Kant concluded that we had knowledge of synthetic a priori propositions. He went on to maintain that it was extremely important to determine how such knowledge was possible.

The logical positivists agreed with Kant that we had knowledge of mathematical truths, and further that mathematical propositions were a priori. However, they did not believe that any fancy metaphysics, such as the type Kant supplied, was necessary to explain our knowledge of mathematical truths. Instead, the logical positivists maintained that our knowledge of judgments like "all bachelors are unmarried" and our knowledge of mathematics (and logic) were basically the same: all proceeded from our knowledge of the meanings of terms or the conventions of language.

The logical positivists' definitions

Thus the logical positivists drew a new distinction, and, inheriting the terms from Kant, christened it the "analytic/synthetic distinction." They provided many different definitions, such as the following:

• 1. analytic proposition: a proposition whose truth depends solely on the meaning of its terms
• 2. analytic proposition: a proposition that is true by definition
• 3. analytic proposition: a proposition that is made true solely by the conventions of language

(While the logical positivists believed that the only necessarily true propositions were analytic, they did not define "analytic proposition" as "necessarily true proposition" or "proposition that is true in all possible worlds.")

Synthetic propositions were then defined as:

• synthetic proposition: a proposition that is not analytic

These definitions applied to all propositions, regardless of whether they were of subject-predicate form. Thus under these definitions, the proposition "It is raining or it is not raining," was classified as analytic, while under Kant's definitions it was neither analytic nor synthetic. And the proposition "7 + 5 = 12" was classified as analytic, while under Kant's definitions it was synthetic.

Kant vs. the logical positivists

If Kant and the logical positivists employed different definitions of the terms "analytic proposition" and "synthetic propositions," then what did they disagree about?

With regard to the issues related to the distinction between analytic and synthetic propositions, Kant and the logical positivists did not disagree about what "analytic" and "synthetic" meant. This would only be a terminological dispute. Instead, they disagreed about whether knowledge of mathematical and logical truths could be obtained merely through an examination of one's own concepts. The logical positivists thought yes. Kant thought no.

See also

• Quine's Rejection of the analytic-synthetic distinction

W.V. Quine Willard Van Orman Quine (June 25, 1908 – December 25, 2000), usually cited as W.V. Quine or W.V.O. Quine but known to his friends as Van, was one of the most influential American philosophers and logicians of the 20th century. ...

References

• Stanford Encyclopedia of Philosophy entry