The analytic–synthetic distinction (also called the analytic–synthetic dichotomy) is a semantic distinction, used primarily in philosophy to distinguish propositions (in particular, statements that are affirmative subject–predicate judgments) 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.
1.1 Conceptual containment 1.2 Kant's version and the a priori / a posteriori distinction 1.3 The ease of knowing analytic propositions 1.4 The possibility of metaphysics
2 Logical positivists
2.1 Frege and
3 Two-dimensionalism 4 Quine's criticisms
5 Peikoff's criticisms 6 See also 7 Footnotes 8 References and further reading 9 External links
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 but related
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," that is, occupy space. (A7/B11)
Each of these statements is an affirmative subject-predicate judgment, and, in each, the predicate concept is contained within the subject concept. The concept "bachelor" contains the concept "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 alone." "All creatures with hearts have kidneys."
Kant's own example is:
"All bodies are heavy," that is, have mass. (A7/B11)
As with the previous examples classified as analytic propositions, each of these new statements 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 "alone"; "alone" 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". Kant's version and the a priori / a posteriori distinction Main article: A priori and a posteriori In the Introduction to the Critique of Pure Reason, Kant contrasts his distinction between analytic and synthetic propositions with another distinction, the distinction between a priori and a posteriori propositions. He defines these terms as follows:
a priori proposition: a proposition whose justification does not rely upon experience. Moreover, the proposition can be validated by experience, but is not grounded in experience. Therefore, it is logically necessary. a posteriori proposition: a proposition whose justification does rely upon experience. The proposition is validated by, and grounded in, experience. Therefore, it is logically contingent.
Examples of a priori propositions include:
"All bachelors are unmarried." "7 + 5 = 12."
The justification of these propositions does not depend upon experience: one need not consult experience to determine whether all bachelors are unmarried, nor whether 7 + 5 = 12. (Of course, as Kant would grant, experience is required to understand the concepts "bachelor", "unmarried", "7", "+" and so forth. However, the a priori / a posteriori distinction as employed here by Kant refers not 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 include:
"All bachelors are unhappy." "Tables exist."
Both of these propositions are a posteriori: any justification of them would require one's experience. The analytic/synthetic distinction and the a priori / a posteriori distinction together yield four types of propositions:
analytic a priori synthetic a priori analytic a posteriori synthetic a posteriori
Kant posits the third type as obviously self-contradictory. Ruling it
out, he discusses only the remaining three types as components of his
epistemological framework—each, for brevity's sake, becoming,
respectively, "analytic", "synthetic a priori", and "empirical" or "a
posteriori" propositions. This triad will account for all propositions
The ease of knowing analytic propositions
Part of Kant's argument in the Introduction to the Critique of Pure
"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 are synthetic a priori propositions, and that we know them. That they are synthetic, he thought, is obvious: the concept "equal to 12" is not contained within the concept "7 + 5"; and the concept "straight line" is not contained within the concept "the shortest distance between two points". From this, Kant concluded that we have knowledge of synthetic a priori propositions. Gottlob Frege's notion of analyticity included a number of logical properties and relations beyond containment: symmetry, transitivity, antonymy, or negation and so on. He had a strong emphasis on formality, in particular formal definition, and also emphasized the idea of substitution of synonymous terms. "All bachelors are unmarried" can be expanded out with the formal definition of bachelor as "unmarried man" to form "All unmarried men are unmarried", which is recognizable as tautologous and therefore analytic from its logical form: any statement of the form "All X that are (F and G) are F". Using this particular expanded idea of analyticity, Frege concluded that Kant's examples of arithmetical truths are analytical a priori truths and not synthetic a priori truths.
Thanks to Frege's logical semantics, particularly his concept of analyticity, arithmetic truths like "7+5=12" are no longer synthetic a priori but analytical a priori truths in Carnap's extended sense of "analytic". Hence logical empiricists are not subject to Kant's criticism of Hume for throwing out mathematics along with metaphysics.
(Here "logical empiricist" is a synonym for "logical positivist".) The origin of the logical positivist's distinction The logical positivists agreed with Kant that we have knowledge of mathematical truths, and further that mathematical propositions are a priori. However, they did not believe that any complex metaphysics, such as the type Kant supplied, are 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) are in the basic sense the same: all proceeded from our knowledge of the meanings of terms or the conventions of language.
Since empiricism had always asserted that all knowledge is based on experience, this assertion had to include knowledge in mathematics. On the other hand, we believed that with respect to this problem the rationalists had been right in rejecting the old empiricist view that the truth of "2+2=4" is contingent on the observation of facts, a view that would lead to the unacceptable consequence that an arithmetical statement might possibly be refuted tomorrow by new experiences. Our solution, based upon Wittgenstein's conception, consisted in asserting the thesis of empiricism only for factual truth. By contrast, the truths of logic and mathematics are not in need of confirmation by observations, because they do not state anything about the world of facts, they hold for any possible combination of facts. — Rudolf Carnap, Autobiography: §10: Semantics, p. 64
Logical positivist definitions Thus the logical positivists drew a new distinction, and, inheriting the terms from Kant, named it the "analytic/synthetic distinction". They provided many different definitions, such as the following:
analytic proposition: a proposition whose truth depends solely on the meaning of its terms analytic proposition: a proposition that is true (or false) by definition analytic proposition: a proposition that is made true (or false) 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 for Kant it was analytic by virtue of its logical
form. And the proposition "7 + 5 = 12" was classified as analytic,
while under Kant's definitions it was synthetic.
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 a puzzle
that has plagued philosophy for some time, namely: 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
"Water is H2O"
is taken to express two distinct propositions, often referred to as a
primary intension and a secondary intension, which together compose
The primary intension of a word or sentence is its sense, i.e., is the
idea or method by which we find its referent. The primary intension of
"water" might be a description, such as watery stuff. The thing picked
out by the primary intension of "water" could have been otherwise. For
example, on some other world where the inhabitants take "water" to
mean watery stuff, but, where the chemical make-up of watery stuff is
not H2O, it is not the case that water is H2O for that world.
The secondary intension of "water" is whatever thing "water" happens
to pick out in this world, whatever that world happens to be. So if we
assign "water" the primary intension watery stuff then the secondary
intension of "water" is H2O, since H2O is watery stuff in this world.
The secondary intension of "water" in our world is H2O, which is H2O
in every world because unlike watery stuff it is impossible for H2O to
be other than H2O. When considered according to its secondary
intension, "Water is H2O" is true in every world.
If two-dimensionalism is workable it solves some very important
problems in the philosophy of language.
analytic propositions – propositions grounded in meanings, independent of matters of fact. synthetic propositions – propositions grounded in fact.
Quine's position denying the analytic-synthetic distinction is summarized as follows:
It is obvious that truth in general depends on both language and extralinguistic fact. ... Thus one is tempted to suppose in general that the truth of a statement is somehow analyzable into a linguistic component and a factual component. Given this supposition, it next seems reasonable that in some statements the factual component should be null; and these are the analytic statements. 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. — Willard v. O. Quine, "Two Dogmas of Empiricism", p. 64
To summarize Quine's argument, the notion of an analytic proposition
requires a notion of synonymy, but establishing synonymy inevitably
leads to matters of fact – synthetic propositions. Thus, there
is no non-circular (and so no tenable) way to ground the notion of
While Quine's rejection of the analytic–synthetic distinction is
widely known, the precise argument for the rejection and its status is
highly debated in contemporary philosophy. However, some (for example,
Boghossian) argue that Quine's rejection of the distinction is
still widely accepted among philosophers, even if for poor reasons.
Paul Grice and
P. F. Strawson criticized "Two Dogmas" in their 1956
article "In Defense of a Dogma". Among other things, they argue
that Quine's skepticism about synonyms leads to a skepticism about
meaning. If statements can have meanings, then it would make sense to
ask "What does it mean?". If it makes sense to ask "What does it
mean?", then synonymy can be defined as follows: Two sentences are
synonymous if and only if the true answer of the question "What does
it mean?" asked of one of them is the true answer to the same question
asked of the other. They also draw the conclusion that discussion
about correct or incorrect translations would be impossible given
Quine's argument. Four years after Grice and Strawson published their
paper, Quine's book
It seems to me there is as gross a distinction between 'All bachelors are unmarried' and 'There is a book on this table' as between any two things in this world, or at any rate, between any two linguistic expressions in the world; — Hilary Putnam, Philosophical Papers, p. 36
Analytic truth defined as a true statement derivable from a tautology
by putting synonyms for synonyms is near Kant's account of analytic
truth as a truth whose negation is a contradiction. Analytic truth
defined as a truth confirmed no matter what, however, is closer to one
of the traditional accounts of a priori. While the first four sections
of Quine's paper concern analyticity, the last two concern a priority.
Putnam considers the argument in the two last sections as independent
of the first four, and at the same time as Putnam criticizes Quine, he
also emphasizes his historical importance as the first top rank
philosopher to both reject the notion of a priority and sketch a
methodology without it.
Jerrold Katz, a one-time associate of Noam Chomsky, countered the
arguments of "Two Dogmas" directly by trying to define analyticity
non-circularly on the syntactical features of sentences.
All necessary (and all a priori) truths are analytic
Analyticity is needed to explain and legitimate necessity.
It is only when these two theses are accepted that Quine's argument holds. It is not a problem that the notion of necessity is presupposed by the notion of analyticity if necessity can be explained without analyticity. According to Soames, both theses were accepted by most philosophers when Quine published "Two Dogmas". Today, however, Soames holds both statements to be antiquated. He says: "Very few philosophers today would accept either [of these assertions], both of which now seem decidedly antique." Peikoff's criticisms Philosopher Leonard Peikoff, in his essay "The Analytic-Synthetic Dichotomy", expands upon Ayn Rand's analysis. He posits that:
The theory of the analytic-synthetic dichotomy presents men with the following choice: If your statement is proved, it says nothing about that which exists; if it is about existents, it cannot be proved. If it is demonstrated by logical argument, it represents a subjective convention; if it asserts a fact, logic cannot establish it. If you validate it by an appeal to the meanings of your concepts, then it is cut off from reality; if you validate it by an appeal to your percepts, then you cannot be certain of it.
To Peikoff, the critical question is: What is included in the meaning of a concept? He rejects the idea that some of the characteristics of a concept's referents are excluded from the concept. Applying Rand's theory that a concept is a "mental integration" of similar existents, treated as "units", he argues that concepts stand for and mean the actual existents, including all their characteristics, not just those used to pick out the referents or define the concept. He states,
Since a concept is an integration of units, it has no content or meaning apart from its units. The meaning of a concept consists of the units — the existents — which it integrates, including all the characteristics of these units.... The fact that certain characteristics are, at a given time, unknown to man, does not indicate that these characteristics are excluded from the entity — or from the concept.
Furthermore, he argues that there is no valid distinction between "necessary" and "contingent" facts, and that all truths are learned and validated by the same process: the application of logic to perceptual data. Associated with the analytic-synthetic dichotomy are a cluster of other divisions that Objectivism also regards as false and artificial, such as logical truth vs. factual truth, logically possible vs. empirically possible, and a priori vs. the a posteriori. See also
Holophrastic indeterminacy Internal–external distinction Sense and reference Two-dimensionalism
^ Rey, Georges. "The Analytic/Synthetic Distinction". The Stanford
References and further reading
Baehr, Jason S. (October 18, 2006). J. Fieser; B. Dowden, eds. "A
Priori and A Posteriori". The Internet Encyclopedia of
Boghossian, Paul. (1996). "Analyticity Reconsidered". Nous, Vol. 30,
No. 3, pp. 360–391.
Cory Juhl; Eric Loomis (2009). Analyticity. Routledge.
Kant, Immanuel. (1781/1998). The Critique of Pure Reason. Trans. by P.
Guyer and A.W. Wood, Cambridge University Press .
Rey, Georges. (2003). "The Analytic/Synthetic Distinction". The
Stanford Encyclopedia of Philosophy, Edward Zalta (ed.).
Soames, Scott (2009). "Chapter 14: Ontology, Analyticity and Meaning:
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