The analytic–synthetic distinction (also called the analytic–synthetic dichotomy) is a conceptual distinction, used primarily in philosophy to distinguish propositions into two types: analytic propositions and synthetic propositions. Analytic propositions are true simply by virtue of their meaning, while synthetic propositions are not. However, philosophers have used the terms in very different ways. Furthermore, philosophers have debated whether there is a legitimate distinction since Willard Van Orman Quine's critique of the distinction in his 1951 article "Two Dogmas of Empiricism".
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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 (1781/1998, A6-7/B10-11). There, he restricts his attention to affirmative subject-predicate judgments, and defines "analytic proposition" and "synthetic proposition" as follows:
Examples of analytic propositions, on Kant's definition, include:
Kant's own example is:
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 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:
Kant's own example is:
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 "unhappy"; "unhappy" 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."
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:
Examples of a priori propositions include:
The justification of these propositions does not depend upon experience: One does not need to consult experience to determine whether all bachelors are unmarried, or whether 7 + 5 = 12. (Of course, as Kant would have granted, experience is required to know 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:
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:
Kant thought the third type is self-contradictory, so he discusses only three types as components of his epistemological framework. However, Stephen Palmquist treats the analytic a posteriori not only as a valid epistemological classification but also as the most important of the four for philosophy.[1]
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 to take the subject and "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, to know 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.
Thus, for example, one need not consult experience 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.
After ruling out the possibility of analytic a posteriori propositions, and explaining how we can obtain knowledge of analytic a priori 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.
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
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 "12" is not contained within the concept "5," or the concept "7," or the concept "+." And the concept "straight line" is not contained within the concept "the shortest distance between two points." (B15-17) From this, Kant concluded that we have knowledge of synthetic a priori propositions. He went on to maintain that it is extremely important to determine how such knowledge is possible.
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 emphasised 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 recognisable as tautologous and therefore analytic from its logical form: any statement of the form "All X that are (F and G) are F". This expanded idea of analyticity was able to show that all Kant's examples of arithmetical and geometrical truths are analytical apriori truths not synthetic apriori 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"[2]
(Here "logical empiricist" is a synonym for "logical positivist")
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 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 by new experiences. Our solution ... consisted in asserting empiricism only for factual truth. By contrast, the truths of logic and mathematics are not in need of confirmation by observations".[3]
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:
(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:
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.
With regard to the issues related to the distinction between analytic and synthetic propositions, Kant and the logical positivists agreed 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 that it could be. Kant thought that it could not.
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 a satisfactory 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 and Berit Brogaard.
Any given sentence, for example, the words,
is taken to express two distinct propositions, often referred to as a primary intension and a secondary intension, which together compose its meaning.[4]
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, and 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 means H2O in every world.
If two-dimensionalism is workable it solves some very important problems in the philosophy of language. Saul Kripke has argued that "Water is H2O" is an example of the necessary a posteriori, since we had to discover that water was H2O, but given that it is true (which it is) it cannot be false. It would be absurd to claim that something that is water is not H2O, for these are known to be identical.
In 1951, W.V. Quine published the essay "Two Dogmas of Empiricism" in which he argued that the analytic–synthetic distinction is untenable. In the first paragraph, Quine takes the distinction to be the following:
In short, Quine argues that the notion of an analytic proposition requires a notion of synonymy, but these notions are parasitic on one another. Thus, there is no non-circular (and so no tenable) way to ground the notion of analytic propositions.
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 (e.g., Boghossian, 1996) 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 Word and Object was released. In the book Quine presented his theory of indeterminacy of translation.
In "Speech acts", John R. Searle argues that from the difficulties encoutered in trying to explicate analiticity by appeal to specific criteria, it does not follow that the notion itself is void.[5] Considering the way which we would test any proposed list of criteria, which is by comparing their extension to the set of analytic statements, it would follow that any explication of what analyticity means presupposes that we already have at our disposal a working notion of analyticity.
In "'Two Dogmas' revisited", Hilary Putnam argues that Quine is attacking two different notions. Analytic truth defined as a true statement derivable from a tautology by putting synonyms for synonyms are 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 apriority and sketch a methodology without it.[6]
Jerrold Katz, an onetime associate of Noam Chomsky's, countered the arguments of Two Dogmas directly by trying to define analyticity non-circularly on the syntactical features of sentences.[7][8][9]
In his book Philosophical Analysis in the Twentieth Century, Volume 1 : The Dawn of Analysis, Scott Soames (pp 360–361) has pointed out that Quine's circularity argument needs two of the logical positivists' central theses to be effective:
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.
Novelist and philosopher Ayn Rand was particularly critical of the analytic-synthetic distinction. In her 1968 essay, Introduction to Objectivist Epistemology, she stated that
the “analytic-synthetic” dichotomy which, by a route of tortuous circumlocutions and equivocations, leads to the dogma that a “necessarily” true proposition cannot be factual, and a factual proposition cannot be “necessarily” true.
She claimed that the dichotomy forces philosophers to subjectively separate propositions into definitions, which are true, but factually irrelevant, and attributes, which are empirically factual, but may or may not be true under certain circumstances. This distinction leads people into believing that universal and fundamental truths such as "man is a rational animal" are mere definitions and logically unimportant, while contingent, empirical truths such as "dogs have fur" are the only valid kind of statements.
Objectivist philosopher Leonard Peikoff, in his essay “The Analytic-Synthetic Dichotomy,” expands upon 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 the real entities referred to by a concept (which he calls "referents" or "existents") are either included or excluded from the concept . Instead, a concept is an ever-growing hierarchy of referents that are synthesized as part of the process by which knowledge about the concept is acquired. 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 believes that there is no distinction between "necessary" and "contingent" truths, that all truths are learned and validated by the same process of observation. Such distinctions emanating from the analytic-synthetic dichotomy lead to other false and artificial splits, such as logical truth vs. factual truth, logically possible vs. empirically possible, and a priori vs. the a posteriori.