Theanalytic–synthetic distinction is asemantic distinction used primarily inphilosophy to distinguish between propositions (in particular, statements that are affirmativesubject–predicate judgments) that are of two types:analytic propositions andsynthetic propositions. Analytic propositions are true or not true solely by virtue of their meaning, whereas synthetic propositions' truth, if any, derives from how their meaning relates to the world.[1]
While the distinction was first proposed byImmanuel Kant, it was revised considerably over time, and different philosophers have used the terms in very different ways. Furthermore, some philosophers (starting withWillard Van Orman Quine) have questioned whether there is even a clear distinction to be made between propositions which are analytically true and propositions which are synthetically true.[2] Debates regarding the nature and usefulness of the distinction continue to this day in contemporaryphilosophy of language.[2]
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The philosopherImmanuel Kant uses the terms "analytic" and "synthetic" to divide propositions into two types. Kant introduces the analytic–synthetic distinction in the Introduction to hisCritique of Pure Reason (1781/1998, A6–7/B10–11). There, he restricts his attention to statements that are 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 statements is an affirmative subject–predicate judgment, and, in each, the predicate concept iscontained 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:
Kant's own example is:
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 thedefinition 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".So the philosophical issue is: What kind of statement is "Language is used to transmit meaning"?
In the Introduction to theCritique of Pure Reason, Kant contrasts his distinction between analytic and synthetic propositions with another distinction, the distinction betweena priori anda posteriori propositions. He defines these terms as follows:
Examples ofa priori propositions include:
The justification of these propositions does not depend upon experience: one need not consult experience to determine whether all bachelors are unmarried, nor whether7 + 5 = 12. (Of course, as Kant would grant, experience is required to understand the concepts "bachelor", "unmarried", "7", "+" and so forth. However, thea priori–a posteriori distinction as employed here by Kant refers not to theorigins of the concepts but to thejustification of the propositions. Once we have the concepts, experience is no longer necessary.)
Examples ofa posteriori propositions include:
Both of these propositions area posteriori: any justification of them would require one's experience.
The analytic–synthetic distinction and thea priori–a posteriori distinction together yield four types of propositions:
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", "synthetica priori", and "empirical" or "a posteriori" propositions. This triad accounts for all propositions possible. Examples of analytic and examples ofa posteriori statements have already been given, for synthetica priori propositions he gives those in mathematics and physics.
Part of Kant's argument in the Introduction to theCritique 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 needs merely to take the subject and "extract from it, in accordance with the principle of contradiction, the required predicate" (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 area priori; there are noa posteriori analytic propositions. It follows, second: There is no problem understanding how we can know analytic propositions; we can know them because we only need to consult our concepts in order to determine that they are true.
After ruling out the possibility of analytica posteriori propositions, and explaining how we can obtain knowledge of analytica priori propositions, Kant also explains how we can obtain knowledge of synthetica posteriori propositions. That leaves only the question of how knowledge of synthetica priori propositions is possible. This question is exceedingly important, Kant maintains, because all scientific knowledge (for him Newtonian physics and mathematics) is made up of synthetica priori propositions. If it is impossible to determine which synthetica priori propositions are true, he argues, then metaphysics as a discipline is impossible. The remainder of theCritique of Pure Reason is devoted to examining whether and how knowledge of synthetica priori propositions is possible.[3]
Over a hundred years later, a group of philosophers took interest in Kant and his distinction between analytic and synthetic propositions: thelogical positivists.
Part of Kant's examination of the possibility of synthetica priori knowledge involved the examination of mathematical propositions, such as
Kant maintained that mathematical propositions such as these are synthetica 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 synthetica priori propositions.
Although not strictly speaking a logical positivist,Gottlob Frege's notion of analyticity influenced them greatly. It included a number of logical properties and relations beyond containment:symmetry,transitivity,antonymy, ornegation 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 "AllX that are (F andG) areF". Using this particular expanded idea of analyticity, Frege concluded that Kant's examples of arithmetical truths are analyticala priori truths andnot synthetica priori truths.
Thanks to Frege's logical semantics, particularly his concept of analyticity, arithmetic truths like "7+5=12" are no longer synthetica priori but analyticala priori truths inCarnap's extended sense of "analytic".Hence logical empiricists are not subject to Kant's criticism of Hume for throwing out mathematics along with metaphysics.[4]
(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 area 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 thatall 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 uponWittgenstein'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.[5][6]
— Rudolf Carnap, "Autobiography": §10: Semantics, p. 64
Thus the logical positivists drew a new distinction, and, inheriting the terms from Kant, named it the "analytic-synthetic distinction".[7] 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 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 tosemantics inanalytic philosophy. It is a theory of how to determine thesense and reference of aword and thetruth-value of asentence. It is intended to resolve a puzzle that has plagued philosophy for some time, namely: How is it possible to discover empirically that anecessary truth istrue? Two-dimensionalism provides an analysis of the semantics of words and sentences that makes sense of this possibility. The theory was first developed byRobert Stalnaker, but it has been advocated by numerous philosophers since, includingDavid Chalmers andBerit Brogaard.
Any given sentence, for example, the words,
is taken to express two distinctpropositions, often referred to as aprimary intension and asecondary intension, which together compose itsmeaning.[8]
The primaryintension of a word or sentence is itssense, i.e., is the idea or method by which we find its referent. The primary intension of "water" might be a description, such aswatery 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 meanwatery 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.
Thesecondary intension of "water" is whatever thing "water" happens to pick out inthis world, whatever that world happens to be. So if we assign "water" the primary intensionwatery stuff then the secondary intension of "water" is H2O, since H2O iswatery stuff in this world. The secondary intension of "water" in our world is H2O, which is H2O in every world because unlikewatery 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.Saul Kripke has argued that "Water is H2O" is an example of thenecessarya posteriori, since we had to discover that water was H2O, but given that it is true, it cannot be false. It would be absurd to claim that something that is water is not H2O, for these are known to beidentical.
Rudolf Carnap was a strong proponent of the distinction between what he called "internal questions", questions entertained within a "framework" (like a mathematical theory), and "external questions", questions posed outside any framework – posed before the adoption of any framework.[9][10][11] The "internal" questions could be of two types:logical (or analytic, or logically true) andfactual (empirical, that is, matters of observation interpreted using terms from a framework). The "external" questions were also of two types: those that were confused pseudo-questions ("one disguised in the form of a theoretical question") and those that could be re-interpreted as practical, pragmatic questions about whether a framework under consideration was "more or less expedient, fruitful, conducive to the aim for which the language is intended".[9] The adjective "synthetic" was not used by Carnap in his 1950 workEmpiricism, Semantics, and Ontology.[9] Carnap did define a "synthetic truth" in his workMeaning and Necessity: a sentence that is true, but not simply because "the semantical rules of the system suffice for establishing its truth".[12]
The notion of a synthetic truth is of something that is true both because of what it means and because of the way the world is, whereas analytic truths are true in virtue of meaning alone. Thus, what Carnap calls internalfactual statements (as opposed to internallogical statements) could be taken as being also synthetic truths because they requireobservations, but some external statements also could be "synthetic" statements and Carnap would be doubtful about their status. The analytic–synthetic argument therefore is not identical with theinternal–external distinction.[13]
In 1951,Willard Van Orman Quine published the essay "Two Dogmas of Empiricism" in which he argued that the analytic–synthetic distinction is untenable.[14] The argument at bottom is that there are no "analytic" truths, but all truths involve an empirical aspect. In the first paragraph, Quine takes the distinction to be the following:
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 itsa 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.[15]
— 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 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 (for example,Paul Boghossian)[16] argue that Quine's rejection of the distinction is still widely accepted among philosophers, even if for poor reasons.
Paul Grice andP. F. Strawson criticized "Two Dogmas" in their 1956 article "In Defense of a Dogma".[17] Among other things, they argue that Quine'sskepticism 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 bookWord and Object was released. In the book Quine presented his theory ofindeterminacy of translation.
InSpeech Acts,John Searle argues that from the difficulties encountered in trying to explicate analyticity by appeal to specific criteria, it does not follow that the notion itself is void.[18] Considering the way that 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:[19]
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;[20]
— Hilary Putnam,Philosophical Papers, p. 36
Analytic truth defined as a true statement derivable from atautology 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 ofa 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.[21]
Jerrold Katz, a one-time associate ofNoam Chomsky, countered the arguments of "Two Dogmas" directly by trying to define analyticity non-circularly on the syntactical features of sentences.[22][23][24] Chomsky himself critically discussed Quine's conclusion, arguing that it is possible to identify some analytic truths (truths of meaning, not truths of facts) which are determined by specific relations holding among some innate conceptual features of the mind or brain.[25]
InPhilosophical Analysis in the Twentieth Century, Volume 1: The Dawn of Analysis,Scott Soames pointed out that Quine's circularity argument needs two of the logical positivists' central theses to be effective:[26]
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."[26]
This distinction was imported from philosophy into theology, withAlbrecht Ritschl attempting to demonstrate that Kant's epistemology was compatible with Lutheranism.[27]
The usual charge against Carnap's internal/external distinction is one of 'guilt by association with analytic/synthetic'. But it can be freed of this association
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