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The analytic-synthetic distinction is a conceptual distinction, used primarily in philosophy to distinguish propositions into two types: analytic propositions and synthetic propositions. Analytic propositions are those which are true simply in virtue of their meaning while synthetic propositions are not, however, philosophers have used the terms in very different ways. Furthermore, whether there is a legitimate distinction to be made has been widely debated among philosophers since W. V. Quine's critique of the distinction in the middle of the twentieth century.


Conceptual containment

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:

  • 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 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 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 version

One common criticism is that Kant's notion of "conceptual containment" is highly metaphorical, and thus unclear.

Another 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.

Kant's version 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 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
  • 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 are 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

Ludwig von Mises' response to the Kantian challenge

The economists Ludwig von Mises and Hans-Hermann Hoppe developed their own account of the a priori.


1.- We have senses.

2.- We have a volitional consciousness, and self-awareness.

3.- When exploring the external world we hypothesize about what we sense and measure. Given that we may never know ultimate causes we form a theory or hypothesis until new data no longer fits the model and then we build a new one.

To quote Hoppe:

"The second assumption of empiricism formulates the extension and application of the first assumption to problems of causality, causal explanation, and prediction. According to empiricism, to explain causally or predict a real phenomenon is to formulate a statement of either the type "if A, then B" or, should the variables allow quantitative measurement, "if an increase (decrease) in A, then an increase (decrease) in B."

As a statement referring to reality (with A and B being real phenomena), its validity can never be established with certainty, that is, by examining the proposition alone, or of any other proposition from which the one in question could be logically deduced. The statement will always be and always remain hypothetical, its veracity depending on the outcome of future observational experiences which cannot be known in advance. Should experience confirm a hypothetical causal explanation, this would not prove that the hypothesis was true. Should one observe an instance where B indeed followed A as predicted, it verifies nothing. A and B are general, abstract terms, or in philosophical terminology, universals, which refer to events and processes of which there are (or might be, in principle) an indefinite number of instances. Later experiences could still possibly falsify it.

And if an experience falsified a hypothesis, this would not be decisive either. For if it was observed that A was not followed by B, it would still be possible that the hypothetically related phenomena were causally linked. It could be that some other circumstance or variable, heretofore neglected and uncontrolled, had simply prevented the hypothesized relationship from actually being observed. At the most, falsification only proves that the particular hypothesis under investigation was not completely correct as it stood. It needs some refinement, some specification of additional variables which have to be watched for and controlled so that we might observe the hypothesized relationship between A and B. But, to be sure, a falsification would never prove once and for all that a relationship between some given phenomena did not exist, just as a confirmation would never definitively prove that it did exist."

4.- In human action, actors choose, err, succeed and have purpose. They think in terms of cause and effect, and this is proven by the fact that acting means intervening in what otherwise would have been the chain of causality --wishing for an outcome different from the one expected had no action been taken.

5.- Humans can investigate the external world because they have evolved to understand reality in order to constantly improve their lifestyle. Our brains developed through evolution in response to stimuli, from cells to primates, through varying degrees of awareness.

6.- Reality can be understood only in terms of cause and effect and correlations that Aristotle referred to the Law of Identity. "The apple falls from the tree" means understanding or *assigning* the label of "apple", "falling", and "tree" to very specific objects and phenomena.

7.- The human mind understands and can investigate external, non-human phenomena because it understands cause and effect, relations, identity, etc. These are aspects or categories of the human mind that have to match external reality successfully for there to be a proper understanding of causality.

8.- The human mind fits reality since it itself is an evolutionary byproduct of reality or, more specifically, because consciousness has degrees of self-awareness and our self-awareness level is sufficient for us to question our own awareness and ponder its significance and implications.

9.- Self-awareness provides us with the tools to assign correctly (send rockets to the moon, predict price control effects) the causes, effects and correlations around us.

10.- The bridge between the mind and external empirical observations is the synthetic a priori since it is not analytical or a posteriori, neither idealist nor tautological, nor empirical in the "using the senses" meaning of the word. Explains Hoppe:

"Mises points out that both requirements are fulfilled by what he terms the axiom of action, i.e., the proposition that humans act, that they display intentional behavior. Obviously, this axiom is not derived from observation—there are only bodily movements to be observed but no such thing as actions—but stems instead from reflective understanding. And this understanding is indeed of a self-evident proposition. For its truth cannot be denied, since the denial would itself have to be categorized as an action. But is this not just plain trivial? And what has economics got to do with this? Of course, it had previously been recognized that economic concepts such as prices, costs, production, money, credit, etc., had something to do with the fact that there were acting people. But that all of economics could be grounded in and reconstructed based on such a trivial proposition and how, is certainly anything but clear. It is one of Mises's greatest achievements to have shown precisely this: that there are insights implied in this psychologically speaking trivial axiom of action that were not themselves psychologically self-evident as well; and that it is these insights which provide the foundation for the theorems of economics as true a priori synthetic propositions."


The Misesian methodological dualism implies that it is counterproductive to try to apply empirical techniques to the study of human action’s basic properties, laws and principles, as one may think it is necessary for the natural sciences. This methodological dualism, the link between empirical reality and a priori knowledge, provides a unique insight based on purposeful action by men. Responding to Kant, the synthetic/analytic and a priori/a posterior classification was reformulated and grounded on categories of action by Mises, so what seemed to be idealism to Kantians and Randians alike, in fact turns out to be an epistemological tool. The validity of the synthetic a priori proposition as a method for validating knowledge proved essential in the development of the Austrian school of economics. Indeed, the entire work of Mises’s version of Economics is based on an a priori method of axiomatic-deductive reasoning.

In the realm where there is no action — no purposeful behavior — we can undertake the study of such phenomena using empirical tools in varying degrees. But even those, vastly used throughout the ages, require “pure” tools such as math, logic and geometry based on a — now evident — synthetic a priori foundation. That Praxeology itself is the basis for the synthetic a priori itself has been further developed by Hoppe. Thus, Praxeology provides their cognitive validity too, through the Misesian matching of the mind with reality, as “pure” sciences, neither requiring experimental validation nor open to Popper’s idea of falsification, but merely being illustrated by experiments and history at their core.

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.

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.

The possibility of metaphysics

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.

The logical positivists

The origin of the logical positivists' distinction

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 within 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 proposition", 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.

Quine's criticism

In 1951, W.V. Quine published his famous 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:

  • analytic propositions - propositions grounded in meanings, independent of matters of fact.
  • synthetic propositions - propositions grounded in fact.

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.

References and further reading

See also

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