I attend a small gathering of philosophers and guest speakers in my local town where we are sometimes lucky enough to get a professor from some university or college to come to give guest lectures.

Recently, we had one such lecturer, but after he was done giving his talk, I had to leave before the discussion began.

He talked heavily about Kant, and Kant's distinction between analytic and synthetic propositions.

I was going to ask him about this during our discussion period at the end of his talk, but considering I had to leave, I will ask you fine folk instead:

He had a slide with the following points:

  • Analytical a priori
  • Analytical a posteriori
  • Synthetic a priori
  • Synthetic a posteriori

But I never understood what these were, and/or the difference between them.

Could anyone kindly explain this to me, so that I don't have to look a fool at next weeks get-together?

  • 2
    You can see the first paragraphs here – Mauro ALLEGRANZA Nov 17 '14 at 17:18
  • @MauroALLEGRANZA That article explains the difference between analytical and synthetical, but not between analytical a priori and analytical a posteriori for example. If you understand the difference, would you mind explaining it to me? – ViRALiC Nov 17 '14 at 18:45
  • The class of analytical a posteriori is empty. Synthetic a posteriori is the "standard" empirical knowledge; the peculiar Kantian contribution is with synthetic a priori, that is the foundation for arithmetic and geometry. See Immanuel Kant: Metaphysics : "In an analytic claim, the predicate is contained within the subject. In the claim, "Every body occupies space," the property of occupying space is revealed in an analysis of what it means to be a body." 1/3 – Mauro ALLEGRANZA Nov 18 '14 at 8:04
  • "The subject of a synthetic claim, however, does not contain the predicate. In, "This tree is 120 feet tall," the concepts are synthesized or brought together to form a new claim that is not contained in any of the individual concepts. The Empiricists had not been able to prove synthetic a priori claims like "Every event must have a cause," because they had conflated "synthetic" and "a posteriori" as well as "analytic" and "a priori." Then they had assumed that the two resulting categories were exhaustive." 2/3 – Mauro ALLEGRANZA Nov 18 '14 at 8:04
  • 1
    And here: philosophy.stackexchange.com/q/474/2953 – Keelan Nov 18 '14 at 9:10

A proposition is analytic if true or false in virtue of its meaning only. The contradiction of an analytic truth is nonsense. Example: red is a colour. Bachelors are unmarried.

It is synthetic if true or false in virtue of the world. The contradiction of a synthetic truth is meaningful (albeit false). Example: human blood is red. John is a bachelor.

It is known a priori if you don't need experience to know its truth value (example: math and conceptual analysis), a posteriori otherwise (scientific truth, facts).

Intuitively, analytic and a priori seem to go together, and synthetic and a posteriori as well. You don't need experience if the meaning only is at stake, otherwise you do need input from the world. Kant however assumed that some mathematical and metaphysical statements are synthetic a priori, a priori because they are known by intuition only, yet synthetic because their contradiction is not absurd. Example: the axioms of euclidean geometry. One can formulate consistent non-euclidean geometries, but Euclid's axioms are true in virtue of physical space and known a-priori (because according to Kant, space is a condition of experience).

This assumption was challenged afterwards (notably, euclidean geometry is not the geometry of physical space, so math axioms might be pure linguistic conventions).

Finally Quine challenged the analytic synthetic distinction on the ground that one cannot distinguish clearly the linguistic and factual components of a sentence. Quine believed there is no such thing as a-priori meaning.

A third important, related dichotomy is necessity / contingency. Traditionnaly, empiricists conflate analycity and necessity but Kripke challenged this (he assumes some metaphysical necessities are synthetic, such as gold's atomic number).

I've never heard of analytic a posteriori, although Kripke gave examples of analytic contingency, such as the choice of a conventional measurement unit.

  • Analytic a posteriori are discussed here philosophy.stackexchange.com/questions/474/…, Kripke's example is "the evening star is the morning star". But according to Kant "it would be absurd to found an analytic judgment on experience." – Conifold Nov 26 '14 at 2:59
  • I don't agree. Kripke gave an example of a posteriori necessity not analycity. Logical empiricists conflated the two but not Kripke. The example of measuring unit I gave in my answer is actually a case of a priori contingency, but I think that for Kripke, analicity and a priori go together. – Quentin Ruyant Nov 26 '14 at 11:07

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