I'm asking here about what exactly constitutes aposteriori statement.

The idea is that an aposteriori statement is one whose truth necessitate experiential evidence to be established. like in empirical sciences. But are there other examples of aposteriori justfication other than empirical evidence. For example suppose one presents an axiomatic theory about ethics, now if acceptance of the axioms of this theory is subject to agreement with the morality of the majority of human authorities on that subject as a final arbiter, then would such a system be considered as an aposteiori justified axiomatic system? Similar thing about for example an axiomatic system about some language, or about music, or even about some art, at the end the axioms would be subject to the agreement with human tastes, inclinations, etc..that are experiencing that language, music or art. So there is some experience deciding what kind of axioms to be chosen for a theory to be acceptable in those fields, they are not just accepted apriori depending on capturing of some intuitive meaning, or being analytic of that meaning, or some other apriori pragmatic purpose. Would those systems qualify as aposteriori justified, even though it is not quite empirical the kind of justification that is involved with them?

  • I am puzzled as to how the "experiencing" of language, music or art is not empirical. Isn't the "agreement with the majority of human authorities" what psychologists and sociologists conduct empirical studies for? Palmquist did advocate "a posteriori analyticity", see What are examples of analytic a posteriori knowledge? which might be in the vicinity, there are also distinctions between directly and indirectly empirical (relative a priori) statements, the latter condensing empirical experience over longer time periods.
    – Conifold
    Commented Jun 7, 2018 at 23:28
  • I thought that empirical evidence involves rigorous ways of experiential encounter whereby experiments and observations are conducted under specific controlled conditions, I don't think we could raise evidence of that rigorous kind on a AXIOMATIC theories about ethics, art, etc.., yes definitely there are tastes, preferences, moralities of humans into play here, but even in the most pure formal system (the apriori ones) there are imaginative, intuitive, conceptual experiences involved and much of those are grounded in experience.
    – Zuhair
    Commented Jun 8, 2018 at 7:00
  • You may need to provide a precise definition of empirical to get a precise answer. As mentioned, Palmquist argues for analytic a posteriori. But also, Kripke suggests the possibility of necessary a posteriori (in Identity and Necessity), and Kant suggests a "transcendental" form of justification (iep.utm.edu/apriori). Your examples of axiomatic ethics or aesthetics seems like a variation on Platonic forms, knowledge of which is presumably a posteriori and perhaps could be argued to be non-empirical.
    – Greg S
    Commented Jun 9, 2018 at 3:27
  • It seems that you are thinking of hard sciences only, "experiments and observations under specific controlled conditions" are often unrealistic in social and human sciences (think of history or economics), this does not make them any less empirical. And there is little point to "axiomatic" theories there. Unlike both types of sciences ethics, art, etc., are not after "truth about the world", so "justification" has a very different meaning in them, if any. As for theories about ethics, art, etc., those belong to descriptive empirical science just like any other study of human artifacts.
    – Conifold
    Commented Jun 9, 2018 at 19:58

2 Answers 2


Most people would consider the concept of non-empirical a posteriori impossible.

A posteriori knowledge is by definition empirical: "A posteriori" means roughly "after" - here referring to the fact that such knowledge came after we experience the world.

Note that the two examples you give:

subject to agreement with the morality of the majority of human authorities....


would be subject to the agreement with human tastes, inclinations, etc..that are experiencing that language, music or art.

Are both things that you have to go out into the world and assess through experience (by interviewing people, studying government documents and critical reviews), i.e. they would constitute empirical knowledge, not theoretical knowledge.

You seem to confusing hard sciences (i.e. physics, chemistry, biology, etc...) with empirical sciences (pretty much any science is empirical - that is what distinguishes science from mathematics or philosophy).

  • I prefer to define science as a Factual discipline, and by then we can have non-empirical sciences of which part of mathematics and logic are examples, an perhaps even some sectors of philosophy that might emerge.
    – Zuhair
    Commented Jun 8, 2018 at 6:46
  • My problem is that even some pure formal theories, which are labeled apriori, are subject to this "agreement" criterion for their acceptance? take for example "classical logic", not everyone agrees to it, so its axioms are accepted just because the majority of logicians preferred it. So in what sense I would consider the agreement condition by authorities, that I've spoken about in the head post,as constituting a kind of "empirical" evidence for the truth of the proposed axiomatic system?
    – Zuhair
    Commented Jun 8, 2018 at 6:52
  • @Zuhair you seem to be mixing the colloquial definitions of "fact" and "science" with the philosophical ones. In Epistemology, a fact is considered to a be a true statement that is verifiable empirically, and science is the study of empirical truths. Math and logic are not considered part of science but their own separate domain - the statements of math and logic are not falsifiable the way the statements of physics and chemistry are. See Hume's fork and Karl Popper's demarcation criterion. Commented Jun 8, 2018 at 16:59
  • Ok, no problem really. it is just a matter to terminology, to me a "fact" is nothing but a 'true statement', now 1+1=2 is an arithmetical fact, however it is NOT an empirical fact, to me science is any factual discipline so it can subsume logic and mathematics. However, you are also right since commonly and as you said Epistemologically it is agreed that the term "fact" to be reserved to "empirically verifiable data", then no problem of course mathematics and logic won't be named as such and they won't be science since the later mean a factual discipline. My way is broader.
    – Zuhair
    Commented Jun 9, 2018 at 9:33

One way of defining a posteriori would be something knowable "dependent on experience." One way of defining empirical is "dependent on sensory experience," or "dependent primarily on sensory experience."1 If we assume that reasoning and thought are not sensory processes, then we obviously have things we know, which are dependent on experience yet are not dependent primarily on sensory experience. These might include as you suggest ethical or artistic principles. Theoretical physics might be a good example of a field that has an indirect relation to empirical evidence. Perhaps knowledge of platonic forms or essence could be included here.

However, under the more abstract definition as dependent on sensory experience, it's likely the systems you describe would be considered empirical. In this interpretation, we might say "the distinction between a priori and a posteriori thus broadly corresponds to the distinction between empirical and nonempirical knowledge" [emphasis mine] (https://www.iep.utm.edu/apriori/). Perhaps an exception would be transcendental knowledge (e.g. "cogito ergo sum").

1 It might be worthwhile to note that per wikipedia (https://en.wikipedia.org/wiki/Empirical_evidence) empirical has a root of empeiría (ἐμπειρία) meaning experience. I think based on Kant, the terms are roughly synonymous. However, in the context of empiricism it seems we would want to emphasize sensory experience as being the primary basis (or at least part of the basis) for knowledge to consider it empirical if we want the terms to be different at all.

  • can you explain what "primarily" mean in that context? I mean a precise definition of it. Also if we adopt the "primarily sensory dependence" definition of empirical, then what would the systems I've presented qualify as: they won't be empirical, yes, but are they apriori or aposteriori?
    – Zuhair
    Commented Jun 9, 2018 at 9:37
  • "Primarily" suggests a range of views, but a precise version here would be scientific (empirical) falsifiability. Anything which draws upon observation, fact, or experience regarding the world is a posteriori. While a purely mathematical theory of music might be a priori, one that considers certain combinations of sounds superior (in a non-falsifiable sense) with some basis in e.g. personal experience or human physiology would be a posteriori. So for this precise view of empirical, such a theory would be non-empirical a posteriori.
    – Greg S
    Commented Jun 11, 2018 at 17:51

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