In the introduction of the critique of pure reason, Kant says

"That all our knowledge begins with experience there can be no doubt. For how is it possible that the faculty of cognition should be awakened into exercise otherwise than by means of objects which affect our senses. [...] But, though all our knowledge begins with experience, it by no means follows that all arises out of experience. For, on the contrary, it is quite possible that our empirical knowledge is a compound of that which we receive through impressions, and that which the faculty of cognition supplies from itself"

but then he defines "a priori knowledge" in the following way

"in speaking of knowledge which has its sources in experience, we are wont to say, that this or that may be known a priori, because we do not derive this knowledge immediately from experience, but from a general rule, which, however, we have itself borrowed from experience. [...] By the term “knowledge a priori,” therefore, we shall in the sequel understand, not such as is independent of this or that kind of experience, but such as is absolutely so of all experience."

These two statements seem to contradict one another, because if all knowledge has its deepest source in experience, then there is some degree of "a posteriori" in every synthetic judgement. For example, in physics one can say "energy is conserved", but there is no way that this is a priori, as we draw this conclusion by looking at the world.

  • Suppose we were living in a totally liquid universe ( like fishes) , suppose also the that we were deprived of the sense of sight , maybe in that case we would not have ever thought of the concept of a collection of distinct/ discrete objects, and consequently we would never have thought the concept of number, of addition, , of equal collections, etc. In that case there would be no arithmetic.

  • So, our arithmetical concepts and our arithmetical knowledge is occasionned by the fact that we experience discrete objects. This is the empirical origin of this knowkledge.

  • But this is not the foundation of our arithmetical knowledge. The proposition that 2+3=5 is not grounded on the fact that I have experienced many times that 2 apples joinded to 3 apples make a collection of 5 apples. Knowledge requires universality and necessity which cannot be provided by induction and empirical generalizations. The truth " 2+3=5" is founded on a priori principles ( of which we become aware after having first thought of this truth).

" Coming from " refers to psychological/ empirical/chronological origin.

" Being derived from" refers to logical and objective foundation/justification.

  • Kants point is to show that the following reasoning is not valid :

(1) All our knowledge begings with experience.

(2) If A begins with B, then B is A's principle, A's foundation.

(3) Therefore, experience is the foundation of all our knowledge [empiricist thesis]

According to Kant , premise (1) is true, but premise (2) is false. He shows this by distinguising " coming from" and " being founded on/ deriving from".

  • 1
    I can see the difference, thank you! Still i have some troubles accepting a priori synthetic judgments in physics. There is no foundation on the statement "the quantity of matter remains unchanged", only empirical knowledge. – user35319 May 13 '20 at 6:56
  • Kant considers that this principle can be proved, using a transcendental argument: it is a condition of the possibility of experience; we could not experience a change in case we hadn't phis principle at hand. Reference: Critique of Pure Reason, Analyitic Of Principles, first analogy of experience. - I do not claim that Kant's argument is convincing. - For a detailed summary, you may have a look at Routledge Contemporary Intro. , Classic modern philosophy. – user37859 May 13 '20 at 9:00
  • plato.stanford.edu/entries/kant-science/#Mec – user37859 May 13 '20 at 9:09

You have to keep in mind that Kant is working with a very exact definition of the difference, here. A priori comes down to proactively, in the sense that a question to be answered a priori can have all its cases posed (hence the answers are necessary, and in the analytic cases relatively trivial) by the mind "spontaneously," if you will. Experience by itself is passive, knowledge that happens to you versus knowledge that you "do."

Nevertheless, outside of ethics, this "strength" of the a priori is an illusion, Kant notes: without reference to more particular intuitions, we can only pose a vague range of actual questions. Or, worse, we end up even with unanswerable questions, which defeat the a priori all the more.

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