For Kant, the analytic/synthetic distinction and the a priori/a posteriori distinction are fundamental building blocks in his philosophy. In this essay I shall first provide a short explanation of the distinction between a priori and a posteriori knowledge. I will then outline the distinction Kant provides in his ‘Critique of Pure Reason’ between analytic and synthetic judgements. Next I will describe and evaluate Kant’s idea of synthetic a priori statements and explain how this is indeed crucial to his philosophy as a whole. Following this I shall critically compare this concept with the ideas of logical empiricists, emphasising the essay ‘Denial of the Synthetic A Priori’ by O. A. Johnson. And finally I will argue that the idea of a synthetic a priori statement is indeed significant in Kant’s work and thus hugely influential post-Kantian philosophy.

Kant’s goal, when writing the Critique, was essentially to provide a bridge between the two opposing epistemological standpoints of rationalism and empiricism.  In particular he wished to counteract Hume’s refutation of metaphysics which was based on the division between matters of fact and relations of ideas. The first step in this task is to distinguish between a priori and a posteriori (empirical) knowledge. A statement is a priori when it can’t be proven from experience, even though experience may be needed in order for us to know it . On the other hand a statement or principle is knowable a posteriori when it can be proven or disproven from experience. Kant recognises that our knowledge starts with experience but that this is not the limit of our knowledge, experience may make knowable to us claims that are not derived from experience. For example a baby needs language (something gained through experience) to develop understanding of abstract or non-empirical concepts.

The second distinction Kant makes is between analytic and synthetic judgements. To Kant, an analytic judgement is when the predicate contains within it the concept of the subject. Kant uses the example ‘all bodies are extended’ (b11-b12) as the concept of extension is already contained in that of a body. Another example of this may be ‘all bachelors are unmarried men’ as it is impossible for the concept of a bachelor to not include within it the predicate of being an unmarried man. To Kant analytic judgements do therefore not extend our knowledge but merely explicate our concepts. A synthetic judgement, on the other hand, is a judgement whose predicate concept is not contained within its subject concept. In other words the predicate that it connects with the concept of the subject is not contained within it. The connection between subject and predicate in the analytic sense is ‘thought through identity’ whereas in the synthetic sense it is ‘thought without identity’; the subject and predicate are connected through a synthesis, a connection of two elements that were not previously joined. Kant uses the example all bodies are heavy (B12) to exemplify a synthetic judgement as the concept of weight is not contained within that of a body, this is something we add to it through it experience. Kant argues that the principle of contradiction can therefore be used to determine the truth of analytic judgements but not synthetic ones. For synthetic judgements this principle provides knowledge that they are contradictory and thus cannot be true or non-contradictory and therefore may potentially be true.

However, how does this distinction relate to the necessary a priori, and contingent empirical (a posteriori) knowledge? To philosophers like Leibniz and Hume all necessary a priori judgements must be analytic whereas contingent a posteriori judgements must be synthetic. However Kant argues that this is not necessarily true; although all a posteriori judgements are indeed synthetic not all necessary a priori judgements are analytic. For example, the law of causation ‘every event has a cause’ is necessary so therefore must be a priori, yet it is not analytic as the concept of an event does not contain within it the concept of being an effect. To Kant, metaphysical judgements such as this are therefore a priori and synthetic; they cannot be derived purely from logic or experience. Has Kant, therefore, merely led us to Hume’s previous conclusion that it is impossible for us to gain metaphysical knowledge? To Kant the answer would be yes if it weren’t for the synthetic a priori judgements of mathematics and geometry; judgements not even Hume had rejected. Leibniz had argued that mathematical judgements are true due to the principle of contradiction and they are therefore analytic, for example ‘a square has four sides’ is true because four sidedness is in the concept of a square, similarly ‘7+5=12’ is true in the same way i.e. it’s truth can be reached via purely logical principles. However, Kant argues ‘In all theoretical sciences of reason synthetic a priori judgements are contained as principles’ (B14) thus the concept of ‘7+5’ does not contain within it the concept of ‘12’, we require intuition to show us what 7 added to 5 is equal to. Furthermore the principle of contradiction can only show us that ‘7+5≠12’ is a contradiction if we add further mathematical (not logical) premises to it. There is, therefore, a form of synthesis that is needed to connect the subject of a particular sum (e.g. ‘7+5’) to its predicate (‘12’) meaning, for Kant, Leibniz’s supposition that mathematics can be derived from logic is false. Therefore both Leibniz and Hume’s explanations fail to provide an accurate source for our knowledge; they both fail to account for the possibility of synthetic a priori judgements thus opening ‘the door to demonstrating, against Hume, the possibility of metaphysics’.

What we have seen so far is that the basic task of Kant’s Critique of Pure Reason was to show how synthetic a priori propositions are possible; this was the foundation upon which Kant built his whole transcendental philosophy. However some have argued there are problems with Kant’s reasoning. One of these criticisms is concerned with the distinction between analytic and synthetic judgements. Kant defines an analytic statement as ‘belongs to the subject as something which is covertly contained, but merely breaking it up into those constituent concepts that have all along been thought in it’; they add ‘nothing to the predicate through the concept of the subject’ (B11). How is the relation of one concept containing another to be determined? When Kant refers to ‘breaking up’ the proposition into concepts it seems there is some ambiguity. For example, stating ‘the black cat is black’ must be analytic as the concepts of ‘black’ and ‘cat’ are clearly contained within the ‘black cat’. Yet how can the concept of ‘7’ or ‘5’ not be contained by the concept of 12 by this same reasoning? If something being ‘covertly contained’ is understood in terms of us thinking whether the predicate is either inside or outside the concept of the subject then the difference between analytic and synthetic becomes purely and individual introspective distinction. Does this mean Kant guilty of Psychologism? Does this narrow definition ‘covertly contained’ mean judgements can be analytic or synthetic depending on the person? Kant would argue not. To Kant, analytic judgements provide the basis for the way we construct definitions rather than merely presupposing them. He believes there must be ‘core elements in concepts’ otherwise we would not be able to have knowledge of the content of our concepts. Therefore Kant’s idea of concepts is not guilty of psychologism.

Furthermore, Kant has been accused of confusing two different versions of the distinction between analytic and synthetic judgements and it is for this reason that he has come up with the notion of synthetic a priori knowledge. According to this argument Kant’s concept of the ‘analytic’ is advancing two different criteria for the same concept. The first is that a judgement is analytic if its truth is determined by the conceptual meanings of the terms involved i.e. ‘bachelor’ and ‘unmarried man’. The second is that its truth is self-evident yet it does not extend our knowledge. These two conceptions of the term differ due to the fact that a judgement could be true conceptually without being self-evidently true i.e. since they require reasoning to make them true. Synthetic a priori judgements would thus be analytic by Kant’s own reasoning. Gardner states that these may be better described as ‘non-obvious analytic judgements’.

The idea of the synthetic a priori has also been harshly criticised by the twentieth century logical empiricists such as Herbert Feigl and A.J. Ayer. In ‘Logical Empiricism’ Feigl states that ‘all forms of empiricism agree in repudiating the existence of synthetic a priori knowledge’ and this is the exact thing that Oliver A. Johnson focuses on in his essay ‘Denial of the Synthetic a priori’. Johnson believes this problem to be ‘one of the most important in all of philosophy’ and sets to explore whether the classification the empiricist statement ‘no synthetic propositions are a priori’ is itself a priori or a posteriori. He states that the logical empiricist may argue it is a posteriori. This would mean it would be an empirical hypothesis that could be disproved by empirical evidence specifically a synthetic a priori statement itself. However would this really disconfirm the statement? He gives the example of the empirical hypothesis ‘all swans are white’, this hypothesis is disconfirmed as soon as a black (or any non-white) swan is discovered (echoing Hume’s problem of induction). However if the statement ‘no synthetic propositions are a priori’ is known a posteriori it must be theoretically able to be disconfirmed by sense data, just as the with the swan example. Can we therefore lay down the criteria, as we can with colours, that would make it possible to empirically discover that a synthetic proposition is also a priori? Johnson argues that we can’t as the notion of a priori cannot be observed. However it could be argued that if there were synthetic a prioris they could be observed as easily as a black swan. All that would be necessary would be for someone to write a synthetic a priori proposition on a piece of paper and let us look at it. Thus the statement ‘no synthetic propositions are a priori’ is theoretically capable of being proven by a posteriori evidence, and is therefore a posteriori. However he does go on to say that although a proposition must be expressed empirically for it to be communicated it doesn’t mean the two things are the same. The observation of the words on the paper would only disconfirm the proposition ‘no synthetic statements are written on paper’. However would the person who wrote the statement on the paper tell us it is synthetic a priori? If so would then only hear his voice along with reading the paper. We never observe that either any synthetic proposition is a priori or any synthetic a priori proposition, we don’t observe any proposition at all. He states the reason is that propositions are intrinsically unobservable thus the production of a synthetic a priori proposition could not disconfirm ‘no synthetic propositions are a priori’ empirically since a necessary condition of an a posteriori proposition is that it be theoretically capable of disconfirmation. The proposition cannot be a posteriori because of this reasoning and must be, in conclusion a priori. Johnson therefore goes through an interesting method of providing a possible counter argument to Kant’s idea, yet reasons that in the end Kant’s reasoning is viable enough to provide a solid grounding for the rest of the Critique.

In conclusion, Kant’s idea of synthetic a priori is hugely significant for his philosophy as a whole. It provides the essential bridge between rationalist and empiricist epistemology and in doing so gives probably the best account for the plausibility of metaphysical knowledge that sceptics like Hume had repudiated. To quote Nietzsche ‘it is high time to replace the Kantian question, ‘How are synthetic judgments a priori possible?’ by another question, ‘Why is belief in such judgments necessary?’’ Yet contrary to Nietzsche it is my belief that not only is Kant’s reasoning necessary, I agree with Johnson in saying it is one of the most important problems in philosophy, one that I believe Kant solved.

Excuse the lack of proper referencing, I had formatting issues converting from Word.


Feigl, H., (1947) Logical Empiricism. Twentieth Century Philosophy. ed. D. D. Runes.

Gardner, S., (1999) Kant and the Critique of Pure Reason. Routledge: London.

Hume, D., (2008) Enquiry Concerning Human Understanding. Oxford University Press: Oxford

Johnson, O. A., (1960) Denial of the Synthetic a priori. Philosophy. 35(134)

Kant, I., (1797) Critique of Pure Reason. Trans. Norman Kemp Smith 1997. Palgrave Macmillan

Mates., B (1986) The Philosophy of Leibniz. Oxford University Press: Oxford

Nietzsche, F., (2003) Beyond Good and Evil. Trans. R.J. Hollingdale. Penguin Classics.

Russell, B., (2001) The Problems of Philosophy. Oxford Paperbacks: Oxford


10 thoughts on “The Importance of the Synthetic A Priori in Kant’s First Critique

    • No? What I aimed to do was to give a brief exposition of Kant’s arguments for the basis of the synthetic a priori. It would take much more than a short essay to relate it to every concept in the CPR (space/time etc etc.)


      • Yup. I am aware of the hugeness of the required exposition of the ideas that would be exhaustive.

        But you wrote “And finally I will argue that the idea of a synthetic a priori statement is indeed significant in Kant’s work and thus hugely influential post-Kantian philosophy.” And all I’m saying is that I’m not getting the mentioned significance.


      • Right you are, I didn’t really mention much post-Kantian philosophy, except for the examples in the essay, which since they are commenting on Kant could be considered under that category (though they are obviously not Hegel/Schopenhaur etc).

        However, I think throughout the essay you get an understanding of the importance of the synthetic a priori as a foundation of Kant’s philosophy at least; as the bridge between rationalism and empiricism.


  1. i found it interresting; but you that O.A. Johnson is not a common philosopher, it would have been better to write a brief of his biography in order to give your paper more value.


  2. Pingback: Hume's Fork Explained - Fact / Myth

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