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===Theory of perception===
{{Main|Critique of Pure Reason}}
Kant defines his theory of perception in his influential 1781 work the ''Critique of Pure Reason'', which has often been cited as the most significant volume of metaphysics and [[epistemology]] in modern philosophy.[{{Cite web |url=https://plato.stanford.edu/entries/kant/ |title=Archived copy |access-date=29 May 2019 |archive-date=14 November 2019 |archive-url=https://web.archive.org/web/20191114014720/https://plato.stanford.edu/entries/kant/ |url-status=live }}] Kant maintains that understanding of the external world had its foundations not merely in experience, but in both experience and ''a priori'' concepts, thus offering a ''non-empiricist critique of rationalist philosophy'', which is what has been referred to as his Copernican revolution.[{{cite web |url=http://encyclopedia2.thefreedictionary.com/Kant%2c+Immanuel |title=Kant, Immanuel definition of Kant, Immanuel in the Free Online Encyclopedia |publisher=Encyclopedia2.thefreedictionary.com |access-date=26 February 2014 |archive-date=2 March 2014 |archive-url=https://web.archive.org/web/20140302135203/http://encyclopedia2.thefreedictionary.com/Kant%2c+Immanuel |url-status=live }}]
Firstly, Kant [[Analytic–synthetic distinction|distinguishes between analytic and synthetic propositions]]:
# '''Analytic proposition''': a proposition whose predicate concept is contained in its subject concept; ''e.g.'', "All bachelors are unmarried," or, "All bodies take up space."
# '''Synthetic proposition''': a proposition whose predicate concept is not contained in its subject concept; ''e.g.'', "All bachelors are alone," or, "All bodies have weight."
An analytic proposition is true by nature of the meaning of the words in the sentence — we require no further knowledge than a grasp of the language to understand this proposition. On the other hand, a synthetic statement is one that tells us something about the world. The truth or falsehood of synthetic statements derives from something outside their linguistic content. In this instance, weight is not a necessary [[predicate (grammar)|predicate]] of the body; until we are told the heaviness of the body we do not know that it has weight. In this case, experience of the body is required before its heaviness becomes clear. Before Kant's first Critique, empiricists (cf. Hume) and rationalists (cf. [[Gottfried Wilhelm Leibniz|Leibniz]]) assumed that all synthetic statements required experience to be known.
Kant contests this assumption by claiming that elementary mathematics, like arithmetic, is synthetic ''a priori'', in that its statements provide new knowledge not derived from experience. This becomes part of his over-all argument for [[transcendental idealism]]. That is, he argues that the possibility of experience depends on certain necessary conditions — which he calls ''a priori'' forms — and that these conditions structure and hold true of the world of experience. His main claims in the "[[Critique of Pure Reason#I. Transcendental Doctrine of Elements|Transcendental Aesthetic]]" are that mathematic judgments are synthetic ''a priori'' and that [[space]] and [[time]] are not derived from experience but rather are its preconditions.
Once we have grasped the functions of basic arithmetic, we do not need empirical experience to know that 100 + 100 = 200, and so it appears that arithmetic is analytic. However, that it is analytic can be disproved by considering the calculation 5 + 7 = 12: there is nothing in the numbers 5 and 7 by which the number 12 can be inferred.[{{cite book |last1=Kant |first1=Immanuel |title=Prolegomena to Any Future Metaphysics |url=http://www.gutenberg.org/files/52821/52821-h/52821-h.htm |access-date=22 March 2020 |at=§ 2 |archive-date=1 August 2020 |archive-url=https://web.archive.org/web/20200801234756/http://www.gutenberg.org/files/52821/52821-h/52821-h.htm |url-status=live }}] Thus "5 + 7" and "the cube root of 1,728" or "12" are not analytic because their reference is the same but their sense is not — the statement "5 + 7 = 12" tells us something new about the world. It is self-evident, and undeniably ''a priori'', but at the same time it is synthetic. Thus Kant argued that a proposition can be synthetic and ''a priori''.
Kant asserts that experience is based on the perception of external objects and ''a priori'' knowledge.[The German word ''Anschauung'', which Kant used, literally means 'looking at' and generally means what in philosophy in English is called "perception". However it sometimes is rendered as "intuition": not, however, with the vernacular meaning of an indescribable or mystical experience or sixth sense, but rather with the meaning of the direct perception or grasping of sensory phenomena. In this article, both terms, "perception" and "intuition" are used to stand for Kant's ''Anschauung''.] The external world, he writes, provides those things that we sense. But our mind processes this information and gives it order, allowing us to comprehend it. Our mind supplies the conditions of space and time to experience objects. According to the "transcendental unity of apperception", the concepts of the mind (Understanding) and perceptions or intuitions that garner information from phenomena (Sensibility) are synthesized by comprehension. Without concepts, perceptions are nondescript; without perceptions, concepts are meaningless. Thus the famous statement: "Thoughts without content are empty, intuitions [perceptions] without concepts are blind."{{rp|193-4 (A 51/B 75)}}
Kant also claims that an external environment is necessary for the establishment of the self. Although Kant would want to argue that there is no empirical way of observing the self, we can see the logical necessity of the self when we observe that we can have different perceptions of the external environment over time. By uniting these general representations into one global representation, we can see how a transcendental self emerges. "I am therefore conscious of the identical self in regard to the manifold of the representations that are given to me in an intuition because I call them all together '''my''' representations, which constitute '''one'''."{{rp|248 (B 135)}}
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