A priori in the context of "Organon"

Transcendental idealism is a philosophical system founded by German philosopher Immanuel Kant in the 18th century. Kant's epistemological program is found throughout his Critique of Pure Reason (1781). By transcendental (a term that deserves special clarification) Kant means that his philosophical approach to knowledge transcends mere consideration of sensory evidence and requires an understanding of the mind's innate modes of processing that sensory evidence.

In the "Transcendental Aesthetic" section of the Critique of Pure Reason, Kant outlines how space and time are pure forms of human intuition contributed by our own faculty of sensibility. Space and time do not have an existence "outside" of us, but are the "subjective" forms of our sensibility and hence the necessary a priori conditions under which the objects we encounter in our experience can appear to us at all. Kant describes time and space not only as "empirically real" but transcendentally ideal.

The Critique of Pure Reason (German: Kritik der reinen Vernunft; 1781; second edition 1787) is a book by the German philosopher Immanuel Kant, in which the author seeks to determine the limits and scope of metaphysics. Also referred to as Kant's "First Critique", it was followed by his Critique of Practical Reason (1788) and Critique of Judgment (1790). In the preface to the first edition, Kant explains that by a "critique of pure reason" he means a critique "of the faculty of reason in general, in respect of all knowledge after which it may strive independently of all experience" and that he aims to decide on "the possibility or impossibility of metaphysics".

Kant builds on the work of empiricist philosophers such as John Locke and David Hume, as well as rationalist philosophers such as René Descartes, Gottfried Wilhelm Leibniz and Christian Wolff. He expounds new ideas on the nature of space and time, and tries to provide solutions to the skepticism of Hume regarding knowledge of the relation of cause and effect and that of René Descartes regarding knowledge of the external world. This is argued through the transcendental idealism of objects (as appearance) and their form of appearance. Kant regards the former "as mere representations and not as things in themselves", and the latter as "only sensible forms of our intuition, but not determinations given for themselves or conditions of objects as things in themselves". This grants the possibility of a priori knowledge, since objects as appearance "must conform to our cognition...which is to establish something about objects before they are given to us." Knowledge independent of experience Kant calls "a priori" knowledge, while knowledge obtained through experience is termed "a posteriori". According to Kant, a proposition is a priori if it is necessary and universal. A proposition is necessary if it is not false in any case and so cannot be rejected; rejection is contradiction. A proposition is universal if it is true in all cases, and so does not admit of any exceptions. Knowledge gained a posteriori through the senses, Kant argues, never imparts absolute necessity and universality, because it is possible that we might encounter an exception.

In Immanuel Kant's philosophy, a category (German: Categorie in the original or Kategorie in modern German) is a pure concept of the understanding (Verstand). A Kantian category is a characteristic of the appearance of any object in general, before it has been experienced (a priori). Following Aristotle, Kant uses the term categories to describe the "pure concepts of the understanding, which apply to objects of intuition in general a priori…" Kant further wrote about the categories: "They are concepts of an object in general, by means of which its intuition is regarded as determined with regard to one of the logical functions for judgments." The categories are the condition of the possibility of objects in general, that is, objects as such, any and all objects, not specific objects in particular. Kant enumerated twelve distinct but thematically related categories.

A choropleth map (from Ancient Greek χῶρος (khôros) 'area, region' and πλῆθος (plêthos) 'multitude') is a type of statistical thematic map that uses pseudocolor, meaning color corresponding with an aggregate summary of a geographic characteristic within spatial enumeration units, such as population density or per-capita income.

Choropleth maps provide an easy way to visualize how a variable varies across a geographic area or show the level of variability within a region. A heat map or isarithmic map is similar but uses regions drawn according to the pattern of the variable, rather than the a priori geographic areas of choropleth maps. The choropleth is likely the most common type of thematic map because published statistical data (from government or other sources) is generally aggregated into well-known geographic units, such as countries, states, provinces, and counties, and thus they are relatively easy to create using GIS, spreadsheets, or other software tools.