Categorical logic is now a well-defined field based on type theory for intuitionistic logics, with applications in functional programming and domain theory, where a cartesian closed category is taken as a non-syntactic description of a lambda calculus.

* Categorical distribution: for discrete random variables with a finite set of values.

** Categorical grants may be spent only for narrowly defined purposes and recipients often must match a portion of the federal funds.

Immanuel Kant, a great influence for Rawls, similarly applies a lot of procedural practice within the practical application of The Categorical Imperative, however, this is indeed not based solely on ' fairness '.

* Level, for a Categorical variable in statistics, the different values that such a variable can have

This led to the most important part of Kant's ethics, the formulation of the Categorical Imperative, which is the criterion for whether a maxim is good or bad.

Categorical random variables are normally described statistically by a categorical distribution, which allows an arbitrary K-way categorical variable to be expressed with separate probabilities specified for each of the K possible outcomes.

Categorical logic is a branch of category theory within mathematics, adjacent to mathematical logic but more notable for its connections to theoretical computer science.

Caml ( originally an acronym for Categorical Abstract Machine Language ) is a dialect of the ML programming language family, developed at INRIA and formerly at ENS.

" Exact Inference for Categorical Data ".

Categorical imperative is a method for determining right from wrong by thinking through the ethical valence of an act, regardless of motive.

Categorical propositions can be categorized into four types on the basis of their quality, quantity, and distribution.

Moreover, Kant saw a good will as acting in accordance with a moral command, the " Categorical Imperative ": " Act according to those maxims that you could will to be universal law.

Even though an example like the one above regarding the orange would not be something that required the practical application of The Categorical Imperative, it is important to draw distinction between Kant and Rawls, and note that Kant's Theory would not necessarily lead to the same problems Rawls ' does-i. e., the cutting in half of the orange.

Categorical sentences may then be abbreviated as follows:

" For Kant, practical reason has a law abiding quality because the Categorical imperative is understood to be binding one to one's duty rather than subjective preferences.

Categorical data is a grouping of data into discrete groups, such as months of the year, age group, shoe sizes, and eye colors.

* Categorical logic

Categorical logic -- Clocked logic -- Cointerpretability -- College logic -- Combinational logic -- Combinatory logic -- Computability logic -- Conditional -- Conditional proof -- Conjunction elimination -- Conjunction introduction -- Conjunctive normal form -- Consequent -- Constructive dilemma -- Contradiction -- Contrapositive -- Control logic -- Converse ( logic ) -- Converse Barcan formula -- Cotolerance -- Counterfactual conditional -- Curry's paradox

Categorical models of bunched logic are given by doubly closed categories, which are both cartesian closed and symmetric monoidal closed.

* Categorical logic, a branch of category theory within mathematics with notable connections to theoretical computer science

# Deontological ethics, notions based on ' rules ' i. e. that there is an obligation to perform the ' right ' action, regardless of actual consequences ( epitomized by Kant's notion of the Categorical Imperative )

Categorical equivalence has found numerous applications in mathematics.

* Categorical data analysis-Data sets used in the book, An Introduction to Categorical Data Analysis, by Agresti are provided on-line by StatLib.

** Immanuel Kant's Categorical Imperative, which roots morality in humanity's rational capacity and asserts certain inviolable moral laws.

Categorical products are a particular kind of limit in category theory.

* Borceux, F. Handbook of Categorical Algebra: vol 1 Basic category theory ( 1994 ) Cambridge University Press, ( Encyclopedia of Mathematics and its Applications ) ISBN 0-521-44178-1

Social cognition: Categorical person perception.

It is often said that the Categorical Imperative is the same as The Golden Rule.

Schopenhauer's criticism of the Kantian philosophy expresses doubt concerning the absence of egoism in the Categorical Imperative.

Schopenhauer claimed that the Categorical Imperative is actually hypothetical and egotistical, not categorical.

Schopenhauer specifically targeted the Categorical Imperative, labelling it cold and egoistic.

* Herrlich, Horst: Categorical topology 1971-1981.

* Herrlich, Horst & Strecker, George E .: Categorical Topology-its origins, as examplified by the unfolding of the theory of topological reflections and coreflections before 1971.

* Categorical Exclusion ( CATEX ): As discussed above, the government may exempt an agency from the process.

* Categorical Pretreatment Standards are issued to industrial users ( also called " indirect dischargers ") contributing wastes to POTW.

Work in set theory showed that almost all ordinary mathematics can be formalized in terms of sets, although there are some theorems that cannot be proven in common axiom systems for set theory.

However, in certain axiom systems for constructive set theory, the axiom of choice does imply the law of the excluded middle ( in the presence of other axioms ), as shown by the Diaconescu-Goodman-Myhill theorem.

This theorem showed that axiom systems were limited when reasoning about the computation which deduces their theorems.

The field of mathematics known as proof theory studies formal axiom systems and the proofs that can be performed within them.

Many formalists would say that in practice, the axiom systems to be studied will be suggested by the demands of science or other areas of mathematics.

Hilbert's goals of creating a system of mathematics that is both complete and consistent were dealt a fatal blow by the second of Gödel's incompleteness theorems, which states that sufficiently expressive consistent axiom systems can never prove their own consistency.

Other formalists, such as Rudolf Carnap, Alfred Tarski and Haskell Curry, considered mathematics to be the investigation of formal axiom systems.

Formalism is thus silent on the question of which axiom systems ought to be studied, as none is more meaningful than another from a formalistic point of view.

" In any of these systems, removal of the one axiom which is equivalent to the parallel postulate, in whatever form it takes, and leaving all the other axioms intact, produces absolute geometry.

In mathematics, Zermelo – Fraenkel set theory with the axiom of choice, named after mathematicians Ernst Zermelo and Abraham Fraenkel and commonly abbreviated ZFC, is one of several axiomatic systems that were proposed in the early twentieth century to formulate a theory of sets without the paradoxes of naive set theory such as Russell's paradox.

Lines and points are undefined terms in absolute geometry, but assigned meanings in the theory of real numbers in a way that is consistent with both axiom systems.

: In systems thinking it is an axiom that every influence is both cause and effect.

The axiom systems most often considered in reverse mathematics are defined using axiom schemes called comprehension schemes.

For example, in traditional systems of logic ( e. g., classical logic and intuitionistic logic ), every statement becomes true if a contradiction is true ; this means that such systems become trivial when dialetheism is included as an axiom.

* Gödel's speed-up theorem, showing that some mathematical proofs can be drastically shortened in stronger axiom systems

The axioms defining antimatroids as set systems are very similar to those of matroids, but whereas matroids are defined by an exchange axiom ( e. g., the basis exchange, or independent set exchange axioms ), antimatroids are defined instead by an anti-exchange axiom, from which their name derives.

In contemporary use by mathematical logicians, the term refers to several branches of pure mathematics whose study involves careful attention to formal axiom systems and formal definability.

One can extend absolute geometry by adding different axioms about parallel lines and get incompatible but consistent axiom systems, giving rise to Euclidean or hyperbolic geometry.

A conceptual model is a representation of some phenomenon, data or theory by logical and mathematical objects such as functions, relations, tables, stochastic processes, formulas, axiom systems, rules of inference etc.

See for minimal axiom systems inside which the Sylvester – Gallai theorem can be proved.