Theories of deduction

thumb|Peter Abelard, a French philosopher, theologian and preeminent logician, put forward the theory of conceptualism. In metaphysics, conceptualism is a theory that explains universality of particulars as conceptualized frameworks situated within the thinking mind. Intermediate between nominalism and realism, the conceptualist view approaches the metaphysical concept of universals from a perspective that denies their presence in particulars outside the mind's perception of them. Conceptualism is anti-realist about abstract objects, just like immanent realism is (their difference being that i

Psychologism is a family of philosophical positions, according to which certain psychological facts, laws, or entities play a central role in grounding or explaining certain non-psychological facts, laws, or entities. The word was coined by Johann Eduard Erdmann as Psychologismus, being translated into English as psychologism.

In philosophy of mathematics, logicism is a school of thought comprising one or more of the theses that – for some coherent meaning of 'logic' – mathematics is an extension of logic, some or all of mathematics is reducible to logic, or some or all of mathematics may be modelled in logic. Bertrand Russell and Alfred North Whitehead championed this programme, initiated by Gottlob Frege and subsequently developed by Richard Dedekind and Giuseppe Peano.

emphasis on form over content or meaning in the arts, literature, or philosophy

a set of problem-solving methods that involve expressing problems and their solutions in ways that a computer could execute

philosophical view expounded by Bertrand Russell

Conventionalism is the philosophical attitude that fundamental principles of a certain kind are grounded on (explicit or implicit) agreements in society, rather than on external reality. Unspoken rules play a key role in the philosophy's structure. Although this attitude is commonly held with respect to the rules of grammar, its application to the propositions of ethics, law, science, biology, mathematics, and logic is more controversial.

Illuminationism (Persian حكمت اشراق hekmat-e eshrāq, Arabic: حكمة الإشراق ḥikmat al-ishrāq, both meaning "Wisdom of the Rising Light"), also known as Ishrāqiyyun or simply Ishrāqi (Persian اشراق, Arabic: الإشراق, lit. "Rising", as in "Shining of the Rising Sun") is a philosophical and mystical school of thought introduced by Shahab al-Din Suhrawardi (honorific: Shaikh al-ʿIshraq or Shaikh-i-Ishraq, both meaning "Master of Illumination") in the twelfth century, established with his Kitab Hikmat al-Ishraq (lit: "Book of the Wisdom of Illumination"), a fundamental text finished in 1186. Written w

study of the semantics, or interpretations, of formal and natural languages

Dialetheism (; from Greek 'twice' and 'truth') is the view that there are statements that are both true and false. More precisely, it is the belief that there can be a true statement whose negation is also true. Such statements are called "true contradictions", dialetheia, or nondualisms.

Fictionalism is a view in philosophy that posits that statements appearing to be descriptions of the world should not be construed as such, but should instead be understood as cases of "make believe", thus allowing individuals to treat something as literally true (a "useful fiction").

200px|thumbnail|right|Trivialism in First-order logic#Logical symbols|symbolic logic; Read as "given any proposition, it is a true proposition."

Ramism was a collection of theories on rhetoric, logic, and pedagogy based on the teachings of Petrus Ramus, a French academic, philosopher, and Huguenot convert, who was murdered during the St. Bartholomew's Day massacre in August 1572.

Polylogism is the belief that different groups of people reason in fundamentally different ways (coined from Greek poly 'many' + logos 'logic'). The term is attributed to Ludwig von Mises, who claimed that it described Marxism and other class-based social philosophies. In the Misesian sense of the term, a polylogist ascribes different forms of "logic" to different groups, which may include groups based on race, gender, class, or time period.

in the philosophy of language, a theory of truth holding that truth is a property of sentences

In the philosophy of mathematics, ultrafinitism, ultraintuitionism, strict formalism, strict finitism, actualism, predicativism, and strong finitism are various philosophies of mathematics with aspects of finitism and intuitionism. Common to these philosophies is their objection to the totality of number theoretic functions like exponentiation over natural numbers.

Context-based approach to semantics