PropositionA proposition is a central concept in the philosophy of language, semantics, logic, and related fields, often characterized as the primary bearer of truth or falsity. Propositions are also often characterized as being the kind of thing that declarative sentences denote. For instance the sentence "The sky is blue" denotes the proposition that the sky is blue. However, crucially, propositions are not themselves linguistic expressions.
EmpiricismIn philosophy, empiricism is an epistemological view that holds that true knowledge or justification comes only or primarily from sensory experience. It is one of several competing views within epistemology, along with rationalism and skepticism. Empiricism emphasizes the central role of empirical evidence in the formation of ideas, rather than innate ideas or traditions. However, empiricists may argue that traditions (or customs) arise due to relations of previous sensory experiences.
Automated theorem provingAutomated theorem proving (also known as ATP or automated deduction) is a subfield of automated reasoning and mathematical logic dealing with proving mathematical theorems by computer programs. Automated reasoning over mathematical proof was a major impetus for the development of computer science. While the roots of formalised logic go back to Aristotle, the end of the 19th and early 20th centuries saw the development of modern logic and formalised mathematics.
AestheticsAesthetics (also esthetics) is the branch of philosophy concerned with the nature of beauty and the nature of taste; and functions as the philosophy of art. Aesthetics examines the philosophy of aesthetic value, which is determined by critical judgements of artistic taste; thus, the function of aesthetics is the "critical reflection on art, culture and nature". Aesthetics studies natural and artificial sources of experiences and how people form a judgement about those sources of experience.
Gödel's incompleteness theoremsGödel's incompleteness theorems are two theorems of mathematical logic that are concerned with the limits of in formal axiomatic theories. These results, published by Kurt Gödel in 1931, are important both in mathematical logic and in the philosophy of mathematics. The theorems are widely, but not universally, interpreted as showing that Hilbert's program to find a complete and consistent set of axioms for all mathematics is impossible. The first incompleteness theorem states that no consistent system of axioms whose theorems can be listed by an effective procedure (i.
AtheismAtheism, in the broadest sense, is an absence of belief in the existence of deities. Less broadly, atheism is a rejection of the belief that any deities exist. In an even narrower sense, atheism is specifically the position that there no deities. Atheism is contrasted with theism, which in its most general form is the belief that at least one deity exists. The first individuals to identify themselves as atheists lived in the 18th century during the Age of Enlightenment.
René DescartesRené Descartes (deɪˈkɑːrt or UKˈdeɪkɑːrt; ʁəne dekaʁt; Latinized: Renatus Cartesius; 31 March 1596 – 11 February 1650) was a French philosopher, scientist, and mathematician, widely considered a seminal figure in the emergence of modern philosophy and science. Mathematics was central to his method of inquiry, and he connected the previously separate fields of geometry and algebra into analytic geometry. Descartes spent much of his working life in the Dutch Republic, initially serving the Dutch States Army, later becoming a central intellectual of the Dutch Golden Age.
LogicismIn the philosophy of mathematics, logicism is a programme 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.
Quantifier (logic)In logic, a quantifier is an operator that specifies how many individuals in the domain of discourse satisfy an open formula. For instance, the universal quantifier in the first order formula expresses that everything in the domain satisfies the property denoted by . On the other hand, the existential quantifier in the formula expresses that there exists something in the domain which satisfies that property. A formula where a quantifier takes widest scope is called a quantified formula.
William JamesWilliam James (January 11, 1842 – August 26, 1910) was an American philosopher, historian, and psychologist, and the first educator to offer a psychology course in the United States. James is considered to be a leading thinker of the late 19th century, one of the most influential philosophers of the United States, and the "Father of American psychology". Along with Charles Sanders Peirce, James established the philosophical school known as pragmatism, and is also cited as one of the founders of functional psychology.
Age of EnlightenmentThe Age of Enlightenment or the Enlightenment, also known as the Age of Reason, was an intellectual and philosophical movement that occurred in Europe, especially Western Europe, in the 17th and 18th centuries, with global influences and effects. The Enlightenment included a range of ideas centered on the value of human happiness, the pursuit of knowledge obtained by means of reason and the evidence of the senses, and ideals such as natural law, liberty, progress, toleration, fraternity, constitutional government, and separation of church and state.
