Rosalie Iemhoff (born 1969) [1] is a Dutch logician whose research interests include intuitionistic logic and proof theory. She is a professor in the Department of Philosophy and Religious Studies at Utrecht University, [2] and an editor-in-chief of the Journal of Philosophical Logic . [3] She is also a member of the editorial board of the Stanford Encyclopedia of Philosophy. [4]
After earning a master's degree in mathematics from the University of Amsterdam in 1995, [5] Iemhoff completed a PhD in mathematical logic there in 2001. [2] Her dissertation, Provability Logic and Admissible Rules, was jointly promoted by Anne Sjerp Troelstra, Dick de Jongh, and Albert Visser. [6] [7]
She was a postdoctoral researcher at the University of California, San Diego and a Marie Curie Fellow at TU Wien, before becoming an assistant professor at Utrecht University in 2006. [2] [5] She was promoted to associate professor in 2010 and full professor in 2019. [5]
In the philosophy of mathematics, intuitionism, or neointuitionism, is an approach where mathematics is considered to be purely the result of the constructive mental activity of humans rather than the discovery of fundamental principles claimed to exist in an objective reality. That is, logic and mathematics are not considered analytic activities wherein deep properties of objective reality are revealed and applied, but are instead considered the application of internally consistent methods used to realize more complex mental constructs, regardless of their possible independent existence in an objective reality.
Luitzen Egbertus Jan "Bertus" Brouwer was a Dutch mathematician and philosopher who worked in topology, set theory, measure theory and complex analysis. Regarded as one of the greatest mathematicians of the 20th century, he is known as one of the founders of modern topology, particularly for establishing his fixed-point theorem and the topological invariance of dimension.
Proof theory is a major branch of mathematical logic and theoretical computer science within which proofs are treated as formal mathematical objects, facilitating their analysis by mathematical techniques. Proofs are typically presented as inductively-defined data structures such as lists, boxed lists, or trees, which are constructed according to the axioms and rules of inference of a given logical system. Consequently, proof theory is syntactic in nature, in contrast to model theory, which is semantic in nature.
Understood in a narrow sense, philosophical logic is the area of logic that studies the application of logical methods to philosophical problems, often in the form of extended logical systems like modal logic. Some theorists conceive philosophical logic in a wider sense as the study of the scope and nature of logic in general. In this sense, philosophical logic can be seen as identical to the philosophy of logic, which includes additional topics like how to define logic or a discussion of the fundamental concepts of logic. The current article treats philosophical logic in the narrow sense, in which it forms one field of inquiry within the philosophy of logic.
Jan Łukasiewicz was a Polish logician and philosopher who is best known for Polish notation and Łukasiewicz logic. His work centred on philosophical logic, mathematical logic and history of logic. He thought innovatively about traditional propositional logic, the principle of non-contradiction and the law of excluded middle, offering one of the earliest systems of many-valued logic. Contemporary research on Aristotelian logic also builds on innovative works by Łukasiewicz, which applied methods from modern logic to the formalization of Aristotle's syllogistic.
George Stephen Boolos was an American philosopher and a mathematical logician who taught at the Massachusetts Institute of Technology.
Ruth Barcan Marcus was an American academic philosopher and logician best known for her work in modal and philosophical logic. She developed the first formal systems of quantified modal logic and in so doing introduced the schema or principle known as the Barcan formula. Marcus, who originally published as Ruth C. Barcan, was, as Don Garrett notes "one of the twentieth century's most important and influential philosopher-logicians". Timothy Williamson, in a 2008 celebration of Marcus' long career, states that many of her "main ideas are not just original, and clever, and beautiful, and fascinating, and influential, and way ahead of their time, but actually – I believe – true".
Provability logic is a modal logic, in which the box operator is interpreted as 'it is provable that'. The point is to capture the notion of a proof predicate of a reasonably rich formal theory, such as Peano arithmetic.
Bastiaan Cornelis van Fraassen is a Dutch-American philosopher noted for his contributions to philosophy of science, epistemology and formal logic. He is a Distinguished Professor of Philosophy at San Francisco State University and the McCosh Professor of Philosophy Emeritus at Princeton University.
In mathematical logic, a judgment or assertion is a statement or enunciation in a metalanguage. For example, typical judgments in first-order logic would be that a string is a well-formed formula, or that a proposition is true. Similarly, a judgment may assert the occurrence of a free variable in an expression of the object language, or the provability of a proposition. In general, a judgment may be any inductively definable assertion in the metatheory.
Philosophy of logic is the area of philosophy that studies the scope and nature of logic. It investigates the philosophical problems raised by logic, such as the presuppositions often implicitly at work in theories of logic and in their application. This involves questions about how logic is to be defined and how different logical systems are connected to each other. It includes the study of the nature of the fundamental concepts used by logic and the relation of logic to other disciplines. According to a common characterisation, philosophical logic is the part of the philosophy of logic that studies the application of logical methods to philosophical problems, often in the form of extended logical systems like modal logic. But other theorists draw the distinction between the philosophy of logic and philosophical logic differently or not at all. Metalogic is closely related to the philosophy of logic as the discipline investigating the properties of formal logical systems, like consistency and completeness.
Peter Henry George Aczel was a British mathematician, logician and Emeritus joint Professor in the Department of Computer Science and the School of Mathematics at the University of Manchester. He is known for his work in non-well-founded set theory, constructive set theory, and Frege structures.
Dirk van Dalen is a Dutch mathematician and historian of science.
Sergei Nikolaevich Artemov is a Russian-American researcher in logic and its applications. He currently holds the title of Distinguished Professor at the Graduate Center of the City University of New York where he is the founder and head of its research laboratory for logic and computation. His research interests include proof theory and logic in computer science, optimal control and hybrid systems, automated deduction and verification, epistemology, and epistemic game theory. He is best known for his invention of logics of proofs and justifications.
Juliet Floyd is professor of philosophy at Boston University. Her strongest research interests lie in early analytic philosophy and she has used early analytic philosophy as a lens to examine a diverse array of topics.
Richard Zach is a Canadian logician, philosopher of mathematics, and historian of logic and analytic philosophy. He is currently Professor of Philosophy at the University of Calgary.
Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the study of deductively valid inferences or logical truths. It examines how conclusions follow from premises based on the structure of arguments alone, independent of their topic and content. Informal logic is associated with informal fallacies, critical thinking, and argumentation theory. Informal logic examines arguments expressed in natural language whereas formal logic uses formal language. When used as a countable noun, the term "a logic" refers to a specific logical formal system that articulates a proof system. Logic plays a central role in many fields, such as philosophy, mathematics, computer science, and linguistics.
Dutch philosophy is a broad branch of philosophy that discusses the contributions of Dutch philosophers to the discourse of Western philosophy and Renaissance philosophy. The philosophy, as its own entity, arose in the 16th and 17th centuries through the philosophical studies of Desiderius Erasmus and Baruch Spinoza. The adoption of the humanistic perspective by Erasmus, despite his Christian background, and rational but theocentric perspective expounded by Spinoza, supported each of these philosopher's works. In general, the philosophy revolved around acknowledging the reality of human self-determination and rational thought rather than focusing on traditional ideals of fatalism and virtue raised in Christianity. The roots of philosophical frameworks like the mind-body dualism and monism debate can also be traced to Dutch philosophy, which is attributed to 17th century philosopher René Descartes. Descartes was both a mathematician and philosopher during the Dutch Golden Age, despite being from the Kingdom of France. Modern Dutch philosophers like D.H. Th. Vollenhoven provided critical analyses on the dichotomy between dualism and monism.
Alice Geraldine Baltina ter Meulen is a Dutch linguist, logician, and philosopher of language whose research topics include genericity in linguistics, intensional logic, generalized quantifiers, discourse representation theory, and the linguistic representation of time. She is a professor emerita at the University of Geneva.
Laurina Christina (Rineke) Verbrugge is a Dutch logician and computer scientist known for her work on interpretability logic and provability logic. She completed her PhD at the University of Amsterdam in 1993 under the supervision of Dick de Jongh, Anne Troelstra, and Albert Visser.
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