In the context of computability theory, the term "low" usually refers to a classification of degrees of unsolvability or computably enumerable (c.e.) sets that are relatively "simple" in terms of their Turing degrees. Specifically, a set (or degree) is said to be low if it is computationally weak in a certain sense.

Alfred North Whitehead was an English mathematician and philosopher known for his work in various fields, including philosophy of science, metaphysics, logic, and education. His major works reflect his systematic approach to philosophy and his interest in process and change. Here are some of his most notable works: 1. **"Principia Mathematica" (1910-1913)** - Co-authored with Bertrand Russell, this monumental work aimed to establish a solid foundation for mathematics using formal logic.

Bertrand Russell (1872–1970) was a British philosopher, logician, mathematician, historian, and social critic. He is best known for his work in mathematical logic and analytical philosophy, making significant contributions to a wide range of fields, including philosophy of language, epistemology, ethics, and political theory. Russell was a prominent figure in the development of modern logic and is one of the founders of analytic philosophy, along with figures like G.E.

"Failure to refer" is a term commonly used in legal and medical contexts, though its meaning can vary depending on the specific field. Generally, it refers to a situation where an individual, such as a healthcare provider or a professional, does not direct a patient or client to another expert or specialist when necessary, potentially resulting in harm or inadequate care.

Logical atomism is a philosophical belief primarily associated with the work of early 20th-century philosophers, notably Bertrand Russell and Ludwig Wittgenstein. It is a logical theory that proposes that the world consists of a series of atomic facts or simple propositions that can be combined to describe more complex realities.

Gerald Sacks is an American mathematician known for his contributions to the field of mathematical logic, particularly in the areas of recursion theory and model theory. He has worked on topics such as the structure of certain mathematical models and the relationships between different levels of mathematical infinities. Sacks is also known for the Sacks forcing technique, which is a method used in set theory to construct models with certain desirable properties. His work is significant in understanding the foundations of mathematics and the nature of mathematical truth.

Greg Hjorth is a noted mathematician primarily known for his contributions to the field of logic and set theory, particularly in areas related to the foundations of mathematics, model theory, and descriptive set theory. He has published numerous research papers and articles addressing complex topics within these domains.

Jean-Yves Béziau is a prominent philosopher and logician known for his work in the fields of logic, philosophy, and the foundations of mathematics. He has contributed to various areas, including non-classical logics, paraconsistent logics, and the philosophy of mathematics. Béziau is also recognized for his research on the relationships between logic, language, and philosophical inquiry.

Paul Bernays (1888–1979) was a significant figure in the fields of mathematics and logic. He was born in Switzerland and later became a prominent mathematician and philosopher, particularly known for his work in foundational mathematics, logic, and the philosophy of mathematics. Bernays is often associated with the development of predicate logic and contributions to set theory.

A "filter quantifier" is a concept that can be found in various fields, but it is most commonly associated with logic, mathematics, and computer science, particularly in the context of quantified expressions in formal systems or programming languages. In logical and mathematical contexts, filter quantifiers can be understood as operators that restrict the domain of discourse to a certain subset defined by specific properties or conditions.

Yehoshua Bar-Hillel (1915-1975) was a prominent Israeli philosopher, linguist, and computer scientist known for his contributions to the fields of artificial intelligence, linguistics, and philosophy of language. He was a key figure in the development of natural language processing and was involved in early work that laid the groundwork for AI research in these areas.

Tarski's World is an educational software tool designed to help students learn the principles of formal logic, particularly the semantics of predicate logic. It was developed by philosopher and logician Alfred Tarski and his pedagogical approach is used in various logic and philosophy courses. In Tarski's World, users interact with a virtual environment that allows them to create and manipulate three-dimensional shapes and objects.

Meronomy is a term used in various fields, including philosophy, linguistics, and information science, to refer to the study of parts and the relationships between parts and wholes. The term derives from the Greek words "meros," meaning "part," and "nomos," meaning "law" or "norm." In philosophy, particularly in ontology, meronomy examines how entities are composed of parts and explores the hierarchical relationships among those parts.

Supervenience is a philosophical concept that describes a relationship between different sets of properties or facts, often used in discussions about the relationship between the mental and the physical, or between moral properties and non-moral properties. The idea is that if one set of properties (the supervenient properties) changes, there must be a change in the other set of properties (the subvenient properties) as well.

Consistency can refer to several different concepts depending on the context in which it is used. Here are a few of the most common interpretations: 1. **General Definition**: Consistency refers to the quality of being uniform or coherent over time. It implies stability and reliability in behavior, performance, or characteristics. 2. **In Psychology**: Consistency can relate to a person's behavior and attitudes across different situations.

Gentzen's consistency proof is a significant achievement in mathematical logic, particularly in the study of formal systems and their foundational properties. Proposed by Gerhard Gentzen in the 1930s, this proof addresses the consistency of Peano Arithmetic (PA), which is a foundational system for number theory.

A Hilbert system is a type of formal proof system used in mathematical logic and proof theory. Named after the mathematician David Hilbert, it is characterized by a set of axioms and inference rules that allow for the derivation of logical statements. Hilbert systems are typically structured to provide a framework for proving theorems in propositional logic and first-order logic.

A Pure Type System (PTS) is a type-theoretical framework used in computer science and mathematical logic for defining and analyzing programming languages. It generalizes certain typing systems, allowing for the expression of a wide variety of type theories and their associated computational behaviors. Here are some key aspects of Pure Type Systems: 1. **Basic Structure**: A PTS consists of a set of types and terms, along with rules for how types can be constructed from each other and how terms can be typed.

Benjamin Franklin (1706–1790) was an American statesman, inventor, scientist, printer, and writer who is one of the Founding Fathers of the United States. He played a crucial role in the American Enlightenment and the development of the nation. Franklin is best known for his contributions to the fields of electricity, politics, and diplomacy. His famous experiments with electricity led to the invention of the lightning rod, and he made significant contributions to the understanding of electrical phenomena.

Counter-Enlightenment refers to a set of philosophical and ideological movements and ideas that emerged as a reaction against the principles and values of the Enlightenment. The Enlightenment, which spanned the late 17th to the 18th centuries, emphasized reason, individualism, empiricism, and the belief in progress through science and rational thought. It championed ideas such as human rights, democratic governance, secularism, and the universality of knowledge.