philosophical logic 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 ...

metaphysics Metaphysics is the branch of philosophy that studies the fundamental nature of reality, the first principles of being, identity and change, space and time, causality, necessity, and possibility. It includes questions about the nature of conscio ...

, and the

philosophy of language In analytic philosophy, philosophy of language investigates the nature of language and the relations between language, language users, and the world. Investigations may include inquiry into the nature of meaning, intentionality, reference, the ...

, the problem of absolute generality is the problem of referring to absolutely everything. Historically, philosophers have assumed that some of their statements are absolutely general, referring to truly everything. In recent years, logicians working in the logic of quantification and

paradox A paradox is a logically self-contradictory statement or a statement that runs contrary to one's expectation. It is a statement that, despite apparently valid reasoning from true premises, leads to a seemingly self-contradictory or a logically u ...

have challenged this view, arguing that it is impossible for the logical quantifiers to range over an absolutely unrestricted domain. Philosophers who deny the possibility of absolutely unrestricted quantification (often called ''generality relativists'') argue that attempting to speak absolutely generally generates paradoxes such as Russell's or Grelling's, that absolute generality leads to indeterminacy due to the

Löwenheim–Skolem theorem In mathematical logic, the Löwenheim–Skolem theorem is a theorem on the existence and cardinality of models, named after Leopold Löwenheim and Thoralf Skolem. The precise formulation is given below. It implies that if a countable first-orde ...

, or that absolute generality fails because the notion of "object" is relative. Philosophers who believe that we can indeed quantify over absolutely everything (known as ''generality absolutists''), such as

Timothy Williamson Timothy Williamson (born 1955) is a British philosopher whose main research interests are in philosophical logic, philosophy of language, epistemology and metaphysics. He is the Wykeham Professor of Logic at the University of Oxford, and fel ...

, may respond by noting that it is difficult to see how a skeptic of absolute generality can frame this view without invoking the concept of absolute generality. A 2006 book, ''Absolute Generality'', published by

Oxford University Press Oxford University Press (OUP) is the university press of the University of Oxford. It is the largest university press in the world, and its printing history dates back to the 1480s. Having been officially granted the legal right to print book ...

, contains essays on the subject written by both the leading proponents and opponents of absolutely unrestricted quantification.

References

Paradoxes {{logic-stub

See also

References