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 philosophic ...

metaphysics Metaphysics is the branch of philosophy that examines the basic structure of reality. It is traditionally seen as the study of mind-independent features of the world, but some theorists view it as an inquiry into the conceptual framework of ...

, and the

philosophy of language Philosophy of language refers to the philosophical study of the nature of language. It investigates the relationship between language, language users, and the world. Investigations may include inquiry into the nature of Meaning (philosophy), me ...

, 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 or apparently true premises, leads to a seemingly self-contradictor ...

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-order ...

, 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, 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 publishing house of the University of Oxford. It is the largest university press in the world. Its first book was printed in Oxford in 1478, with the Press officially granted the legal right to print books ...

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

References

Paradoxes Philosophical problems Concepts in metaphysics {{logic-stub

See also

References