In philosophical logic, metaphysics, and the philosophy of language, the problem of absolute generality is the problem of referring to absolutely everything.[1] Historically, philosophers have assumed that some of their statements are absolutely general, referring to truly everything.[1] In recent years, logicians working in the logic of quantification and paradox have challenged this view, arguing that it is impossible for the logical quantifiers to range over an absolutely unrestricted domain.[2]
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, or that absolute generality fails because the notion of "object" is relative.[3]
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.[4]
A 2006 book, Absolute Generality, published by Oxford University Press, contains essays on the subject written by both the leading proponents and opponents of absolutely unrestricted quantification.[5]
^ abAugustín Rayo; Gabriel Uzquiano (2006). Rayo, Augustín; Uzquiano, Gabriel (eds.). Absolute Generality. Oxford: Oxford University Press. CiteSeerX 10.1.1.365.3334.
^Glanzberg, Michael (2004). "Quantification and Realism*". Philosophy and Phenomenological Research. 69 (3): 541–572. doi:10.1111/j.1933-1592.2004.tb00518.x. Retrieved 6 September 2020.
^Priest, Graham (17 September 2007). "Absolute Generality". Notre Dame Philosophical Reviews. University of Notre Dame. Retrieved 6 September 2020.
logic, metaphysics, and the philosophy of language, the problem of absolutegenerality is the problem of referring to absolutely everything. Historically...
various linguistic settings. He frequently collaborates with Jc Beall. Absolutegenerality Contextualism "Glanzberg, Michael". Rutgers Department of Philosophy...
temperature. Additional laws have been suggested, but have not achieved the generality of the four accepted laws, and are generally not discussed in standard...
Philosophy Compass. --------, and Gabriel Uzquiano, eds., 2006. AbsoluteGenerality Oxford University Press. Bertrand Russell, B., 1903. The Principles...
serves a similar purpose to the more common phrase, "without loss of generality" (WLOG). The legal use of the term is somewhat specialized. As glossed...
^{eb}-{R^{b}}_{ecd}\tau ^{ae}} The latter can be shown by taking (without loss of generality) that τ a b = λ a μ b {\displaystyle \tau ^{ab}=\lambda ^{a}\mu ^{b}}...
solved by powerful frequency domain mathematical techniques of great generality, such as the Laplace transform, Fourier transform, Z transform, Bode plot...
V^{*};\mathbb {F} \right)} . Tensor products can be defined in great generality – for example, involving arbitrary modules over a ring. In principle,...
more) monomers can occupy the same location. Although it is simple, its generality gives insight about the physics of polymers. In this model, monomers are...
Leonhard Euler Gauss Joseph Fourier Law of continuity History of calculus Generality of algebra Elementary Calculus: An Infinitesimal Approach Nonstandard...
which such a theorem exists are called Euclidean domains, but in this generality, uniqueness of the quotient and remainder is not guaranteed. Polynomial...
Banach space L 1 ( S , μ ) {\displaystyle L_{1}(S,\mu )} Without loss of generality, one can assume that f is real, because one can split f into its real...
[g(X)]=\int _{-\infty }^{\infty }g(x)\,\mathrm {d} F_{X}(x).} In even greater generality, X could be a random element in any measurable space, in which case the...
little or no decoration, and lacked much complexity in design. These generalities of fascist architecture contributed to the simple aesthetics the edifices...
Electrical charges are omitted from subsequent equations for the sake of generality K a = [ H ] [ A ] [ HA ] {\displaystyle K_{a}={\frac {{\ce {[H] [A]}}}{{\ce...
the book on arithmetic concerns like the field of definition, but in it covers in full generality many scheme-theoretic results stated in this article....
\lambda _{1}} and x the component in which v has maximum absolute value. Without loss of generality assume vx is positive since otherwise you simply take...
If b ≠ 0, the function is called an affine function (see in greater generality affine transformation). Linear algebra is the branch of mathematics concerned...
biblical view of sexual relations is consistently within the pattern of absolute mutual commitment, reflecting God's commitment to his people. And the assumption...
population by conducting a series of questions and then extrapolating generalities in ratio or within confidence intervals. A person who conducts polls...
characteristics that are lost in the voluptuous indolence that enthrals the generality of the western Asiatics." — The English in India, and other sketches,...
disclose its evaluation criteria or decision processes beyond broad generalities, such as long-term citizen population-related goals. One of the government's...
ordinal variable on a scale 1, ..., K. For simplicity, and without loss of generality, we assume y is a non-decreasing vector, that is, yi ≤ {\displaystyle...
the x i {\displaystyle x_{i}} fall in some partially ordered set. For generality, each observation ( x i , y i ) {\displaystyle (x_{i},y_{i})} may be given...
the negative is only an abstraction of the other, and in the highest generality even an abstraction of thought itself." A study of the few sentences under...
Global Information