Paul Weiss

 

From Science and Sanity, 1933 by Alfred Korzybski

 

SUPPLEMENT II

THE THEORY OF TYPES

BY PAUL WEISS*

 

      It would seem from the interpretation that Whitehead and Russell put on the theory of types,[1] that it is impossible or meaningless to state propositions which have an unrestricted possible range of values, or which, in any sense, are arguments to themselves. Thus on the acceptance of the principle that statements about all propositions are meaningless,2 it would be illegitimate to say, "all propositions are representable by symbols"   "all propositions involve judgment,"   "all propositions are elementary or not elementary," and if no statement could be made about all the members of a set,3 it would be impossible to say, "all meanings are limited by a context,"   "all ideas are psychologically conditions,"   "all significant assertions have grammatical structures," etc., all of which are intended to apply to themselves as well. The theory seems also to make ineffective a familiar form of refutation. General propositions are frequently denied because their enunciation or acknowledgment depends on the tacit supposition of the truth of a contradictory or contrary proposition. Such refutations assume that the general proposition should be capable of being an argument of the same type and to the same function as its own arguments, so that according to Whitehead and Russell, they fallaciously refute "by an argument which involves a vicious circle fallacy."4

      That these limitation on the scope of assertions or on the validity of refutations are rarely heeded is apparent even from a cursory examination of philosophical writings since 1910, Thus Russell, apropos to Bergson's attempt to state a formula for the comic say,5, "It would seem to be impossible to find any such formula as M. Bergson seeks. Every formula treats what is living as if it were mechanical, and is therefore by his own rules a fitting object of laughter." The characterisation of all formulæ, even though it refers to a totality, seems to Mr. Russell to be of the same type as the formulæ characterized.


    1 Chap. II., Principia Mathematica.
    2 P. 37, ibid. (second edition).       3 P. 37., ibid.       4 P. 38, ibid.
    5 "Prof. Guide to Laughter," Cambridge Review, Vol. 32, 1912, and Jourdain's Philosophy of Mr. B*tr*nd R*ss*ll, pp. 86-7
    * [Reprinted from MIND: a Quarterly Review of Psychology and Philosophy. Vol. XXXVII., N.S., No. 147 ; with minor corrections.]

 

      If the theory were without any embarrassments of its own, and were indispensable for the resolution of the so-called paradoxes1 (which no one seems to believe), there would be nothing to do but to acknowledge the impossibility of cosmic formulations, as well as the inadequacy of philosophic criticisms, and to pass charitably over such remarks as Russell's as mere accidents in a busy life. However, the statement of the theory itself involves the following difficulties in connection with (1) its scope, (2) its applicability to propositions made about it, and (3) its description.

1. It is either about all propositions or it is not.

A. If it were about all propositions it would violate the theory of types and be meaningless or self-contradictory.

B. If it were not about all propositions, it would not be universally applicable. To state it, its limitations of application would have to be specified.   (Etc.)

( pages 737-738 )

 

Selected bibliographic

Author Peirce, Charles S. (Charles Sanders), 1839-1914. Title Collected papers of Charles Sanders Peirce / edited by Charles Hartshorne and Paul Weiss. Publisher Bristol, England : Thoemmes Press, 1998. Description 8 v. : ill. ; 23 cm. ISBN 1855065568 (set) Language English Note Originally published: Cambridge : Harvard University Press, 1931-58. Note Includes bibliographical references and indexes. Contents v.1. Principles of philosophy -- v. 2. Elements of logic -- v. 3. Exact logic -- v. 4. The simplest mathematics -- v. 5. Pragmatism and pragmaticism -- v. 6. Scientific metaphysics -- v. 7. Science and philosophy -- v. 8. Reviews, correspondence, and bibliography. Subject Philosophy, Modern -- 20th century. Pragmatism. Science -- Philosophy. Format Book Library GTU 2

Author Peirce, Charles S. (Charles Sanders), 1839-1914. Uniform Title [ Works. English. 1994] Title The collected papers of Charles Sanders Peirce [electronic resource]. Publisher Charlottesville, Va. : InteLex Corporation, 1994. Series InteLex Past Masters ISBN 1570852227 (web) Language English Note Title from title screen (as viewed on July 13, 2004). The Past Masters The Collected Works of Charles Sanders Peirce contains the complete eight volume edition of The Collected Papers of Charles Sanders Peirce, edited by Charles Hartshorne and Paul Weiss (vols. 1-6), and Arthur Burks (vols. 7-8) published by Harvard University Press. Note Access restricted to subscribers. Subject Philosophy, Modern. Pragmatism. Logic. Reasoning. Semiotics. Format Book Computer file Online Library UCB 3

Author Peirce, Charles S. (Charles Sanders), 1839-1914. Title Collected papers. Edited by Charles Hartshorne and Paul Weiss. Publisher Cambridge, Belknap Press of Harvard University Press, 1960- Description v. in illus., diagrs., tables. 25 cm. ISBN 0674138007 Language English Note LIB. HAS: v. 1-2 and v. 5-6 (c1963) Contents v. 1-2. Principles of philosophy and Elements of logic.--v. 3-4. Exact logic (published papers) and The simplest mathematics.--v. 5-6. Pragmatism and pragmaticism and Scientific metaphysics. Subject Philosophy. Format Book Library SRLF UCLA UCD GTU UCSD UCI UCB 4

Author Peirce, Charles S. (Charles Sanders), 1839-1914. Title Collected papers of Charles Sanders Peirce, edited by Charles Hartshorne and Paul Weiss. Publisher Cambridge, Harvard University Press, 1960- Description 6 v. in 3. illus., diagrs., tables. 24 cm. Language English Contents 1-2. Principles of philosophy. Elements of logic.--3-4. Exact logic. The simplest mathematics.--5-6. Pragmatism and pragmaticism. Scientific metaphysics. Subject Peirce, Charles S. (Charles Sanders), 1839-1914. Philosophy. Format Book Library UCSB 5

Author Peirce, Charles S. (Charles Sanders), 1839-1914. Title Collected papers. Edited by Charles Hartshorne and Paul Weiss. Publisher Cambridge, Belknap Press of Harvard University Press 1958. Description 8v. illus., diagrs., tables. Language English Contents v. 1-2. Principles of philosophy and Elements of logic. -v. 3-4. Exact logic (published papers) and The simplest mathematics.-v. 5-6. Pragmatism and pragmaticism and Scientific metaphysics.-v. 7. Science and philosophy, edited by A. W. Burks.-v. 8. Reviews, correspondence, and bibliography, edited by A. W. Burks. Subject Philosophy. Format Book Library UCSC 6

Author Peirce, Charles S. (Charles Sanders), 1839-1914. Title Collected papers. Edited by Charles Hartshorne and Paul Weiss. Publisher Cambridge : Belknap Press of Harvard University Press, 1974-1979, c1935-1961. Description 8 v. in 4 illus. 25 cm. Language English Note Vols. 7-8 edited by A. W. Burks. Note Includes bibliographical references. Contents v. 1-2. Principles of philosophy and Elements of logic. 1 v.--v. 3-4. Exact logic (published papers) and The simplest mathematics. 1 v.--v. 5-6. Pragmatism and pragmaticism and Scientific metaphysics. 1 v.--v. 7-8. Science and philosophy and reviews, correspondence, and bibliography. 1 v. Subject Philosophy. Format Book Library UCLA 7

Author Peirce, Charles S. (Charles Sanders), 1839-1914. Title Collected papers, edited by Charles Hartshorne and Paul Weiss. Publisher Cambridge : Harvard University Press, 1931-60. Description 8 v. in 7 ports., diagrs., facsim. 24 cm. Language English Note Vols. 7-8 edited by A. W. Burks. Note Bibliography: v. 8, p. 251-330. Contents v.1. Principles of philosophy.--v.2 Elements of logic.--v.3. Exact logic (published papers)--v.4. The simplest mathematics.--v.5. Pragmatism and pragmaticism.--v.6. Scientific metaphysics.--v.7. Science and philosophy.--v.8. Reviews, correspondence, and bibliography.

 

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Last updated 12 Dec 04

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