Skip to main content
×
Home
    • Aa
    • Aa

LOGIC IN THE TRACTATUS

Abstract
Abstract

I present a reconstruction of the logical system of the Tractatus, which differs from classical logic in two ways. It includes an account of Wittgenstein’s “form-series” device, which suffices to express some effectively generated countably infinite disjunctions. And its attendant notion of structure is relativized to the fixed underlying universe of what is named.

There follow three results. First, the class of concepts definable in the system is closed under finitary induction. Second, if the universe of objects is countably infinite, then the property of being a tautology is $\Pi _1^1$ -complete. But third, it is only granted the assumption of countability that the class of tautologies is ${\Sigma _1}$ -definable in set theory.

Wittgenstein famously urges that logical relationships must show themselves in the structure of signs. He also urges that the size of the universe cannot be prejudged. The results of this paper indicate that there is no single way in which logical relationships could be held to make themselves manifest in signs, which does not prejudge the number of objects.

    • Send article to Kindle

      To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      LOGIC IN THE TRACTATUS
      Available formats
      ×
      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your Dropbox account. Find out more about sending content to Dropbox.

      LOGIC IN THE TRACTATUS
      Available formats
      ×
      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your Google Drive account. Find out more about sending content to Google Drive.

      LOGIC IN THE TRACTATUS
      Available formats
      ×
Copyright
Corresponding author
*DEPARTMENT OF PHILOSOPHY BOSTON UNIVERSITY BOSTON, MA 02215, USA E-mail: max@whythis.net
Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

W Ackermann . (1937). Die widerspruchsfreiheit der allgemeinen mengenlehre. Mathematische Annalen, 114, 305315.

A Avron . (2003). Transitive closure and the mechanization of mathematics. In F. D Kamareddine . editor. Thirty five Years of Automating Mathematics. Dordrecht: Springer, pp. 149171.

J Barwise . (1975). Admissible Sets and Structures. Berlin: Springer-Verlag.

J Barwise . (1977). On Moschovakis closure ordinals. Journal of Symbolic Logic, 42(2), 292296.

T Bays . (2001). On Tarski on models. Journal of Symbolic Logic, 66(4), 17011726.

K Fine . (2010). Towards a theory of part. Journal of Philosophy, 107(11), 559589.

J Floyd . (2001). Number and ascriptions of number in Wittgenstein’s Tractatus . In J. Floyd and S. Shieh , editors. Future Pasts. Cambridge, MA: Harvard University Press, pp. 145193.

R Fogelin . (1976). Wittgenstein. London: Routledge and Kegan Paul.

P Frascolla . (1997). The “Tractatus” system of arithmetic. Synthese, 112(3), 353378.

L Henkin . (1950). Completeness in the theory of types. Journal of Symbolic Logic, 15(2), 8191.

L Kirby . (2009). Finitary set theory. Notre Dame Journal of Formal Logic, 50(3), 227244.

P Mancosu . (2010). Fixed- versus variable-domain interpretations of Tarski’s account of logical consequence. Philosophy Compass, 5(9), 745759.

M Potter . (2009). The logic of the Tractatus . In D. M. Gabbay and J. Woods , editors. From Russell to Church, Volume 5 of Handbook of the History of Logic. Amsterdam: Elsevier, pp. 255304.

B. Rogers & K Wehmeier . (2012). Tractarian first-order logic: Identity and the N-operator. Review of Symbolic Logic, 5(4), 538573.

I Rumfitt . (2006). ‘Yes’ and ‘no’. Mind, 109(436), 781824.

T Smiley . (1996). Rejection. Analysis, 56, 19.

S Soames . (1983). Generality, truth-functions, and expressive capacity in the Tractatus . Philosophical Review, 92(4), 573589.

P Sullivan . (2004). The general form of the proposition is a variable. Mind, 113(449), 4356.

G Sundholm . (1992). The general form of the operation in Wittgenstein’s Tractatus . Grazer Philosophische Studien, 42, 5776.

J Väänänen . (2001). Second order logic and foundations of mathematics. Bulletin of Symbolic Logic, 7(4), 504520.

K Wehmeier . (2004). Wittgensteinian predicate logic. Notre Dame Journal of Formal Logic, 45, 111.

K Wehmeier . (2008). Wittgensteinian tableaux, identity, and codenotation. Erkenntnis, 69(3), 363376.

S Yablo . (1993). Paradox without self-reference. Analysis, 53(4), 252–252.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

The Review of Symbolic Logic
  • ISSN: 1755-0203
  • EISSN: 1755-0211
  • URL: /core/journals/review-of-symbolic-logic
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×

Keywords:

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 236 *
Loading metrics...

Abstract views

Total abstract views: 821 *
Loading metrics...

* Views captured on Cambridge Core between 12th January 2017 - 27th July 2017. This data will be updated every 24 hours.