David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Journal of Philosophical Logic 26 (2):181-222 (1997)
Formal systems are standardly envisaged in terms of a grammar specifying well-formed formulae together with a set of axioms and rules. Derivations are ordered lists of formulae each of which is either an axiom or is generated from earlier items on the list by means of the rules of the system; the theorems of a formal system are simply those formulae for which there are derivations. Here we outline a set of alternative and explicitly visual ways of envisaging and analyzing at least simple formal systems using fractal patterns of infinite depth. Progressively deeper dimensions of such a fractal can be used to map increasingly complex wffs or increasingly complex 'value spaces', with tautologies, contradictions, and various forms of contingency coded in terms of color. This and related approaches, it turns out, offer not only visually immediate and geometrically intriguing representations of formal systems as a whole but also promising formal links (1) between standard systems and classical patterns in fractal geometry, (2) between quite different kinds of value spaces in classical and infinite-valued logics, and (3) between cellular automata and logic. It is hoped that pattern analysis of this kind may open possibilities for a geometrical approach to further questions within logic and metalogic
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
|Through your library||Configure|
References found in this work BETA
No references found.
Citations of this work BETA
No citations found.
Similar books and articles
Sara L. Uckelman (2013). Medieval Disputationes de Obligationibus as Formal Dialogue Systems. Argumentation 27 (2):143-166.
Catarina Dutilh Novaes (2011). The Different Ways in Which Logic is (Said to Be) Formal. History and Philosophy of Logic 32 (4):303 - 332.
Gary Mar & Paul St Denis (1999). What the Liar Taught Achilles. Journal of Philosophical Logic 28 (1):29-46.
Shahid Rahman & Helge Rückert (2001). Dialogical Connexive Logic. Synthese 127 (1-2):105 - 139.
Douglas Walton (2003). Is There a Burden of Questioning? Artificial Intelligence and Law 11 (1):1-43.
Carlo Cellucci (1992). Gödel's Incompleteness Theorem and the Philosophy of Open Systems. In Daniel Miéville (ed.), Kurt Gödel: Actes du Colloque, Neuchâtel 13-14 Juin 1991, pp. 103-127. Travaux de logique N. 7, Université de Neuchâtel.
Erik C. W. Krabbe (1985). Formal Systems of Dialogue Rules. Synthese 63 (3):295 - 328.
Erick C. W. Krabbe (1984). Formal Systems of Dialogue Rules. Synthese 58 (2):295 - 328.
Richard D. Campbell (1996). Describing the Shapes of Fern Leaves: A Fractal Geometrical Approach. Acta Biotheoretica 44 (2).
Added to index2009-01-28
Total downloads13 ( #100,596 of 1,089,053 )
Recent downloads (6 months)1 ( #69,801 of 1,089,053 )
How can I increase my downloads?