Notre Dame Journal of Formal Logic

Peeking at the Impossible

Chris Mortensen


The question of the interpretation of impossible pictures is taken up. Penrose's account is reviewed. It is argued that whereas this account makes substantial inroads into the problem, there needs to be a further ingredient. An inconsistent account using heap models is proposed.

Article information

Notre Dame J. Formal Logic Volume 38, Number 4 (1997), 527-534.

First available in Project Euclid: 10 December 2002

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 03B60: Other nonclassical logic


Mortensen, Chris. Peeking at the Impossible. Notre Dame J. Formal Logic 38 (1997), no. 4, 527--534. doi:10.1305/ndjfl/1039540768.

Export citation


  • [1]Mortensen, C., Inconsistent Mathematics, Kluwer, Dordrecht, 1995.
  • [2]Mortensen, C., ``The Leibniz continuity condition, inconsistency and quantum dynamics,'' Journal of Philosophical Logic, vol. 26 (1997), pp. 377--89.
  • [3] Penrose, R., ``On the cohomology of impossible figures,'' Structural Topology, vol. 17 (1991), pp. 11--16.
  • [4] Penrose, R., ``Mathematics of the impossible,'' pp. 324--34 in The Artful Eye, edited by R. Gregory et al., Oxford University Press, Oxford, 1995.
  • [5] Penrose, L. S., and R. Penrose, ``Impossible objects, a special type of visual illusion,'' British Journal of Psychology, vol. 49 (1958), p. 31.
  • [6] Priest, G., ``Inconsistent models of arithmetic, Part 1: Finite models,'' The Journal of Philosophical Logic, vol. 26 (1997), pp. 223--35.
  • [7] van Bendegem, J. P.,``Strict, yet rich, finitism," pp. 61--79, in First International Symposium on Gödel's Theorem, World Scientific, Singapore, 1993.