Notre Dame Journal of Formal Logic

The Irrelevance of Distribution for the Syllogism

Wallace A. Murphree


While accepting that distribution is a coherent notion, I argue that it is nevertheless irrelevant to the working of the syllogism. Instead, I propose: (i) that a term's being distributed or undistributed in a proposition is its capacity to be replaced in a truth-preserving substitution with a narrower or a wider term; (ii) that which capacity the term has is determined by whether it occurs as the predicate of a negative or of an affirmative statement of the proposition; and (iii) that it is only the term's occurrence as the predicate of a negative or an affirmative statement–rather than its distribution value–that is relevant to syllogistic entailment.

Article information

Notre Dame J. Formal Logic Volume 35, Number 3 (1994), 433-449.

First available: 21 December 2002

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Digital Object Identifier

Zentralblatt MATH identifier

Primary: 03A05: Philosophical and critical {For philosophy of mathematics, see also 00A30}


Murphree, Wallace A. The Irrelevance of Distribution for the Syllogism. Notre Dame Journal of Formal Logic 35 (1994), no. 3, 433--449. doi:10.1305/ndjfl/1040511349.

Export citation


  • [1] Barker, S., The Elements of Logic, McGraw-Hill, New York, 1965.
  • [2] Englebretsen, G., ``Defending Distribution," Dialogos, vol. 45 (1985), pp. 157--159.
  • [3] Geach, P., Reference and Generality: An Examination of Some Medieval and Modern Theories, Cornell University Press, New York, 1962.
  • [4] Geach, P., ``The Doctrine of Distribution," Mind, vol. LXV (1956), pp. 67--74.
  • [5] Geach, P., ``Distribution: A Last Word," Philosophical Review, vol. LXIX (1960), pp. 396--398.
  • [6] Johnstone, H., ``Pairs of Negative Syllogistic Premises Yielding Conclusions," Logique et analyse, vol. 85--86 (1979), pp. 109--110.
  • [7] Katz, B., and A. Martinich, ``The Distribution of Terms," Notre Dame Journal of Formal Logic, Vol. XVII (1976), pp. 279--283.
  • [8] Kelley, D., The Art of Reasoning, Norton, New York, 1990.
  • [9] Murphree, W., Numerically Exceptive Logic: A Reduction of the Classical Syllogism, Peter Lang, New York, 1991.
  • [10] Sommers, F., ``Distribution Matters," Mind, vol. LXXXIV (1975), pp. 27--46.
  • [11] Toms, E., ``Mr. Geach on Distribution," Mind, vol. LXXIV (1965), pp. 428--431.
  • [12] Williamson, C., ``Traditional Logic as the Logic of Distribution Values," Logique et analyse, vol. 14 (1971), pp. 729--746.