Implication and What There is

  • Louis O. Kattsoff


There is one other relation in logic that needs to be considered. That is the relation symbolized by ‘ → ’ and interpreted as ’implies, or ‘if ..., then ...’ These two interpretations reveal the existence of an ambiguity in the semantics of ‘ →. ’ My problem may be stated somewhat in this fashion: what, if anything, about what there is does the relation symbolized by ‘ → ’ and interpreted in various ways intend to mirror ? What others thought it represented is an historical question whose answer is to be found in the works of Leibniz, Aristotle, and all other logicians who laid the foundations of logical theory. But even if I should turn this into an historical study. I would then have indicated what these philosophers intended. And I am not here concerned with that type of historical study. Rather, what I want to determine is the underlying element that causes this type of relation to be introduced. In other words, why is it necessary to have such an element in a language at all?


Historical Study Truth Table Logical Theory Logical Schema Linguistic Form 
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  1. 1.
    All the difficulties Strawson finds in the interpretation of logic have their root in this: cf. Introduction to Logical Theory, (New York: John Wiley and Sons, 1953). Warnock also points up the same type of thing in Quine in his article “Metaphysics in Logic,” Proceedings of the Aristotelian Society,N.S. LI, 1950–51, pp. 196 ff.Google Scholar
  2. 2.
    John Wisdom, “Metaphysics,” Proceedings of the Aristotelian Society, N.S. LI, 1950–51, pp. i ff.Google Scholar

Copyright information

© Martinus Nijhoff, The Hague, Netherlands 1956

Authors and Affiliations

  • Louis O. Kattsoff
    • 1
  1. 1.University of North CarolinaUSA

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