Abstract
In this chapter we deepen our characterization of propositions and study the basic structures of propositional implication. Here is, then, a short, but slightly unconventional (because more philosophical), introduction to standard two-valued logic. We need this introduction, not only for completeness, given that propositions are contents of practical reasoning, but primarily because the implicational structure of propositions is the paradigm of implicational structure. This is part of the ontological primacy of the contents of contemplative thinking. We make use of most of this chapter in the following ones.
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This name is adopted from Wilfrid Sellars, ‘Presupposing’, The Philosophical Review, 63 (1954): 197–215. Keith Lehrer has informed me that these dialectical principles are similar to what Paul Grice has called rules of conversational implicature.
Since there is no ultimate form of a proposition or an argument, it follows that there is no purely formal proof of non-implication, consistency or non-validity. Since philosophical analyses are strong co-implications, the non-analyzability of a concept cannot be proven formally. This is a most important principle that philosophers often forget. And this is often joined to the idea that unanalyzable concepts cannot be related by implications. This denial of bridging implications leads to false principles like the socalled naturalistic fallacy or Hume’s guillotine. (See pp. 21 and 332ff.)
J. Barkley Rosser, Logic for Mathematicians, McGraw-Hill, New York. 1953, Chapter IV, pp. 55–76.
In H-N. Castañeda, ‘On the Semantics of the Ought-to-Do’, Synthese 21 (1970): 449–468, reprinted in G. Harman and D. Davidson, eds., Semantics of Natural Language (Dordrecht: Reidel Publishing Co., 1972).
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© 1982 D. Reidel Publishing Company, Dordrecht, Holland
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Castañeda, HN. (1982). Propositional Structure and Propositional Implication. In: Castañeda, HN. (eds) Thinking and Doing. Philosophical Studies Series in Philosophy, vol 7. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-9888-5_3
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DOI: https://doi.org/10.1007/978-94-010-9888-5_3
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