Semantics of logic

Summary

In logic, the semantics of logic or formal semantics is the study of the semantics, or interpretations, of formal and (idealizations of) natural languages usually trying to capture the pre-theoretic notion of entailment.

Overview

The truth conditions of various sentences we may encounter in arguments will depend upon their meaning, and so logicians cannot completely avoid the need to provide some treatment of the meaning of these sentences. The semantics of logic refers to the approaches that logicians have introduced to understand and determine that part of meaning in which they are interested; the logician traditionally is not interested in the sentence as uttered but in the proposition, an idealised sentence suitable for logical manipulation.[citation needed]

Until the advent of modern logic, Aristotle's Organon, especially De Interpretatione, provided the basis for understanding the significance of logic. The introduction of quantification, needed to solve the problem of multiple generality, rendered impossible the kind of subject–predicate analysis that governed Aristotle's account, although there is a renewed interest in term logic, attempting to find calculi in the spirit of Aristotle's syllogisms, but with the generality of modern logics based on the quantifier.

The main modern approaches to semantics for formal languages are the following:

See also

References

  • Jaakko Hintikka (2007), Socratic Epistemology: Explorations of Knowledge-Seeking by Questioning, Cambridge: Cambridge University Press.
  • Ilkka Niiniluoto (1999), Critical Scientific Realism, Oxford: Oxford University Press.