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A theory of propositions. (English) Zbl 1368.03010
This paper proposes that we should take a proposition to be an ordered pair whose first member is a well-formed formula (of some appropriate formal language) and whose second member is a model (in the sense of model theory) of the fragment of the formal language needed to form that wff. It then argues cogently that a proposition so understood can fulfill the roles usually ascribed to propositions:
(i)
They are the objects of such attitudes as belief and desire.
(ii)
They are expressed by (declarative) sentences uttered in contexts.
(iii)
They can be expressed in different languages and can be the objects of belief (etc.) of different agents.
(iv)
They are the primary bearers of truth values.
(v)
They are the objects of logic and of properties such as logical truth and satisfaction and of relations such as logical consequence and equivalence, when logic is used to provide norms for rationality and to explain behavior.
The concept of proposition proposed is then distinguished from rival concepts prominent in current or historical discussions, and its advantages over them explained. The final part of the paper explains how the paper does not do more than what it proposes, because doing so would have the effect of limiting the generality and consequently the usefulness of the concept of proposition defined.
MSC:
03A05 Philosophical and critical aspects of logic and foundations
03B05 Classical propositional logic
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