Concept
Modal operator
Overview
A modal connective (or modal operator) is a logical connective for modal logic. It is an operator which forms propositions from propositions. In general, a modal operator has the "formal" property of being non-truth-functional in the following sense: The truth-value of composite formulae sometimes depend on factors other than the actual truth-value of their components. In the case of alethic modal logic, a modal operator can be said to be truth-functional in another sense, namely, that of being sensitive only to the distribution of truth-values across possible worlds, actual or not. Finally, a modal operator is "intuitively" characterized by expressing a modal attitude (such as necessity, possibility, belief, or knowledge) about the proposition to which the operator is applied.
Overview adapted from Wikipedia (CC BY-SA 4.0; see the article history for authors).
Possible passages
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Any such select set is called the set of postulates, or premises, from which the reasoning proceeds. The reasoning is nothing else than the exhibition of the whole pattern of general conditions involved in the pattern derived from the selected postulates.
Alfred North Whitehead, Science and the modern world
States what Modal operator is.
The copula is the sign denoting that there is an affirmation or denial; and thereby enabling the hearer or reader to distinguish a proposition from any other kind of discourse. Thus, in the proposition, The earth is round, the Predicate is the word _round_, which denotes the quality affirmed, or (as the phrase is) predicated: _the earth_, words denoting the object which that quality is affirmed of, compose the…
John Stuart Mill, A System of Logic
States what Modal operator is.
On the other hand an event-particle is defined so as to exhibit this character of being a route of approximation marked out by entities posited in sense-awareness. A definite event-particle is defined in reference to a definite punct in the following manner: Let the condition {sigma} mean the property of covering all the abstractive elements which are members of that punct; so that an abstractive set which satisfies…
Alfred North Whitehead, The Concept of Nature The Tarner Lectures Delivered in Trinity College, November 1919
States what Modal operator is.
Philosophers who discussed Modal operator
Related ideas
- Belief
- Deontic logic
- Subjunctive possibility
- Propositional variable
- Logical connective
- Propositional logic
- Knowledge
- Value theory
- Modal logic
- Accessibility relation
- Causality
- Logical truth
- Quantifier (logic)
- De dicto and de re
- Truth function
- Possible world
- Proposition
- Doxastic logic
- Epistemic modal logic
- Alethic modality
- Scope (logic)
- Predicate variable
Place in the tradition
Part of Doxastic logic.