|Modal logic: the modal logic is an extension of classical logic to systems in which possibility and necessity can also be expressed. Different approaches use operators to express "necessary" and "possible", which, depending on the placement within formulas, can let claims of different strengths win. E.g. there is an object which necessarily has the property F/it is necessary that there is an object with the property F. The introduction of possible worlds makes quantification possible for expressing possibility (There is at least one world in which ...) and necessity (For all worlds is valid ...). See also operators, quantifier, completion, range, possible worlds._____________Annotation: The above characterizations of concepts are neither definitions nor exhausting presentations of problems related to them. Instead, they are intended to give a short introduction to the contributions below. – Lexicon of Arguments. |
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Modal logic/Language/Bigelow/Pargetter: at the end we get an orthodox language of modal logic: it is an extension of the classical language of Tarski in two respects:
1. extension of the referents of individual constants so that they can also include Possibilia
2. addition of rules for modal operators.
That does not mean that this is the only right way.
Possibilia we do not claim their existence for semantic reasons either. But there are good non-semantic reasons for believing in them.
Modal Logic/Modality/Intuition/Bigelow/Pargetter: our intuitions are deceptive here.
Some of our intuitions even contradict each other:
E.g. Principle of the distribution of disjunction:
((a v b) would be > would be g) > ((a would be > would be g) u (b would be > would be g)).
That seems to be true. For example, "If you ate or drink, you would be my prisoner." "So if you ate, you would be my prisoner and if you drank, you would be my prisoner."
Problem: this principle cannot be added to our axiom system._____________Explanation of symbols: Roman numerals indicate the source, arabic numerals indicate the page number. The corresponding books are indicated on the right hand side. ((s)…): Comment by the sender of the contribution.
J. Bigelow, R. Pargetter
Science and Necessity Cambridge 1990