Certain and Uncertain Inference with Indicative Conditionals
- URL: http://arxiv.org/abs/2207.08276v2
- Date: Fri, 28 Apr 2023 14:52:43 GMT
- Title: Certain and Uncertain Inference with Indicative Conditionals
- Authors: Paul \'Egr\'e and Lorenzo Rossi and Jan Sprenger
- Abstract summary: We develop a trivalent semantics for the truth conditions and the probability of the natural language conditional.
We show systematic correspondences between trivalent and probabilistic representations of inferences in either framework.
The result is a unified account of the semantics and indicative of conditionals that can be fruitfully applied to analyzing the validity of conditional inferences.
- Score: 0.3437656066916039
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: This paper develops a trivalent semantics for the truth conditions and the
probability of the natural language indicative conditional. Our framework rests
on trivalent truth conditions first proposed by W. Cooper and yields two logics
of conditional reasoning: (i) a logic C of inference from certain premises; and
(ii) a logic U of inference from uncertain premises. But whereas C is monotonic
for the conditional, U is not, and whereas C obeys Modus Ponens, U does not
without restrictions. We show systematic correspondences between trivalent and
probabilistic representations of inferences in either framework, and we use the
distinction between the two systems to cast light, in particular, on McGee's
puzzle about Modus Ponens. The result is a unified account of the semantics and
epistemology of indicative conditionals that can be fruitfully applied to
analyzing the validity of conditional inferences.
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