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Against Deductive Closure

Theoria 83 (2):103-119 (2017)

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  1. Risky belief.Martin Smith - 2022 - Philosophy and Phenomenological Research 106 (3):597-611.
    In this paper I defend the claim that justification is closed under conjunction, and confront its most alarming consequence — that one can have justification for believing propositions that are unlikely to be true, given one's evidence.
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  • The joint aggregation of beliefs and degrees of belief.Paul D. Thorn - 2018 - Synthese 197 (12):5389-5409.
    The article proceeds upon the assumption that the beliefs and degrees of belief of rational agents satisfy a number of constraints, including: consistency and deductive closure for belief sets, conformity to the axioms of probability for degrees of belief, and the Lockean Thesis concerning the relationship between belief and degree of belief. Assuming that the beliefs and degrees of belief of both individuals and collectives satisfy the preceding three constraints, I discuss what further constraints may be imposed on the aggregation (...)
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  • The Normative Force of Logical and Probabilistic Reasoning in Improving Beliefs.Corina Strössner - 2019 - Theoria 85 (6):435-458.
    There is a deep tension between logical and probabilistic norms of belief. This article illustrates the normative force that is associated with these frameworks by showing how rather unrestricted belief bases can be improved by undergoing logical and probabilistic reflection. It is argued that probabilistic reasoning accounts for the reliability of the conclusions one can draw from the beliefs. Most importantly, reliability commands us to care for the increasing uncertainty of conjunctions of beliefs. Deductive logic captures the agent's commitment towards (...)
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  • Impossibility Results for Rational Belief.Gerhard Schurz - 2019 - Noûs 53 (1):134-159.
    There are two ways of representing rational belief: qualitatively as yes-or-no belief, and quantitatively as degrees of belief. Standard rationality conditions are: consistency and logical closure, for qualitative belief, satisfaction of the probability axioms, for quantitative belief, and a relationship between qualitative and quantitative beliefs in accordance with the Lockean thesis. In this paper, it is shown that these conditions are inconsistent with each of three further rationality conditions: fallibilism, open-mindedness, and invariance under independent conceptual expansions. Restrictions of the Lockean (...)
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