Impossibility Results for Rational Belief

Noûs ◽  
2017 ◽  
Vol 53 (1) ◽  
pp. 134-159 ◽  
Author(s):  
Gerhard Schurz
Keyword(s):  
Rational Belief ◽  
Impossibility Results

BELIEF-REVISION, THE RAMSEY TEST, MONOTONICITY, AND THE SO-CALLED IMPOSSIBILITY RESULTS

2008 ◽  
Vol 1 (4) ◽  
pp. 402-423
Author(s):  
NEIL TENNANT
Keyword(s):  
Belief Revision ◽  
Impossibility Result ◽  
Rational Belief ◽  
Methodological Error ◽  
Ramsey Test ◽  
Impossibility Results ◽  
Definition Of ◽  
New Diagnosis ◽  
Made In ◽  
Monotonicity Principle

Peter Gärdenfors proved a theorem purporting to show that it is impossible to adjoin to the AGM-postulates for belief-revision a principle of monotonicity for revisions. The principle of monotonicity in question is implied by the Ramsey test for conditionals. So Gärdenfors’ result has been interpreted as demonstrating that it is impossible to combine the Ramsey test for conditionals with the basic postulates for rational belief-revision. It is shown here that this interpretation of Gärdenfors’ result is unwarranted. A new diagnosis is offered of a methodological error made in the statement of the key principle of monotonicity. Crucial applications of this principle in Gärdenfors’ proof require one to regard as revisions what are really expansions. If monotonicity is stated only for genuine revisions, then Gärdenfors’ proof does not go through. Nor can it; for, when the monotonicity principle for revisions is correctly formulated, one can actually establish a contrary consistency result. This requires only a slight adjustment to the postulates of AGM-theory, in order to ensure that the three operations of expansion, contraction, and revision trichotomize the domain of theory-changes. It is further shown that being careful in this way about the proper domains of definition of the three operations of expansion, contraction, and revision also disposes of another, more direct, impossibility result, due to Arló-Costa, that targets the Ramsey test.

Conclusion

2017 ◽  
Author(s):  
Ralph Wedgwood
Keyword(s):  
Rational Choice ◽  
Mental State ◽  
Rational Belief ◽  
True Proposition ◽  
The Other ◽  
Relevant Notion

It is explained how the conception of rationality proposed earlier in this book can set the agenda for the study of rational belief and rational choice. Part of the task will be to investigate the kind of ‘rational probability’ that was introduced in Chapter 9; the other part will be to study the conditions under which each kind of mental state counts as ‘correct’. There are reasons for thinking that the relevant notion of correctness must be such that in the case of belief, a correct belief is a belief in a true proposition, and in the case of choice, it is ‘akratic’ to choose something if one is fully confident that it is not correct to choose it. It is explained what light this approach could shed on the traditional issues about rational belief and rational choice.

Is Rationality Normative?

2017 ◽  
Author(s):  
Ralph Wedgwood
Keyword(s):  
Rational Choice ◽  
Rational Belief ◽  
False Beliefs ◽  
Ought Implies Can ◽  
Normative Concept ◽  
Original Meaning ◽  
Formal Theories

In its original meaning, the word ‘rational’ referred to the faculty of reason—the capacity for reasoning. It is undeniable that the word later came also to express a normative concept—the concept of the proper use of this faculty. Does it express a normative concept when it is used in formal theories of rational belief or rational choice? Reasons are given for concluding that it does express a normative concept in these contexts. But this conclusion seems to imply that we ought always to think rationally. Four objections can be raised. (1) What about cases where thinking rationally has disastrous consequences? (2) What about cases where we have rational false beliefs about what we ought to do? (3) ‘Ought’ implies ‘can’—but is it true that we can always think rationally? (4) Rationality requires nothing more than coherence—but why does coherence matter?

On Identifying the Problem of Evil and the Possibility of Its Theist Solution

2018 ◽  
Author(s):  
John Bishop
Keyword(s):  
Problem Of Evil ◽  
Rational Belief ◽  
Alternative Conception ◽  
Viable Alternative ◽  
Cognitive Level ◽  
The Problem Of Evil ◽  
The Face ◽  
Argument From Evil ◽  
Existential Problem ◽  
Foundational Problem

The argument of this chapter is that the foundational problem of evil is the existential problem of maintaining hopeful commitment to virtuous living in the face of all that may undermine human fulfilment. Dealing with this problem at the cognitive level involves commitment to a view of reality as favourable to practical commitment to ethical ideals. An intellectual problem of evil then arises to the extent that it seems that the fact of evil is evidence against the truth of the salvific worldview we are inclined to adopt for dealing with it. In relation to theism’s ‘revelatory’ worldview, this intellectual problem is expressible as an Argument from Evil. A ‘normatively relativized’ version of the Argument from Evil is proposed that seeks to exclude rational belief in the ‘personal omniGod’. As a viable alternative conception of God is possible, however, the Argument fails to justify outright atheism.

Reasoning Without the Conjunction Closure

Episteme ◽  
2021 ◽  
pp. 1-14
Author(s):  
Alicja Kowalewska
Keyword(s):  
Computational Complexity ◽  
Error Rate ◽  
Cognitive Abilities ◽  
Rational Belief ◽  
Rational Agents ◽  
Confidence Levels

Abstract Some theories of rational belief assume that beliefs should be closed under conjunction. I motivate the rejection of the conjunction closure, and point out that the consequences of this rejection are not as severe as it is usually thought. An often raised objection is that without the conjunction closure people are unable to reason. I outline an approach in which we can – in usual cases – reason using conjunctions without accepting the closure in its whole generality. This solution is based on the notion of confidence levels, which can be defined using probabilities. Moreover, on this approach, reasoning has a scalable computational complexity adaptable to cognitive abilities of both rationally bounded and perfectly rational agents. I perform a simulation to assess its error rate, and compare it to reasoning with conjunction closure.

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