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Doxastic logic

Doxastic logic
The original uploader was Magnus Manske at English Wikipedia. Later versions were uploaded by Optimager at en.wikipedia. · Public domain · source

Overview

Doxastic logic is a type of logic concerned with reasoning about beliefs.

The term doxastic derives from the Ancient Greek δόξα (doxa, "opinion, belief"), from which the English term doxa ("popular opinion or belief") is also borrowed. Typically, a doxastic logic uses the notation

B

c

x

{\displaystyle {\mathcal {B}}_{c}x}

to mean "reasoner

c

{\displaystyle c}

believes that

x

{\displaystyle x}

is true", and the set

B

c

:

{

b

1

,

…

,

b

n

}

{\displaystyle \mathbb {B} _{c}:\left\{b_{1},\ldots ,b_{n}\right\}}

denotes the set of beliefs of

c

{\displaystyle c}

. In doxastic logic, belief is treated as a modal operator.

There is complete parallelism between a person who believes propositions and a formal system that derives propositions. Using doxastic logic, one can express the epistemic counterpart of Gödel's incompleteness theorem of metalogic, as well as Löb's theorem, and other metalogical results in terms of belief.

Overview adapted from Wikipedia (CC BY-SA 4.0; see the article history for authors).

Possible passages

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  1. 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 Doxastic logic is.

    Read the chapter · Open in the reader

  2. But it seems to us that they are misled by the ambiguity of the name. For argumentation signifies two things under one name, because any discussion respecting anything which is either probable or necessary is called argumentation, and so also is the systematic polishing of such a discussion. When then they bring forward any statement of this kind,--"Since she has had a child, she has lain, with a man," they bring…

    Marcus Tullius Cicero, The Orations of Marcus Tullius Cicero, Volume 4

    States what Doxastic logic is.

    Read the chapter · Open in the reader

  3. This complete quantity of the extent in relation to such a condition is called universality (universalitas). To this corresponds totality (universitas) of conditions in the synthesis of intuitions. The transcendental conception of reason is therefore nothing else than the conception of the totality of the conditions of a given conditioned. Now as the unconditioned alone renders possible totality of conditions, and…

    Immanuel Kant, The Critique of Pure Reason

    States what Doxastic logic is.

    Read the chapter · Open in the reader

Related ideas

Place in the tradition

Part of Outline of philosophy.

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