Thought ISSN 2161-2234
The Logic of the Knowledge Norm
Julian J. Schlöder
University of Amsterdam
e knowledge norm of assertion is the subject of a lively debate on when someone is in a position
to assert something. However, not much has been said about the logic that underlies such debate.
In this paper, I propose a formalisation of the knowledge norm in a deontic logic that aims
to be explanatory and conceptually sound. Aerwards, I investigate some problems that this
formalisation makes visible. is reveals some signicant limitations of the underlying logic: it can
neither contain Axiom 4 (transitivity) nor Axiom C4 (density). Moreover, sentences of the form p
and I have not asserted that p appear to licence a violation of deontic rules.
Keywords assertion; assertibility: knowledge norm of assertion; deontic logic; deontic paradoxes
1 A logical form of the knowledge norm
Timothy Williamson (2000) famously defends the thesis that knowledge is the norm of
assertion. To evaluate the consequences of accepting this norm, I rst translate it into the
language of deontic logic.
1.1 Deontic logic
Let ♢ and ◽ be deontic modal operators (‘permitted’ and ‘obligatory’) and add operators
for knowledge (K)andassertion(A). For now, let’s assume that the logic governing ◽ and
♢ satises the KD4 axioms.
(K) ◽(φ → ψ) → (◽φ → ◽ ψ).
(D) ◽φ → ♢ φ.
(4) ♢♢ φ → ♢ φ.
(N) ⊢ φ entails ⊢ ◽ φ.
ese are typical assumptions about deontic modals insofar as they can be found in new
and old textbooks (Chellas 1980; Garson 2013) and in the semantics literature on deontic
modals (see Parsons 2013 for discussion). I will further clarify the role of the transitivity
axiom (4) later in the discussion.
1.2 e knowledge norm of assertion
Williamson endorses a prohibitive version of the knowledge norm: that one is permit-
ted to assert that ponlyif one knows that p. ere are two prima facie reasonable
Correspondence to: E-mail: firstname.lastname@example.org
Thought 7 (2018) 49–57 © 2018 The Thought Trust and Wiley Periodicals, Inc. 49