Abstract
The main burden of this chapter is to defend the knowledge account of the norm of assertion—one must: assert p only if one knows p, from a model-theoretical perspective. I start with a classification of three different kinds of norms of assertion, i.e., semantic, pragmatic, and epistemic and focus on the epistemic normativity for assertion in this chapter. I take it as a starting point that the ultimate concern of making an assertion is to transmit true information via the embedded assertoric force in assertion that the agent performs, which can be in turn characterized by virtue of the agent’s epistemic attitude toward the propositional content of whatever the agent asserts. Then, I examine three popular accounts of epistemic norms of assertion, including the truth account, the justified belief (or warrant) account, and the knowledge account.
I next examine, from a model-theoretic perspective, how to stipulate the required semantic rule for modal-operator A for assertion in the standard Kripke models for epistemic logic, containing the modal operators K (knowing), A (asserting), B (believing), and Bj (having justified belief), in accordance with each account and show that each has certain difficulties. I then show that the required semantic rule for Aφ can hardly be stipulated merely by the truth of φ in related accessible states, nor the appeal to Bφ or Bj. However, I show that the knowledge account can be defended by proposing a kind of models referred to as TWA-models (‘TW’ for Timothy Williamson). This is an application of my previous work, “TW-models for logic of knowledge-cum-belief” (Yang 2013). TW-models for a logic of knowledge and belief, a kind of Kripke models in character, with reflexivity as the sole accessibility relation, satisfy the main theses of Timothy Williamson’s knowledge first epistemology. The required semantic rule for Kφ is stipulated in the standard way, but the semantic rule for B (correspondingly, for Bj) is given in a way such that the truth value of Bφ at a given state will be determined by the truth value of Kφ (correspondingly, Bφ) in some related states.
The construction of TWA-models will be specified, and the semantic rules for A will be given in a way such that the truth value of Aφ at a given state can be determined by virtue of the truth values of the corresponding Kφ in the accessible states. This will provide a model-theoretical justification of the knowledge rule. Some by-products will be mentioned briefly.
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Notes
- 1.
See, for example, Williamson (2000, pp. 240, 241): “Assertion is a kind of speech act that we perform.” Also Kemp (2013, p. 107): “assertion is individualistic in the sense that the matter of whether or not an agent asserts a proposition the agent expresses is entirely determined by the agent’s intentions.”
- 2.
See, for example, Williamson (2000, p. 258): “the default use of declarative sentences is to make assertions.”
- 3.
See Mark (2010, pp. 163–164): “In order for an utterance to have assertoric force, it must also be subject to the cognitive and social safeguards that distinguish assertion…both from other illocutionary acts and from other forms of information transfer.”
- 4.
For the sake of simplicity, we may for the time being treat “One rationally believes…,” “One reasonably believes…,” “One has justification to believe…,” “One justified believes…,” etc., as synonyms, similarly for the phrases “justified belief,” “reasonable belief,” “rational belief,” “having justification for belief,” “warranted belief.” Henceforth, I shall use the term “justified belief” or justification.
- 5.
According to Douven, the rational credibility account is implied by two of our basic commitments, namely (a) our aiming to be rational and (b) the belief-assertion parallel, according to which belief is subvocalized assertion. It is noteworthy that Douven criticized that Williamson is committed to the belief-assertion parallel, because he holds that “occurrently believing p stands to asserting p as the inner stands to the outer” (Williamson 2000, p. 255). But this criticism seems to ignore Williamson’s account of belief in his knowledge first epistemology that belief can only be characterized in terms of knowledge.
- 6.
The recent development of justification logic can be found in a series of work by Artemov (1995, 2001, 2006, 2008), Artemov and Nogina (2005), and Fitting (2005). The initial justification logic system, namely, the Logic of Proofs (LP), was firstly introduced in Artemov (1995); a more general approach to common knowledge based on justified knowledge can be found in Artemov (2006). Fitting (2005) firstly provides epistemic semantics and established completeness for LP.
- 7.
For example, Unger (1975, Chap. 6), Williamson (1996, 2000, Chap. 11), DeRose (2002, p. 180): “One is positioned well-enough to assert that P iff one knows that P”; Stanley (2005, pp. 10, 11): “[A]ssertion is…conceptually connected to knowledge…one ought only to assert what one knows”; Hawthorne (2004, p. 23): “The practice of assertion is constituted by the rule/requirement that one assert something only if one knows it”; to mention a few. Perhaps, the earliest version of knowledge account can be found in G. E. Moore’s work, when he claims that “by asserting p positively you imply, though you don’t assert, that you know that p” (1962, p. 277, see also 1960, p. 125).
- 8.
Typically, this is the root of the well-known Moore’s paradox―“P, and I don’t know that P” (Moore 1962).
- 9.
For instance,
-
1.
R to be reflexive, i.e., ∀w∈S, Rww, the Kripke models would satisfy ( T).
-
2.
R to be transitive, i.e., ∀w, u,v∈S, Rwu∧ Ruv→ Rwv, the Kripke models would satisfy ( 4).
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3.
R to be equivalence, i.e., with reflexivity, transitivity, and also symmetry, the Kripke models would satisfy ( T) + ( 4) + ( 5).
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4.
R to be transitive and Euclidean (∀w, u,v∈S, R wu∧ R wv→ R uv), but not reflexive, the Kripke models would satisfy ( K) + ( 4) + ( 5).
-
5.
R to be serial, i.e., ∀x ∈S∃y R xy ( no end-point included), the Kripke models would satisfy ( D).
Again, taking CPC—classical propositional calculus as the underlying system, we may have some well-known modal systems, such as System K ( = CPC + ( N) + ( K)), System T ( = K + ( T)), System S4 ( = T + ( 4)), System S5 ( = S4 + ( 5)). Of course, the rule of Necessitation is required—( N) Form ⊢| one can get ⊢□|.
Usually we may have systems K, T, S4, S5 for knowledge and assertion. But some may reject ( T), so the modal operator A would behave like the modal operator for believing. Accordingly, it is suggested that we should take so-called KD45 or weak S5, by adding ( D B ) to K45 yields the so-called KD45 or weak S5. Some take both K45 and KD45 as appropriate for a logic of assertion.
-
1.
- 10.
A quite popular one is to appeal to S5. But in this case, there would be no difference between knowledge and assertion. Assertion collapses into knowledge.
- 11.
I have summarized there Williamson’s knowledge-first epistemology in terms of the following theses:
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Knowing is a state of mind.
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Knowing is factive.
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The broadness of knowing (Externalist approach).
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The primeness of knowing (Knowledge first!).
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Take knowledge as central to our understanding of belief.
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Cognitive-homeless thesis.
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The knowledge account of evidence—One’s knowledge is just one’s evidence.
-
The knowledge account of assertion—Assert p only if one knows that p.
I acknowledged that TW-models would not deal with the knowledge account of assertion, and this will be settled in TWA-models in this chapter.
-
- 12.
Accordingly, we need to add into the language in use one more modal operator, say IK, so that IKφ is to mean “the agent is actually in a position to know φ.” The corresponding semantic rule for IK will be stipulated in the following way: M, s⊨ IK φ iff φ∈δ( s).
- 13.
- 14.
As Davidson (2001, p. 90) rightly remarked, there are no such conventions governing the formation of intentions. So I can only put forth a primitive function here.
- 15.
Davidson (2001, p. 91) notes that “It is a mistake to suppose that if an agent is doing something intentionally, he must know that he is doing it.” This indicates that Aφ→KAφ would not hold. But it seems beyond reasonable doubt to claim that the agent must know that she knows what she asserts, otherwise, it would be difficult to show how she could do this intentionally.
- 16.
In short, on TWA-models, the knowledge account of assertion satisfies the following conditions: (a) A|→|; (b) A|→B|; (c) A|→BK|; and (d) A|→Bjφ.
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Acknowledgment
Previous versions of this paper were presented at Asian Workshop on Philosophical Logic (February 15-17, 2012, Japan Advanced Institute of Science and Technology (JAIST), Ishikawa, Japan), and Workshop on Logic, Philosophy, and Computation (October 19, 2012, Institute of Information Science, Academia Sinica, Taiwan). I am deeply grateful to all participants on these occasions for their helpful remarks and comments. I also thank anonymous referees and Duen-Min Deng for their valuable comments and suggestions.
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Yang, Sm. (2014). A Defense of the Knowledge Account of Assertion: From a Model-Theoretic Perspective. In: Hung, TW. (eds) Communicative Action. Springer, Singapore. https://doi.org/10.1007/978-981-4585-84-2_3
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