Dialogue Semantics for Bilateralism: Towards a Multi-Agent Account –Abstract– September 15, 2015

Dialogue Semantics for Bilateralism:
Towards a Multi-Agent Account
–Abstract–
September 15, 2015
According to bilateralists like Greg Restall (Restall, 2005, 2013) the meaning
of the logical constants, and thus the nature of logical consequence, can be given
in terms of how such vocabulary effects conversational positions: collections of
assertions and denials. According to the bilateralist a statement of logical consequence such as
Γ `∆
is to be understood as telling us that the position [Γ : ∆] which involves asserting
all of the sentences in Γ and denying all of the sentences in ∆ involves a clash.
Similarly, the validity of the classical left negation rule
Γ ` ∆, A
Γ , ¬A ` ∆
[¬L]
tells us about a certain connection between denying a statement and asserting
its negation, namely that any position in which denying A results in a clash is
also one where asserting ¬A will result in a clash. As a story about logical consequence and the meaning of the logical constants this very attractive, providing
an intuitive justification for the rules of the classical sequent calculus in broadly
normative pragmatic terms. As it stands, though, this approach faces two difficulties.
• Assertions are social acts which involve multiple agents, but no explicit
connection to social interaction is made by Restall or other similar bilateralists such as (e.g. Ripley (2013)). As it stands there is nothing which
distinguishes these ‘assertions in the void’ from something private and
mental.
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• The notion of a Clash is underspecified. All we are given in the above references are some general constraints on clashes (corresponding to various
structural rules) as well as that an assertion and a denial of the same sentence clash.
What we will do here is show how a bilateralist can overcome these difficulties
by grounding the bilateralist approach to logical consequence more firmly in
multi-agent social interaction. In particular we will introduce a novel kind of
dialogue game, ‘agreement games’1 , which involve two agents—red and black—
attempting to explain their individual conversational positions to one another
in such a way as to avoid disagreement, attempting to find some common ground
between their positions.
According to this account the notion of a clash in a collection of assertions
and denials is actually parasitic on a multi-agent notion of a clash. A paradigm
case of two conversational positions conflicting is when red asserts (resp. denies) a sentence which black denies (resp. asserts). Call a pair of conversational positions for which this is the case jointly incoherent. A pair of positions
clashes whenever every way of expanding them in accordance with the rules of
our agreement games results in positions which are jointly incoherent. That is
to say, pairs of positions which clash have conflicting conversational commitments. We can then think of a position [Γ : ∆] as involving a clash whenever it
can be divided up into positions [Γr : ∆r ] and [Γb : ∆b ] such that (i) these two
positions clash, and (ii) [Γ : ∆] = [Γr ∪ Γb : ∆r ∪ ∆b ].
A winning strategy in these games for either player shows that the union of
their positions [Γr ∪ Γb : ∆r ∪ ∆b ] does not clash, and thus is an invalid sequent.
Interestingly, winning strategies in these games can involve an interesting variety of ‘social asymmetry’, where only the actions of one player are able to avoid
brining their positions into conflict.
Bibliography
Restall, G. (2005). Multiple Conclusions. In P. Hájek, L. Valdes-Villanueva, and
D. Westerstøahl (Eds.), Logic, Methodology and Philosophy of Science: Proceedings
of the Twelfth International Congress, pp. 189–205. College Publications.
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A variant of the model construction games in §16.3 of van Benthem (2014).
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Restall, G. (2013). Assertion, Denial and Non-classical Theories. In K. Tanaka,
F. Berto, E. Mares, and F. Paoli (Eds.), Paraconsistency: Logic and Applications,
pp. 81–99. Dordrecht: Springer.
Ripley, D. (2013). Paradoxes and Failures of Cut. Australasian Journal of Philosophy 91(1), 139–164.
van Benthem, J. (2014). Logic in Games. Boston: MIT Press.
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