Abstract
Across languages, certain logically natural concepts are not lexicalized, even though they can be expressed by complex expressions. This is for instance the case for the quantifier not all. In this paper, we propose an explanation for this fact based on the following idea: the logical lexicon of languages is partly shaped by a tradeoff between informativity and cost, and the inventory of logical expressions tends to maximize average informativity and minimize average cost. The account we propose is based on a decision-theoretic model of how speakers choose their messages in various situations (a version of the Rational Speech Act model). EARLY ACCESS
Highlights
The Aristotelian square of opposition consists of the following four categories of logical statements: 1. Universal (A): All As are Bs.2
To substantiate an account of this type, we need to a) establish that the choice between I and O is partly governed by probabilistic informativity, and b) that there are good reasons to think that across contexts I is more informative than O. Before turning to these issues, we will provide a model of message choice which captures the reasoning we have just sketched, inspired by the Rational Speech Act model of pragmatics (RSA) model of pragmatics (Goodman & Stuhlmüller 2013)
Because the pragmatic listener would interpret both ‘some’ and ‘not all’ as meaning ‘some but not all’, both are going to be informative, and our proposal in this paper could not work if we modeled the
Summary
The Aristotelian square of opposition consists of the following four categories of logical statements: 1. Universal (A): All As are Bs. Katzir & Singh (2013) generalize Horn’s idea by proposing that at a certain level, logical operations are expressed in terms of certain primitives; this has the consequence that E and O have more complex representations This is in line with findings suggesting that monotonedecreasing operators are harder to process than monotone-increasing ones (Geurts & van Der Slik 2005). As to the observed cognitive cost of sentences containing negation and other monotone-decreasing operators, it should be noted that such sentences tend to be syntactically more complex than their ‘positive’ counterparts, so that we should not conclude that this cost is tied to the logical meaning of the relevant operators We discuss these points with more details, in connection with recent proposals that are to some extent related to ours..
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