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17/06/2021 Seminari del GLiF, a càrrec de Peter Sutton (UPF)

17/06/2021 Seminari del GLiF, a càrrec de Peter Sutton (UPF)

The Problem of the Many and the semantics of countability" a càrrec de Peter Sutton (UPF)

14.06.2021

 

 

Data: dijous 17 de juny del 2021

Hora: 12.00 h

Accés: en línia, amb Collaborate (enllaç: eu.bbcollab.com/guest/cbd918ec0de7403f94ba44b0a67b7a2d)

Resum:

The problem of the many (Geach 1962/1980; Lewis 1993/1999; and Unger 1980) relates to a paradox-generating line of reasoning. The problem is usually formulated in terms of nouns such as cloud and mountain:  

There are entities that can clearly be truly described as one mountain or one cloud., but it is less clear what is in the extension of singular count expressions such as mountain and cloud even in situations in which it is clear that there is one mountain or one cloud. Take mountain, suppose we select some region of land that is a good candidate to demarcate the boundaries of the mountain. A problem arises, because there are many other marginally different, but equally valid ways of drawing the boundary.  Since these competing extensions are genuinely as good as one another, then either all of these extensions count as one mountain or none of them do. Either way, we do not have one mountain, contrary to what we know to be true.

 


The problem of the many is most frequently discussed in the context of philosophical metaphysics.  However, in this talk, I argue that the problem is directly relevant to semantic, mereological analyses of countability and numerals.  First, I argue that vagueness is orthogonal to the problem of the many, since the problem arises for nouns that are not vague in the way that cloud and mountain are.  Second, I claim that problem-of-the-many cases are genuinely problematic for the leading mereological theories of count nouns (e.g., Chierchia 2015; Landman 2016, Rothstein 2017), all of which, I argue, falsely predict either that count nouns such as mountain are not count, or that there are many mountains in situations such as the one above.

To address this challenge to theories of countability, I propose that we should opt for a logically weaker mereological criterion than proposed in the above theories. The criterion I propose is weak quantization.  A predicate P is weakly quantized iff at most one of any two non-overlapping parts of a P is a P.  Count nouns denote weakly quantized sets relative to a world and a context.

The wider relevance of this proposal is what it implies for the formal underpinnings of counting and individuation in natural languages.  In particular, it suggests that counting based on extensional non-identity, as formalised in the cardinality function of classical, extensional set theory (in which | X | is the number of unique members of X), only approximates the cardinality function encoded by natural language grammars.

When we carry these considerations through into the semantics of numerals, we arrive at a semantic solution to the problem of the many.  In natural languages, provided that the set of entities being counted is weakly quantized, multiple entities that are not identical to one another, such as those aligned with the different ways of drawing the boundary of a mountain, can still count as one.

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