Rick Nouwen is in Brussels for a CRISSP lecture series. His handouts are now available for download:

• Lecture 1: Quantifiers
• Lecture 2: Numerals and modification
• Lecture 3: Intensification

The schedule, title and abstract of the Nouwen Lectures are now available.

Title: Scales and expressions of quantity and degree
Schedule: 15 October (15:30-18:30), 16 October (10:30-13:30), 17 October (13:00-16:00)

Abstract

Scales play a central role in the semantics of many natural language phenomena. In these lectures, I focus on three kinds of scalar operators: (i) quantifiers, semantically complex operators that form scales themselves; (ii) numeral modifiers, operators that express manipulations of the numerical scale, and (iii) intensifiers, operators that highlight regions on a scale of degrees. The common theme I focus on is that these kinds of operations are not always purely scalar, but that they are semantically and pragmatically complex.

Lecture 1: Quantifiers
One of the success stories of formal semantics is the programme of “Generalised Quantifiers” (e.g. Barwise and Cooper 1981). It is almost impossible to overstate the importance of the abundance of insights and tools that emerged from this programme. This notwithstanding, I will highlight several complications that make it that the denotations offered by generalised quantifier theory are in several different ways overly simple. That is, the semantic and pragmatic effects of quantifiers are not fully covered by relations between sets and cardinalities, and the scales such relations form.

Lecture 2: Modified numerals
In the second lecture, I will zoom in on the numerical scale and ways in which natural language allows for quantification on the basis of this scale. Geurts and Nouwen 2007 show that modified numerals with superlative morphology, like “at least 4”, do not have a purely scalar meaning but that there has to be some epistemic component to them: “John found at least 4 marbles” seems to convey that the speaker does not know exactly how many marbles John found. In more recent work on this topic, it has become clear that the precise nature of this epistemic flavour is very hard to pin down. I will highlight some interesting aspects of the resulting discussion. In addition, I will be looking at more complications, especially those offered by prepositional numerals like “up to 100” and I will compare the numerical scale to the spatial structures that form the normal domain of prepositions like “up to”.

Lecture 3: Intensifiers
Finally, I will turn to adjectives and their intensifiers. Simple unmarked adjectives are interpreted with respect to a cutoff point on a scale, the so-called standard of comparison. For “John is tall” to be true, John has to be taller than some (context-dependent) degree of height. It is often believed that intensifiers like “very” are essentially vague scalar operations manipulating this standard. “John is very tall” is just as vague as “John is tall”, but the standard of comparison for being “very tall” is simply higher than that for “tall”. I will argue that in many cases, however, it is not the case that intensifiers directly encode the amplification or slackening of the relevant standard. In particular, I will be looking at cases of intensification where the modifier is lexically transparent, as in “surprisingly tall” or “ridiculously tall”. I will argue that a lot of intensification comes about not by scalar operation, but by an indirectly provided signal of the speaker regarding his emotive or evaluative attitude to the sentence.

Barwise, Jon, and Robin Cooper. “Generalized quantifiers and natural language.” Linguistics and philosophy 4.2 (1981): 159-219.
Geurts, Bart, and Rick Nouwen. “‘At least’et al.: the semantics of scalar modifiers.” Language (2007): 533-559.

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