Previous research has shown that children go through a stage in which they know that the number words each refer to a distinct numerosity, yet do not know which numerosity each number word picks out (Wynn, 1992). How do children attain this level of knowledge? We explore the possibility that particular properties of how number words are used within sentences inform children of the semantic class to which they belong. An analysis of transcripts of the spontaneous speech of three one- and two-year-old children and their parents (from the CHILDES database; MacWhinney & Snow, 1990) suggests that the relevant cues are available as input in parents ’ speech to children, and that children generally honour these properties of number words in their own speech. Implications of this proposal for word learning more generally are discussed.

Semantic vector models have proven their worth in a number of natural language applications whose goals can be accomplished by modelling individual semantic concepts and measuring similarities between them. By comparison, the area of semantic compositionality in these models has so far remained underdeveloped. This will be a crucial hurdle for semantic vector models: in order to play a fuller part in the modelling of human language, these models will need some way of modelling the way in which single concepts are put together to form more complex conceptual structures. This paper explores some of the opportunities for using vector product operations to model compositional phenomena in natural language. These vector operations

We explore the use of the landing page content in sponsored search ad selection. Specifically, we compare the use of the ad’s intrinsic content to augmenting the ad with the whole, or parts, of the landing page. We explore two types of extractive summarization techniques to select useful regions from the landing pages: out-of-context and in-context methods. Out-of-context methods select salient regions from the landing page by analyzing the content alone, without taking into account the ad associated with the landing page. In-context methods use the ad context (including its title, creative, and bid phrases) to help identify regions of the landing page that should be used by the ad selection engine. In addition, we introduce a simple yet effective unsupervised algorithm to enrich the ad context to further improve the ad selection. Experimental evaluation confirms that the use of landing pages can significantly improve the quality of ad selection. We also find that our extractive summarization techniques reduce the size of landing pages substantially, while retaining or even improving the performance of ad retrieval over the method that utilize the entire landing page.

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Default reasoning occurs whenever the truth of the evidence available to the reasoner does not guarantee the truth of the conclusion being drawn. Despite this, one is entitled to draw the conclusion “by default” on the grounds that we have no information which would make us doubt that the inference should be drawn. It is the type of conclusion we draw in the ordinary world and ordinary situations in which we find ourselves. Formally speaking, ‘nonmonotonic reasoning’ refers to argumentation in which one uses certain information to reach a conclusion, but where it is possible that adding some further information to those very same premises could make one want to retract the original conclusion. It is easily seen that the informal notion of default reasoning manifests a type of nonmonotonic reasoning. Generally speaking, default statements are said to be true about the class of objects they describe, despite the acknowledged existence of “exceptional instances” of the class. In the absence of explicit information that an object is one of the exceptions we are enjoined to apply the default statement to the object. But further information may later tell us that the object is in fact one of the exceptions. So this is one of the points where nonmonotonicity resides in default reasoning.

Frege Arithmetic (FA) is the second-order theory whose sole non-logical axiom is Hume’s Principle, which says that the number of F s is identical to the number of Gs if and only if the F s and the Gs can be one-to-one correlated. According to Frege’s Theorem, FA and some natural definitions imply all of second-order Peano Arithmetic. This paper distinguishes two dimensions of impredicativity involved in FA—one having to do with Hume’s Principle, the other, with the underlying second-order logic—and investigates how much of Frege’s Theorem goes through in various partially predicative fragments of FA. Theorem 1 shows that almost everything goes through, the most important exception being the axiom that every natural number has a successor. Theorem 2 shows that the Successor Axiom cannot be proved in the theories that are predicative in either dimension. 1

Jackson’s black-and-white Mary teaches us that the propositional content of perception cannot be fully expressed in language. In one of the earliest and best replies to Frank Jackson’s knowledge argument, Horgan claimed, in effect, that the argument illegitimately draws a metaphysical conclusion – that physicalism is false – from an epistemic premise – that physically omniscient Mary would not know everything. Horgan’s response has become standard. And, as it happens, I think it is correct. 1 But although physicalism survives unscathed, Jackson’s thought experiment does hold an important lesson. 2 It suggests, I shall argue, that the propositional content of perception is ineffable, in the sense that it cannot be fully expressed in language. This conclusion will be reached by considering a puzzle about perception posed by a slightly modified version of Jackson’s thought experiment. As will become clear, the puzzle has affinities * Earlier drafts were improved thanks to Michael Glanzberg, Benj Hellie,

The present form of mathematical logic originated in the twenties and early thirties from the partial merging of two different traditions, the algebra of logic and the logicist tradition (see [27], [41]). This resulted in a new form of logic in which several features of the two earlier traditions coexist. Clearly neither the algebra of logic nor the logicist’s logic is identical to the present form of mathematical logic, yet some of their basic ideas can be distinctly recognized within it. One of such ideas is Boole’s view that logic is the study of the laws of thought. This is not to be meant in a psychologistic way. Frege himself states that the task of logic can be represented “as the investigation of the mind; [though] of the mind, not of minds” [17, p. 369]. Moreover Frege never charges Boole with being psychologistic and in a letter to Peano even distinguishes between the followers of Boole and “the psychological logicians ” [16, p. 108]. In fact for Boole the laws of thought which are the object of logic belong “to the domain of what is termed necessary truth ” [2, p. 404]. For him logic does not depend on psychology, on the contrary psychology depends on logic insofar as it is only through an investigation of logical operations that we could obtain “some probable

“Like everything metaphysical the harmony between thought and reality is to be found in the grammar of language.” Wittgenstein, Zettel 55 I. Behold analytic truths; for they can serve to indicate that issues hitherto considered metaphysical are actually semantic. With this way of putting the moral of my paper, the reader may easily get the impression that I am trying to revive some tenet of ‘the linguistic turn’. The moral is impeccably described—still, what I am after is a different revolution. My aim is to get a better handle on the most prominent turn in the philosophy of language over the past half century, a contribution that continues to be widely misunderstood: Saul Kripke’s Naming and Necessity lectures held in 1970. The presumed metaphysical consequences of these lectures mostly turn out to be illusory. In fact, by ushering in rigid designation and metaphysical necessity, Kripke has introduced what is at

As a middle school mathematics teacher, I was frequently frustrated by what went on in the classroom. Theorists and practitioners in other subject areas have worked to explicitly link the role of human agency to their respective disciplines and to find ways to apply school knowledge in reasonably realistic contexts. In language arts, science, and history, emphasis on