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" Nominalization, Specification, and Investigation "
Lawrence, Richard Wyley
MacFarlane, John; Mancosu, Paolo
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Latin Dissertation
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English
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| Record Number
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904152
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TL3fc2n2qb
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| Main Entry
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Lawrence, Richard Wyley
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Nominalization, Specification, and Investigation\ Lawrence, Richard WyleyMacFarlane, John; Mancosu, Paolo
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| College
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UC Berkeley
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| Date
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2017
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2017
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| Abstract
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What does it mean for something to be an /object/, in the broad sense inwhich numbers, persons, physical substances, and reasons all play therole of objects in our language and thought? I argue for anepistemological answer to this question in this dissertation. Thesethings are objects simply in the sense that they are answers toquestions: they are the sort of thing we search for and specify duringinvestigation or inquiry. They share this epistemological role, but donot necessarily belong to any common ontological category.I argue for this conclusion by developing the concept of an/investigation/, and describing the meaning of nouns like `number' interms of investigations. An investigation is an activity structured bya particular question. For example, consider an elementary algebraproblem: what is the number x such that x^2 - 6x + 9 = 0?Beginning from this question, one carries out an investigation bysearching for and giving its answer: x = 3. On the view I develop,nouns like `number' signify the /kind/ of question an investigationaddresses, since they express the range of its possible answers.`Number' corresponds to a `how many?' question; `person' corresponds to`who?'; `substance' to one sense of `what?'; `reason' to one sense of`why?'; and so on.I make use of this idea, which has its roots in Aristotle's/Categories/, to solve a puzzle about what these nouns mean. As Fregepointed out in the /Foundations of Arithmetic/, it seems to beimpossible for (1) The number of Jupiter's moons is four.to be true while (2) Jupiter has four moons.is false, or vice versa. These sentences are just two different ways ofexpressing the same thought. But on a standard analysis, it is puzzlinghow that can be so. Every contentful expression in (1) has an analogue in(2), except for the noun `number'. If the thought is the same whether ornot it is expressed using `number', what does that noun contribute? Isthe concept it expresses wholly empty? That can't be right: `number' isa meaningful expression, and its presence in (1) seems to make thatsentence /about/ numbers, in addition to Jupiter and its moons. So whydoesn't it make a difference to the truth conditions of the sentence?The equivalence between these two sentences is famous, but it is hardlya unique example. To say that Galileo discovered Jupiter's moons isjust to say that the /person/ who discovered them was Galileo.Likewise, to say that Jupiter spins rapidly because it is gaseous isjust to say that the /reason/ it spins rapidly is that it is gaseous.So the same puzzle that arises for `number' also arises for `person',`reason', and other nouns of philosophical interest. If they aresignificant, what contribution do they make?Because the problem is general, I pursue a general solution. Thesentences which introduce the nouns in these examples are known as/specificational/ sentences, because the second part specifies what thefirst part describes. In (1), for example, `four' specifies the number ofJupiter's moons. I argue that we should analyze specificationalsentences as pairing questions with their answers. At a semantic level,a sentence like (1) is analogous to a short dialogue: "How many moons doesJupiter have? Four." This analysis is empirically well supported, andit unifies the theoretical insights behind other approaches. Mostimportantly, it solves the puzzle. According to this analysis, (1)asserts no more or less than the answer it gives, which could also begiven by (2); that is why they are equivalent. But it differs from (2) byexplicitly marking this assertion as an answer to the `how many?'question expressed by `the number of Jupiter's moons'. That is why thetwo sentences address different subject matters and have different uses.In order to formulate this analysis in a contemporary logical framework,I apply the concept of an investigation in the setting ofgame-theoretical semantics for first-order logic. I argue thatquantifier moves in semantic games consist of investigations. Astraightforward first-order representation of the truth conditions ofspecificational sentences then suffices to explicate the question-answeranalysis. In the semantic games which characterize the truth conditionsof a specificational sentence, players carry out investigationsstructured by the question expressed in the first part of the sentence.When they can conclude those investigations by giving the answerexpressed in the second part, the sentence is true.The game semantics characterizes objects by their role ininvestigations: objects are whatever players can search for and specifyas values for quantified variables in the investigations that constitutequantifier moves in the game. This semantics thus captures the sense inwhich objects are answers to questions. I use this account to offer anew interpretation of Frege's claim that numbers are objects. His claimis not about the syntax of number words in natural language, but aboutthe epistemological role of numbers: numbers are the sort of thing wecan search for and specify in scientific investigations, as sentenceslike (1) reveal.
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MacFarlane, John; Mancosu, Paolo
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UC Berkeley
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