Nominalization, Specification, and Investigation

What does it mean for something to be an /object/, in the broad sense in/nwhich numbers, persons, physical substances, and reasons all play the/nrole of objects in our language and thought? I argue for an/nepistemological answer to this question in this dissertation. These/nthings are objects simply in the sense that they are answers to/nquestions: they are the sort of thing we search for and specify during/ninvestigation or inquiry. They share this epistemological role, but do/nnot necessarily belong to any common ontological category./nI argue for this conclusion by developing the concept of an/n/investigation/, and describing the meaning of nouns like `number' in/nterms of investigations. An investigation is an activity structured by/na particular question. For example, consider an elementary algebra/nproblem: what is the number x such that x^2 - 6x + 9 = 0?/nBeginning from this question, one carries out an investigation by/nsearching for and giving its answer: x = 3. On the view I develop,/nnouns like `number' signify the /kind/ of question an investigation/naddresses, since they express the range of its possible answers./n`Number' corresponds to a `how many?' question; `person' corresponds to/n`who?'; `substance' to one sense of `what?'; `reason' to one sense of/n`why?'; and so on./nI make use of this idea, which has its roots in Aristotle's/n/Categories/, to solve a puzzle about what these nouns mean. As Frege/npointed out in the /Foundations of Arithmetic/, it seems to be/nimpossible for/n(1) The number of Jupiter's moons is four./nto be true while/n(2) Jupiter has four moons./nis false, or vice versa. These sentences are just two different ways of/nexpressing the same thought. But on a standard analysis, it is puzzling/nhow that can be so. Every contentful expression in (1) has an analogue in/n(2), except for the noun `number'. If the thought is the same whether or/nnot it is expressed using `number', what does that noun contribute? Is/nthe concept it expresses wholly empty? That can't be right: `number' is/na meaningful expression, and its presence in (1) seems to make that/nsentence /about/ numbers, in addition to Jupiter and its moons. So why/ndoesn't it make a difference to the truth conditions of the sentence?/nThe equivalence between these two sentences is famous, but it is hardly/na unique example. To say that Galileo discovered Jupiter's moons is/njust to say that the /person/ who discovered them was Galileo./nLikewise, to say that Jupiter spins rapidly because it is gaseous is/njust to say that the /reason/ it spins rapidly is that it is gaseous./nSo the same puzzle that arises for `number' also arises for `person',/n`reason', and other nouns of philosophical interest. If they are/nsignificant, what contribution do they make?/nBecause the problem is general, I pursue a general solution. The/nsentences which introduce the nouns in these examples are known as/n/specificational/ sentences, because the second part specifies what the/nfirst part describes. In (1), for example, `four' specifies the number of/nJupiter's moons. I argue that we should analyze specificational/nsentences as pairing questions with their answers. At a semantic level,/na sentence like (1) is analogous to a short dialogue: "How many moons does/nJupiter have? Four." This analysis is empirically well supported, and/nit unifies the theoretical insights behind other approaches. Most/nimportantly, it solves the puzzle. According to this analysis, (1)/nasserts no more or less than the answer it gives, which could also be/ngiven by (2); that is why they are equivalent. But it differs from (2) by/nexplicitly marking this assertion as an answer to the `how many?'/nquestion expressed by `the number of Jupiter's moons'. That is why the/ntwo sentences address different subject matters and have different uses./nIn order to formulate this analysis in a contemporary logical framework,/nI apply the concept of an investigation in the setting of/ngame-theoretical semantics for first-order logic. I argue that/nquantifier moves in semantic games consist of investigations. A/nstraightforward first-order representation of the truth conditions of/nspecificational sentences then suffices to explicate the question-answer/nanalysis. In the semantic games which characterize the truth conditions/nof a specificational sentence, players carry out investigations/nstructured by the question expressed in the first part of the sentence./nWhen they can conclude those investigations by giving the answer/nexpressed in the second part, the sentence is true./nThe game semantics characterizes objects by their role in/ninvestigations: objects are whatever players can search for and specify/nas values for quantified variables in the investigations that constitute/nquantifier moves in the game. This semantics thus captures the sense in/nwhich objects are answers to questions. I use this account to offer a/nnew interpretation of Frege's claim that numbers are objects. His claim/nis not about the syntax of number words in natural language, but about/nthe epistemological role of numbers: numbers are the sort of thing we/ncan search for and specify in scientific investigations, as sentences/nlike (1) reveal.

Advisor: MacFarlane, John
Mancosu, Paolo