UC Berkeley

What does it mean for something to be an /object/, in the broad sense in

which numbers, persons, physical substances, and reasons all play the

role of objects in our language and thought? I argue for an

epistemological answer to this question in this dissertation. These

things are objects simply in the sense that they are answers to

questions: they are the sort of thing we search for and specify during

investigation or inquiry. They share this epistemological role, but do

not 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' in

terms of investigations. An investigation is an activity structured by

a particular question. For example, consider an elementary algebra

problem: what is the number x such that x^2 - 6x + 9 = 0?

Beginning from this question, one carries out an investigation by

searching for and giving its answer: x = 3. On the view I develop,

nouns like `number' signify the /kind/ of question an investigation

addresses, 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 Frege

pointed out in the /Foundations of Arithmetic/, it seems to be

impossible 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 of

expressing the same thought. But on a standard analysis, it is puzzling

how 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 or

not it is expressed using `number', what does that noun contribute? Is

the concept it expresses wholly empty? That can't be right: `number' is

a meaningful expression, and its presence in (1) seems to make that

sentence /about/ numbers, in addition to Jupiter and its moons. So why

doesn't it make a difference to the truth conditions of the sentence?

The equivalence between these two sentences is famous, but it is hardly

a unique example. To say that Galileo discovered Jupiter's moons is

just to say that the /person/ who discovered them was Galileo.

Likewise, to say that Jupiter spins rapidly because it is gaseous is

just 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 are

significant, what contribution do they make?

Because the problem is general, I pursue a general solution. The

sentences which introduce the nouns in these examples are known as

/specificational/ sentences, because the second part specifies what the

first part describes. In (1), for example, `four' specifies the number of

Jupiter's moons. I argue that we should analyze specificational

sentences as pairing questions with their answers. At a semantic level,

a sentence like (1) is analogous to a short dialogue: "How many moons does

Jupiter have? Four." This analysis is empirically well supported, and

it unifies the theoretical insights behind other approaches. Most

importantly, it solves the puzzle. According to this analysis, (1)

asserts no more or less than the answer it gives, which could also be

given by (2); that is why they are equivalent. But it differs from (2) by

explicitly marking this assertion as an answer to the `how many?'

question expressed by `the number of Jupiter's moons'. That is why the

two 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 of

game-theoretical semantics for first-order logic. I argue that

quantifier moves in semantic games consist of investigations. A

straightforward first-order representation of the truth conditions of

specificational sentences then suffices to explicate the question-answer

analysis. In the semantic games which characterize the truth conditions

of a specificational sentence, players carry out investigations

structured by the question expressed in the first part of the sentence.

When they can conclude those investigations by giving the answer

expressed in the second part, the sentence is true.

The game semantics characterizes objects by their role in

investigations: objects are whatever players can search for and specify

as values for quantified variables in the investigations that constitute

quantifier moves in the game. This semantics thus captures the sense in

which objects are answers to questions. I use this account to offer a

new interpretation of Frege's claim that numbers are objects. His claim

is not about the syntax of number words in natural language, but about

the epistemological role of numbers: numbers are the sort of thing we

can search for and specify in scientific investigations, as sentences

like (1) reveal.