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.