doing different things. But this means only that they ended up making differ-

ent entries (entries of different precision) in their observation logs because of

differences in the degree of accuracy of their observations.

Saying this might seem painfully obvious. However, once again it does have

repercussions on what philosophers are saying and doing”or trying to say and

to do. The set of available answers determines partly the set of presuppositions

that an inquirer has access to. Hence the questions that one can legitimately

ask will depend on factors such as the state of experimental technology. Ergo,

it is futile to set limits to an inquirer™s inquiries in logical or other purely

conceptual terms. Hence the problem of demarcation that loomed so large

for Popper, and to a lesser extent for the logical positivists, is not a purely

philosophical one. Any full answer to it will depend on the current state of

scienti¬c research.

4. Knowledge Statements

In order to make progress here, we have to investigate further the nature

of interrogative inquiry. We have to uncover the logical form of questions,

answers, and their presuppositions. For one important thing, what can be said

of the presuppositions of questions? First, I have to explain what the true

logic of questions and answers is, which in practice means showing how ques-

tions and answers are treated in the right kind of epistemic logic. (For a fuller

account, see Hintikka 2003; Hintikka, Halonen, and Mutanen 1998.) In using

this logic, the ingredients of one™s language include the resources of some ¬xed

¬rst-order language plus a sentence-initial epistemic operator K. Since the par-

ticular knower we are talking about is largely irrelevant, for the purposes of

this chapter this operator K can here usually be thought of as expressing an

Socratic Epistemology

88

impersonal “it is known that.” Its meaning can be captured by thinking of it as

a universal quanti¬er ranging over the scenarios (courses of events) left pos-

sible by what is known. In game-theoretical semantics, K mandates a choice

by the falsi¬er of one of those epistemically possible scenarios.

For simplicity, in what follows, our formulas are always assumed to be in a

negation normal form”that is, in a form where the logical constants are

∼, &, ∨, (∃x) ∀x, =

and where all negation-signs (∼) occur pre¬xed to an atomic sentence or an

identity.

The novel ingredient in my epistemic logic is the independence indicator /

(the slash). Its meaning can be seen from an example or two. The sentence

K(∃x) S[x] (1)

says that in every possible scenario compatible with what is known, there exists

among its members an individual, call it x, such that S[x]. What this amounts

to is saying that it is known that there exists an x such that S[x].

But what does it mean to assert the following?

K(∃x/K) S[x] (2)

Here, the independence of (∃x) of K indicated by the slash (/) means that

the individual x satisfying S[x] must be chosen independently of the choice of

any particular scenario compatible with what is known. Hence the choice of x

might as well be made before the choice of a scenario signaled by K. In other

words, there is some one and the same individual x that in all those scenarios

satis¬es S[x]. In other words, (2) means that it is known of some particular

individual x that S[x]. And this is unmistakably what it means to know who or

what satis¬es S[x]. In brief, if the variable x ranges over persons, (2) says that

it is known who (call him or her x) is such that S[x].

Ordinary language examples of (1) and (2) might be:

It is known that someone murdered Roger Akroyd (3)

It is known who murdered Roger Akroyd (4)

Or, if the question is raised personally,

I know who murdered Roger Akroyd (5)

Here, the difference between (∃ x) and (∃ x/K) is essentially that between some-

one and who (in other examples some other wh-word, such as what, where,

when, . . . . ). The same difference can be said to separate knowledge of proposi-

tions from knowledge of objects (of any logical type)”in other words, knowl-

edge of entities that perhaps could also be called knowledge of id-entities.

Presuppositions and Other Limitations 89

Similar remarks apply to subordinate propositional questions. Consider the

following propositions:

K(S1 ∨ S2 ) (6)

K(S1 ( ∨ /K)S2 ) (7)

The former says that it is known that S1 or S2 . The latter says that it is known

whether S1 or S2 . Thus the relation of ∨ to (∨/K) is like the relation of that to

whether.

These concepts and distinctions can be generalized. Excluding nested inter-

rogative constructions (as well as constructions with why or how), any knowl-

edge statement can be said to be of the form

KS (8)

where S is like a ¬rst-order sentence (in negation normal form) except that

some existential quanti¬ers (∃x) have been replaced by (∃x/K) and some dis-

junction signs ∨ by (∨/K). These slashed expressions constitute the question

ingredient in our formal (but interpreted) language. The propositional ques-

tion indicator (∨/K) expresses knowledge of propositions whereas (∃x/K)

expresses knowledge of objects (entities; in this case, individuals).

5. Questions and Their Desiderata

This explains the nature of knowledge statements. But what do they have to do

with questions? The answer is very simple. Semantically speaking, a question is,

at bottom, a request for information (knowledge). To specify this information

is to specify the epistemic state that the questioner wants to be brought about.

Any ¬rst-person knowledge statement can serve this purpose. A knowledge

statement corresponding to a direct question is called its desideratum. For

instance, the desideratum of the question

Who murdered Roger Ackroyd? (9)

is

I know who murdered Roger Ackroyd (5)

or, if the question is an impersonal one, (3). And the logical form of (3) or (9)

is, of course, (2).

Different questions correspond to non-equivalent desiderata and equiv-

alent questions to equivalent desiderata. One way in which the notion of

desideratum helps our analysis of interrogative inquiry is that it enables us to

deal with ways of answering questions by means of questions. In the original

explanation of inquiry by questioning, some ¬xed conclusion was postulated

as being given at the outset of the inquiry. This might seem to restrict the appli-

cability of interrogative inquiry tremendously, for only in the case of why- and

Socratic Epistemology

90

how-questions do we know at the outset of an inquiry what its conclusions will

be. This apparently restrictive assumption can be disarmed by assigning the

desideratum of a question to the role of the “conclusion.” The entire inquiry

will then amount to our attempt to answer this “big,” or principal question,

with the help of answers to several “small,” or operative questions.

A question can thus play two different roles in inquiry. Answering it may

be the aim of the entire game”namely, in the case of a principal question. But

answering an operative question is merely one step in the process of hopefully

answering the principal question. Again, the distinction between principal

and operative questions is not recent news. For instance, as Richard Robinson

(1971) has shown, Aristotle™s injunction against the fallacy of petitio principii

was originally a warning against asking (“petitioning”) the principal question

when asking a number of the operative ones is in order.

In general, the desideratum of a question determines much of its logical

behavior and most of its logical properties. An important example is offered

by the very notion of presuppositions we are interested in here. The presup-

position of (9) is

I know that someone murdered Roger Ackroyd. (10)

More generally, the presupposition of a question whose desideratum is of the

form (2) is (1).

6. Presuppositions of Questions

The general characterization of the presupposition of a question is now easy.

As you can see, the presupposition (1) of the question whose desideratum is

(2) is obtained from (2) by leaving out the slashed /K. This holds in general.

If the desideratum of a question (8), its presupposition is obtained from (8)

by omitting all expressions of the form /K. This is a good example of how the

independence (slash) notation enables us to carry out a simple and uniform