the question of whether these peculiarities necessarily mean that the con-

stituent in question is not trivially inconsistent.) In the second example, we

have, according to traditional terminology, two possible individuals that are not

compossible.

Hence we have also to countenance constituents that are not trivially incon-

sistent when we are dealing with the notion of information. These constituents

must be thought of as specifying alternative possibilities that language users

(and logic users) have to keep an eye on. The result is a new concept of infor-

mation that we might call “surface information.” In a perfectly natural sense,

it is surface information rather than depth information that our propositions

can be used to codify in the ¬rst place. It is the kind of information that we

human beings in fact convey, receive, and apply.

Surface information corresponds to a kind of probability (which we might

call “surface probability”) in the same way in which depth information cor-

responds to the usual (depth) probability. By the same token as in the case

of information, the notion of subjective probability with which we actually

traf¬c in real life is surface probability. Indeed, the great theorist of subjec-

tive (personal) probability, L. J. Savage (1967), is on record as maintaining

that the appropriate notion of subjective probability must behave (to use the

terminology of this chapter rather than Savage™s) like surface probability.

Surface information behaves in some ways like depth information, and in

some other ways unlike it. The most striking difference is that purely logical

inference can enhance one™s surface information. By the same token, not all

logical truths are surface tautologies. Likewise, as Savage already pointed out

in effect, surface probability is not invariant with respect of logical equivalence.

It is important to realize that surface information is, Savage notwithstand-

ing, an objective notion. Or, strictly speaking, we have to say that it is as

objective as the language that is being used, for at least qualitatively speaking,

the notion of surface information is determined by that language.

A fascinating insight here is that in the most practical terms imaginable,

surface information can be fully as valuable as depth information, and can even

Socratic Epistemology

196

be said in a sense to be about reality. The reason is that before I have actually

eliminated an inconsistent constituent, so to speak, from the normal form of

the totality of my knowledge, I have to be prepared for its truth, just as much

as in the case of a consistent constituent. In terms of the light-hearted example

just given, as long as I do not know that a universal consoler, in the sense

explained earlier cannot exist, I have to be prepared to meet such a person and

possibly make preparations for such an encounter. What if he tries to seduce

my unhappy niece? When I come to know the inconsistency, I will of course

be relieved of the need of such precautions. But this relief is not automatic,

and will involve some deductive labor whose amount cannot be mechanically

predicted. It does not make any difference to my preparations, or my failure to

take such preparations, whether the elimination of the offending constituent

takes place deductively on the basis of factual evidence. More generally, there

is no way of making the distinction between depth information and surface

information on the basis of the informed person™s reactive behavior.

On the logical level, the inseparability of surface information and depth

information shows up in the fact that there is no computable method of telling,

in general, whether we have eliminated enough inconsistent constituents to

tell that a given ¬rst-order consequence relation holds or does not hold. (This

“fact” is, of course, but another alias of the unsolvability of the decision prob-

lem for ¬rst-order logic.)

This inseparability (in a sense) of conceptual and factual information seems

to have been Quine™s insight. As such, it is a most astute idea. There is a sense in

which Quine is right, on the surface of things. In a sense, factual and conceptual

(logical) truths are inseparable and have a similar effect on a language user™s

behavior. But it is not feasible, even from a behavioristic point of view, to try to

deny a distinction altogether. For it can sometimes be ascertained behavioris-

tically whether a given agent is rejecting a certain proposition”for instance, a

certain constituent”for factual or conceptual reasons. For these two types of

reasons come from an agent™s previous exploratory or deductive enterprises.

And these two types of activity are obviously distinguishable behavioristically.

But, behaviorism aside, what we obviously need here is a ¬ner distinction than

the crude analytic versus synthetic distinction that was, in effect, a distinc-

tion between no factual information and some factual information. We need a

sense of information that is factual in the sense of helping one to cope with the

world but that can be increased by purely logical means. It seems unlikely that

we can even understand how computers can contribute to our intellectual and

material well-being without some such concept of surface information. For,

unlike telescopes or microscopes, computers do not help us in enhancing our

store of factual information in the sense of depth information.

This concept of surface information is an idea whose time has come. It can

be seen to play a crucial role in important human activities. For instance, what

happens when we explain something? The explanation does not add any factual

information to the explanandum. An answer is provided by the recent theory

Who Has Kidnapped Information? 197

of explanation that I have developed with Ilpo Halonen. (See Hintikka and

Halonen 2005.) The gist of the theory is the use of suitable logical interpolation

results. Suppose that a ¬rst-order proposition G is a logical consequence of

F. In order to see that this consequence relation holds, it must be seen that

those constituents that are in the normal form of F but not in that of G are all

inconsistent. Eliminating them does not add to the depth information of F, just

because they are inconsistent, but it increases the surface information of F.

When suitably normalized, the interpolation formula I shows how the two

kinds of reasons why a constituent can be inconsistent play out in the particular

case at hand. It spells out what individuals there exist in a model of F that help

to make it a model of G, too, and how the individuals in a model of G must

be related to those in the models of F. This obviously amounts to a kind of

account or explanation of why G logically follows from F. For instance, if one

wants to bring about G by making F true, the interpolation formula I tells one

what kinds of individuals one must create or introduce for the purpose and

how they must be related to all the other individuals in the purported model

(or system, in physics-speak). If this does not amount to an explanation of how

(and why) the truth of F makes the truth of G necessary, it is hard to see what

could be.

This shows, in fact, a remarkable feature of logical proofs. Suitably normal-

ized, they not only show that the consequence G follows from the premise(s) F,

they also show in a perfectly good sense why the consequence relation holds.

This goes a long way toward explaining the usefulness of logical inference in

applications.

Empirical explanations can be thought of as showing that the explanandum

E follows from the antecedent condition A on the basis of a background

theory T. “The” explanation will then be the interpolation formula for the

logical consequence.

(T ⊃ E)

A (2)

Such an explanation shows what it is about the antecedent conditions A that

enables the explainer to subsume E under the general theory T. It explains why

E is necessitated by A, given the background theory T. Such explanations do

not add to the depth information of A or to that of (T ⊃ E), but they typically

add to their surface information.

In brief, explanation is a matter of enhanced surface information, illustrat-

ing the function of this concept.

So far, I have not discussed how we can”if we can”assign numerical mea-

sures to information, either depth or surface information. Before discussing

this problem, it is relevant to point out that it does not affect the special case of

zero information. This is the case in which all the relevant constituents occur in

the distributive normal form of a proposition. Take, for instance, a depth tau-

tology. All consistent constituents of a given depth occur in its normal form.

It does not exclude any actually realizable possibilities and hence does not

Socratic Epistemology

198

convey any depth information. The only possible course of action is to assign

to it zero (depth) information.

This incontrovertible conclusion has a considerable philosophical interest.

It means that in ¬rst-order languages, logical truths are depth tautologies, and

vice versa. The philosophical interest of this result lies in part in its being a

refutation of Quine™s claim that logical truths can be considered as analytic in

his sense”that is, purely conceptual. We can now see that that claim is simply

and plainly wrong.

This conclusion is not belied, either, by there being alternative “non-

classical” logics. Their existence carries little conviction until their precise

nature, prominently including their semantics, has been spelled out. Brie¬‚y, as

far as I can judge the situation, neither constructivistic nor intuitionistic logics

quali¬es as counterexamples. Constructivistic logics ensue from classical logics

by imposing stricter conditions on the Skolem functions that produce the “wit-

ness individuals” that show the truth of a quanti¬cational proposition. Intu-

itionistic logics ought to be considered as variants of epistemic logics, and not

alternatives to ¬rst-order logic. And as far as the new independence-friendly

logic is concerned, Jouko Vaananen (2002) has shown that distributive normal

¨¨ ¨

forms exist also in it, even though they are no longer unique. But what about

languages that are not semantically complete”in other words, whose logic has

no complete formal proof method? The simplest such logics include IF ¬rst-