Hintikka - Halonen 2005_Explanation-Retrospective Reflexions

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JAAKKO HINTIKKA and ILPO HALONEN

EXPLANATION: RETROSPECTIVE REFLECTIONS

In John Austin’s obituary in the Times, it is said that if his influence has

turned out to be different from what he hoped it to be, that is just what he

hoped it would be. The responses that the lead paper of this number have

provoked and the other developments it has prompted are different from

what we initially hoped them to be, but they have in fact turned out to be

just what we could for collateral reasons have hoped for. Indeed, they haveled us to form in our minds interesting perspectives on the state of the art

of explanation – or at least of the philosophical study of explanation.

In the simplest possible terms, this study used to be dominated by

a dichotomy of two types of approaches to explanation. They can be

characterized equally briefly as follows:

(A) Explanation by subsumption. According to this type of view, to

explain an explanandum is to show that it is a special case of a

wider generalization.

(B) Causal theories of explanation. According to this type of

view, to explain e.g., an event is to show that it is a causalconsequence of its antecedents.

It is not claimed that this contrast is exhaustive. For instance, unificationist

approaches to explanation deserve a separate treatment.

This distinction is not without its usefulness. Unfortunately, it has been

badly muddled by philosophers. One reason for this muddle is that the

distinction (A)–(B) has been assimilated to another distinction or pseudo-

distinction. This distinction is supposed to be a contrast between two

different views as to what the means of explanation are.

(a) According to one alleged type of view, to explain something is

to find an inferential or other logico-linguistic relation betweenthe propositions that are usually called the explanandum and

the explanans. This is supposed to instantiate what is called the

deductivist view of explanation.

Synthese (2005) 143: 207–222 © Springer 2005



208 JAAKKO HINTIKKA AND ILPO HALONEN

(b) According to the other type of idea, the gist of explanation lies

in discovering an actual relation of dependence between what

is expressed by the explanandum and the explanans.

The reason why an assimilation of the contrast (A)–(B) to the con-

trast (a)–(b) is misleading is that the latter distinction is fallacious, and

fallacious in a pernicious way. For naturally whatever dependence rela-

tions there are between what is expressed by the explanandum and by

the explanans must be expressed in language with the help of logical and

linguistic relations. In general, all that can be expressed in language about

reality is expressed through the properties and relations of its symbols. As

Wittgenstein once expressed this fact of a language speaker’s life,

. . . if one says “How am I supposed to know what he means, all I can see are merely his

symbols”, then I say: “How is he supposed to know what he means, all that he has are

merely his symbols”. (MS 108, p. 277)

If one internalizes this fact, one sees that the critics of so-called deductiv-

ism are fighting a bogeyman of their own imagination. Of course, saying

this does not mean that each and every logico-semantical relation expresses

an actual relation in the world which one’s language can be used to speak

about. Moreover, those formal relations cannot be restricted to deductive

ones.

Indeed, one of the main jobs of the most important logical concepts,

the quantifiers, is to express such actual dependencies. For how can you

express in a logical language the dependence relation between two vari-

ables? Obviously by the dependence of the quantifiers on each other to

which they are bound. For instance, in a sentence of the form

(1) (∀x)(∃y)F [x, y]

the value of y depends on the value of x. Moreover, this is the only way

in which dependencies between real-life variables can be expressed in an

applied logical language on the first-order level. Indeed, the task of ex-

pressing dependence relations between variables is an important part of the

job description of quantifiers. This aspect of the semantics of quantifiers

for a long time did not receive appropriate attention. When it did, in what is

known as independence-friendly logic, it led to a substantial strengthening

of the expressive powers of the new first-order quantificational languages

as compared with the received first-order logical languages. These newlanguages are known as independence-friendly (IF) languages. Their se-

mantics is obtained from the well-known game-theoretical semantics for

the received first-order languages merely by allowing moves prompted by



EXPLANATION: RETROSPECTIVE REFLECT IONS 209

quantifiers to be informationally independent of other similar moves on

which they would otherwise depend.

Yet the alleged distinction (a)–(b) is still raising its ugly head in the

discussion about explanation. Even though we obviously failed to makeour thinking clear in the original lead paper, our basic outlook on explan-

ation was and is that that it is essentially a matter of discovering a pattern

of dependencies of different factors in the explanatory situation. Our pro-

ject was to find what the logical structure of such dependence analysis is.

Yet our (admittedly half-baked) reliance on logical interpolation theorems

resulted in our approach being classified as an (a)-type or propositional

approach. Even though the misunderstanding may very well be our fault,

it is important to correct it.

Some thinkers in fact seem to assume that any account of explanation

which is formulated in terms of logical relations between the explanandum,

the explanans and whatever other propositions relevant to an account of

explanation there may be, must be a subsumption account, in other wordssimilar to Hempel’s covering law account. Such an assumption is incorrect,

however, as will be spelled out below.

In spirit, if not in letter, our line of thought was, and is, more in line

with (B)- type approaches than (A)-type ones. However, causal theories

of explanation seem to us to suffer of important weaknesses. The im-

portant matter in explanation is pattern of dependencies between different

factors in an explanatory situation. Now the traditional notion of cause is

hopelessly too narrow to capture all the different types of dependence and

independence between variables. The causal relation is antisymmetric, and

hence incapable of handling all logically possible patterns of dependence,

for instance mutual ones. (Such mutual dependencies are found in quantumtheory according to Hintikka, forthcoming.)

Moreover, what the precise logico-linguistic way is of expressing sup-

posed causal relations is a complicated philosophical problem, whereas

the representation of dependence is one of the routine tasks of logical

constants, as was seen. Hence to rely on the notion of cause instead of more

general and more pliable notion of dependence is a questionable approach.

Even though we do not want to exhume Hume here, it is relevant to recall

that causal relations are not directly observable, in contrast to relations of

actual dependence which few philosophers seem to have any quarrel with.

(Even Hume relied on the idea of “constant conjunction”.) It even looks

more promising to try to analyze the ordinary discourse notion of cause on

the basis of a satisfactory theory of explanation than to analyze explanationin terms of the received notion of cause. We are avoiding all appeals to

causal or nomic links beyond what can be expressed in terms of observ-




able dependencies. However, this does not mean that we do not consider

dependence relations as a part of the objective reality that explanations are

addressed to. If someone wants to follow the example of Alexander Bird

in his paper above and to call such actual dependence relations “metaphys-ical”, we do not want to object. However, we do not include in the notion

of dependence anything more than what can be expressed by the resources

of first-order logic, rightly understood.

Both Hitchcock and Keränen and Salmon take us to defend in our target

paper an (A)-type approach, and therefore a (a)-type one. The fault for the

misunderstanding is undoubtedly ours, but the fact is that our aims were

almost diametrically opposed to what is ascribed by these authors to us.

With enemies like us, Hitchcock and Keränen and Salmon do not need

friends – at least if they were willing to accept the help of logic-based

arguments. The real disagreement between us and them does not concern

the nature of explanation, but what we cannot help considering their bias

against what they call deductivism. We do not want to come down tooharshly against these three authors, however, for the same bias unfortu-

nately is quite widespread among contemporary philosophers, including

analytic ones.

However, disagreements between our respective views must be re-

gistered. Keränen and Salmon write apropos our target paper that “it seems

strange that an attempt to capture intuitions about explanations should

omit considerations of causality”. We find this statement to represent a

strange perspective on the philosophical problem of explanation. We do

not believe that any philosopher should base his or her arguments on the

gut feelings that are euphemistically called “intuitions”. In the target article

we were charting the logical and epistemological structure of the processof explanation, not to imitate philosophers’ misinterpretation of Chom-

sky’s methodology (Hintikka 1999). We would find it strange indeed to

approach explanation without considering dependence relations, but we

are suspicious of attempts to posit metaphysical causal powers to back up

such relations of dependence.

There are in any case many accounts of events which are referred to as

explanations in ordinary usage even though they are not obviously causal.

A rich lode of such explanations is constituted by accounts of people’s

behavior by reference to what they know or believe. Even though attempts

have been made to ascribe a causal role to beliefs, such explanations are

routinely accepted by people who do not believe that causality plays any

role in them.This is enough to show that the emphases (a) and (b) are not mutually

exclusive. This exempts us among other things from making much weather




about the distinction between the explanandum and the explanans as pro-

positions on the one hand and what they express on the other hand. But we

have not seen yet how the two frameworks can actually be reconciled, that

is, how a concrete dependence of the explanandum from its antecedents ismanifested in language. In this respect, the original paper left much to be

desired, which justifies some of the criticisms levelled at it in the other es-

says appearing here. The general scheme assumed there was that to explain

why the explanandum D obtains is to deduce it from a background theory

T and certain ad explanandum conditions (not unlike initial conditions or

boundary conditions) A. Thus we have

(2) (T & A) D .

The explanans (“the explanation”) is then obtained by applying an inter-

polation theorem to

(3) A (T ⊃ D ).

In the original paper we used Craig’s well-known interpolation theorem,

applying it to the simple test case where D is of the form P (b). The ap-

plication presupposes that P does not occur in A nor b in T . (They can

thus be written A[b] and T [P ].) The interpolation formula H [b]does not

contain P , and it satisfies

(4) A[b] H [b],

(5) H [b] (T [P ] ⊃ P(b)).

On the assumptions move, (5) implies

(6) T [P ] (∀x)(H [x] ⊃ P (x)).

The suggestion was that in some sense H [b] is the explanation.

But does H [b] really show in down-to-earth terms why it is the case that

P(b)? What was given in the original paper as an answer to this question

was only a lame reference to how H [b] is constructed from a suitably

normalized proof of (3). It is excusable if this reference did not satisfy

everybody. After completing the target paper, the situation has changed

radically. We have been able to prove a new interpolation theorem which

will be called the explanatory interpolation theorem. It brings out much

than Craig’s old theorem the relevant aspects of an explanatory situation.

This theorem uses a simplified method of Beth’s tableau method. Be-cause of the completeness of the tableau method, we can consider all

consequence relations as being proved by this method. The rules of this

simplified version can be stated as follows:




(i) For each open branch on the left, form the conjunction of all the

formulas needed for bridges to the right side.

(ii) Form a disjunction of all the conjunctions (i).

(iii) From bottom up (i.e., in the order reverse to the rule application inthe proof of (F G)) carry out step by step the following quantifier

introductions:

(a) Replace an individual constant introduced by existential instanti-

ation on the left by a new variable x and prefix the formula by (∃x)

(different x for different applications of (a) or (b)).

(b) Replace each individual constant introduced to the left side from

the right side by an application of universal instantiation on the

left side by a variable y and prefix the formula by (∀y) (different

y for different application of (a) or (b)).

It is easily seen that the sentence IL obtained serves as an interpolation

formula, in other words, the following holds:

F I L I L G.

Now I L can be seen to contribute to the explanation of the conclusion

F G in a striking way. The premise F describes a certain kind of struc-

ture or, rather, a number of alternative structures, and likewise for G. Then

each existential quantifier in I L specifies an individual occurring in one of

these alternative structures which must exist and which serves to show that

a structure specified by F must be also a structure specified by G.

Likewise, each universal quantifier occurring in I L specifies a general

truth about one of the structures specified by F which can be applied to

the individuals occurring in the structures specified by G so as to help to

show that the structures specified by F are also structures specified by G.

(Notice that these general truths about F may involve the individuals said

to exist by the existential quantifiers of F .)

That I L can be said in a very striking sense to be an explanation (or a

part of an explanation) why G follows logically from F . More explicitly

expressed, I L tells what it is about the structures specified by F that makes

the models of F to be also models of G. We can also define a mirror-image

(dual) interpolation formula I R which tells us which individuals exist in the

structures specified by G and which general laws hold in these structures

that guarantee that it G follows logically from F :

The explanatory interpolation theorem shows the actual real-life con-nection between the premise and the conclusion. The left-hand interpol-

ation sentence spells out those features of a structure which satisfies F

that make it a structure which also satisfies G. Suppose that your task is




to bring it about that G. Knowing that G is logically implied by F does

not automatically help you to do so, even if you know that F is true. But

knowing the left-hand interpolation sentence I L provides a blueprint of

making sure that G. For I L shows what kind of structure you have to findor to construct in order to realize G, in that it lists the individuals that

have to exist and the general laws that bind them together which guarantee

this result. By replacing existential quantifiers by Skolem functions we

can even think of these general laws as dependence relations between the

elements of the structure that satisfies F .

In a similar way you can see that I R describes a structure such that if it

exists, G is automatically true. And the fact that I R is a trivial consequence

of I L means in effect that the two structures are the same, except that

they are described from a different perspective, or else that the structure

specified by I R is in the same sense a part of the structure described by I L.

The interpolation sentences I L and I R thus spell out how the models

satisfying F also satisfy G. They show how the latter literally depend onthe former. And this “how” includes both the individuals that mediate the

dependence and the relations that tie them together. If spelling out this

dependence is not an explanation why G follows from F , it is hard to see

what could possibly be.

These observations thus show that a logical proof of G from F can

serve to produce a genuine explanation of the consequence relation. Of

course not every proof does so. It is a part of the mission of proof theory

to find the normal forms of proofs which can serve such a purpose and

to which other proofs can be reduced. Kreisel was thus right when he

emphasized that proof theory is not only a study how logical truths and

logical consequence relations can be proved. It also serves to show howother important information can be extracted from logical proofs.

The actual burden in explaining the explanandum is thus to find the

ad explanandum data A[b] for which (2) holds. As a by-product of the

explanation we do obtain a kind of covering law, viz. (∀x)(H [x] ⊃ P (x)).

There is thus a grain of truth in the subsumption idea. But in the actual

process of explanation this covering law plays no role. Explanation does

not consist in deducing the explanandum from the covering law.

In everyday explanations as well as in legal ones T [P ] need not be a

general scientific law. Rather, it is often all the background information

which we keep fixed for the sake of explanation in order to study the role

of some one factor in the situation in which we happen to be especially

interestedThis becomes even clearer when it is recalled how the explanatory

interpolation theorem operates in our account. It is there applied to (3),




that is to say, with the ad explanandum premise playing the role of F .

This premise is what has to be discovered interrogatively in the actual

process of explanation. Now, as was seen, the explanatory interpolation

formula literally lists the different individuals that the inquirer has to findfor the purpose, plus the dependencies between them and other individu-

als that suffice to imply the explanandum (jointly with the background

theory). The order of the quantifiers which specify these individuals and

their interconnections even reproduces the order in which they make their

appearance in the interrogative inquiry involved in the explanation. This is

the sense in which the explanatory interpolation formula is a summary of

the actual process of explanation.

Even though we did not reach a satisfactory account in the target paper,

these new insights should satisfy amply Sintonen’s request of providing

an explanation why explanations are explanatory on our account. They are

also relevant to other papers. For instance, Christopher Hitchcock endorses

the view (which he attributes to J. Woodward) that what is characteristicof explanations bring out the dependence of the explanandum on the initial

conditions or, as he expresses the idea, “how the explanandum would have

been different had the initial conditions been different in different ways”.

This comes close to the dependence idea, expect perhaps for the fact that

concomitant variation is only an indication of dependence, not its neces-

sary condition. Hitchcock argues, undoubtedly correctly, that our initial

account did not do justice to this idea. What we failed to do was to bring

out sufficiently clearly how this dependence is manifested. What we should

have emphasized is that the interpolation sentence not only summarizes the

deduction A (T ⊃ D ), but shows how the fact that A makes it necessary.

The explanatoriness of an explanation does not come from the backgroundtheory, but from the connection between A, T and D that the explanatory

interpolation theorem brings out.

It also follows that there can be genuine explanations in mathematics.

We do not indulge here in a closer study of such explanations, however.

An example may illustrate what has been said. Some writers of logic

textbooks try to impress students by showing that deductions can produce

surprising conclusions. They take the old line of a song “Everybody loves

my baby, but my baby only loves me” and show that as if by magic it

implies that I am my baby. What is there to be said by way of explaining

the curious consequence? Let us see. We can put b = my baby, m = me,

L(x, y) = x loves y , T = (∀x)L(x, b), A = (∀x)(L(x,b) ⊃ (x = m)),

D = (b = m). Then, a simple deduction of A (T ⊃ D) might run asfollows:




(1) (∀x)(L(b, x) ⊃ (x = m)) (2) (∀x)(L(b, x) ⊃ (b = m))

(3) L(b, b) ⊃ (b = m) from (1) (4) (∃x) ∼ L(x,b) from (2)

(7) ∼ L(b, b) from (3) (8) (b = m) from (3) (5) (b = m) from (2)

bridge to (6) bridge to (5) (6) ∼ L(b, b) from (4)

According to the explanatory interpolation theorem,

I L = I R = (∼ L(b, b) ∨ (b = m)) = (L(b, b) ⊃ (b = m)).

This calls the bluff of the textbook writers. The surprising conclusion

is the result of a mistranslation. In ordinary usage, “everybody loves

my baby” does not imply that my baby loves my baby. (Ordinary lan-

guage uses the exclusive interpretation of quantifiers, not the inclusive in

Jaakko Hintikka’s terminology.) The apparently surprising conclusion is

explained by this mistranslation. And this explanation is precisely whatthe interpolation sentence provides.

Another example is offered by the well-known “curious incident of

the dog in the night-time” in Conan Doyle. There the ad explanandum

premises say (i) that there was a trained watchdog in the stable, in brief

(∀x)D(x), and (ii) that no dog barked at the thief, in short (∀x)(D(x) ⊃

∼ B(x,t)). The general truths about the situation are (i) that the master

of all the dogs in stable was the stable master, in short (∀x)(∀y)((D(x) &

M(y,x)) ⊃ s = y ) and (ii) that the only person a watchdog does not bark

at is its master, in short (∀x)(∀y)((D(x) & ∼ B(x,y)) ⊃ M(y,x)). The

conclusion is that the stable master was the thief or s = t . The tableau for

A (T ⊃ D ) will look like this:

(1) (∃x)D(x) (3) (∀x)(∀y)((D(x) & M(y,x)) ⊃ s = y )

(2) (∀x)(D(x) ⊃∼ B(x,t) & (∀x)(∀y)((D(x) & ∼ B(x,y)) ⊃ M(y,x)) ⊃ s = t

(4) D(δ) from (1) (8) s = t from (3)

(5) (D(δ) ⊃∼ B(δ,t ) from (2) (9) (∃x)(∃y)(D(x) & M(y,x) & s = y )

∨(∃x)(∃y)(D(x) & ∼ B(x,y) & ∼ M(y,x)) from (3)

(6) ∼ D(δ) (7) ∼ B(δ, t) from (5) (10) (∃x)(∃y)(D(x) & M(y, x) & s = y )

closure from (5) from (9)

(11) (∃x)(∃y)(D(x) & ∼ B(x, y) & ∼ M(y,x))

from (9)

(12) D(δ) & M(t,δ) & s = t from (10)

(13) D(δ) & ∼ B(δ,t) & ∼ M(t,δ) from (11)

(14) D(δ) (15) M(t,δ) (16) s = t

from (12) fro m (12) from (12)

bridge closure

(17) D(δ) (18) ∼ B(δ,t ) (19) ∼ M(t,δ)

from (13) fro m (13) from (13)

bridge bridge closure




According to the explanatory interpolation theorem, we have here

I L = (∃x)(D(x)& ∼ B(x,t)) = I R.

In other words, what in the observed circumstances explains why the sta-blemaster was the thief is the fact that there was a watchdog in the stable

who did not bark at the thief. This is of course precisely the explanation

Sherlock Holmes offered to the good inspector. And, indeed, given the

general truths T , there is no way for I L to be true unless the thief was the

stablemaster.

The literature on explanation is full of examples of attempted ex-

planations that fail, usually in the form of what are supposed to be

counter-examples to Hempel’s covering law account of explanation. It

seems to us a welcome change to have a couple of examples of successful

explanation to contemplate.

Another example illustrates the character of the implication I L I R as

a trivial one. In it the relevant entailment is

(7) (∃x)(∀y)L(x, y) (∀y)(∃x)L(x, y).

We can take, e.g., L(x, y) = x loves y . The tableau might look like

(1) (∃x)(∀y)L(x, y) (2) (∀y)(∃x)L(x, y)

(3) (∀y)L(α, y) from (1) (4) (∃x)L(x,β) from (2)

(5) L(α,β ) from (3) (6) L(α,β ) from (4)

Here I L = (1), I R = (2). What this triviality reflects is obvious. A situation

in which someone, say α, loves everyone, is automatically one in which

anyone, say β , is loved by someone, viz. α .

What is there to be said on the basis of the explanatory interpolation

theorem about the problems of explanation in general and about the other

contributions to this number in particular? There is more to be said by way

of an answer than can be exhausted in this paper. A few salient points can

nevertheless be made.

The explanatory interpolation theorem applies more widely than

Craig’s old theorem. Craig’s interpolation theorem applied to the con-

sequence relation F G is vacuous if F and G share the same nonlogical

constants. In the relevant application this means (in terms of our example,

cf. (3)–(6)) that both P and b occur in A. In contrast, no such restriction is

needed for the applicability of the explanatory interpolation theorem.In contrast, no such restriction is needed for the applicability of the

explanatory interpolation theorem. Since it was seen to yield genuine ex-

planations, Gerhard Schurz is entirely right in claiming (as against our




original paper) that perfectly good explanations are possible even when

Craig’s interpolation theorem does not apply. What remains true is that if

b occurs in T , we obtain (5) but not (6). Then no covering law is implied by

T [P , b]. This shows in fact an important qualification to any version of thecovering law idea. In our original paper, it was maintained that a covering

law is available as a kind of by-product of any successful explanation.

This could have been a partial vindication of the covering law idea. Now

it turns out that even this partial vindication is too generous in that there

are perfectly good explanations which do not have a covering law as their

by-product.

This amounts to a kind of refutation of the covering law idea. Hence our

account of explanation is not by any stretch of imagination a subsumption

(covering law) account. As a consequence, the real or alleged counter-

examples to Hempel’s theory of explanation do not necessarily have any

applicability to our account.

What also remains true is that the relevant interpolation theorem doesnot apply when F is logically false or G logically true. In the application

to (3) this means that A must not be self contradictory and (T ⊃ D ) must

not be logically true.

Moreover, if T is logically true, (3) reduces to A D. This case

scarcely qualifies as one of explanation, for an inquirer cannot in such a

situation ascertain the truth of the ad explanandum conditions A without

ipso facto ascertaining the truth of the explanandum D. The same obvi-

ously holds when T is some other kind of conceptual truth, for instance

arithmetical or geometrical. This is illustrated by the flagpole example

of Bromberger’s. In it, the general truth involved is geometrical one.

Hence on our account it does not rate as an instance of explanation. As aconsequence, the flagpole example not only does not constitute a counter-

example to our account (contrary to what Hitchcock and Keränen and

Salmon think) but indirectly supports it.

The ad explanandum premise A is also indispensable in explanation –

at least in the kind of explanation we are dealing with. Admittedly, there

are views like Putnam’s (reported by Sintonen) according to which explan-

ation typically consists in deriving explananda from a general theory alone.

Such a view might first seem totally unrealistic, for a completely general

theory typically does not entail any particular facts without the help of ad

explanandum premises, such as initial conditions or boundary conditions.

Speaking in general terms, an important aspect of explanation that is re-

vealed by the explanatory interpolation theorem is that the explanatorinessof explanations is a matter of the connection that there obtains between

the background theory, ad explanandum data and the explanandum itself.




It is not a matter, contrary what e.g., Hitchcock seems to think, concerning

primarily the nature of the background theory. In everyday explanations,

the role of the background theory can be played simply by those relevant

factors which do not depend on the factor (e.g., a certain person) whoserole in the genesis of the explanandum one is interested in.

There is a different (though not unrelated) question concerning the

rationale of explanations. It may be expressed in the form of Wesley Sal-

mon’s onetime title question: Why ask why? In other words, what does an

inquirer gain cognitively by finding explanations for various phenomena?

We are inclined to consider answers in terms of systematization or unific-

ation dangerously vague. Is there a more clearly definable “commodity”

that is acquired through an explanatory process?

Now such elimination of merely apparent possibilities is the hallmark

of what has been called surface information (Hintikka 1970, 2003). Sur-

face information is objective, and it can be of great practical value precisely

because it amounts to the elimination of prima facie possible but in (lo-gical) reality impossible alternatives. Admittedly, not all such elimination

increases our surface information according to its technical definition. But

this is due merely to the fact that the definition of surface information that

is found in the literature is calculated to capture only such elimination

of spurious possibilities that goes beyond propositional logic and even

beyond monadic quantification theory. The notion of surface information

could in principle be redefined so as to cover also the propositional and the

monadic case.

With this qualification in mind, it can be said that explanation in the

sense - considered here increases – or forces us to increase – our surface in-

formation. In view of the fact that surface information is our objective (andoften quite useful) commodity, this serves to explain why explanations are

indeed valuable, in other words, why one should ask why.

Indeed, looking at the relationship from the other end it can be said

that the practice of explanation offers probably the most vivid example

of the role of surface information in science and everyday life. We hope

that our analysis of explanation will enhance philosophers’ interest in the

important but badly neglected distinction between surface information and

depth information.

This brings out an important dimension in explanation. A deductive

interpolation sentence has normally the more surface information the more

layers of quantifiers it contains, in other words, the more complex it is in

this respect. This put the entire philosophical discussion of explanation ina quaint light. For among the examples of explanation actually analyzed

in the literature there are few – probably none – in which the explanatory




interpolation sentence is more complicated than the formulas of monadic

predicate logic. What this means is that the entire discussion has been

conducted by reference to examples which are so simple as not to be rep-

resentative of what makes successful explanations interesting. This holdsin particular of the numerous “counter-examples” to Hempel. Even when

they tell against the letter of Hempel’s views, the attention paid to them in

the literature is excessive, for because their relative triviality they are not

likely to bring out what makes genuine explanations explanatory.

Even the examples we have used are by the same token fairly element-

ary, and not fully representative of the enhancement of surface information

that was seen to be the gist of the nontriviality of good explanations. Their

plausibility as explanations is due to the fact that in them certain prima

facie possibilities were successfully eliminated.

We cannot here offer a line-by-line commentary on all the different

papers. In all of them, there are interesting comments on our shared prob-

lems, and useful corrections to our target paper. This is especially true of Gerhard Schurz’s paper. Some remarks that hopefully have some general

interest can nevertheless be made. Sintonen argues that explanation is a

wider concept than we are assuming in that explanation of phenomena is

part of theory formation. In apparent contrast to this fact we apparently

assume that the background theory remains constant during the process

of explanation. A similar idea of a wider role of explanation in science

underlies other views of explanation, too, such as unificationist ones. We

are sure that Sintonen and others are right about the ordinary force of the

term “explanation”. However, the course we have taken seems to be by

far the best for the purpose of understanding the structure of the process

of explanation. For the purpose, it is not so important that the backgroundtheory is fixed, but that the desideratum (or the class of desiderata) remains

constant in the course of the process. Now in actual scientific thinking

theory formation cannot be reduced to finding an explanation for so far

known facts. The essential purposes of a new theory include ways of

discovering new previously unknown facts that the theory can explain,

thereby confirming it and perhaps separating it from other theories. And

by definition no rules can be given for explaining unknown data. It is for

this reason why scientific reasoning cannot be reduced to “inferences to the

best explanation”. Such a reduction would mean neglecting the dynamic

and progressive aspect of theory formation. Each datum, new or old, has

to be explained in the sense we have been dealing with: separately and

from some one given theory or theory version. Thus the core meaning of explanation is bound to be explaining given data on the basis of a given

background theory.




The givenness of the theory need not be absolute.

Two aspects of Alexander Bird’s contribution call for clarifications. He

speaks of “contrastive” explanations which are targeted on a certain feature

of the explanandum. There need not be anything wrong about using suchlocutions. However, in a certain sense all explanation is contrastive, as we

tried to explain in the target article. For when explanation is analyzed in

epistemic terms, it inevitably involves a choice of queried and unqueried

ingredients of the explanandum.

Bird also distinguishes from each other subjective and objective ex-

planations. Once again such a distinction is viable and sometimes even

illuminating. But it should not deflect our interest away from the question

as to what objective factors (e.g., structural factors) typically make prima

facie subjective explanations subjectively explanatory.

We have nothing but praise to offer on the details of Diderik Batens’

able paper. However, his overall approach differs from ours in ways that

deserve serious attention. At the bottom of the difference, there seems tolurk something of the same alienation of deductive relations in philosoph-

ers’ thinking from what an analysis of those logical relations in effect tells

us about actual dependence relations in the world.

Batens is in any case absolutely right in calling attention to the cases

in which there are inconsistencies in the background theory T or in the

ad explanandum data A. We should have discussed this kind of case in

the target paper, for it is not only a possible one in realistic inquiry but a

frequently occurring one. However, we do not find any need to resort to any

unusual logic here, for the kind of dependence analysis that is exemplified

by the explanatory interpolation theorem goes a long way toward hand-

ling even the contradictory cases. Take for instance Batens’ intentionallyoversimplified case in which

T = (∀x)(Q(x) ∨ P(x)) & (∃x)(R(x) & ∼ R(x))

A =∼ Q(a)

Explanandum = D = P(a).

Here a simple tableau derivation of A (T ⊃ P (a)) might run as follows:

(1) ∼ Q(a)(2) (∀x)(Q(x) ∨ P(x)) & (∃x)(R(x) & ∼ R(x)) ⊃ P (a)

(3) (∃x)(∼ Q(x) & ∼ P(x)) ∨ (∀x)(∼ R(x)∨ ∼∼ R(x))

(4) P (a)

(5) (∃x)(∼ Q(x) & ∼ P(x))

(6) (∼ Q(a) & ∼ P (a))

(7) ∼ Q(a) (8) ∼ P (a)

bridge closure




This is precisely the kind of explanation Batens wants to capture. Here it is

obtained automatically, without any need of adjustments, complete with an

interpolation sentence. And the explanation works in the same way as in

the consistent case. It shows that there is in the ad explanandum data thatnecessitates the implication from the background theory to the explanan-

dum. The reason Batens cannot avail himself to this line of thought is that

in paraconsistent logic that he prefers to employ the conclusion does not

hold. But this is a self-inflicted problem that we do not have to worry about.

A dependence analysis accounts for the puzzle more economically than a

switch in logic.

Such an analysis does not help us if the crucial consequence relation

A (T ⊃ D) holds only in virtue of the inconsistency. This is shown

in our normalized tableau method by the fact that all the paths (branches)

close on the one side of the tableau or the other (or both). In such cir-

cumstances the kind of quasi-explanation just mentioned is clearly useless.

But the realistic response on the part of an inquirer to such an eventualityis not to adopt some fancy new logic but to realize that one of his or

her assumptions has to be rejected. In terms of the interrogative model,

this means suspending (“bracketing”) one of the answers (or one of the

initial premises). The choice of the answer to be bracketed can typically

be guided by a dependence analysis, but it remains a strategic decision for

which binding definitory rules cannot always be given.

Batens’ approach seems to be predicated on an awkward view of the

role of so- called rules of inference in logic. He appears to think that they

so to speak codify our strategies of passing from one sentence to another.

But this is simply not the whole story. The validity of rules of inference

depends on the semantical rules that relate our language to reality andthereby determine the meaning of our sentences. Hence when someone

tells us that he or she will henceforth use paraconsistent logic or some

other “nonclassical” logic, in the most literal sense of the word he or she

is beginning to talk about something else. What is said may be fine and

dandy, but the nonclassical logician owes us a realistic translation to our

old idiom or some other explanation as to how his or her new discourse is

relevant to the old problems formulated in terms of classical logic. Logic

is not only a medium of inference. It is in the first place a medium of

representation.

It may well be that Batens’ ingenious use of certain nonclassical logics

can be translated to the language of bracketing and unbracketing. However,

the correspondence is not obvious, and there are good reasons to think that it will be rather complicated. The most important reason is that the

inference rules of logic are what has been called definitory rules. They do




not tell what a reasoner should do, but what he or she is allowed to do in

the “game” of logical inference. By so doing, they in a sense define that

game. It is only the strategic rules that guide an inquirer’s actual decisions.

Strategic rules do not permit or mandate what an inquirer does. Followingone of them depends on the inquirer’s utilities, which are for him or her to

choose.

But it was just seen in effect that decisions to bracket an answer are

strategic in nature. Hence it is most unlikely that they can be captured by

any rules of inference, classical, nonclassical, paraconsistent or whatnot.

REFERENCES

Halonen, Ilpo and Hintikka, Jaakko: 2003, ‘Toward the Theory of the Process of Explana-

tion’, this volume.

Hintikka, Jaakko: 1970, ‘Surface Information and Depth Information’, in Jaakko Hintikkaand Patrick Suppes (eds), Information and Inference, D. Reidel, Dordrecht, pp. 263–297.

Hintikka, Jaakko: 1999, ‘The Emperor’s New Intuitions’, Journal of Philosophy 96, 127–

147.

Hintikka, Jaakko: 2003, ‘A Distinction Too Few or Too Many?’, in Carol Gould (ed.),

Constructivism and Practice: Toward a Historical Epistemology, Roman & Littlefield,

Lanham, Maryland, pp. 47–74.

Hintikka, Jaakko: forthcoming, ‘On the Logical Foundations of Quantum Theory’.

Wittgenstein, Ludwig: 2000, Wittgenstein’s Nachlass, The Bergen Electronic Edition,

Oxford University Press.

Department of Philosophy

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