costa & french, partial structures and the logic of azande

North American Philosophical Publications

Partial Structures and the Logic of AzandeAuthor(s): Newton da Costa and Steven FrenchSource: American Philosophical Quarterly, Vol. 32, No. 4 (Oct., 1995), pp. 325-339Published by: University of Illinois Press on behalf of the North American Philosophical PublicationsStable URL: http://www.jstor.org/stable/20009835 .Accessed: 25/06/2011 06:03

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American Philosophical Quarterly Volume 32, Number 4, October 1995

PARTIAL STRUCTURES AND THE LOGIC OF AZANDE

Newton da Costa and Steven French

The inconsistent people I have known have not seemed to have a higher ratio of false

beliefs to true ones than those who make a superhuman effort to maintain consistency at

all costs. True, people who are compulsively consistent will probably save themselves

certain false beliefs, but I'm afraid they will also miss many true ones! (R. Smullyan, 5000

B.C. and Other Philosophical Fantasies, St. Martin's Press 1983, p. 40)

__ j

Introduction

V V HY should one be consistent in one's

beliefs?1 Because, it is typically answered, beliefs are beliefs that certain propositions are true and the structure of the set of

propositions, the framework on which they

hang, is that of classical logic, in which in?

consistency leads to triviality and the ex?

plosion of the belief set. Thus, on what is

sometimes referred to as the "rationalist"

view, the Principle of Non-Contradiction is

taken to be one of the most fundamen?

tal?perhaps the most fundamental?of

the assorted struts and spars in the frame?

work of rationality (Lukes 1970). This view has, over the past several years,

come under concerted attack. In particular, there has recently been something of a

"boom" in the study of inconsistency, with

workers from a number of fields tracking its

prevalence across a range of putative "kinds"

or forms of reasoning: formal, scientific and

"natural." One conclusion that has been

reached echoes Kyburg's renowned claim

that "the demand for consistency is appropri? ate for angels, not men" (Kyburg 1987, p. 141) and efforts have been made to demonstrate

that, within suitable (re-)formulations, the

existence of inconsistency is not fatal to

(appropriate) notions of rationality. The de?

velopment of such formulations and the

concomitant reappraisal of our under?

standing of what it is to be rational is an

on-going endeavor, and it is not yet clear

what is to replace what Elster calls the "thin"

account of rationality sketched above.

In a series of recent works (da Costa 1989; da Costa and French 1990a, 1990b, 1991,

1993a, 1993b; French 1991) we have at?

tempted to lay down the basis of an alter?

native account in which inconsistency is

analysed in model theoretic terms. In par? ticular, our central claim is that inconsis?

tency can be accommodated through the

introduction of so-called "partial struc?

tures," within the model-theoretic ap?

proach, in terms of which one can formally define a notion of "partial," or "pragmatic," truth. This allows for a more accurate re?

flection of our actual doxastic circum?

stances and formally incorporates an

element of fallibility sufficient to prevent an inconsistent belief set from blowing up in our faces. On this account, certain beliefs,

namely those that Sperber designates as

"representational" (1982), are to be repre? sented not as "belief that p is true," where

p is some proposition, but rather as "belief

that p is partially true," where p is a "semi

propositional representation." Our aim in the present paper is to extend

this treatment to the phenomenon of

325

326 / AMERICAN PHILOSOPHICAL QUARTERLY

"cross-cultural" inconsistency: where the

beliefs of another culture appear inconsis?

tent in our terms. In particular, we shall ex?

amine the well known and much discussed case of Zande witchcraft beliefs, although

we suspect that other examples, such as the beliefs of the Nuer, can be treated in a simi?

lar way. It is the purported existence of such

examples that supplies much of the grist to

the relativists' mill and offers the most ob?

vious challenge to the rationalist, who is

caught between the devil of (at its most ex?

treme) logical relativism and the deep blue sea of writing off an entire culture as irra?

tional. A possible escape route is provided

by the Principle of Charity which rejects, as

a genuine translation, any translation of the

utterances of representatives of the culture

concerned that involves the attribution of

inconsistent beliefs. In effect, to be a set of

beliefs, the set must be consistent and the

"thin" account of rationality regains its uni?

versality. Again, Charity, as such, has also

come under fire in recent years, yet some?

thing like it must be presupposed to get the

translation off the ground, even to begin to

talk of the beliefs of another culture. The

nature of this "something" and its location within the kind of account we are con?

cerned to elaborate here will be discussed towards the end of this essay.

Let us consider, then, perhaps the most

famous case study of a putative set of in?

consistent beliefs.

Zande Reasoning

The example of Zande witchcraft beliefs

has acquired the status of a cultural datum

against which successive philosophers can

test their particular views of rationality. As

recorded by Evans-Pritchard (1937), the

Azande believe that certain individuals are

witches, by virtue of their possessing "witch?

craft substance" (see Evans Pritchard, pp. 21

23, for a discussion of the nature of this

substance)2. Being a witch is a heritable

trait: the witchcraft substance is inherited

by the same-sex offspring of a witch. Attri?

butions of the activity of witchcraft are

made to explain a variety of events and are

determined through the use of "oracles," such as that of the "poisoned chicken." Typi? cally, a dose of benge, a naturally occurring toxin, will be administered to the hapless fowl and the result will be associated with the an? swers to a particular question regarding a

particular putative case of witchcraft.

Since a Zande clan can be delineated as

a group of biologically interrelated indi?

viduals, it would seem to follow that if one

member of a clan is found to be a witch, all

members of the same sex of the clan must

be witches. The Azande, however, do not ac?

cept such an inference.

The argument has been clearly expressed by Jennings:

1. All and only witches have witchcraft sub?

stance;

2. Witchcraft substance is always inherited by the same-sexed children of a witch;

3. The Zande clan is a group of persons re?

lated biologically to one another through the male line;

4. Man A of clan C is a witch;

5. Every man in clan C is a witch. (Jennings 1989.)

The Azande appear to accept the premises but not the conclusion. As Evans-Pritchard

said, in one of the most reproduced remarks

in the literature on this topic, Azande see

the sense of this argument but they do not

accept its conclusions, and it would involve the

whole notion of witchcraft in contradiction were they to do so (Evans-Pritchard, p. 34).

How, then, should we respond to this re?

fusal to face the epistemic facts?

Responses

One obvious response is to write off the

Azande as irrational, illogical, child-like even. Ignoring the suggestion of cultural

imperialism inherent in such a response, it

collapses into implausibility once one notes

that the Azande could not be described as

particularly child-like in their other, non

magical, dealings. As Cooper notes, in a re?

cent discussion that we shall analyse in more detail shortly, such a view implies a

THE LOGIC OF AZANDE / 327

degree of cultural schizophrenia on the part of the Azande that is clearly difficult to

maintain (Cooper 1975, p. 247). Evans

Pritchard emphasizes that "most of their

talk is common-sense talk, and their refer?

ences to witchcraft, whilst frequent enough, bear no comparison in volume to their talk

about other matters. Similarly, though Azande often perform ritual it takes up

very little of their time in comparison with

more mundane occupations" (p. 20). Towards the end of his work he further

remarks, with regard to Zande beliefs, that

when we see how an individual uses them we

may say that they are mystical but we cannot

say that his use of them is illogical or even

that it is uncritical. I had no difficulty in using Zande notions as Azande themselves use them. Once the idiom is learnt the rest is

easy, for in Zandeland one mystical idea fol? lows on another as reasonably

as one com?

mon-sense idea follows on another in our

own society (p. 541).

There is, then, some sort of logical structure

here, sufficient to allow inferences of one

form or another to be made.

Cooper also recalls Horton's argument that the response of illogicality trades on an

incorrect analogy between the scientific

and magico-religious frameworks. It views

spirits as some kind of primitive, personi? fied causes, whereas they should be taken as analogous to the highly theoretical enti?

ties of, say, physics. This forms part of a gen? eral criticism that earlier accounts of

magico-religious thought adopted an incor? rect or inaccurate analogy with certain con?

ceptions of scientific beliefs. There is an

analogy to be drawn, but it is obviously de?

pendent on an appropriate characterization

of science. This is a view with which we

heartily concur, as will be made clear below, and in this respect, like Cooper, we see our?

selves as working within the approach

broadly outlined by Horton in his classic

paper "African Traditional Thought and

Western Science" (1967; see also Horton

1982). Alternative responses can be divided be?

tween those that are broadly rationalist and

those that are equally broadly relativist.

Zande witchcraft beliefs pose a particular

problem for the rationalist, with her em?

phasis on the "laws" of logic, and in particu? lar the Principle of Non-Contradiction, as a

critical supporting strut in the fundamental

framework of rationality (Lukes 1970). Those of the relativist persuasion are cor?

respondingly keen to exploit the example,

using it as further grist to their anti-ration?

alist mill. Barnes and Bloor, in particular, have homed in on the rationalist invocation

of these "laws of logic," noting that:

it is ironic that logicians, who expose with admirable ruthlessness how problematic, variable and difficult to ground patterns of inference are, and who freely confess how

very little is agreed upon by the totality of

practitioners in their field, are turned to

again and again to provide constraints upon the possibilities of rational thought. Just as there is always a certain demand for iron laws of economics, s? there seems always to be a demand for iron laws of logic (1982, p. 45, fn. 40).

We shall not rehearse here the three steps to relativism presented by Barnes and

Bloor, but shall simply note that Zande be?

liefs appear to provide a prima facie exam?

ple of an alternative conceptual scheme in

which not only those beliefs that are held to be true are different, but also the very framework of justification and rationality.

The obvious rationalist response, then, is to invoke some form of the Principle of

Charity and claim that in abstracting the

above argument from Zande utterances,

something has gone awry with the transla?

tion. If due attention is paid to the context

and an alternative translation manual con?

structed, the appearance of inconsistency will be removed (see Cooper, p. 240 and p. 249, for criticisms). Of course, the precise form of the Principle that is invoked here

will have to be attended to very carefully; at the very least, it would seem, it would

have to rule out those translations that do not preserve classical logic (or else the Bar? nes and Bloor line regains its bite). Quine's views on this point are well known, but a


relativist is hardly going to accept the pre?

sumption that quantum mechanics should

be favored over Zande witchcraft beliefs

when it comes to applying the Principle of

Minimum Mutilation!

We shall return to a consideration of the

Principle of Charity after we have outlined

our own position, but it is worth noting the

following at this stage. First of all, the Prin?

ciple is by no means uncontroversial and

both criticisms and modifications abound.

Secondly, a form of the Principle, and it

needs to be made clear which form, plays a

crucial role in Davidson's argument against the very idea of a conceptual scheme (1973;

and, more recently, the very idea of a sub?

ject-object distinction; see Davidson 1989). This forms part of Davidson's response to

relativism, which is to cut it off at the knees

before it even has a chance to get off the

ground. The problem, of course, is that un?

restricted use of the Principle of Charity re?

moves the possibility of irrational belief

sets at the very outset, since they cannot be

translated as such (although, for Davidson, a belief must be a rational belief to be a

belief!). Thus the criticism is that we should

at least allow for the possibility of irration?

ality, if our framework of rationality is to

have any distinguishing power at all. Hav?

ing said that, we certainly do not wish to

reject all principles analogous to that of

Charity, since some foothold needs to be

chipped out if translation is to get off the

ground. We believe there does exist such a

Principle that avoids the pitfalls associated

with the former and, most importantly (!), meshes quite nicely with the view to be pre?

sented below.

Returning to the central point above, there has been a recent reengagement of

the rationalist-relativist debate in this spe? cific context with the emphasis on the na?

ture and role of alternative logics. Let us

consider this latest round of skirmishing in

more detail.

"Witchcraft has its own logic, its own

rules of thought... (Evans-Pritchard, p. 79). Barnes, and later, Jennings, have taken this

claim seriously and suggest that Zande

witchcraft beliefs are embedded within a

non-standard logic, so that within the global

system of beliefs plus logic, there is simply no contradiction (Barnes 1976; Jennings

1989). Logic itself is characterized as "those

shared patterns of thought which are so?

cially selected from among the various pat? terns of thought to which we are naturally inclined" (Jennings, p. 275; recall also Bar?

nes and Bloor, p. 45).

Leaving this naturalist claim aside, there

is no indication as to what kind of logic is

in use in the Zande case. Of course, for Bar?

nes, Bloor, and Jennings, logics, or kinds of

logic, are culturally specific; this is all part and parcel of their relativism. But here the

rationalist has the opportunity to pull the

rug out from under them, by arguing

against cultural specificity on the grounds that the embedding alternative logic is

identical to that proposed in the case of cer?

tain (Western) scientific theories.

This is the line adopted by Cooper who, as we have indicated, follows Horton in re?

garding certain magico-religious proposi? tions, such as those expressed by Zande

witchcraft beliefs, as analogous to highly theoretical scientific ones. Where he differs

from Horton is in his emphasis on under?

standing the logical relations between so

called "primitive" beliefs, rather than the

beliefs themselves. Cooper's specific pro?

posal is to advocate Lukasiewicz's three

valued logic L3, as elaborated and applied

by Reichenbach to the foundations of

quantum mechanics. In L3, propositions

may possess the three "truth values" of

true, false and indeterminate and so the

presumption that every proposition is

either true or false is rejected.

Cooper then adopts a two-stage ap?

proach. First, it must be shown that, if

"primitive thought" is embedded in L3, the

inconsistencies are dissolved, and second

that the system of "primitive" beliefs actu?

ally is embedded in L3. The first stage would

be achieved, he argues, if magico-religious inconsistencies can be shown to be analo?

gous to quantum ones. Thus he claims that, in the specific case of Zande beliefs, if one


of the premises of (a form of) Jennings' ver?

sion of the argument above is assigned the

truth-value "indeterminate," the inconsis?

tency is avoided. (He also considers the

case, of Nuer beliefs about twins and sub?

jects them to the same analysis.) The prem? ise that Cooper seizes upon is Jennings'

premise 2, regarding the heritability of

witchcraft substance. This, he claims, is re?

garded by the Azande as an in principle un

testable proposition, akin to those analysed

by Reichenbach in quantum mechanics.

In achieving the second stage of this ac?

count, the question must be answered as to

whether the Azande actually do regard

propositions such as that expressed in

premise 2 as having an indeterminate truth

value. Cooper approaches an answer to this

question indirectly by noting, first of all, that outside the domain of the magical or

religious, "primitive" reasoning can be em?

bedded in classical logic. He then puts for?

ward as a "reasonable hypothesis" that the

classical form is abandoned in this domain

precisely because it is an area where test?

ability and verification is least available.

Secondly, he repeats the oft-noted observa?

tion that the reaction of the natives when

the contradictions are pointed out to them

is one of indifference, or lack of interest.

Thus, Evans-Pritchard records that

"Azande do not perceive the contradiction

as we perceive it, because they have no

theoretical interest in the subject, and those

situations in which they express their be?

liefs in witchcraft do not force the problem upon them" (p. 25; we shall have occasion

to return to this quote). According to Coo?

per, "This would be precisely the attitude we would expect of someone who treated

the rogue propositions as indeterminate, which would then become analogous to

those which, according to Reichenbach, we

can ignore without danger" (Cooper, p.

251). Finally, Cooper notes that the distinction

between his two stages is somewhat artifi?

cial, since a good reason for thinking that a

system of beliefs is embedded in a non-clas?

sical logic is precisely that difficulties such

as apparent inconsistencies are removed if

such a logic is applied. As he notes in his

concluding remarks, he holds no special brief for L3; it may be that different non

classical logics might be suitable for differ? ent belief systems. What is important is the

spirit of such an approach. We have looked at Cooper's work in

some detail because it represents one of the

few examples in this debate of someone not

only acknowledging the existence of alter?

native logics in this context, but actually ap?

plying a specific formalism to a specific set

of beliefs. Cooper has, however, been criti?

cized in forceful terms by Salmon (1978), who represents the contrary position, that

native reasoning can be captured perfectly well by standard, classical logic.

The central plank of Salmon's critique is

that, in extending Horton's analogy, Cooper has confused "not directly testable" with

"in principle untestable." The highly theo?

retical propositions of science are only indi?

rectly testable but in this they have a

character very different from those of quan? tum mechanics that Reichenbach considered.

Thus, even if propositions concerning the

heritability of witchcraft substance are re?

garded as highly theoretical, this provided no grounds for assigning them an indeter?

minate truth value. And Cooper provides no evidence that Azande regard such

propositions as untestable in principle. Furthermore, regarding Cooper's claim

that the attitude of Azande to the inconsis?

tency is one of indifference, Salmon argues that this cannot provide evidence that the

proposition in question has an indetermi? nate truth value. Her reasoning is as follows. An example of such a proposition would be

"All Azande are witches and not all Azande are witches." If this conjunction is assigned an indeterminate truth value, then so must

be each of the conjuncts, given the truth ta?

bles of L3. However, the statement "Not all

Azande are witches" is not regarded as inde?

terminate by Azande themselves; indeed,

they possess a post-mortem test to determine if someone is a witch or not and on the basis of past results of this test, they would regard


the statement as true. Indifference, then, does not imply indeterminacy.

Salmon also questions Cooper's claim

that Azande are indifferent to inconsistency in her own attempt at a resolution, which

falls under the "charitable" approach. She

contends that rather than expressing indif?

ference towards the conclusion of the argu? ment, Azande actively reject it and remain

within the framework of classical two-val?

ued logic by applying a form of the reductio and rejecting one or other of the premises.

Thus, as Evans-Pritchard notes, when faced

with the argument they either deny premise 1, and claim that witchcraft substance may, in certain cases, be "cool" and inoperative, or they deny premise 2 and claim that the

heritability of witchcraft substance is re?

stricted to very close relatives of the pur?

ported witch. Thus, Salmon concludes, "There is no contradiction when the stand?

ards of ordinary two-valued logic are em?

ployed" (p. 452). This particular exchange has been re?

prised in the pages of The British Journal

for the Philosophy of Science, where Tri?

plets responding to Barnes, has argued that

Azande regard the conclusion of the argu? ment as false and reject one or more of the

premises, keeping within the bounds of

standard Aristotelian logic (Triplett 1988). Jennings' reply is illustrative: these re?

sponses?of rejection of one or other of the

premises?are individual reactions rather

than socially instituted responses and thus

do not represent features of established

Zande thought or logic. According to Jen?

nings, Evans-Pritchard does not say that

Azande revise their beliefs when presented with the argument, he simply records that

they avoid seeing the inconsistency. In par?

ticular, there is no evidence that they actu?

ally regard inconsistent statements of the

kind introduced by Salmon as false.

How then do they live with the inconsis?

tency? On Jennings' account, the answer is

arrived at by considering the fundamental

distinction between practice and the theo?

retical implications of a set of beliefs. Again,

turning to Evans-Pritchard: "In practice

they regard only close paternal kinsmen of a known witch as witches. It is only in the?

ory that they extend the imputation to all a

witch's clansmen" (p. 24). Following Barnes

in adopting a broadly Wittgensteinian line on meaning and use, particularly as applied to negation, Jennings' view is nicely encap? sulated in the aphorism, "The difficulty in

being told that it is raining and not raining is not that it is a contradiction but that we

cannot both take and not take the um?

brella" (p. 284).

Jennings' response makes it absolutely clear that his camp is proceeding from an

entirely different view of the nature of logic from that represented by Salmon and Tri?

plett. A full evaluation would obviously lead us well away from our central concern

in this paper. Nevertheless, it is worth em?

phasizing the sharpness of the split between

the social and personal or psychological as?

pects of logic, on the Barnes-Jennings ac?

count. The implication would seem to be

that Zande social thought is non-classical in

form, whereas "personal" reasoning, as evi?

denced in their rejection of premises 1 or 2, follows the classical standard. Such a di?

vorce of social reasoning from the personal is implausible. That said, the distinction be?

tween "theoretical" and "practical" levels is a useful one to draw (as long as both are

embraced by personal reason), and we shall

return to it below.

Salmon's argument that Zande logic can?

not be Lukasiewicz's L3 is correct but, as

Cooper himself would point out, it rules

out only one kind of non-classical logic and

there are many others available to choose

from. One possibility is that Zande logic is

paraconsistent (da Costa, French and

Bueno, forthcoming); with paraconsistent calculi, as is well known, inconsistency does

not produce a collapse into triviality. However, our intention in this work is to

take a different tack. Let us return to Coo?

per's paper. Towards the end he notes that

it could be objected to his approach that

even if Azande do not regard propositions

concerning witchcraft as testable, still, they believe them and this is sufficient for incon


sistency to arise at the doxastic level. Coo?

per's response is illuminating; he questions whether the sense of "belief" that is appro?

priate here is one that is problematic for his

approach. "For not every use of 'believe' is

best rendered by 'hold to be true' (which is

the troublesome sense)" (p. 252). This is

precisely the thread we have been trying to

develop in our work on inconsistency in sci?

entific and "natural" reasoning.

Partial Structures and

representational belief

At the heart of our account lies a model

theoretic approach to knowledge and be?

lief. Such an approach has been developed most notably in the philosophy of science, and although it embraces a variety of posi? tions, it has at its core the notion that scien?

tific theories are to be regarded as families

of models. (The principal proponents of

this view are Suppes, Beth, van Fraassen,

Suppe, and Giere; an excellent introduc?

tion to the programme can be found in

Chapter 1 of Suppe 1989). In our own work we have tried to press the claim that such

models should be taken to be open-ended and as providing only partial maps of the

relevant domains. The technical tools for

developing such a claim formally were set

down by Mikenberg, da Costa and Chuaqui

(1986) who introduced the notion of a

"partial structure." Essentially, they mod?

ify the Tarskian model-theoretic notion "a sentence s is true in some interpretation /" to give "a sentence 5- is partially or quasi true in a partial interpretation 3 relative to some set P of 'established' sentences." A

partial structure is then a model-theoretic structure whose relations between the ele?

ments of the model, representing the indi?

viduals in the domain concerned, are not

fully specified. The technical details are

given in Mikenberg et. aVs work and in the

appendices to our own papers cited above.

What is important for the present discus?

sion is the introduction of partiality and the

concomitant attitude that scientific theories

should be regarded as partially true only. In

particular, this allows for the accommoda

tion of inconsistent theories?such as

Bohr's theory of the atom?within one's

philosophy of science. Such theories are to

be regarded as partially true, with the in?

consistency acting as a heuristic "signpost" to a consistent successor (da Costa and

French 1993a). More recently, we have extended this ap?

proach to cover so-called "natural" reason?

ing, in particular in the area of statistical

appraisal and analysis, where people appear to reason according to a set of heuristic pro? cedures that deviate quite markedly from

those of, say, standard Bayesian methodol?

ogy (da Costa and French 1993b). Follow?

ing the line that statistical mistakes are an

indicator, not of irrationality, but of igno? rance of the most appropriate model to ap?

ply in a given situation (Nisbett and Ross

1980; Giere 1988), we have argued that those models that are regarded as less than

completely adequate (in the standard sense

that includes empirical success, simplicity etc.) may still be useful and hence consid?

ered as partially true, in the formal sense

mentioned above (see also Kahnemann, Slovic and Tversky 1982; Cherniak 1984).

What we are principally interested in

here is the attitude that is, or should be,

adopted towards these partial structures. In a work that deserves rather more attention

than it has received hitherto, Sperber makes an important and fruitful distinction

between "factual" and "representational" beliefs (Sperber 1982). The former are be?

liefs in propositions regarded as true in the

standard correspondence sense, whereas

the latter are beliefs in what Sperber calls a "semi-propositional representation," re?

garded, we claim, as partially true in our

sense. With representational beliefs, unlike

factual beliefs, there is awareness of a rep? resentation or interpretation. The key

move, as Sperber notes, is to get away from

the standard philosophical examples of

propositions, such as "The grass is green." What anthropologists, and scientists in gen?

eral, are interested in is something more

complex, more open-ended and partial ?what Sperber calls a "semi-propositional


representation." Philosophers tend to be

locked into this view of belief as a "propo sitional attitude," which obscures the fact

that a person can have doxastic attitudes to

"objects," for want of a better word, that are

not propositions in the strict sense of that

which is true or false in the correspondence sense. A semi-propositional representation is neither true nor false in this sense, but it

may be partially true in that it is conceptu?

ally incomplete (that is, as Sperber puts it, it

contains elements whose conceptual content

is not fully specified). Just as propositions are

associated with standard (complete) struc?

tures so semi-propositional (or quasi-propo

sitional) representations are associated with

partial structures.

Inconsistency is then no longer a prob? lem: "If one finds oneself holding two mu?

tually inconsistent ideas and reluctant to

give up either, there is a natural fallback

position which consists in giving one of

them a semi-propositional form" (Sperber,

p. 171). Holding inconsistent factual beliefs

is a problem, not because of any violation

of a particular classical logical principle, but

because of practical barriers, such as Jen?

nings' example of not being able to both

carry and not carry an umbrella.

How are representational beliefs to be

contextually distinguished from those of

factual form? Sperber offers the following:

The semi-propositional character of cultural beliefs is implicitly acknowledged in one of two ways. In some cases people offer exe?

geses of their beliefs, and, while sharing be?

liefs, wonder, argue or even fight about

interpretations. In other cases, when you

ask the people what their cultural beliefs

mean, what they imply, how they fit with

everyday facts etc., they beg off, saying: 'It

is the tradition', 'Our ancestors knew', or

something to that effect. Whether the

proper interpretation is considered a se?

cret lost or a secret to be discovered (or both), a clear if implicit distinction is made

between holding a belief and knowing how to interpret it. This distinction only makes sense if these are semi-propositional be?

liefs (pp. 175-176).

The application of all this to Zande witch? craft beliefs is transparent. Let us consider

again what Evans-Pritchard tells us:

The Zande notion of witchcraft is incompat? ible with our ways of thought. But it must also be said that even to the Azande there is

something peculiar about the action of witchcraft. Normally it can be perceived only in dreams. It is not an evident notion but transcends sensory experience. They do not

profess to understand witchcraft entirely. They know that it exists and works evil, but

they have to guess at the manner in which it works. Indeed, I have frequently been struck when discussing witchcraft with Azande by the doubt they express about their subject, not only in what they say, but even more in their manner of saying it....They feel out of their depth in trying to describe the way in

which witchcraft accomplishes its ends. That it kills people is obvious, but how it kills them cannot be known precisely. They tell you that

perhaps if you were to ask an older man or witchdoctor he might give you more infor? mation (p. 82).

We have already noted that Azande reject, in a more or less ad hoc fashion, one of the

premises of Jennings' form of the argument and thus satisfy the first of Sperber's two

ways in which the semi-propositional char?

acter can be acknowledged. The above pas?

sage reveals that they also satisfy the

second. There are two aspects to this that

we would like to draw attention to. The first

is the elements of vagueness and doubt con?

cerning the operation of witchcraft; the sec?

ond is the appeal to higher authorities.

Considering the former, this is one of sev?

eral reasons given by Evans-Pritchard as to

why Azande do not perceive the contradic?

tion (p. 478). Vaguely formulated beliefs are

less easily verified or falsified by experi? ence, and less easily brought into conflict

with other beliefs. It is not clear how both

evidence and other beliefs impact on such

beliefs because of their vague, imprecise na?

ture. There is a certain incompleteness with

regard to their conceptual content that al?

lows for a degree of slack in their connec?

tions with other beliefs and which can be

captured by this notion of a partial struc


ture, where the relations between the ele? ments are not fully specified.

But what is striking here is the analogy with "lay" beliefs and "natural" reasoning. Consider a lay person's understanding of

electricity, for example; most lay people would not profess to understand electricity

entirely (certainly not in quantum field

theoretic terms); most would have to guess at the manner in which it works; most

would express a degree of doubt about the

subject and so on. Another example would

be Newtonian mechanics. It has been

shown that in situations where the use of

this theory would be most appropriate, peo?

ple tend to resort to a pre-Newtonian model (Giere 1988). Again, the issue is not

one of irrationality, but rather of employing an inappropriate or less than fully adequate

model (that is, one that is only partially cor?

rect); and we would extend this to Zande

beliefs.

Evans-Pritchard also notes that "contra?

dictions between their beliefs are not no?

ticed by Azande because the beliefs are not

all present at the same time but function in

different situations. They are therefore not

brought into opposition" (p. 475; see also p. 28 and later, p. 540). Again there is a clear

analogy with scientific and "lay" beliefs.

Different scientific theories, modeling suffi?

ciently different domains, may in fact be

fundamentally inconsistent with one an?

other. Thus, there is a well known "incom?

patibility," to use a rather coy term, between relativity theory and quantum me?

chanics, which, at the foundational level, breaks out into a full-blown inconsistency. As long as the two theories function in dif?

ferent situations, this inconsistency is not

noticeable at the formal level. If, however, unification is to be achieved?and some

would say this is neither desirable nor pos? sible?some form of reconciliation will

have to be effected, by modifying and "fill?

ing in" one or both of the structures in ques? tion. It has also been suggested that

internally inconsistent theories, such as

Bohr's, can be dealt with in the same way,

by regarding the theory as divided into self

consistent sub-theories (see da Costa and

French 1993a for criticisms). A similar strategy has been advocated in

the case of self-deception, where inconsis?

tency also arises (da Costa and French

1990a). More generally, the "plasticity" of our lay beliefs as functions of specific situ?

ations, to paraphrase Evans-Pritchard (p.

540), seems plausible enough. Driven by the

pragmatics of our circumstances as we are,

only the most angelically rational can avoid

using a particular belief, or belief set, in one

situation and another, contradictory, in a

different situation. It is only when we are

pushed to set the two together that the in?

consistency becomes glaring. With factual

beliefs we may be so pushed in very short

order, whereas with those that can be de?

scribed as representational the push may be

towards a state of epistemic virtue only, and

thus correspondingly weaker.

Regarding the appeal to higher authori?

ties, the role of the princes in Zande culture

is crucial. Death due to the action of witch? craft (and all deaths can be so attributed)

must be avenged; and typically the venge? ance is executed by means of lethal magic.

The attribution of witchcraft action to a cer?

tain witch will be made by means of the poi? son oracle. It is then up to the prince to

decide as to how vengeance is to be ex?

acted: by the physical killing of the witch,

by compensation, or by lethal magic. Inter?

estingly enough, under British rule, only the

method of magic was permitted and here

again problems arise: "It may be observed here... That if it were known that the death of a man X had been avenged upon a witch Y then the whole procedure would be re?

duced to an absurdity because the death of

Y is also avenged by his kinsmen upon a

witch Z" (Evans-Pritchard, p. 27). But con?

firmation of the efficacy of the magic is

achieved via the poison oracle of the kins? men of the witch's victim, which in turn is

confirmed by the prince's oracle. Only then

may the kinsmen cease their mourning. And?this is the important point?the names of the victims of vengeance magic are kept secret by both the kinsmen and the

prince. Regarding this system, Evans


Pritchard writes, "Its fallaciousness is veiled so long as everybody concerned keeps si?

lent about the victims of their vengeance

magic" (p. 27). He continues,

Since the names of victims of vengeance are

kept secret the contradiction is not apparent, for it would only be evident if all deaths were taken into consideration and not any one

particular death. So long therefore as they are able to conform to custom and maintain

family honour Azande are not interested in the broader aspects of vengeance in general.

They saw the objection when I raised it but

they were not incommoded by it (p. 28).

But what of the princes? Surely they must

be aware of the contradiction? And indeed

they are, since they know the outcome of

every death in their provinces:

When I asked Prince Gangura how he ac?

cepted the death of a man both as the action of vengeance-magic and of witchcraft he smiled and admitted that all was not well

with the present-day system. Some princes said that they did not allow a man to be

avenged if they knew he had died from

vengeance-magic, but I think they were ly?

ing. One cannot know for certain, for even if a prince were to tell the kin of a dead man

that he had died from vengeance-magic and

might not be avenged he would tell them in secret and they would keep his words a se? cret. They would pretend to their neighbours that they were avenging their kinsman and after some months would hang up the bark

cloth of mourning as a

sign that vengeance was accomplished, for they would not wish

people to know that their kinsman was a

witch.

Consequently if the kinsmen of A avenge his death by magic on B and then learn that B's kinsmen have ceased mourning in sign of

having accomplished vengeance also, they believe that this second vengeance is a pre? tence. Contradiction is thereby avoided

(ibid., pp. 28-29).

Again, the means by which contradiction is

kept from breaking out into the open are

made clear in these passages. It is worth recalling at this point Evans

Pritchard's remark: "Azande do not per? ceive the contradiction as we perceive it

because they have no theoretical interest in

the subject, and those situations in which

they express their beliefs in witchcraft do not

force the problem upon them" (p. 25; our

emphasis). The kinds of situations Azande

find themselves in when engaging in every?

day activities to not cause them to face the

inconsistencies in their beliefs. Time and

again in his book, Evans-Pritchard empha? sizes the particularity of witchcraft, the way its actions are specific to particular places, times and people: "Witchcraft is a variable

factor in time as well as in space and gives

peculiar value to particular times as it does

to particular places or persons" (p. 72). And

again, "Witchcraft is a causative factor in

the production of harmful phenomena in

particular places, at particular times, and in

relation to particular persons" (ibid.). It is

this particularity that prevents the inconsis?

tency from becoming apparent, a mecha?

nism common across cultures. It is certainly true with regard to the statistical fallacies

exhibited in "natural reasoning." Subjects remain unaware of the fallacious nature of

their reasoning because "the relevant in?

stances are not coded appropriately" (Tver

sky and Kahnemann 1974, p. 1130). The

instances remain particularized and are not

combined in such a way as to reveal just what is going on. Again, it is this fundamen?

tal aspect of the problem that ultimately ex?

plains how the contradictions persist. Nevertheless, as we noted in our other

work, the models themselves are not wholly

inadequate, but are at least partially suc?

cessful. Those employed in statistical rea?

soning may be strictly fallacious, in the

sense of not adhering to the accepted can?

ons of such reasoning, and thereby failing to be maximally successful, but they never?

theless give a better than 50-50 chance of

getting the right answer. They may be re?

garded, according to Cherniak, as heuristic

rules of thumb that are at least partially suc?

cessful and satisfactory to that extent. (Such models may form part of a satisfying, rather

than optimizing, strategy). There is some?

thing similar to be said about Zande models


of witchcraft and magic, although here, of

course, there is only the appearance of suc?

cess. Thus, Evans-Pritchard notes, "Azande

insist that magic must be proved efficacious

if they are to employ it" (p. 444) and "The

test of magic is experience" (p. 466). As he

goes on to point out, the reason there is the

appearance of success is that "Magic is only made to produce events which are likely to

happen in any case?e.g., rain is produced in the rainy season and held up in the dry season; pumpkins and bananas are likely to

flourish?they usually do so. Magic is not

asked to achieve what is unlikely to occur"

(p. 476). Also:

Not too much is claimed for magic. Gener?

ally, in the use of productive magic it is only claimed that success will be greater by the use of magic than it would have been if no

magic had been used. It is not claimed that

without the aid of magic a man must

fail?e.g. a man will catch many termites,

even though he does not use termite-medi? cines (ibid.).

It is noteworthy, however, that Azande rec?

ognize that the action of magic is different

from that of empirical practices and ac?

knowledge that there is something mysteri? ous about it. Again the element of vague? ness enters, as Evans-Pritchard reports that

with respect to the question, how do

Azande think their magic works?, "They do not think very much about the matter (p.

463). A similar account could be given of

the lay attitude to the action of electricity.

Returning to the role of the princes, we

see how the second of Sperber's charac?

teristic indicators of the holding of repre? sentational beliefs is exemplified. It is they

who are taken to possess a complete, or at

least a more complete, representation of

what is going on. Again, there are clear

similarities with lay and scientific reason?

ing. Pressed for an explanation of the action

of electricity, a lay person might appeal to

their college physics professor, Carl Sagan, or a physics textbook! Even at the level of

scientific beliefs there will be similar ap?

peals; someone working within quantum field theory might appeal to an expert in

solid state physics. Even within a particular

discipline there will typically be divisions of

technical expertise. Indeed, it has been sug?

gested, on the basis of these and similar

examples, that the model of the one re?

searcher, boldly going where no one has

gone before, is no longer an adequate

epistemic representation (Hardwig 1985;

1991). Thus, there is a distinction to be drawn in

our account between the lay (Western) per? son, attempting to draw statistical infer?

ences or describing the notion of the nature

of electricity, and the statistician or physi? cist, respectively, and likewise, between the

"lay" Azande, questioned by Evans

Pritchard about witchcraft and the action of

magic, and the princes. In all cases the ap?

propriate model is one that is conceptually

incomplete and partial, but the difference

between the lay person, whether Zande or

Western, and the scientist or prince, is that

in the former case, the fallaciousness of the

reasoning, or the inconsistency of the be?

liefs, is not apparent, for the reasons given above, whereas in the latter Bohr was per?

fectly well aware of the contradictory na?

ture of his model of the atom and both

hoped and worked for a consistent succes?

sor. Likewise, the princes are aware of the

inconsistent nature of the Zande system and acknowledge its deficiencies. The only difference, perhaps, is that the princes typi?

cally do not search for a more consistent

successor, since the current system serves

their purposes. Our thesis, then, is that Zande witchcraft

beliefs are best modeled by partial struc?

tures that can accommodate their loose and

incomplete aspect. Again, Evans-Pritchard

contends that such beliefs "are not indivis?

ible ideational structures but are loose as?

sociations of notions.-.In real life they do not function as a whole but in bits" (p. 540). And, of course, it is when the "bits" are

brought together that the inconsistencies

become apparent. The doxastic attitude of

Azande towards this model is one of doubt, as Evans-Pritchard also makes clear:


To what extent have Azande faith in magic? I have found that they always admit that the issue of a rite is uncertain. No one can be sure that his medicines will achieve the re? sults aimed at. There is never the same de?

gree of confidence as in routine empirical activities (p. 466).

Thus these beliefs should be regarded as

representational, rather than factual. This

provides a doxastic system capable of al?

lowing for the accommodation of the incon

sistencies, since such beliefs are not

regarded as true, in the correspondence sense, but as partially or quasi-true only.

(The appropriate doxastic logic will then be

a paraconsistent one.) Furthermore, this approach removes the

sting from relativism. The slogan, "Differ?

ent cultures live in different cognizable worlds," makes sense only if the relevant

beliefs are taken to be beliefs in certain

propositions as true. That is, it makes sense

only if the cultural beliefs considered, such

as Zande witchcraft beliefs, are factual be?

liefs. But they clearly are not. As Sperber himself notes:

If people of different cultures did hold ap?

parently irrational factual beliefs, then it

might be acceptable to try and reformulate the content of these beliefs so as to establish their rationality, even at the cost of having to

imagine different cognizable worlds. But there is no reason, either theoretical or em?

pirical, to assume that the apparently irra? tional beliefs reported by anthropologists and historians are factual beliefs. No theo?

retical reason: the very fact that, when as?

sumed to be factual, these beliefs appear irrational is reason enough to assume, on the

contrary, that they are representational be?

liefs with a semi-propositional content,

thereby avoiding the costs of relativism. No empirical reason: look in the literature for evidence as to the exact attitude people have toward their 'beliefs'; what little evi? dence there is supports the view that the beliefs we are dealing with are repre? sentational and have a

semi-propositional content (p. 175).

What, then, of charity?

Charity and Explicability

Those who advocate the use of some

form of the Principle of Charity typically do so in terms of an appeal to Context. This is

Salmon's response to Cooper's suggestion above, for example, and she, like Triplett af?

ter her, argues that careful attention to the

cultural context reveals that there is no

need to step outside the bounds of the

standard framework of rationality to un?

derstand what is going on. Likewise, follow?

ing Sperber, we have appealed to the

context regarding doubt and the role of

authority to support our analysis. Clearly, if

understanding piggybacks on translation, then some such principle is required to get the whole process off the ground.Some?

thing has to be taken for granted if the cir?

cle of belief and meaning is to be broken

and the first steps towards understanding taken. However, the form of the Principle of Charity originally proposed by Davidson

is unacceptable, as it immediately rules out

of court any translation that involves the

attribution of inconsistent beliefs (unless such beliefs are written off as irrational).

Our discussion above was intended to press the claim that this would not do justice to

the very context that we are urged to con?

sider. When presented with the argument that makes the inconsistency explicit,

Azande might reject one or more premises, rather than swallow the explicit contradic?

tion, but this is a localized response. In their

daily practice the inconsistencies are simply not allowed to become manifest at the fac? tual level. The further inconsistency con?

cerning the results of witchcraft and

vengeance magic drives this point home.

What is required is some principle that, like charity, would compel us to consider

the appropriate context but that would not

immediately rule out attributions of incon?

sistency. Henderson has put forward a Prin?

ciple of Explicability which not only seems

to do the trick but also meshes nicely with

our distinction between representational and factual beliefs (Henderson 1987).


The decisive element in Henderson's ap?

proach is a fine-grained analysis of the

process of constructing a translation man?

ual that breaks it down into earlier and later

stages. In the former, a "first-approxima? tion" manual is constructed, adequate for

translating the sentences of "everyday us?

age." It is during this stage that the Princi?

ple of Charity is necessary, both in practice and in principle; and it is here that the es?

tablishment of the rationalist's "bridge? head" can be located. It is against the

background of generally successful first-ap?

proximation translation manuals that a "re?

fined" translation manual is elaborated.

This process proceeds by fine-tuning the

first-approximation manuals and is guided

by a "Principle of Explicability," which con?

strains the translator to attribute explicable, rather than "correct" or "consistent," be?

liefs to the speakers of the source language.

According to Henderson, "when engaged in this later task, the concern is with expla?

nation" (p. 238). It is only at this stage that

the social scientist or anthropologist be? comes concerned with explaining native be

liefs and "only by using the first

approximation translation manual can we

acquire much of the evidence in terms of

which the ensuing explanatory endeavor

proceeds" (ibid.). Refined translation de?

pends upon first approximation translation as its basis; the latter provides the data for the former.

Thus, Henderson notes, Evans-Pritchard's

explanation of the Zande failure to per? ceive the contradictions inherent in their

witchcraft beliefs and the futility of their

magic in general?namely the cultural limi?

tations imposed on the sharing and flow of

information?depends crucially on his first

approximation translations which provide the basis for his identification of these be?

liefs at the level of the refined translation.

Henderson goes on to claim that an impor? tant role in this translatory/explanatory en?

deavor can be taken by psychological

theory and in particular he mentions the

work of Nisbett and Ross in accounting for

statistical error in natural reasoning. In our terms, what the first-approxima?

tion manual translates are the factual be

liefs of the natives. Such beliefs will typi?

cally be about matters of observation and,

recalling what we've just noted concerning the way the first-approximation feeds into

the refined translation as data, there is a

clear analogy here with the empirical sub?

structures of the model theoretic approach to scientific theories. As Suppes has long declared, the empirical data are also struc?

tured and must themselves be modeled be?

fore, and if, it is to be embedded into a more

inclusive theoretical super-structure. At this level the appropriate logic would

be classical, not because of some blind ad?

herence to the law of non-contradiction (as an absolute a priori principle, say) but be?

cause of pragmatic considerations, such as

indicated in Jennings' remark about carry?

ing an umbrella. It is upon such considera?

tions that charity piggy-backs. The logic of

the bridgehead, then, is classical.

Refined translation manuals, of course, translate representational beliefs, and here

explicability is what matters. At the refined

level the translator's toolbox will include a

variety of formal frameworks, including those of paraconsistent doxastic logics.

Thus the logic of representational belief

may well be highly non-classical.

Returning, for a final time, to "Witch?

craft, Oracles and Magic" and the continu?

ation of that most famous of quotes

regarding Zande logic, we find:

Witchcraft has its own logic, its own rules of

thought, and..these do not exclude natural

causation. Belief in witchcraft is quite consis? tent with human responsibility and a rational

appreciation of nature. First of all a man must carry out an activity according to tradi?

tional rules of technique, which consist of

knowledge checked by trial and error in each

generation. It is only if he fails in spite of adherence to these rules that people will im?

pute his lack of success to witchcraft (p. 79).

Conclusion

Clearly, then, we agree with the intellec

tualist line adopted by Horton and others, who claim that scientific and "native" (and

"natural") reasoning are of the same kind.


Our work can be seen as an attempt to

highlight the commonalities underlying them. Zande witchcraft beliefs are akin to

the theoretical beliefs of Western science; the trick is to find the most appropriate way of representing the latter. Where we differ

from Horton?and Cooper?is with regard to what should be taken as the correct

model of science; thus this work can also be seen as another piece of support for the

partial structures approach. It is in this re?

spect that we agree with the symbolists who are adamant that native beliefs are not be? liefs in propositions regarded as true (in the

correspondence sense). This is correct, but

then neither are scientific beliefs; and so,

finally, our work can be seen as part of a

wider programme to move philosophy away from a fixation with propositions and

correspondence truth.

University of S?o Paulo

University of Leeds

Received March 29,1995

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NOTES

1. An earlier version of this paper was presented to a meeting of The Alexander Society, in the Dept. of Philosophy, University of Manchester and at the Senior Seminar of the Dept. of Philosophy at the

University of Leeds. The authors would like to thank the participants at both meetings, but espe? cially the students?both undergraduate and postgraduate?in Manchester and Chris Kenny in

Leeds, for many useful and illuminating comments. The responsibility for any further deficiencies is, of course, entirely ours. The authors would also like to thank Otavio Buero for his comments on an earlier version of this paper.

2. Patrick Suppes has long pressed the claim that scientific data are never presented "raw" but

always as structured in one form or another. Likewise this particular cultural datum is structured in terms of Evans-Pritchard's account. The cultural presuppositions underlying this account have been noted (Traweek 1992, pp. 435-37); thus, in a sense, what we are presenting here is an analysis not of Zande beliefs per se but of such beliefs as structured by Evans-Pritchard.

costa & french, partial structures and the logic of azande

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