What Is a Problem That We May Solve It?

What Is a Problem That We May Solve It? Author(s): Thomas Nickles Source: Synthese, Vol. 47, No. 1, Scientific Method as a Problem-Solving and QuestionAnswering Technique (Apr., 1981), pp. 85-118 Published by: Springer Stable URL: http://www.jstor.org/stable/20115620 . Accessed: 15/03/2011 04:59 Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at . http://www.jstor.org/page/info/about/policies/terms.jsp. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use. Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at . http://www.jstor.org/action/showPublisher?publisherCode=springer. . Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed page of such transmission. JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected].

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THOMAS

WHAT

NICKLES

IS A PROBLEM MAY

SOLVE

THAT WE IT?1

The

con of problems and of problem-solving behavior analysis in my judgment, to the general the most promising stitutes, approach can also of science illuminate methodology today. Such analysis studies in the various foundational theories of science. Yet special a notable as to problems in attention and questions increase despite units of and for philosophical and despite the emergence of analysis, models of scientific later Kuhn, (in problem-solving inquiry Popper's an and especially writings, Laudan2), we are still far from possessing account to ask what a of problems. We have only begun adequate is and what an 'account' of problems should do. problem I claim that any adequate must the 'theory' of problems satisfy extended list of logical and historical conditions I of adequacy which set out below. To satisfy these constraints, an account of problems of the research activities must, to some extent, explain the possibility and capabilities them. Although listed, and must certainly not exclude most of these constraining are truistic claims about science conditions and about problems, my own still developing is of problems conception comes the only one I know which to satisfying close them. (This is similar to that employed conception by the cognitive psychologist, Walter Reitman, and the polymath, Herbert Simon, however.) While I believe I say that much of what my topic is scientific problems, to problems extends in general. After I shall continue my critical setting out my list of conditions, now in in Nickles, accounts 1980e) of problem I shall trace major deficiencies of the best now of science to available problem solving model (Laudan's) to what problems are. I conclude insufficient attention themselves by and by indicating its place in a richer my own account presenting theory of inquiry than we have yet developed. examination (begun the literature. Then

Synthese 47 (1981) 85-118. Copyright

?

1981 by D. Reidel

0039-7857/81/0471-0085 $03.40. Publishing

Co., Dordrecht,

Holland,

and Boston,

U.S.A

86

THOMAS

I. REQUIREMENTS

A.

Logical

and Conceptual

NICKLES

AN

OF

OF

ACCOUNT

PROBLEMS

Requirements

exist and some are known. (How is that possible?) are dis are sometimes solved, i.e., their solutions is is (How inquiry inquiry possible?) possible. are identical only if their solutions 3. Problems (or their classes of are This claim does not admissible identical. (Caution: solutions) a It have solutions. that may alternative, deny problem incompatible asserts if the class of that P and Q are the same problem only 1. Problems 2. Problems covered. Thus

for solutions admissible solutions for each is the class of admissible the other.) are identical only if the problems 4. Theories solutions) (problem are solve identical. they 5. Two distinct problems may be solved by the same theory and in the same range that sense may have the same solution and, a fortiori, of

admissible

solutions

(else

one

theory

could

solve

only

a single

problem). 6. A problem

theories (else may be solved by two or more distinct to the same problem). there could be no competitive solutions to goals which have not been 7. Problems exist only in relation achieved. within existence historical have objective bodies of 8. Problems some are Some and discovered, theory, practice, goals. problems or only partially known. The discovery remain unknown process may

be gradual. 9. Two scientists same things about

can have it and

can

the same problem without the knowing different the from problem approach

even from different fields. directions, are (putative) problem 10. Theories solutions are theories. are subproblems 11. Some problems

B. Evidence

that Problems

Have

solutions, of

Conceptual

but not all problem

larger problems.

Depth

(see also C)

see how a can be very puzzling. E.g., we cannot we or two and is what know; powerful given possible, phenomenon or theories clash. obvious intuitively principles 1. Problems

WHAT

IS A

PROBLEM

THAT

WE

MAY

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87

are ill structured, and for substantive problems no reasons. there exists formal, methodological) E.g., a is solution. for whether (Reitman, determining something algorithm 1964; Simon, 1973.) a about when reliable make 3. Despite 2, scientists judgments near is of been There solved. has unanimity frequently problem 2. Many (vs. purely

scientific

(Kuhn, 1962.) (How is this possible?) agreement. the about can sometimes reliable make 4. Scientists judgments or unsolvability of still unsolved sol problems, including solvability in terms of a given body of theory and the amount of time vability the thus to evaluate to obtain a solution-and and effort required likely success 5. Scientists

and programs.3 research proposals of alternative reliable make (and agree) about the cog judgments im intellectual of problems nitive weighting fruitfulness, (their some know that Scientists and prob centrality). portance, generality, than others. lems are more 1977, p. (Kuhn, 1962; Laudan, interesting

32.) (How is all this possible?) whose overdetermined i.e., problems problems, con cannot be all satisfied (inconsistent constraints/goal-demands are not all overdetermined. but straint (Lugg, sets); problems 1978.) is structured in time rather than 7. The discovery process typically of the solution popping a momentary experience psychological being 6. There

exist

head. (Kuhn, 1977, Ch. 7.) into someone's contexts. 8. Complex reasoning typically occurs in problem-solving is such (How reasoning possible?) and is not all 9. This reasoning falls into many different patterns is rare. induction from the data to a solution inductive. Enumerative to solutions is noninductive (How possible?) problem reasoning in modern solutions 10. Problems and problem (e.g., theories) are science esoteric 1977, p. 236) or 1962; (Kuhn, highly frequently weird 1980). (Shapere, positively tradition and innovation 11. There is an 'essential tension' between in the problem-solving is rooted in science, which process (Kuhn, 1959). in science has been more research tradition-bound 12. Historically, rapidly

than problem innovative and progressive and continuously tradition or research pro not linked to a definite behaviors

solving gram. (Lakatos,

1970; Kuhn,

1977, p. 234; Laudan,

1977).

88

THOMAS

C. Evidence that Conceptual and Cannot Be Removed

NICKLES

Constraints Belong to the Background

to the Problem

Itself

are deeper than others. problems are many and diverse types of intellectual problems besides e.g., determination problems, prob explanation-prediction and in of lems, clarification inconsistency problems problems, or or with other principles, coherence theories, (either internally in natural and others science world alone, not to mention views),4 1. Some 2. There

etc. Some of these prob of pure mathematics, philosophy, problems lem types do not involve empirical data, at least not as an important can be understood apart from the data, component. Many problems and one may be familiar with all the relevant data without seeing the problem. 3. Data

the problem do not constitute sometimes (or the primary that a problem but serve chiefly as evidence (or at least a problem) and relativity.) exists. (E.g., the null experiments deeper problem) are intrinsically and are 4. Some conceptual important problems not merely in the way of solving empirical problems. difficulties and some of those are unsol remain unsolved, 5. Some problems or vable, even though the relevant data, if any, have been explained are explainable.5 can be reformulated in significantly 6. Problems (conceptually) and different ways, formulated more or less completely, transformed, to other in the reduced without essential change problems-all of the empirical data to be explained.6 presentation even when on other problems, can be modeled the 7. Problems The modeling is more substantial is dissimilar. data or subject matter

than the data alone would permit.7 a scientific 8. Recognizing and adequately problem formulating tasks. [Bantz, 1980] can be very challenging on the problem 9. The more constraints solution we know, and the more are more the formulated, sharply and completely sharply they can formulate it. and the better we understand the problem, can be an important a good problem theoretical 10. Formulating or different from the discovery scientific achievement, frequently data of for production explanation.

we

A-l

and

the

'How possibly?'

question

it raises may

not

seem

at all

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To bring out the puzzlement, I point out that erotetic puzzling. as the set logicians such as Belnap and Steel (1976) define a question answers plus a request for an answer satisfying of admissible certain conditions of number, distinctness, and completeness. This is puzzl a question with the set of its possible answers ing because identifying a problem and (analogously) with its set of admissible solutions to generate the following dilemma: Either the possible solu appears tions to a problem are known or they are not. If they are, you do not really have a problem at all, for you have the solution(s). And if they are not known, again, you do not have a problem - for how could you know what it is? In Section V, I argue that there is something - but not everything - right about this apparently and paradoxi backwards cal way of defining problems. the appearance I of paradox, Despite think it offers the only way to answer the Meno The paradox. dilemma is in fact a variant form of the paradox found in Plato's Meno 80d-e: Either you know what you are searching for or you do not.

If you do know, you already have if you do not know, you would on it accidentally; stumbled hence,

And

it, whence inquiry is pointless. not recognize it even if you

is impossible, again, inquiry is to show that the second way out of the paradox is false. You can know what you are looking for without it completely. already having it; you can know it without knowing This most basic problem of inquiry, 'How is inquiry possible?' form. Solving the weak form for a (A-2), has a strong and a weak domain con of problems particular requires only that we specify ditions on what would terminate admissible inquiry (in intellectually on what would count as obtaining the goal of inquiry. The ways), pointless. statement

The

in addition, guidance strong form of the problem of inquiry demands, as to how to search for the goal state, not simply how to recognize it if you happen to stumble upon it. Here we may further distinguish of strength, from the provision of algorithms down to the degrees remarks. One can address the supplying of helpful hints and heuristic of inquiry without the existence of an strong problem presupposing or even a general methodology of a algorithmic discovery procedure sort. So far as scientific weaker an increasing inquiry is concerned, number of 'friends of discovery' (to use Gary Gutting's term) reject the classical and Popperian positivist confine itself to the weak problem of of merely and historical psychological

must that philosophy that the form is inquiry, strong interest. Indeed, I (as one of position

90

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turn the old discovery/justification the more radical 'friends') would on its head. The main job of general methodology, on this distinction of radical view, is not to provide a foundational of theory justification and scientific Rather, objectivity. knowledge, rationality, is concerned with 'heuristics' (in a suitably broad sense). methodology To state the point boldly and without the only legitimate qualification: or at least sort of 'theory of justification' into heuristics, collapses into 'theory of inquiry' for science as an ongoing process. To put the into pursuit. (1977), acceptance collapses point in the terms of Laudan I shall return to this conception of methodology. or 'data' on I do not have space here to defend my other constraints about problems of them are platitudes and about Many little defense. research and therefore need their Despite an to account it is of difficult nature, produce platitudinous problems problems. scientific which

satisfies

(or explains) II. EMPIRICIST

them all. MODELS

OF

PROBLEMS

In my

of scientific problems (1980e), I tested three empiricist models above the constraints and I briefly found them against wanting. a those results here. On the minimal summarize model, empiricist an is in fact of search (observational) problem empirical explanation or prediction - or a process con in search of a method of humanly on it of in the trolling (depending variety empiricism question). to any major writer, this extremum Charity forbids ascribing position for this minimal model satisfies hardly any of our constraints. If a a were datum demand the that it be problem only plus explained at all were placed on what and no restrictions controlled) (predicted, or control, counts as explanation, then we hardly could prediction, have a definite problem, much less a definite conception of problems. The minimal model does not solve even the weak problem of inquiry. The positivist model solves the weak problem of inquiry by adding a methodological to the minimal model component stating what as an explanation, counts etc. For law, confirmation, prediction, one version of the positivist model holds a problem to be a example, in search of Hempelian datum explanation (deductive-nomological, or deductive-statistical; see Hempel, inductive-statistical, 1965). Al us as a this count what would model tells solution, though problem and hence what counts as a genuine the positivist model problem, does

not

even

address

the

strong

problem

of

inquiry-or

rather,

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that it can be fruitfully It is well have denied addressed. positivists known of logical positivist writers that two generations explicitly sort takes place denied that reasoning of a philosophically interesting to be false. In their in context of discovery-a claim now known from but from not view, oddly enough, begins, inquiry problems - and in solutions the tes consists theories-i.e., only problem our of of con said theories! Examination list of ting/justification difficulties It straints reveals many more for the positivist model. in category C, and it fails to handle satisfies none of the conditions it recognizes items in A and B. For example, many just a few types of and (empirical explanation-prediction problems un and of theoretical semantic inconsistency problems as treats when well And it of structured, many clarity). problems them are not (B-2). That is, the positivist model assumes the existence scientific

problems

derivative

for determining like an algorithmic of something logic of justification a problem see when is solved which, Putnam, 1971). By (against of theoretical any consideration background against which, neglecting cannot easily explain and within which, arise, the model problems such items as A-9, B-l, B-4, B-5. This last objection is not entirely fair, since, admittedly, many more explicitly had written about problems, would positivists, they a role in the analysis of problems. frameworks have given theoretical since it is Popper, among major figures, who first stressed the role I term the enriched account the Pop of the theoretical background,

But

perian

model.

a 'problem situation' into a 'problem', a 'frame analyzes Popper a In and the example Popper 'theoretical work', (1972, background'. one of Galileo's p. 172) provides, problems was simply to explain the situation was more complex, since he set the tides, but his problem the the theoretical of view background Copernican problem against was to to it in he and which solve committed, firmly point, attempted terms of his own conjectural of circular (framework) hypothesis inertia. In short, Popper retains the positivist model for problems a more is the total situation but proper, complex thing with problem and his followers (Elsewhere, Popper depth. place more conceptual as on situations inconsistencies between emphasis problem theory and data or between research perian

programs. view.)

theories, and on the importance Hence my model captures only

of metaphysical part of the Pop

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THOMAS

NICKLES

richer conception of problems situa (or rather, problem Popper's or less adequately, him to handle, more all of the tions) enables in our categories A and B. And despite his well known constraints views on logic of discovery, 'method of and conjectures Popper's at least addresses refutations' the strong form of the problem of For solutions (even inquiry. by propounding conjectural problem to criticize 'wild' ones, initially) and proceeding is them, the problem more to and determined and the direction in which fully precisely, look for a better solution may become but still apparent. Interesting can be viewed as defective solutions faulty conjectural 'descriptions' of a/the correct solution. these virtues, problem Despite Popper's a model has trouble with the data in our category C. What makes not is but for the itself its problem deep Popper problem background or setting. This consequence if the only deep be tolerable might were problems represented theories, but that is portant the clash between resolving of and the problems theory,

data which threaten im by anomalous not so. Deep problems, such as that of and electromagnetic classical mechanics Newton's theory of gravitation clarifying not need involve additional theory, directly

and Planck's quantum data to explain at all. In such cases, the explanation and prediction of or discontinuing data may play the less central role of confirming moves or of indicating the existence of a highly concep conceptual our tual (vs. purely observational) Since data C-l through problem. themselves that problems C-10 all presuppose may have conceptual I that is conclude model depth, Popper's inadequate. view implies that one and the same problem may possess Popper's at different theoretical times, in different quite different backgrounds contexts. is explicitly defended in an interesting This conception there is an element of truth article by Andrew Lugg (1978). Although to these suggestions, I argue against Popper in the next and Lugg, a or cannot be its dissociated from that section, problem 'background' 'setting'. On the contrary, part of the problem.

III.

We

must

scientific phenomena

PROBLEMS

the

'background'

AND

THEIR

that part of Popper's with problems problems all other (or at least makes

reject

constitutes

an essential

SETTINGS

model

which identifies all observable explaining strictly derivative problems

of

WHAT

IS A PROBLEM

THAT

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MAY

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from this task). There are a great variety of problems in science, not to mention intellectual in general view (C-2). Popper's problems addresses itself to only one or two categories. But if we reject this of Popper's his component model, we can hardly avoid questioning from their backgrounds and frameworks, separation of problems i.e., from their settings of empiri (to adopt Lugg's term). Even problems cal explanation include many and methodological may conceptual A conceptually constraints. deep problem need include no significant, at all. In any case, why should we component empirical, phenomenal on a problem solution, saying draw a distinction among the constraints that some contribute to the definition of the problem itself while others belong to the background? On what grounds is such a dis tinction to be drawn? of Popper and (1978), building on suggestions Jagdish Hattiangadi a bold claim which advances that Agassi, explains how it is possible no substantial contain He con problems phenomenal component. have the logical structure of incon tends, first, that all problems In addition, sistencies. he rejects Popper's of problems separation on the ground from their contexts, that serious scientific problems have an historical structure and cannot be fully understood apart from that. Let us consider each of these components of Hattiangadi's model

in turn. are logical inconsistencies claim that all problems is untenable. As Laudan the mere logical compatibility of theories (1977) observes, can be a problem if a stronger relation of support or is expected demanded. While the minimal the positivist, and even the empiricist, of problems (as idealized above) leave no room for Popperian models as inconsistencies, from problems of problems except as derivative the same kind of mistake data, it does not help to make explaining all problems to a single type. Ironically, as they make by assimilating I understand cannot handle simple problems model it, Hattiangadi's of explaining our empiricist data-the empirical only thing which can handle adequately.8 models The

a problem of empirical in a theory. The incompleteness to explain, even badly, is unable a phenomenon in its of responsibility. (If, in addition, we suppose that a competing for the first theory can explain ,then is a nonrefuting anomaly in Laudan's Yet it not would do to argue sense, 1977, p. 29.) theory, a that this problem involves contradiction between the pro really Consider

theory domain

94

THOMAS

NICKLES

that the theory cannot that it position explain and the demand in its domain. remains The demand unsatified explain everything by the theory, but this is no logical inconsistency. And it is doubtful even whether the conceptual and physical incoherencies blowups which have plagued several historically theories important physical are accurately termed inconsistencies. Now it is often useful to speak of inconsistencies and incom a sense in broader I it that Hat take (cf. Leplin, patibilities 1980). on to so wants do I and done have I occasion. this, tiangadi myself are difficulties also agree that problems attainment blocking goal are inconsistencies (A-7). But to claim that all problems spreads the too thinly, at the cost of blurring notion of inconsistency important sorts of problems. Hattiangadi between distinctions distinct treats all as overdetermined to B-6. problems contrary problems, an historical second that problems claim, possess Hattiangadi's structure cannot be divorced such that problems from, or even more to recommend their historical has from, situations, distinguished it.9Why does he abandon Popper's distinction of problems from their and frameworks and embrace the inclusion thesis backgrounds (as I shall term it), the thesis that the framework and relevant portions of the background itself? One main reason is that belong to the problem to distinguish this enables Hattiangadi deep from routine problems our data and A C-l second is that it enables him to C-2). (satisfying avoid certain difficulties of individuating problems, given his view that are inconsistencies. all problems I want

to continue the argument in favor of the inclusion thesis by us a more its to that enables deal acceptance contending great explain data in an unforced manner than can those models which reject it. One and obvious immediate is the that inclusion thesis advantage to themselves attain great conceptual permits problems depth. And without this depth, we cannot explain the existence of highly concep tual problems at all, not to mention of empirical science the purely of mathematics The and in our data conceptual problems philosophy. category settings) necessary Popper's discussion historical

C each

themselves (and not simply their imply that problems so have conceptual the inclusion thesis is (I claim) depth, to explain each of them. So far as I can see, models such as to account and Lugg's fail A for this data. fuller badly would cases.

consider

each

item

separately,

with

attention

to

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to answer two objections raised by Lugg It remains, however, is that the inclusion (1978) to the inclusion view. Lugg's first objection thesis permits no distinction between what Max Planck called 'phan run of overdetermined tom problems' and the general problems. are those problems, Phantom of a such as the designing problems which cannot be solved by any change of perpetual motion machine, are "problems which have no setting, while overdetermined problems with accepted belief and practice" solution compatible (1978, p. 2), no on it (B-6). Unlike phantom solution compatible with all the constraints problems, ordinary overdetermined problems can be solved by changing the setting, viz., by rejecting or modifying at least one of the constraints on the problem solution. between reply is that there is no clear, important distinction and overdetermined in phantom problems general. Contrary problems to Lugg, I would say that a significant change of setting alters the to the the setting does not permit a solution problem. Changing a us a to it enables solve related rather, original problem; problem, as were. are it In scientific there often research replacement problem, on a problem solution, good reasons for tinkering with the constraints or rejecting them outright for modifying certain constraints (see My

1980b). For me, unlike Lugg, substantial tinkering alters the are we To be there which deter sure, problem. eventually problems mine to be phantom problems, to alter any because we are unwilling on the problem, and we see that solution of the defining constraints is an the circle and and with rule impossible. Squaring trisecting angle are now known to be phantom science compass problems. Modern also regards the production of a perpetual motion machine of the first as a phantom kind (Lugg's example) rational persons problem. What

Nickles,

have done in the latter case is to give up the goal in question rather than to give up the constraints the problem which define (chiefly conservation of energy). Similarly, Boltzmann gave up his eventually aim to strictly derive the classical law from mechanics (a entropy his parallel aim of deriving time-reversible theory), Planck abandoned the second law for radiation from Maxwell's theory, electromagnetic and physicists the have of classical up given goal reconciling and classical mechanics scientists face electromagnetic theory. When a problem to take be abandon that insoluble, they they particular quest and immediately go on to ask whether (by shifting the problem or goals) leaves them with a new problem altering either constraints

96

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is scientifically But this is the case with all prob which interesting. as overdetermined. lems that scientists recognize between and other over Nor is the distinction problems phantom an even on absolute determined one, problems Lugg's own view, as are simply his discussion Phantom those may suggest. problems the constraints of which scientists decide to problems in resolve the leave inviolate. conflict they constraint/goal (Again, the goal.) Yet there is no such thing as an these cases by abandoning The 'absolute' unalterable constraint. constraints of one absolutely or the the become may generation good approximations outright the phantom of one falsehoods of the next. Therefore, problem next the the solved of become may (and vice problem generation a an occur or to at least shift may versa!), interesting replacement overdetermined

A century solvable. motion ago, a perpetual kind works the second which (one by violating was considered law of thermodynamics) classical second impossible. in this century, Einstein showed that Brownian and Perrin Early second law and, in a sense, constitutes motion violates the classical of kind. and Slater motion the second Later Bohr, Kramers, perpetual - conservation with law of the first of tinkered (1924) thermodynamics a not the intent motion with of energy (although producing perpetual was quickly of conservation Their statistical machine). conception one that am I to is make the familiar but the abandoned, trying point a new as to to is revision claim every response developments. subject to the inclusion thesis is more serious. It is second objection Lugg's problem machine

which of the

is

that the inclusion thesis multiplies Every necessity. problems without the in basis of a problem substantial the changes change conceptual a is and 'radical result bothersome The unnecessary problem. problem to the radical meaning variance and theory vari variance' analogous ance which recent philosophy has plagued of science. On the in we could no longer say that Ptolemy clusion view, Lugg contends, on the problem that of the planets; both worked and Copernicus on the problem of the circulation of both worked Galen and Harvey J. all J. that and C. Smart and Plato, Descartes, blood, (we might add) addressed

the mind-body problem. in (1978) is similar to Pop view of problems Lugg presents a phenomenon a A is task of explaining simply per's. problem proper no The is and has depth. depth supplied by its particular conceptual his of Louis Agassiz's in detailed historical (Yet example setting(s). The

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out the problem of explaining 'erratics', Lugg fleshes by problem to what is tantamount and theoretical background Popper's including the inclusion view and adopt a framework.) Lugg urges us to abandon which would of charity', permit us to say that although 'principle in very different settings, they attacked the Galen and Harvey worked same problem. In short, Lugg opts for the view that basic problems are enduring, while holding that the problems themselves (apart from are their of merely empirical problems explaining settings) This view, I contend, is unhistorical and indefensible. phenomena. it raises the is because second serious, however, objection Lugg's and identity conditions difficult question of individuation for prob is P when and the very lems. How do we tell problems apart, problem as problem Q? On this occasion I can touch this same problem to point out that the question is question only lightly, but I hasten difficult for any theory of problems. is that, when we of the objection My answer to Lugg's formulation are being careful, we do want to say that Ptolemy and Copernicus on rather different problems10 and that Copernicus were working and different Thus Newton attacked problems. quite prob multiplying we are merely lems is a necessity; what are already distinguishing For the same reason that it would be misleading problems. on atomic to say that Democritus and Bohr both worked on the more to it be would than odd that both worked say they theory, same problems.11 There is now a wealth of historical material that I shall confine myself to the documents claims such as these. Here of one and the same logical point that A and B are two formulations

distinct indeed

one also solves (or question) (or answers) problem only if whatever vir solves the Now the Bohr-Kramers-Slater other (answers) (A-3). tual oscillator model of the atom, mentioned solved above, (tem structure of atomic their problem and of the relation of porarily) to matter. Was to any problem it a possible solution of radiation not. not Democritus? Democritus could have understood Obviously even but a the 'Dreim?nnerarbeit', their paper contained though and even if he could have understood it, it single, simple formula; would not have solved any of his problems. For the Greek atomists, atoms did not even have an internal structure. The stability of the atom was no problem for Democritus and his school! Similar remarks could

be made

mind-body

about

problem.12

the Galen-Harvey

problem

and

about

the

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anew that the historical reply it will be objected study of as I am treating it and them, ironically must conclude that no to For have of. the history problems speak by exaggerating of each subtle view leads to the shift, my importance conceptual to a change of problem. A resear conclusion that each shift amounts cher could not even gain a deeper understanding of a problem without on the the since each discovered constraint problem, changing newly no solution would the We could that say change longer problem. on worked the of the for and years many problem Copernicus planets To my problems,

on the blackbody for about six, for the very idea that problem made that their problems shifted. progress suggests they constantly to is inclusion view it makes it Finally, alleged, my impossible explain link Ptolemy with Copernicus and Newton rather why we historically or with Darwin with Freud. than, say, can be (to take the last objection first), problems Surely, however are more or less closely There related without identical. many being can be related. Toulmin ways, needing more study, in which problems Some prob of problems. (1972) suggestively speaks of a 'geneology' Planck

and the offspring of still others. of other problems lems are ancestors on the on other problems, can be modeled Then again, some problems content intellectual basis of mathematical content, form, (physical content, etc.), or both. Still other problems enjoy no such biological to one another. The very fact that a line of inquiry evolves relations over time from problem P to problem Q means that P typically will to be related to Q in ways that it is not related to problems belonging were the of thought. Ptolemy's other departments fairly problems of Copernicus's while Copernicus, close ancestors problems, though closer in time, was perhaps a more distant ancestor of Newton. a con between Moreover, just as the word 'theory' is ambiguous crete achievement 1913 and a subject matter ('Bohr's theory of the own to Heisenberg'; 'Newton's atom' vs. 'atomic theory from Stoney vs. so can 'Newtonian the word be theory'), theory' 'problem' matter and a subject concrete instance versus of the orbit' Mars' 'the Kepler ('Kepler's problem shape - the two-body problem). This is not surprising, since concrete problem' to concrete and atomic theories are solutions theory (for problems, area that addresses of atomic the is subject problems just example) - the kind of use concrete the As scientists word, problems physics. thing given to graduate students to work on for their thesis research ambiguous

between

a

of finding

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very specific indeed. If we employ the label in the 'subject matter' worked on 'the and Copernicus sense, then it is true that both Ptolemy not to both Democritus that but useful still of the say planets' problem the nature of atoms. and Bohr tackled problems concerning sense it is perfectly natural to describe the in the concrete Even a as 'same and relation between Ptolemy's Copernicus's problems are

term (1975)-the to adopt Harold Brown's in different and others, but with respects importantly matter I side with Brown against On this relations. ancestral strong terms in him. of of of constraints criticisms Thinking problems Lugg's in parti and the the differences commonalities facilitates specifying ness/difference same in certain

cular

relation',

cases.

- that on the inclusion view our part of the objection us as we more out from under learn about shift right problems out of the inclusion best answered version them-is my by setting I do in Section V. For now let model of problems more fully, which me say that I do not believe my differences from Lugg on this point as may appear. as are as substantial I prefer to think of a problem a as with determinate pretty something something quite definite, structure, rather than as an historically changing entity. To adopt this The

other

are historical is not at all to deny that problems in the standpoint more important sense. It is not to sacrifice history to Logic. Since on are objectively in a body of humanly my view problems present and aims, they may strictures, theory, data, methodological produced exist all unrecognized and may be discovered constraint gradually, can In I this of way (A-8, A-9). by-constraint speak successively as new con of one and the same problem, sharper reformulations as long as said constraints are already straints are discovered, im in relevant and the corpus e.g., (See, practice. plicit of thought of the black-body But 1978, on the development Nickles, problem.) this very way of speaking then forces me to say that the problem-/or scientist-X with the discovery of (say Planck) changed significantly this new condition. A change of problem in this 'agent' sense need not sense (problem in the previous, be a change of problem 'semantic' Problem in the semantic shifts for-a-body-of-theory-and-practice). sense occur when or the in significant changes goals, methodology, new occur a context the theoretical of (e.g., development theory which has implications for a given problem area, or the abandonment of an old

theory which

strongly

conditioned

the problem).

I suspect

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to draw similar distinctions that Lugg and others of like mind want sense of 'problem', between (b) (a) the agent sense and the semantic in a and (c) changes and the subject-matter the concrete sense, from changes of problem. problem I now complete my limited survey of current conceptions of problems Laudan's model of science - the most by considering problem-solving on and best known of all recent work comprehensive, interesting, I shall then spell out my version problems. cannot consider here other interesting work such as Bunge (1967).

IV.

LAUDANS

PROBLEM-SOLVING

I of the inclusion model. on problems and puzzles,

MODEL

OF

INQUIRY

is in no sense a review of Laudan's rich and fascinating section to the restricted Relative and Its Problems. book, Progress topic of this paper, the book's chief virtues are that (1) it is problem-centered, an account of the i.e., it is a theory of inquiry and not merely unlike of the of concep justification inquiry; (2) empiricist products Laudan the importance of conceptual tions of problems, recognizes out to the the heuristic book (3) nicely brings problems inquiry; to pursuit and pursuit in its attention dimension of inquiry, chiefly natural worthiness of theories; (4) the book has a healthy historicist, as these advances orientation. are, istic, anti-foundational Impressive I shall argue that, in each case, Laudan does not go far enough in the that he has pointed us. direction This

the reader's familiarity with Laudan's Since I must assume book, is intended the following brief summary of the problem solving model to refresh the memory rather than as an adequate merely exposition. is to solve problems. to Laudan, the chief work of science According He distinguishes concerning (roughly, problems empirical problems is like) from conceptual what the world (difficulties which problems to solve empirical He further dis in our efforts arise problems).

unsolved three types of empirical problems: problems tinguishes at solved problems -those which those which no theory has solved; and anomalous least one theory has solved; problems problems has. which a particular theory has not solved but which a competitor a theory may face nonrefuting anomalies In particular, problems a particular but which solved by a competitor solve, theory cannot even

wrongly

(hence,

there

is no

'refuting'

prediction).

Following

WHAT

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101

I think Laudan should recognize (personal communication), no in class of anomalous which need problems, competitor have solved the problems (indeed, there may be no serious competitor in the field) but which a given theory solves incorrectly. Recognizing

Gutting another

this

to the standard is close (which not to give up his Laudan Popperian require no claim that unsolved count (since problems against theory they are solved by none), for we do want to distinguish anomalous solutions from no solutions at all. Laudan several (Ch. 2) also distinguishes types of conceptual as internal such problems, problems, chiefly conceptual ambiguity, class

of anomalous problems sort of anomaly) would

circularity, inconsistency; theory clashes with other widely

problems, which arise when a rules, or principles, methodological

and external theories,

shared world-views.

are appraised the by comparing of their latest theories. Laudan's discussion problem-solving a calculus sum of conceptual the weighted and suggests by which anomalous left unsolved each is subtracted from problems theory by sum of empirical problems the weighted solved. The theory which has score is most the highest and should be effective problem-solving in further 'treated means, (where accepted roughly, 'accepted' a is to research as if it were It rational pursue true'). theory which a rate of the pursued has you do not accept when theory higher success even in the recent past than the accepted theory, though it cannot match success. Rational the latter in overall problem-solving Competing

research success

traditions

in choosing the most progressive ity thus consists theory and tradi in the choice of ever more tion, rather than progress consisting rational theories. A number of criticisms of Laudan's model are possible. I think that in making all appraisal comparative, he swings too far away from the monotheoretic account by assuming that a theory always has serious And his interesting claim that unsolved competitors. problems rarely count against a theory is too strong. (Notice that Laudan could allow them to count against a theory and they would still cancel out in the that of equal process, comparative appraisal provided they were all But for theories intention here is not to my weight compared.) out rehearse the difficulties Laudan's reviewers and critics. pointed by see to our how well account Laudan's fits purpose is, first, My on the problem a constraints as to it and, second, concept appraise

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contribution

to the theory

NICKLES

of inquiry, understood

as a problem

solving

activity. in order, I think Laudan's account first runs Taking our constraints are constitutive into trouble with A-7. Goals of problems, since or are in of obstacles difficulties the way reaching goals. problems some of the the problems, Changing goals will change eliminating The of and their rational altogether. topic goals original problems a is but in and nutshell Laudan's is difficult, appraisal huge difficulty that he makes problem inquiry and solving itself the goal of scientific not simply the means to attain a 'higher' goal such as a true world that these epistemic he denies goals (truth, know picture. Because are rational of scientific goals inquiry (since we can never ledge) know whether we have attained them or how close we are), and since he also

that technological advancement is the aim of Veritas titled and revealingly 'Beyond epilogue, or to without in be left useful appears any Praxis'), serve. to for He purpose justifiable tellectually problem solving the need of human curiosity about the world, but speaks of satisfying our curiosity if we ever became be satisfied that would convinced true of is Laudan's view correct? science Of course, nonepistemic and practical scien utility have been past goals of many knowledge no so need in the exis Laudan have for tists, difficulty accounting tence of scientific communities these among problems possessing that problem is an end in solving goals. But unless he can establish science

explicitly (in his Laudan

denies

the existence and urgency he will have trouble explaining in an ideal, of conceptual (weighting) problems, particularly problems, For will find it difficult Laudanite he scientific community. example, to explain why the incompatibility of two highly successful theories is a serious problem - the more serious the more of different domains and successful the two theories individually. comprehensive rather casual use of the term 'problem' leaves me un Laudan's itself,

A-8 and A-9, but there conditions certain how well his account meets is no reason why Laudan cannot develop his conception of problems so as to incorporate an agent/semantic distinction (see above, p. 99) and other elements of a more detailed account. Laudan's model handles the items in my category B very well, but it does not fully satisfy C-2, C-3, and especially its C-4. Despite on too Laudan's model remains conceptual emphasis problems, as difficulties since it treats conceptual problems merely empiricist,

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in arising in the attempt to solve empirical problems. This is reflected of that the in his view calculus his 'maximin' 68, 124), goal (pp. solved while the number of empirical problems science is to maximize Thus the real goal of number of the conceptual problems. minimizing In the appraisal is empirical for Laudan science solving. problem a counts twice (removing calculus, problem solving an anomalous a a while solution) solving problem difficulty plus adding positive a once this That counts difficulty). (removing just conceptual problem can be brought out by remains too empiricist part of Laudan's model with it another goes too far in the (which perspective contrasting is the central goal of solving conceptual problems opposite direction): are not often solutions inherently science; empirical problem us to solutions evaluate competing help merely interesting-they is suggested This latter perspective by Joseph problems. in and Their Roots 'The Scientific Problems Nature of title, Agassi's a us to this aims science On concep view, give (1964). Metaphysics' to resolve between world coherent, disputes picture, tually deep, conceptual

traditions. Science research (I would (what used to be) metaphysical the (and doing a add) replaces metaphysics by assuming responsibility is really like. better job!) of telling us what the world The obvious way out of this predicament (and one that Laudan seems close to taking) is to abandon the quasi-positivistic distinction the former and between conceptual problems, empirical problems or more less data of observable shallow problems explaining being like In its place we put something and the latter being deep problems. even in which that I am developing, of the problems the conception can have great conceptual depth. The obser problems are but the tip of the problem-iceberg. constraints (E.g., on Planck's to constraints theoretical the deep consider attempt distribution determine and then to explain the black-body law.) does not do justice to C-10. He always model Laudan's Finally, as liabilities for a theory and for the research tradi treats problems But not all problems which arise within it is embedded. tion in which at least a research need be problems tradition for the tradition, we as all have Just know, one (as presuppositions initially. questions empirical vational

can ask a stupid question!), just as we speak of 'good', 'intelligent', so with 'insightful' questions, problems. Good and insightful problems are achievements, not only in successfully initiating inquiry but in the had Heitler and London Think of what that they display. knowledge

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even to pose their problems to know (or to insightfully of conjecture) in molecular the that Laudan's did.13 model way just bonding they cannot the promise of a new research tradition which explain a new whole host of generates interesting, problems, most of which are not yet solved. At the beginning, such questions point to (presup resources to theoretical which have be The yet pose) fully exploited. can at fact that certain important and promising be asked all questions if the questions should rate in favor of a tradition, cannot even arise vs. for a less imaginative (Think of cognitive competitor. psychology in the early 1960's.) Yet Laudan's behaviorism calculus may well give the palm to the less imaginative theory. As a historian of science as well as a philosopher, Laudan can easily appreciate the importance of 'asking the right question', of posing the 'right' problem. By properly (or at least certain kinds of understanding problems as we can overcome also the potentially achievements, problems) serious difficulty for Laudan that a successor theory, by being both in scope and deeper than its predecessor, actually will face more and than its The move (or create) deeper problems predecessor. from a theory which its ten of explains eight problems (to state the

broader

to a successor which point with concreteness) simplistic explains of its of its twenty say, eight thirty problems (including, predecessor's but a different eight) is progressive in one important sense; problems, but it is not progressive to Laudan's calculus according (given reasonable the about in assumptions problem weights). Acceptance science often occurs before Laudan's calculus it should. says The general thrust of several of the above criticisms is that Laudan needs a more detailed account of problems-of their 'fine structure', so to speak-and of how they arise. Such an account, including an treatment of and on of constraints adequate goals conceptually deep to understand is necessary reason the detailed 'empirical' problems, in scientists in that their activities. More engage ing problem solving detail is probably necessary also for Laudan to recover the criteria of of problems which his account needs but identity and individuation lacks. To be fair, I must point out that in Progress Laudan concerned with the broad sweep of inquiry as a problem than with details, and he stressed the tentative nature solving process we can of his account. What, as a about Laudan's model then, say

presently was more

theory of inquiry? I shall try, all too briefly, to establish my claim that Laudan not go far enough along the path that he has pointed out to us.

general Here does

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to the four cardinal virtues of Laudan's work which I reference now at I is this clear the it of section, recognized beginning hope why I think that although Laudan's problem oriented account puts general back on the track (as an account of, and sometime guide methodology for, inquiry, rather than as a foundational appraisal of the products of to say a great deal he needs theory of justification), inquiry-i.e.,

With

more

are and how they arise. I also hope to about what problems on conceptual have shown that, although his emphasis goes problems far toward putting models of and of research empiricist problems in overcoming in their place, Laudan does not quite succeed generally to It the remains and anti tradition. discuss heuristics

foundationalism. to pursuit, the prominence he gives Despite pursuitworthiness, Laudan's model contains noticeable etc., gaps at promise, fertility, a Thus his these loci. calculus research just explains why appraisal or theory is promising formulated program, proposal, newly only or theory being when the proposal, program, appraised already even if a short has a track record of problem success, solving one. (Cf. Frankel, to say that promise himself wants 1980.) Laudan in terms of past achievements be wholly understood when he so much interest in atomism generated remarks: "Similarly, Daltonian the early years of the nineteenth of its century largely because its concrete scientific rather than achievements" (p. 113). promise, is concerned more with future prospect Since heuristic appraisal than cannot

account with past performance, Laudan's is insufficiently heuristic. The same can be said for his treatment of the Duhemian argument prac against crucial tests. Siding with simple logic against historical holds when failure the blame occurs, tice, Laudan that, (pp. 40jf) over all participating should be distributed and theories equally But just as confirmation is more selective than auxiliary hypotheses. this (Glymour, If scientists could not 1980), so is disconfirmation. to locate the blame, because of Duhemian where be no reasons for pressing research in one direction another - a most unheuristic situation.

decide would

logic, there rather than

Laudan's of blame is only interesting reply is that equal assignment the first stage of a two-stage the core theory process. Subsequently, are and all auxiliary hypotheses terms of their evaluated in implicated effectiveness. The blame should be in those located problem solving reasons elements which are least effective. Laudan's all reduces reply for discriminating to Duhemian determination of among premises

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relative

I grant that such reasons are problem solving effectiveness. I but think Laudan's is a cumbersome calculus instrument important, for many such discrimination tasks, Laudan's evaluation (a) pro cedure is shortcircuited often produce by the fact that scientists is more suspect than the others. specific reasons why one component of the forms of the equations involved may help to locate Analysis the source of a conceptual for It is these specific blowup, example. reasons which further In many cases, heuristically guide inquiry. of blame followed of equal assigment by analysis problem solving effectiveness is a procedure which is simply bypassed, (b) It is accurate doubtful whether information the solv concerning problem of each Duhemian include ing effectiveness (which will premise individual components of theories as well as broad, framework prin is available, if Laudan's is applic calculus (c) Even ciples) normally to know? If the able, does it tell the scientist what he really wants is employed calculus in its 'acceptance' it will mode, systematically and conservatively the blame to new, upstart theories allocate rather than to the grand old warhorses which have proven their worth. And if it is employed in the 'pursuit' mode, the bias may be reversed. Either way, we come back to the point that future promise is not a matter of The to calculus simply past performance. appears ignore or to undervalue the finely structured reasoning specific to the case at hand.

Laudan's between and acceptance distinction is over pursuit drawn.14 To a large extent, pursuit of problem to solutions expands swallow last of the old of up acceptance (the vestige theory still more provocatively, Restated to heuristics justification). expands swallow of The of up logic largely justification. point is, many types heuristic to 'accepted' theories as to 'pur appraisal apply as much sued' (which

theories includes

and programs. Certainly methodology more than heuristics) comprehends

of

discovery and justification of the discovery

since the latter are but a late stage acceptance, These claims are spelled out in detail in my (1980a and 1981). process. I can only point out that an accepted Here theory will remain an active center of research only so long as it retains a certain amount of for dealing with still unsolved promise problems. As Ernan McMullin in his perceptive looks to the future emphasizes (1976), promise rather than to the past and is an estimate of the resources of the a theory has been, if its resources theory. No matter how successful

WHAT

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are

turn to have been exhausted, will scientific attention thought a is in and this for abandonment. elsewhere; theory ripe position the first years of this classical mechanics (E.g., consider during as in with the and With research theories science programs century.) of and other procedures products hyperprogressive (paint disciplines and jazz, etc.), the question is not 'What ing, musical composition not even have you done for me?', 'What have you done for me to 'What but do do for me tomorrow?' you promise lately T, A theory can be an require qualification. of the without its being part accepted, background knowledge a center of research activity. And justification is not entirely a matter of heuristic to bold claims are necessary Nevertheless, appraisal. overcome the weight of opposing denies which heuristics tradition, role in rational methodology. any interesting his general line is historicist and naturalistic (in the good Although sense of recognizing access to reality, that that we have no privileged we cannot stand outside of history and gain a God's-eye view of the Ultimately,

these

claims

trusted

Laudan's still smacks too much of posi calculus world), appraisal in tivistic algorithms and confirmation of theory theory justification a sense that goes beyond a critical to interest in scientific reasoning like philosophical foundationism. This is especially true something is at the center of attention. Let me illustrate with when acceptance to Laudan's reference recent attack on convergent realism (Laudan, view of that Laudan's 1980). The nature of the attack again reveals is too problems empiricist. In attempting to trace out rigorously the consequences of the problem too Laudan his in drawing the calculus sticks closely by solving model, et alia are simply wrong to suppose that Popper that a conclusion a over successor to first into its should go theory predecessor, If and thereby explain the success of the predecessor. approximation, success our is overall problem of rational criterion acceptance, solving states Laudan, there is no reason why a successor theory need have any with its predecessor, its laws or mechanisms. connection substantial Now Laudan does have a point. It is too strong to require, without successor reduce in some approximation that any adequate exception, or to its predecessor. in terms of 'final' appraisal But by thinking rather than in terms of the problem acceptance (theory of justification) he overlooks the richly woven solving process (inquiry, heuristics), that normally hold between the two theories of a mature continuities

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by the very nature of conceptually deep problems. Given that a science will have conceptually i.e., problems deep problems, which conditions their constraints, possess among deep theoretical as any that these theoretical and given conditions serve, as much a thing, to define the subject matter of that science, complete break of seems to have in mind would amount to changing the kind Laudan the of the other. In subject. The one theory could hardly be a successor

science mature

as I have shown elsewhere (1976, 1978), limit constraints particular, are one of the most defining conditions. important types of problem are partly defined by conditions of the sort: Any Many problems solution must reduce to this formula in the low frequency adequate limit and to that one in the high frequency limit. To a large degree, are anchored in the theoretical is con which problems background stitutive of them. (This partly explains B-12, to which Laudan himself as Laudan are not as free-floating is strongly committed.) Problems that successor theories nor (cf. Lugg, 1979). In supposing imagines so radically he unwittingly break from their predecessors, mally are shallow, to release the and he threatens implies that problems 'essential tension' between tradition and innovation of which Kuhn In is tension this essential my view, (1959) so revealingly speaks.15 part of the very nature of problems (B-ll). A deep problem, by its very depth, is rooted in a more or less established body of theory; yet it could not be a serious problem at all unless it apparently challenged or at least im that body of theory, thereby calling for innovation agination. This is but one of the reasons why I think Laudan's (justified) attack on convergent a sense too realism goes far. In it is his own 'ad use ventitious Davidson's (to philosophical term16) which puritanism' to conclude leads Laudan that fallibilism about implies skepticism in turn leads him to be (rightly) scientific claims and which of the over-optimistic of Boyd (1973) and Putnam puritanism realism and even a (1976) and, as a result, to think that theoretical view of science are untenable. nonfoundational epistemic

general critical

is mildly natural Laudan he is explicitly historicist, schizophrenic: but his book still makes and anti-foundationist, implicitly and objectivity. the guardians of scientific rationality philosophers Laudan is not quite cured of that old foundationist for a hankering to categorize and judge all framework within which content-neutral content (cf. Rorty, 1979). possible istic,

WHAT

V.

THE

IS A PROBLEM

THAT

CONSTRAINT-INCLUSION

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MODEL

What, then, are problems? My short answer is that a problem consists on the solution plus the demand or constraints of all the conditions that the solution (an object satisfying be found.17 For the constraints) this reason (and for lack of a prettier name), I call it the constraint - in a sense inclusion model of problems. The constraints characterize 'describe' the sought-f or solution. Specific types of problems will, of But what else could a problem in course, possess special features. or can I the demand general include than the constraints plus request? think of nothing that this model leaves out. Does it include too much? It is agreed on all hands that problems a problem do not arise apart from goals and demands. Furthermore, on the solution must in order to be a include at least one constraint well-defined problem at all and in order for inquiry into its solution to be possible. I know of no basis for discriminating those constraints which do belong to the problem proper from those which do not, so I in the problem. For practical purposes, include all constraints only the more a to familiar or more constraints important particular special are mentioned in scientific communication and in problem usually but definition of every single constraint, life; 'constraint', everyday by rules out some conceivable solution as inadmissible and thereby (I helps to define the problem. On my view, nearly every problem a discipline a human or within arising within society will have no difficulty numerous in common; but that fact presents constraints as its name of individuation, for the constraint-inclusion model, on all constraints which individuate implies, also contains problems can handle any in the other models I have reviewed. My model dividuation based on constraints and/or goals at all. can now be The role of our 'data' on problems in this discussion claim)

better appreciated. For these data represent many (though not all) of we want to impose on the problem concept the constraints itself, on to the 'problem' problem. the solution An answer to the question 'What is a problem?' must The constraints satisfy these constraints. a 'describe' what is. Thus task in this paper my collectively problem is a reflexive one. I am inquiring into the nature of problems them selves.

Erotetic I (Unlike Hattiangadi, logic offers one entry to my model. make no sharp distinction between and I and find questions problems;

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some of the logical discussion too formal suggestive, although much to be directly to most that a scientific Recall problems.) applicable a answers set for erotetic is of admissible question, logicians, plus a selection demand on the form of the answer. As Belnap and Steel put it, A

first

presenting

approximation a range

respondent

to the central of

is to make

alternatives a selection

idea

is that each question is to be conceived its subject, from among which alternatives as from a tray of hors d'oeuvres (1976, p. 17). as

as the

object, can a question be defined in terms in terms of its solutions? Doesn't this put the cart before the horse? In science, at least, isn't it the case that our over which hors d'oeuvre arises not from indecisiveness puzzlement we have or available no to choose but because theory precisely answer at all - we can think of none, or at least none which available satisfies known constraints?18 Moreover, how does the erotetic view have different which the same range of ad distinguish questions

But how, many readers will of its answers or a problem

missible horse?'

answers-such and 'What color

color is George as, "What Washington's is George Washington's house?' Or 'What is the melting and 'What is the centigrade?' point of lead in degrees in For the same set of of iron melting degrees centigrade?' point answers the set of admissible for each of these numbers constitutes latter questions and the same set of colors for the former. as answers this problem and Steel avoid by construing Belnap of sentences which 'The the repeat point question. melting complete lead is 327?C and 'The melting point of iron is 1535?C obviously one may wonder answer distinct this whether However, questions. terms in device does not amount to semi-circularly defining questions And must the answer to 'What is the melting of themselves. point of in degrees be a complete centigrade?' rather than simply '327'?19 I do not base my Be that as it may, on formal erotetic any particular, problems lead

(question-repeating)

sen

tence

of scientific conception model follows logic. My not the letter of the erotetic analysis but only the spirit, as expressed as an answer counts is in the central what insight that "Knowing to the question."20 equivalent knowing It is the same move The reader can now anticipate my next move. out Meno to that solves the that we can know viz., point paradox, as an answer what counts in without any answers actually having

WHAT

IS A

PROBLEM

THAT

WE

MAY

SOLVE

IT?

Ill

are indeed unlike Belnap's scientific problems tray Interesting answers a set of full, alternative is rarely available of hors d'oeuvres; is available from the in advance induction). But what (cf. eliminative at all, is some start and must be, if we are to have a problem on the solution(s). And it is precisely of the function constraints as inquiry pro are discovered these constraints, and those which

hand.

to delimit the range of admissible to the problem. solutions a in is in saying that a there of truth my view, Thus, large grain terms its is in of But here I admissible solutions. defined problem a problem to that alter the erotetic doctrine say significantly logicians' can be defined, set of per in terms of the actual not necessarily missible themselves for we may know the problem without solutions - but solutions any permissible rather, in terms of something knowing the range of admissible solutions which determines themselves, the constraints. namely This departure from the standard view also solves the erotetic now set For not of individuation raised above. it is the of problem answers admissible but the constraints which (solutions) (roughly) ceeds,

set that defines determine the former the question and (problem) one problem individuates from another. Two problems differ if and differ. It is of course possible only if (and insofar as) their constraints for distinct sets of constraints to determine the same range (or at least it would be answers; otherwise, overlapping ranges) of admissible a more one to for solve than impossible theory-cum-problem-solution (A-5). problem a bit more fully. The basic idea is that a I now set out the model a a is demand that certain goal be achieved problem plus constraints on the manner the goal is achieved, in which of i.e., conditions on the Here several of solution. clarification adequacy problem points are in order. First, these constraints may not all be known. Usually, as one progresses are uncovered additional constraints toward a the entire problem may exist un Indeed, an investigator discovers it. It follows from in terms of constraints of problems that problems my characterization are entities which have 'objective' existence, just as the constraints themselves have. A problem exists within a body of belief, assump or not anyone and demands whether its tions, practices, recognizes we can out in the theories of presence (A-8). Today point problems detected

to the problem. for a time until

previous

generations

solution

which

went

unrecognized

at the time but were

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nonetheless. present within that historical body of theory and practice as eternal Platonic Such a view does not reify problems entitites of human and The existing independently knowledge aspirations. or Greeks did not fail to solve the mind-body of problem problems nuclear

structure, for in the context of their intellectual did not exist (A-7). these goals, problems left hanging on p. 99 Thus (to answer the objection now see how different people can know different things the same problem, how a problem can be approached even from different fields (A-9),21 and how directions, can

discover

and

articulate

traditions

and

above) we can about one and

from different an investigator a problem the step by step without with the emergence into knowledge of

problem changing constraint. in terms need not (all) be explicitly formalizable Second, constraints of a precise set of features or rules which the solution must satisfy. is room here for what Michael There 'the tacit (1966) called Polanyi model leaves the possibility dimension'.22 tacit of open My on the solution which are not, and perhaps constraints conditions cannot be, fully articulated but whose is indicated in the presence of in and the actions of agreement degree judgments competent or craft. (See Kuhn, of a discipline 1962, and Dreyfus, practitioners your problem may be to find a mug-file 1972). For example, pho underlying each new

the man

who robbed you-and is of faces recognition so same far resisted features The may something analysis. hold true of legal judgment, medical aesthetic diagnosis, judgment, and so on (Wartofsky, 1980). some constraints are more some fundamental than others, Third, are more more or while others remain flexible firmly established, as In the exact such sciences highly developed conjectural. disciplines and law, the constraints structure. may form an elaborate Indeed, the a a a be demand that certain structure in theoretical gap problem may or clash within be filled, or that an incongruity the structure be tograph

of

that has

eliminated. A problem is a set of constraints (better, a constraint structure) plus an a demand on the selec that the object (or object, etc., depending or 'described' by the con tion properties of the demand) delimited or rather, straints be obtained. How is it that constraints, their are non like problems, (for constraints, linguistic formulations can be formulated or described items which in various linguistic

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the problem describe solution? of By their very function a as a counts what solution kind of defining they provide description of the solution. The set of constraints the ad thereby determines to the problem. missible solutions can be defined This explains how a problem in terms of its ad ways),

that one or more of them be plus the demand a the of produced. Roughly speaking, formulation (in my problem ?5 just a description of its solution(s) view) plus the demand. On my view it is literally true that 'Stating the problem is half the solution'! Of course, the description of the solution contained in the statement of the problem does not represent the solution in the desired form; there would be no more profound than 'What otherwise, questions color was Washington's white horse?'

missible

solutions

The resolution of Meno's (A-l, A-2) poses no difficulty for paradox the constraint-inclusion a state model. is possible because Inquiry ment of a genuine question or problem aside from the is, demand, just a description of the answer-the object sought. If enough constraints are

known

to make that means

the

to in clear and well defined problem a as know what count would if vestigators, solution, they on should to stumble can it. the constraints they Moreover, happen and usually do provide positive toward a problem solution. guidance not tell when have found the in what solution but you you They only space to look for it. This view of problems region of the problem the of complex in the context of easily explains possibility reasoning an and to the (B-8, B-9) discovery gives awakening slap long dormant of and It innovation. solves the study discovery strong form as well as the weak form of the problem of inquiry as completely as the strong can be solved, since my model of problems all includes problem on the solution, including algorithmic ones, where they exist. constraints It is easy to see, on the constraint-inclusion how some model, can than one be others how have (C-l), problems deeper might purely (C-2, C-3), how one can initially have a vague conceptual problems a problem

and succeed or fail to establish the existence so on And with the In parti data. problem. remaining a I that it is believe virtue a of and not that cular, my view, defect, Brown's relation' holds between ad 'sameness/difference problems savants dressed at different in different historical circum times, by research traditions stances, or at the same time from different (see hunch about of a genuine

above,

p. 99).

114

THOMAS

NICKLES

On the negative the constraint-inclusion model side, admittedly, needs more development and must more directly address the identity can be guided by the parallel individuation issues. Here the discussion of theories. For I construe not as linguistic discussion problems as conceptual entities but, like theories, structures (plus demands).23 This

move

to conceptual from linguistic structures should not sur a is for what but scientific the for many prise, problem specifications a the intellectual demand solution) plus constructing theory (problem

that the theory be built? And what, new problems?! way of generating University

of Nevada,

in turn, is a theory but a problem's

Reno NOTES

1 Draft Las

read at the University of Nevada, parts of this paper were on scientific at a University of Pittsburgh I have workshop change. Andrew from discussion with Larry Laudan, Lugg, Maurice Finocchiaro, and others. I also gratefully the support of the National Brown acknowledge

Harold

of different

versions

Vegas, benefitted

and

Science Foundation (Grant SOC-7907078). 2 See Kuhn (1977). (1962), Popper (1972), and Laudan 3 Recall that for Kuhn the solvability of the routine (1962) the paradigm 'guarantees' that he terms 'puzzles'. problems 4 of problems, For discussion three kinds Monk of these see, respectively, (1980); Finocchiaro (1969), Laudan (1977), and Leplin (1980). (1980); and Shapere 5 a non-quantum of the black-body Planck's of finding interpretation E.g., problem with of reconciling statistical mechanics the classical radiation law and his problem entropy

law. See Klein

E.g.,

the black-body It was radiation.

cavity Planck, Debye, atomic

(1962), (1966), and Kuhn (1978). as a problem was radiation reformulated problem concerning as a question ideal material treated oscillators by concerning of counting of vibration normal modes Ehrenfest, by Rayleigh,

as a problem et ai, as a problem state transitions and

as a problem of electrons of theory by Lorentz, in 1916, and as a problem of counting by Einstein see Nickles in 1924. For references (1980e).

in the radiation

numbers by Bose occupation 7 see Kuhn's For example, discussion to the second 8 Hattiangadi to his thesis, 9 I have no

in his postscript of the pendulum-efflux problem (1976). (1962) and also Darden that there are a large number of apparent counterexamples acknowledges little to show that appearance differs from reality. but he does or his interesting to discuss the details of Hattiangadi's space position edition

of

itself into tacit debates. thesis that scientific inquiry organizes 10 were to Ptolemy's It is difficult to judge precisely how close Copernicus's problems aims may about Ptolemy and his aims. Copernicus's because of our limited information have differed substantially. 11 have solutions I am not here denying that a problem several, may quite different (A-6).

IS A

WHAT

THAT

PROBLEM

WE

MAY

SOLVE

IT?

115

12 see Matson 1. On the mind-body (1979), Ch. (1966) and Rorty problem, 13 For an illuminating discussion of this case, see Bantz (1980). 14 now de-emphasize in favor Laudan informs me that he would somewhat, acceptance see my (1980a). and pursuit, of pursuit. For more on discovery 15 in mind when have kept this point more he overemphasized the Kuhn himself might of (1962), where he spoils his earlier of revolutions in some passages discontinuity - normal in separate tradition and innovation and rev discussion by locating periods owes to with Gutting and This also science. discussion olutionary something paragraph Lugg. 16 I am indebted. See Davidson (1967), p. 116, and also Rorty (1979), to which 17 owes a good It will be obvious to anyone who that my account knows their work to Reitman this paper was deal (1964, 1965) and to Simon (1977). After completed, to his early essay Professor Simon called my attention (1962), co-authored by Newell to in which of problems and the relation of problem and Shaw, their conception solving is set out explicitly. and to innovation heuristics 18 and '^-predicaments'. See Bromberger (1966) on 'p-predicaments' 19 see Tichy For this last point and others, (1978). 20 and Steel Hamblin (1976), p. 35. (1958), quoted by Belnap 21 on my account, or overlap that the convergence of two Indeed, we should expect, of the fields by a scientist) often will result in rapid problem fields (or the switching can result in a much For pooling better constraints 'fix' on common solving progress. more of the solutions detailed (Here I am problems-i.e., 'descriptions' being sought. to P. William Laudan's view that problems indebted do not exist Bechtel.) interesting is a radical variant of my way of handling until solved by a theory the Meno paradox, is possible. inquiry I agree with Simon that tacit (1966), pp. 22-25, (1976) against Polanyi to solve the Meno is not necessary On the issue of rules and the knowledge paradox. see also Kuhn tacit dimension, (1962), Dreyfus (1972), and Wartofsky (1980). 23 to the This suggests that we treat problems in a manner (insofar as possible) parallel the problem 22 However,

of how

of theories. of the semantic and semantic (For discussion conception conception, see Suppe, as nonlinguistic theories references, 1974, pp. 221jf.) By construing entities, the difficulty the semantic view avoids that each change of formulation is a change of theory-and itself neatly

we

to make

other

solutions) (problem should be analyzed account of the other. conflicts

within

'agent'

sense.

data, practice, or conjectures.

In the

rather

the

individuation

move

issues.

or of can problems Nor be simply matters of belief subjective of belief in the of course (as per Hattiangadi), systems except 'semantic' exist for humanly of bodies sense, problems produced or not anyone ever believed and goals, whether those particular

our

theory, theories

'third world'

same

for problems. This move does not in not our conceptions of theories Might nor problems and problems be tightly linked? If so, neither theories in isolation from the other. An account of one must dovetail with an

want

resolve

If forced than

in his

to choose, I would 'second world'.

place

problems

in Popper's

(1972)

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