Marco Giunti
HATTIANGADI'S THEORY OF SCIENTIFIC PROBLEMS
AND THE STRUCTURE OF STANDARD EPISTEMOLOGIES^{*}
In British Journal for the Philosophy of Science, 39 (1988), pp. 421-439.
1 INTRODUCTION
Hattiangadi's two papers on the structure of problems (see [1978] and [1979]), together with Laudan's book Progress and its Problems,^{1} represent the most complete attempt thus far to ground a whole epistemology on the basic notion of scientific problem.
The most interesting feature of Hattiangadi's system is that both the evaluation of scientific theories and the rules for their acceptance or rejection require the consideration of the historical structure of scientific problems. Hattiangadi has also proposed a logical analysis which is intended to provide the 'unit structure' of all intellectual problems. According to this analysis, all problems arise from logical inconsistencies, while scientific (or deep) problems also have an additional historical structure.
Although Hattiangadi's approach is novel on many significant points, it surprisingly turns out to be an instance of standard epistemology. By this term, I mean any view of science which primarily focuses on the process of theory-choice, and which tries to elaborate a set of evaluation-concepts and of rules for the acceptance or rejection of hypotheses. Standard (or traditional) epistemologies accept the basic postulate:
(TC) (under ideal coditions) scientists choose theories by following methodological rules, which are based on evaluation-concepts.
This is a very usual claim, so entrenched in our epistemological beliefs, that it is often taken as the starting point for understanding the whole dynamics of science. According to this view, the problem of any epistemology consists in establishing what the evaluation-concepts, and the related rules for theory-choice are. An epistemology of this kind is not necessarily normative, since the rules governing the process of theory-choice might be taken as not rationally justifiable. It is my contention that it is reasonable to challenge (TC). I will argue that (TC) is not the only central fact of science, and that, as a consequence, the basic problem of epistemology should be revised.
The second section gives a brief exposition of the motivations and content of Hattiangadi's theory of scientific problems. In the third section; five main criticisms will be presented:
2 HATTIANGADI'S HISTORICAL THEORY OF PROBLEMS (AN IMPROVED VERSION)
Hattiangadi presents his theory of problems as a response to two difficulties of Popper's epistemology, which Hattiangadi interprets as a Socratic view of knowledge. According to this interpretation, science does not (and cannot) yield knowledge in the traditional sense (episteme). However, scientists continue to seek knowledge. It is then very natural to ask:
(a) why should we continue to seek knowledge, if we cannot reach it?Hattiangadi claims that we can easily solve these difficulties, if we accept a problem-based view of science. The answer to the first question is that we seek knowledge 'because we must, in order to solve problems which arise in our beliefs' (Hattiangadi [1978], p. 351). The reason why we must solve problems is not theoretical, but, ultimately, practical. In fact Hattiangadi maintains that all problems are logical inconsistencies, and, since from a contradiction anything follows, a set of inconsistent beliefs cannot have any practical utility. This answer to question (a), besides being very persuasive and clear, has the advantage of not using Popper's concept of verisimilitude, which, in turn, is affected by at at least two other difficulties (see Hattiangadi [1978], pp. 346-7, and [1979], pp. 69-70: 'Popper's answer ... intellectual activity?').(b) If we never have any knowledge, how it is possible that, sometimes, we recognize a certain hypothesis as what we were looking for?
The answer to question (b) is that problems pose some desiderata for a good solution, so that we can recognize whether a certain hypothesis meets these requirements.
According to Hattiangadi, we must distinguish between two main categories of problems. All intellectual problems share the same logical structure, that is, they are contradictions. However, some problems have a further characteristic, depth. Scientific problems fall under this category. Their depth is due to the fact that they arise in theories which are embedded in intellectual traditions. Consequently, to understand scientific problems, we have to consider not only their logical structure, but also their historical structure. I am going to present below Hattiangadi's theory of the historical structure of problems.
Competing intellectual traditions are lineages of theories and problems with a common origin. All the competing traditions which stem from the same origin form an intellectual debate.^{2}
The origin of an intellectual debate is constituted by a problem which arises for a theory. This problem can be solved in different ways, by different theories. Each of these different solutions may be the starting point of a distinct intellectual tradition.
Let us consider Figure 1. T_{0}, is the 'founding theory', and P_{0} is the original problem of the debate. This intellectual debate has two distinct traditions, whose origin is, respectively, T_{1} and T_{2}. Any T_{i} gives a different solution to P_{0}.
In turn any T_{i} will typically give rise to other problems, some of which will be solved by other theories, and so on. The debate in Figure 1, at a later stage, might look as in Figure 2.
There are two remediable, but intriguing, formal problems with Hattiangadi's tree-like representations of intellectual debates. One of them concerns the concept of line of thought in a tradition of an intellectual debate. The other regards the concept of discriminatory problem. These two notions are very important for Hattiangadi's epistemology, since they will be employed to define a set of evaluation-concepts, which allow the appraisal of traditions. These concepts, in turn, are the basis of Hattiangadi's methodological rules for the acceptance or rejection of theories. For this reason, I am going to discuss in some detail Hattiangadi's basic notions of line and discriminatory problem. Tradition 1 in Figure 2 has one line of thought, the line
The problem is with the other branch of the tradition. Should we count this as a unique line or as two different lines? Hattiangadi is not clear on this point, The simplest answer would consist in taking
as two different lines. If we make this choice, we have that [2] has one open problem (P_{5}), while [3] has no open problem. Consequently, tradition 2 is, on the whole, as successful as tradition 1, which also has one line with no open problem. But, according to Hattiangadi, in a case like this we should conclude that tradition 1 dominates tradition 2 (see Hattiangadi [1979], p. 61, schema 7). On the other hand, a tradition dominates the other if, and only if, it has at least one line with no open problem and all the lines of the other tradition have at least some open problems. Consequently, tradition 1 does not dominate tradition 2. We have a contradiction, and we thus must conclude that [2] and [3] are not different lines. We then have one line:
How many open problems does this line have? The most natural answer is one. Nevertheless, according to Hattiangadi's theory, they should be two, P_{5} and P_{6 }even though P_{6} is solved by T_{211}. The basic idea is that P_{6} is still open because it is not solved by a theory which also solves P_{5}. Hattiangadi does not explicitly draw this distinction between solved, but still open, problems, and definitely solved, or closed. problems in a line. This distinction is, however, implicit in his claim that 'a subsequent problem includes within its structure all the earlier problems on that line' (Hattiangadi [1979], p. 55).^{3}
What would it happen if line [4] developed as, respectively, [5] or [6]?
The whole [5] would still count as a unique line, with two open problems, P_{5} and P_{6}.
In [6], T_{212} has solved both problems of T_{21}, P_{5} and P_{6}. As a consequence, T_{211} has been expelled from the line, which now has no open problem.^{4}
Let us now define: a line is closed iff it has no open problem; a line is open iff it has at least one open problem. We can finally define the concept of dominance of a tradition over another tradition. Tradition TR_{1} dominates tradition TR_{2} (in debate D) iff at least one line in TR_{1}is closed, and no line in TR_{2} is closed (see Hattiangadi [1979], p. 61, schema 7).
The relative standing of two traditions is the nearness of one to being dominated by, or dominating, the other one (see Hattiagadi [1979], p. 61).^{5}
A tradition TR (in debate D) is viable iff no other tradition in D dominates TR.
The value of a solution of a problem, in debate D, is given by the difference that it makes to the standing of the different traditions in D.^{6}
Hattiangadi distinguishes between discriminatory and common problems. A problem is discriminatory between two (or more) traditions iff it belongs to just one tradition. A problem is common iff it belongs to all.^{7} To represent discriminatory problems, Hattiangadi uses diagrams of the following kind (see Hattiangadi [1979], p. 58, schema 6):
In Figure 3, there are two different traditions, TR_{1} and TR_{2}. P_{2} is a common problem, P_{1} and P_{3} are discriminatory. Now, assume that the debate in Figure 3 evolves as in Figure 4:
The problem with Figure 4 is that we do not know to which tradition T_{3} belongs. Is T_{3} a solution of P_{2} in TR_{1}, a solution of P_{2} in TR_{2}, or both? The representation of common problems in tree-like diagrams must be improved, if they are to be used to appraise competing traditions by means of the evaluation-concepts previously defined. This is formally accomplished if we represent a common problem as a divided box. Figure 4 will thus become one of the three diagrams in Figure 5
It must be noticed, however, that this graphical device has only solved
the problem of correctly representing traditions (or lines) once they have
been identified. A more substantive difficulty is still open: how could
we actually choose one of the three possibilities of Figure 4? Hattiangadi's
theory does not provide any answer to this question. One would expect the
theories in the same tradition to be somehow related, for instance in a
Lakatosian way - they all share the same basic assumptions or hard-core.
Hattiangadi, however, does not introduce any notion of this kind, so that
the identification of different traditions exclusively relies on the careful
historical study of any specific case.
3 CRITICAL COMMENTS
3.1 Criticism of Hattiangadi's Historical Theory of Problems
Hattiangadi's historical theory suffers from a diffuse instability in the relations between its main concepts. So it poses, in the first place, a quite intriguing formal problem. Its central meaning is, however, rather definite, so that the interpretative problem can be solved. The interpretation given in Section 2 is a step in this direction, and it might be further elaborated, so as to arrive at a completely adequate formulation. The formal inadequacies of the theory are basically due to the ambiguous usage of the concept of line, which sometimes refers to traditions, and, in other occasions, refers to lines.^{8} This ambiguity also leads to deficiencies in the formulation of the notions of dominance, standing, viability, and value of asolution. However, when the distinction between lines and traditions is introduced, and the concept of line is sufficiently elaborated, all these difficulties can be overcome.
But Hattiangadi's historical theory also has some substantive problems. These are concerned with the two properties of lines, conservation and non-recurrence (see footnote 3), which are essential for Hattiangadi's view of problems as historical entities. To modify (or to drop) these two properties would amount to completely changing his theory. But this is precisely what is required, for non-recurrence and conservation are not properties which can reasonably beattributed to real-life scientific problems.
According to the non-recurrence property, if a problem, P, is solved by some theory, in a line, P never occurs again as a problem of some later theory in that line. This property is too strong, for it a-priori rules out cases which can obviously occur. Consider the following example. For Aristotle's biological theory, the appearance of a mutation constitutes a problem, since a particular organism deviates from the essential characters of its species. On the other hand, mutations also are a problem for Darwin's theory of evolution, since his theory requires the occurrence of variations, but no mechanism is provided to account for such a phenomenon. We thus see that two different theories in the same line have the same problem, namely, to explain the phenomenon of mutations. Given Hattiangadi's theory, there are two possible replies to this objection. First, one could deny that Aristotle's essentialist theory and Darwin's theory were in the same line. Or, second, one might claim that although Darwin's problem is similar to the earlier one, it is not identical, because it possesses an additional historical structure. The difficulty with these two replies, however, is that Hattiangadi's concepts of line and problem are too vague to rule out the interpretation that Darwin's and Aristotle's theory were indeed in the same line and that they share the same problem.
Something similar happens with the conservation property: in a (closed) line any problem solved by theory T is also solved by any later theory in that line. This property is arbitrary. In fact it is possible to think of many cases in which two theories in a line do not satisfy such a property. It may be true that there is a continuous line between Parmenides's problem of motion and, for example, Newtonian mechanics. Nevertheless, it seems quite odd to affirm that Newtonian mechanics solves Parmenides's problem.
This arbitrariness of the two properties of lines would disappear if:
(1 ) they followed from Hattiangadi's logical theory of problems; (2) such
a theory were strongly justified by the history of science. But it will
be shown below that neither (1), nor (2), is the case, so that Hattiangadi's
historical theory turns out to be extremely implausible.
3.2 Criticism of Hattiangadi's Logical Theory of Problems
The main thesis of Hattiangadi's analysis of the logical structure of problems is that all intellectual problems are inconsistencies. I have already mentioned one strong motivation for holding this thesis. If all problems are inconsistencies, and if our seeking knowledge consists in trying to solve problems, then the answer to the question 'why do we seek knowledge?' is very simple and convincing: because we must for practical reasons.^{9} The central role of inconsistencies for the development of science has also been stressed by Popper, since a refutation is nothing else than an inconsistency between a theory, hypothesis, or expectation, and a well corroborated basic statement. But, although many problems certainly are inconsistencies, still it seems obvious that there are problems which are not contradictions. At least two large categories of problems, gaps in our knowledge, and formal problems, are of this kind.
A typical knowledge-gap is the problem of measurement. We know that a certain object has a certain (physical) magnitude, but we do not yet know the value. There is no reasonable sense in which a problem of this kind might be interpreted as a contradiction. One might reply that this is not a deep, or scientific, problem. But it is well known that an important part of the scientific activity is concerned with just this kind of problem. For example, according to Newton's theory, the force between two unit masses at unit distance is the same for any two objects. But the value of this constant (the universal gravitation constant) was not known for about a century, until Cavendish devised an apparatus capable to determine such value.^{10}
Formal problems concern the formulation of a theory. These difficulties may sometimes involve inconsistencies, but, if we reduce formal problems to inconsistencies, we lose sight of their peculiar character. Formal problems arise from unstable relations between the main terms of a theory. If we think of a theory as a net-like structure, then the nodes are its terms, and the lines are the statements in which these terms are involved. This structure may be unstable, in the sense that the theoretical statements may not be clearly formulated. The most stable part of a conceptual system is given by its terms (sometimes called concepts or categories), the most variable is given by the relations between terms. To any different configuration of the system' that is, to any fixed set of terms in some fixed relations, a meaning corresponds. If the system is not arbitrary, its meaning oscillates around a central point. The typical formal problem, relative to a system S, consists in trying to stabilize the system, while preserving the central part of its meaning oscillations. If we take this characterization of formal problems, we see that they are problems of interpretation, whose formulation does not essentially involve inconsistencies.
An interesting example of a conceptual system which has a formal problem is the present theory of natural selection. In such a theory there is no shared formulation of the principle of natural selection. However, there is a family of resembling principles (see Bradie and Gromko [1981]). The same holds for the concept of fitness. There are many different interpretations of this concept. Moreover, if we consider just one interpretation, for instance the propensity interpretation of fitness, we discover that there is a family of similar definitions which employ the propensity interpretation of probability in a very unprecise and questionable way.
The theory of the logical structure of problems also has a technical difficulty. For Hattiangadi, a problem is an inconsistent set of statements, I, together with the set, S(I). of all the solutions of I (see Hattiangadi [1978], p. 357: 'A problem ... the solutions').^{11}
E is 'the' explanatory power of I^{12} iff I is an inconsistent set of statements, and E is a consistent set of statements such that: [1] any of its members is a reasonable candidate for truth; [2] E is implied by a consistent subset of I; [3] for any consistent set of statements, E', which is not logically equivalent to E, and also satisfies [1] and [2], there is at least one statement, A, such that A is implied by E, and A is not implied by E' (see Hattiangadi [1978], p. 358: 'My fifth ... for truth', and p. 359: 'Maximality condition ... consequence of B').
C is a solution of I iff I is an inconsistent set of statements, and C is a consistent set of statements which implies 'the' explanatory power, E, of I (see Hattiangadi [1978], p. 358: 'My fourth ... set of statements').
Assume we have a problem, P = (I, S(I)), and let C be a solution of I, that is, C is member of S(I). Since C is a consistent set of statements, there is no problem, P', such that P' = (C, S(C)). This leads to the following result: if the logical structure of problems is analyzed as above, then there can be no solution of a problem which, in turn, leads to another problem. Hattiangadi is of course aware of this difficulty. To overcome it, he allows two further possibilities:
(a) 'A problem may also be solved by an inconsistent set of statements, if the same problem does not arise again in the solution' (Hattiangadi [1978], p.362);There are essentially two difficulties with theses (a) and (b). The first is as follows. Thesis (b) is a definition of a symmetric relation between problems. How should we interpret thesis (a)? If (a) is a definition of 'solution of a problem', when the solution is inconsistent, we have:(b) P is essentially the same problem as Q iff P = (I_{1}, S(I_{1}), and Q = (I_{2}, S(I_{2})), and the intersection of I_{1} and I_{2}, I, is inconsistent, and R = (I, S(I)) is such that S(I) includes both S(I_{1}) and S(I_{2}) (see Hattiangadi [1978], p. 362: 'Thesis seven ... consistent subsets of X).
(a') I_{2} is an inconsistent solution of I_{1} iff I_{1} is an inconsistent set of statements, and I_{2} is inconsistent, and Q is not essentially the same problem as P, whereFrom (a'), and since (b) is symmetric, we obtain that, for any two inconsistent sets of statements, I_{1} and I_{2}, if I_{2}, is an inconsistent solution of I_{1} then I_{1} is aninconsistent solution of I_{2}, But it is quite obvious that the relation x is an inconsistent solution of y should not be symmetric. Consequently, (a) cannot be a definition of such a relation; (a), at most, gives a necessary condition.P = (I_{1}, S(I_{1})) , andQ = (I_{2}, S(I_{2}))
The second difficulty regards thesis (b). Let us consider the example which Hattiangadi discusses on p. 362 of his [1978]. Let X = {A_{1}, ..., A_{n}, B, -B}, Y = {A_{1} ... A_{n}, A_{n+1}, B, -B}, P = ( X, S(X)), and Q = (Y, S(Y)). Assume that A_{n+1}, is aconsistent statement, and that it is not implied by any consistent subset of X. Hattiangadi affirms that Q is essentially the same problem as P. This claim is intuitively plausible, for Y and X have the same 'troublesome pair', B and -B. and Y differs from X just for A_{n+1}, which has been added. Nevertheless, this claim is contradicted by definition (b). In fact, the intersection of X and Y, I, is equal to X. Since A_{n+ 1} is consistent and it is not implied by any consistent subset of X, S(I) does not include S(Y). Consequently, by definition (b), Q is not essentially the same problem as P. If we take this example as an obvious case of two inconsistent sets which have the same problem (as Hattiangadi does), then definition (b) is not adequate.
In conclusion, Hattiangadi's analysis of the logical structure of problems,
if not further elaborated, does not allow the possibility that an inconsistency
of theory T_{1} is solved by theory T_{2}, which is also
inconsistent, but not 'in the same way'. Contrary to his claims, Hattiangadi
has not given any explication of this concept, for theses (a) and (b) are
not, respectively, adequate definitions of the relations x is an inconsistent
solution of y, and x is essentially the same problem as y. If (a) and (b)
are dropped, then Hattiangadi's logical theory implies that a solution
of a problem can
never
lead to any other problem.
3.3 The Relation Between the Logical and the Historical Theory
Hattiangadi repeatedly claims that all problems share the same logical
structure.^{13} If
this logical structure is the one discussed in par. 3.2, such a claim is
unjustified. We have seen in Section 2 that one of the peculiar features
of deep and scientific, problems is that their solutions are theories which,
in turn, have other problems. But we have also seen, in par. 3.2, that
the logical explication of this idea is not tenable. Moreover, if the logical
theory of problems is taken as it stands, then it is incompatible with
such an idea. We can thus conclude that the logical theory of problems
does not support the historical one. The two theories are also incompatible,
unless the logical one is further developed in order to allow inconsistent
solutions of inconsistencies.^{14}
3.4 Criticism of Hattiangadi's Methodology
We have seen in Section 2 that the historical theory defines four evaluation concepts:^{15} domination, standing, viability, and value of a solution. Hattiangadi affirms that the definition of the value of a solution is the basic rule which permits us to understand every other rule regarding the evaluation of scientific theories (see Hattiangadi [1979], pp. 61-2: 'I suggest ... by Popper'). This claim cannot be taken literally, for a definition is not a rule. The definition of an evaluation-term, however, can be the basis for a methodological rule, which, in this case, is:
(R) given an intellectual debate, choose the solution with the highest value.Consider, now the intellectual debate in Figure 6.
According to Hattiangadi's definition, the value of T_{4} is higher than the value of T_{6}, since T_{4} positively affects the standing of its tradition more than T_{6} does. Infact, tradition 2, without T_{4}, has two open problems, while, with T_{4}, has no open problem. On the other hand, tradition 1 has two open problems in both cases. In accordance with (R), we should choose T_{4}. Hattiangadi maintains that:
(a) choices based on (R) are rational;Let us first notice that these two claims correspond to two different aspects of Hattiangadi's methodology. (a) amounts to saying that this methodology is a normative theory; (b) affirms that it is also descriptive.(b) scientists really choose theories (and consequently traditions) in this way.
Let us now consider claim (a), and the example in Figure 6. In what sense is choosing T_{4}, instead of T_{6}, rational? In the given debate, T_{4} is better than T_{6}, but, at a later stage, the standing of the two traditions might be reversed. At that stage, it would be rational to choose the last theory of tradition 1. It then follows that choosing tradition 2 is rational at a certain stage and irrational at a laterstage. This is a rather weak concept of rationality. Also, it is incompatible with the commonly accepted idea, which Hattiangadi seems to share, of a convergence-pattern in the development of science. According to Hattiangadi's model, tradition 1 and tradition 2 might be based on two incompatible, and very different conceptions of the world. It is possible to think of an intellectual debate in which the standing of the two traditions is regularly reversed at later stages. Our knowledge of the world would accordingly oscillate without showing any convergence.
There is also a paradoxical consequence of this view of rationality. Assume that thesis (a) is true, and that all the scientists choose theories according to rule (R), that is, they all are rational. Also assume that there are two competing traditions, TR_{1 }and TR_{2}, and that, very early in the debate, TR_{2} comes to dominate TR_{1}. Then all the scientists of TR_{1} will switch to TR_{2}. Assume that the standing between TR_{1} and TR_{2} remains favorable to TR_{2} for a very long time (say 1,000 years), so that nobody, during this period, chooses and further develops TR_{1}. But now assume that, after 1,000 years, TR_{2} starts accumulating problems, so that the standing between TR_{1} and TR_{2} gets reversed. At that moment, all the scientists will rationally choose the last theory of TR_{1}. In this way, however, 1,000 years of good scientific work and discoveries will be lost. This seems sufficient for concluding that claim (a) is not tenable.
Let us consider, now, claim (b). Whether (b) holds is, essentially, an empirical question. What 'choice-behavior' could confirm (b)? If (b) were true, then scientists should be particularly interested in the history, or genealogy, of the theories they choose. The reason is very simple. Let us consider Figure 7.
According to Hattiangadi's theory, T_{4} is better than T_{8}, for T_{4} makesTR_{1}dominate TR_{2}. But, to realize that T_{4} has a greater value than T_{8}, one must consider the whole intellectual debate. So, if scientists really applied Hattiangadi's rules, they first of all would carefully study the complete history of the theories they choose.^{16} But this is not the case, therefore thesis (b) must be rejected.
A possible reply to this objection is that, in fact, scientists have some knowledge of the historical background of the theories and problems they discuss, even though this knowledge is not acquired by means of a systematic study of the history of science:
If we call certain problems which arise within intellectual disciplines 'deep' problems ... then my thesis is that the structure of 'deep' problems is historical in nature.What Hattiangadi affirms may well be true. Still, this is not sufficient for justifying thesis (b). In order to do this we should be able to show that the'distilled history' that any scientist understands comprehends the whole traditions to which the given problems belong. In fact, if we do not make this assumption, we cannot maintain that scientists really choose theories according to Hattiangadi's rule (R), for this rule, together with the definition of value of a solution (see Section 2) implies that a comparison must be made between the whole traditions under consideration. But this assumption is not plausible, so that the scientists' knowledge of a 'distilled history' cannot provide any justification for thesis (b).
The intellectual who understands the structure of such a problem must, therefore, understand some distilled history of the problem. This is certainly not to say that all intellectuals are historians. In a similar case, a solicitor who knows Common Law may not be a historian of law, even though Common Law may not have a historical structure, insofar as its structure depends upon a history of practise and precedent. In a similar way the scientist studies problems that have a historical structure, yet with this difference, that the structure of deep problems is determined historically not by practise and precedent but in a different manner altogether. (Hattiangadi [1979], pp. 52-3)
4 CONCLUDING REMARKS: HATTIANGADI'S THEORY AND THE STRUCTURE OF STANDARD EPISTEMOLOGIES
To fully appreciate the theoretical significance of Hattiangadi's theory, we must now consider its general structure. Surprisingly enough, this structure is shared by a large group of theories of science, which, to a more superficial analysis, might well seem to be worlds apart. Theories with such a structure will be called standard (or traditional) epistemologies.
Standard (or traditional) epistemologies assume a theory-choice postulate, which can be put in this form:
(TC) scientists choose theories following certain rules, which are based on some evaluation concepts, unless 'disturbing factors impede them.Some standard epistemologies also assume another postulate, which can be called the rationality postulate:
(RC) scientists' rule-based choices are rational.(TC) and (RC) together are equivalent to the thesis of the rationality of the context of appraisal. If a standard epistemology also assumes (RC), it is a normative epistemology.
The basic problem of all standard epistemologies consists in specifying the rules which, according to (TC), guide the scientists' choices. This problem leadsto the problem of specifying the evaluation-concepts on which such rules arebased, and this, in turn, leads to the problem of specifying the nature, orstructure of the theories which the evaluation-concepts are supposed toevaluate.
Consequently, the conceptual architecture of any standard epistemology is asfollows. In the first place, there is a structural theory,^{17}that is, a theory of whata theory is. This structural theory supports definitions of evaluation-concepts,^{18}which in turn support the formulation of choice-rules.^{19}When such rules are specified, a specific version, (TCS), of the theory-choice postulate,^{20}is assumed. In general, (TC) follows from (TCS),^{21} therefore any specific epistemology with this structure is a model of a standard epistemology. Specific normative epistemologies also assume a specific version, (RCS), of (RC).^{22} The methodology of a standard epistemology is the set of its rules together with (TCS) and, eventually, (RCS).^{23}
The most original feature of Hattiangadi's epistemology consists in that the whole system is based on the concept of scientific problem. First, for Hattiangadi, the very notion of scientific theory involves a reference to problems. Theories are conceptual systems in which problems arise, and which are solutions of previous problems. Theories are thus essentially linked to problems, so that we cannot separate them either from the problems which they are designed to solve or from the problems which they raise. This is an important insight about the nature of scientific theories, an insight which has also been expressed by Popper:
My fourth point is that every attempt (except the most trivial) to understand a theory is about to open up a historical investigation about this theory and its problem, which thus become part of the object of the investigation. (Popper [1972], p. 177)Second, the evaluation of theories is ultimately based on the consideration of problems.^{24} In fact, the four evaluation-concepts which Hattiangadi proposes (dominance, standing, viability, and value of a solution) all involve an essential reference to problems (see Section 1). This idea distinguishes Hattiangadi's view from the majority of the standard epistemologies, which are mostly concerned with concepts like (empirical) content, accuracy, simplicity, fruitfulness, confirmation, corroboration, etc. Since these concepts have not led thus far to a satisfactory theory of science, Hattiangadi's problem-based alternative deserves careful attention. Nevertheless, the critical analysis of the preceding section has also shown that Hattiangadi's proposal for a new epistemology has serious difficulties.
We can also wonder whether Hattiangadi has fully exploited the idea that focusing on problems is crucial for a correct understanding of the development of science. This doubt leads us to question the very structure of all standard epistemologies. These systems essentially focus on the process of theory-choice, which is accorded a sort of special status for understanding science. The underlying idea is that if we were able to explain how scientists choose theories, we would have the key for understanding the whole scientific activity and its historical development. Even though this assumption has been, and still is, widely accepted by philosophers of science, its implausibility is quite striking. The process of theory-choice is only a part of the whole complex of scientific activities, and to assume that the dynamics of science can be understood by primarily considering just this process is a conjecture which needs some justification. There is no prima facie evidence in favor of this assumption, but instead there is indirect evidence against it, for all standard epistemologies have thus far failed to give a satisfactory account of the overall development of science.
There is perhaps a historical reason for the central place which the study of the process of theory-choice has acquired in the contemporary philosophy ofscience. This can be traced back to Reichenbach's distinction between the context of discovery and the context of justification, and to the long accepted view that philosophy of science could only be concerned with justification, whilediscovery should be investigated by other disciplines, such as psychology, sociology, history of science, etc. This view is connected to the idea of an essential difference between justification and discovery. While the first would be a rational process, the second would lack this character. Therefore, only justification could undergo a philosophical analysis, while discovery would be the object of specific scientific disciplines. But the clearcut distinction between the two contexts is no longer tenable in the light of the most recent epistemological debate, so that also the central role of the theory-choice process needs to be revised.
Laudan's analysis of the context of pursuit might seem a first step in this direction. For Laudan, to understand the dynamics of science, we must not only consider the theories which scientists accept, but also the theories on which they choose to work, without necessarily committing themselves to their acceptance. Laudan's analysis of pursuit, however, exclusively focuses on the conditions under which the choice to develop a theory is rational. Hence, also Laudan's epistemology maintains theory-choice as its primary object.
If philosophy of science aims to understand science, and its development, in all the relevant aspects, then, besides the context of justification, also discovery is its proper object. Perhaps the most interesting feature of a problem-based approach is that it seems to provide a framework for a unified account of both justification and discovery. Hattiangadi's epistemology shows that the conceptof problem can be used for constructing an explanation of how theories are accepted or rejected. Hattiangadi, however, has not exploited the full potential of this approach, since he has not tried to explain in detail how problems lead to the development of existing theories and to the creation of new theories. An adequate theory of science should deal with these issues, and also with the more traditional questions about acceptance and rejection. Focusing on problems seems to be a promising strategy for elaborating such a theory.
Department of History and Philosophy of Science
Indiana University
NOTES
* I wish to thank Prof. Noretta Koertge for her comments, suggestions, and criticisms.
1. Progress and its Problems (Laudan [1977]) had been published before Hattiangadi's papers, but, as it results from Hattiangadi's autobiographical remarks, his theory was developed independently (see Hattiangadi [1978], pp. 346-7, and p. 355: 'I had for many years ... their history').
2. Hattiangadi uses 'intellectual tradition' and 'intellectual debate', more or less, as synonyms, and they correspond to what I call here 'intellectual debates'. My 'traditions' are called, by Hattiangadi, 'subtraditions', and, sometimes, 'main lines of a tradition', or 'lines'. The problem with Hattiangadi's terminology is that he does not draw a clear distinction between subtraditions (or main lines) and lines. This distinction becomes crucial when he introduces the concept of dominance of a main line upon another main line.
3. This property of lines in a tradition might
be called the conservation-property.
No previous problem is ever
lost along a line. If some problem which arises in theory T_{i}
of a line is not solved together with the other problems which arise in
T_{i}, all the problems of T_{i} remain open, until
a subsequent theory, T_{j}, closes the line. When T_{j}
closes the line (as in [6]) all problems of T_{i} become solved
problems of T_{j}. Note that the closing of the line might not
happen immediately, as in [6]. It might occur much later in the development
of the line. The effect would however be the same.
There is another important property of lines. This
can be called the non-recurrence property (see Hattiangadi [1979],
p. 54: 'But it is ... that line'). In one line, no solved problem reappears
in a successive theory. There is a minor difficulty with this property.
Schema 5 in Hattiangadi [1979], p. 57, has one line which does not satisfy
the non-recurrence property. Specifically, problem B occurs twice in the
same line. I take this to be just a slip of the pen.
4. I must here point out that the concept of expulsion, and the elaboration of the notion of line based on the distinction between solved and closed problems, are not Hattiangadi's. His theory simply lacks a clear notion of line, which, however, is crucial for introducing the concept of dominance, and standing, of a tradition with respect to another tradition. I maintain that the interpretation I give here grasps Hattiangadi's intuitions. However, the main critical points I will make later are independent from this interpretation. This interpretation has the only function to make sure that Hattiangadi's theory can be elaborated so that it is, at least, formally adequate.
5. There is a further problem with this definition. Hattiangadi states the definition for lines, but it is clear that they are main lines, so that they correspond to what I call here traditions (see also footnote 2).
6. I will comment more on these evaluation-concepts in Section 3.4, since they are the basis of Hattiangadi's methodology (see also footnote 15 and Section 4). For the definition of value of a solution see Hattiangadi [1979], p. 60: 'The greater ... the tradition'.
7. There is a minor difficulty with this terminology. Hattiangadi also uses discriminatory in a different sense. A discriminatory problem is a problem whose eventual solution affects the standing of two traditions. If we take this meaning of discriminatory, then all non-common problems, and at least some common problems, are discriminatory, so that, if we are not careful in distiguishing the two senses, we arrive at a plain contradiction: some common problems are both discriminatory and not discriminatory. To avoid this unpleasant consequence, we can retain only the first sense of discriminatory ( = non-common). The second sense can be captured by the concept of value of a solution.
9. It is, however, worth noticing that Hattiangadi's answer to this question heavily rests on the assumption that our 'natural' logic is classical. This assumption is not uncontroversial, it is for instance challenged by those logicians who believe that relevant, and not classical logic, is the underlying structure of our informal reasoning. A part from this difficulty, Hattiangadi's answer also seems to overlook the effectiveness of pragmatic devices in keeping separate potentially inconsistent beliefs. It seems that our need of solving inconsistencies is not so urgent, and so frequent, as Hattiangadi claims.
10. See Kuhn [1962], pp. 25-6: 'first is ... sort of fact', and pp. 27-8: 'In the more mathematical ... a stable solution'.
11. X is an inconsistent (consistent) set of statements iff Cn(X) is inconsistent (consistent), where Cn(X) is the set of all the logical consequences of X. Similarly for statements.
12. Contrary to the usual terminology, according to Hattiangadi, the explanatory power of a theory, I, is not necessarily unique. This follows from his definition of thisconcept (see Hattiangadi [1978], p. 359: 'Corollary to ... selecting solutions').
13. Besides the difficulties which I discuss in the text, this thesis is also affected by a minor one. Hattiangadi gives two distinct characterizations of the logical structure or problems. I have presented the first in the previous paragraph. The second is in Hattiangadi [1979], p. 50: 'Suppose ... structure of problems'. It is never completely clear which logical structure (the first or the second?) all problems are supposed to share. I am assuming here that this common structure is given by the first theory, the 'official' logical theory, which Hattiangadi has discussed throughout his [1978] paper.
14. It is not even clear whether the eventual solution of this difficulty would be sufficient for harmonizing logical and historical theory. The notion of a theory which has many, different, problems would also be needed. It is not prima facie clear how an inconsistency-view of problems can accommodate this concept.
15. What I call evaluation concept is usually called standard, criterion, and, sometimes, (cognitive) value.
16. If a scientist were not a good historian, he might easily choose the wrong theory. He might, for example, prefer T_{8} to T_{4}, because T_{8} unifies two theories, like T_{4} does, but, in addition, T_{8} solves more problems.
17. Hattiangadi's structural theory is provided by his historical theory of problems. More precisely, a scientific theory is defined as the solution of a problem in a given tradition.
18. Hattiangadi's evaluation-concepts are: dominance, standing, viability, and value of a solution (see Sect ion 2).
19. Hattiangadi's choice-rule is (R) (see section 3.4).
20. Hattiangadi's specific version of the theory-choice postulate is assumption (b) (see section 3.4).
21. In fact, in Hattiangadi's epistemology, (TC) follows from (b) (see Section 3.4).
22. Hattiangadi's specific version of the rationality-postulate is assumption (a) (see section 3.4).
23. Instances of standard epistemologies are: logical empiricist views of science, Popper's, Lakatos's, and Laudan's epistemologies. All these theories are also normative. Examples of nonstandard epistemologies are Kuhn's and Feyerabend's theories. These theories are nonstandard because they assume the negation of the theory-choice postulate. In fact, according to Kuhn and Feyerabend, there are no shared rules for the acceptance or rejection of theories. Toulmin's theory (see [1972]) might be classified as 'semi-standard', since the theory-choice postulate is accepted in a weaker form - scientists choose theories according to rules, but these rules vary over time. The most recent developments ofLaudan's thought (see [1984]) go in the same direction.
24. Laudan's book Progress and Its Problems
([1977])
also stresses the importance of problems for the evaluation of theories
(see also footnote 1).
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