Curt Ducasse, Philosophy as a Science, 1941


The Empirical and the Theoretical Tasks of Any Scientific Inquiry

IN THE development of any scientific inquiry -- it makes no difference what its subject matter may be -- experience and reason play parts equally indispensable. To torture the word "experience" in such manner as will pack into its meaning the part of reason, or to do conversely, is a futile procedure whose only fruit could be to save the mere label "empiricism" or "rationalism" for use as an epistemological battle cry. But discernment of the roles of experience and reason in knowledge eliminates the casus belli itself and therefore also the need for battle cries.

1. Experience and Reason. -- A science begins by attempting to discover laws -- regularities -- among its primitive facts. Certain of these facts are observed to resemble one another in certain respects, and these mutually resemblant facts are sometimes observed to be regularly correlated with certain other facts also resembling one another in certain respects. The outcome of such observations is the conceiving of kinds (of which various primitive facts or their elements are cases), and the detecting of the empirical laws we commonly call the properties of things.{1} These laws are more or less venturesome generalizations of the regularities that were found among the facts observed: we venture to believe that they are present also among the unobserved or not yet observed facts of the same kinds.

Even when additional observations confirm the validity of the generalizations, however, the scientific mind is not satisfied. It insists on asking not only what laws there are but -- also why they are what in particular they are; what the exact scope of each is; and whether or how they are connected with one another. It seeks not only knowledge but also understanding of the laws of the field it studies. But demand for explanation of a law empirically discovered is not met by subsumption of it under another more general empirical law. That wax melts when subjected to heat is not explained by mention of the fact that all solids do so under the influence of heat. Explanation of an empirical law is provided only by theory -- by a theory of the sort of fact which the law merely asserts. And the construction of theory is that part of the development of a body of knowledge in which the requirements of reason dictate most completely and obviously. It is, however, already at their behest that we insist on generalizing our observations -- on postulating that the regularities we have experienced are not limited to the particular set of cases in which we have actually experienced them.

Theory, however, is not independent of and, still less, opposable to experience, for the theorizing is about the very laws that observation and experiment have discovered. Moreover, as theory develops, laws hitherto unsuspected are deduced from it, and experience comes gradually to function not so much as a source of material for inductive generalizations, but more and more rather as a test of the validity in experience of laws obtained deductively from theory about certain experienced facts.

This broad sketch of the roles of observation or experience and of reason in the development of scientific knowledge in general is applicable not only to the natural sciences but also to mathematics. E. Goblot{2} points out that

It is through trials that Pythagoras seems to have discovered the curious properties of certain numbers and of certain series of numbers. In this way he found that the sum of consecutive odd numbers is always a perfect square. The sums of consecutive whole numbers and the sums of even numbers also have general properties. Nowadays we should write them as follows:
1 + 2 + 3 + . . . . + n = (n (n + 1))/2

1 + 3 + 5 + . . . . + 2n-1 = n^2
1 + 4 + 6 + . . . . + 2n = n(n+1)

It is one thing, however, to discover empirically such properties of certain numbers, and to confirm more and more, by means of more and more extensive observations of particular numbers of the same kind, the generalization which extends these properties to all numbers of that kind; and it is another thing to prove, deductively, that the properties necessarily hold of all numbers of the given kind. The attempt to provide deductive proof of them, or of other mathematical propositions already for one reason or another regarded as probably true, and to deduce new ones from the same premises, is the sort of task that engages most of the attention of mathematicians.

In the natural sciences, on the other hand, especially in those in which theory is not yet greatly advanced, the task of discovering valid empirical generalizations looms much larger than it does in mathematics. But both sorts of tasks are present in each case. The fundamental difference between the natural sciences and mathematics is not that the method of the former is exclusively empirical and that of the latter exclusively deductive, but that the entities whose properties the natural scientist investigates experimentally are entities merely presented to him by perception, whereas those whose properties the mathematician investigates (also experimentally) are entities created by his own verbal stipulations. The operations to be performed in experimental investigation of the former accordingly are physical operations; in the case of the latter, they are arithmetical or other mathematical operations. But in both cases alike there remains the difference between simply finding, after performance, that a certain operation upon certain entities does have a certain outcome, and proving, independently of such performance, that it must have that very outcome. It is therefore not from difference in this respect that the contrast arises between the probability of natural laws and the necessity of mathematical theorems. It arises on the contrary from the fact that in mathematics all the properties of the entities to be studied are implicitly fixed by the stipulations which created these entities, whereas in natural science the properties of the entities to be studied are not fixed by perceptual observation, since perception does not create but only discloses these entities.

The statements of the defining properties of mathematical entities thus are stipulations, not hypotheses, and their defining properties are therefore known with certainty to start with. But the statements of the defining properties of natural entities always remain hypotheses only, and their defining properties (viz., those from which all their remaining ones can be inferred) are therefore not known to start with but only to end with, and then not with certainty but only with a degree of probability always short of the highest.

In philosophy, observation and theory -- experience and reason -- likewise both enter, and the role of each there is of essentially the same nature as in all other knowledge-seeking enterprises. To show that this is indeed the case, we need first to consider more carefully what exactly theory is in general, and what function it performs, and then to point out of what sort the empirical generalizations of philosophy are, and how the validity of any theory which philosophy constructs to explain or demonstrate them is to be empirically tested. To the first of these two tasks the remaining sections of the present chapter are devoted.

2. Theory, Conjecture, and Law. -- It is sometimes said that a theory is the sort of thing which, when it has received enough confirmation, acquires the status of a law. Theory in this sense of the word would be synonymous with conjectural law. For example, one notices that various pieces of wax have been exposed to heat and that they have melted. One then may form the theory, that is, the conjecture, that when wax is exposed to heat it always melts. This is a conjecture concerning a law of the behavior of wax, i.e., concerning a property of wax, and if experimental investigation confirms it, we then describe the proposition no longer as a theory or conjecture but as a now known law of the behavior of wax.

Theory in the sense of conjecture, however, has no special connection with laws, for there are conjectures that concern not laws but particular facts. An example would be the theory or conjecture that Bacon and not Shakespeare wrote Hamlet. It is obvious that if ever this theory should be proved, the proposition that Bacon wrote Hamlet would not thereupon become describable as a law; for a law is a proposition concerning any case of a given kind, not concerning one particular fact, whether conjectural or established. But although some theories (in the sense merely of conjectures) are thus not conjectural laws, the theories which are about laws -- whether in the sense of being conjectural laws, or in another sense to be described later -- are always at least conjectures, since otherwise we should call what they assert not theory but known fact.

3. Theory as Explanatory Conjecture. -- "Theory," however, seldom means simply conjecture (whether in respect to law or particular fact). Usually it means at least explanatory conjecture; and when scientific theories are mentioned, such as Fourier's theory of heat conduction or the dynamic theory of gases, then theory means in addition conjecture explanatory of laws. But before inquiring into the difference between the sorts of conjectures explanatory of, respectively, laws and particular facts, we must first be clear as to what explanation, no matter of what, essentially consists in.

It is sometimes said that science does not explain but only describes -- that it does not tell us why things happen as they do, but only how they happen. But obviously this is not true unless, to begin with, we force upon the question "Why?" some mystical or foolish meaning not intended by those who, day in and day out, ask it and get it satisfactorily answered. I recently had occasion to ask, for instance, why my oil-burning furnace failed to start when the thermostat called for heat, and my question was eventually answered by the statement that it was because the contact points in the electrical relay had become corroded, and whenever this occurs the electric current no longer passes through. This was exactly the sort of information that my demand for an explanation, through the question "Why?" was meant to elicit. To say that even if that information was true it did not constitute explanation would be simply to refuse to use the word "explanation" in the sense it has in ordinary English, and to force upon it instead, ad damnandum, some unusual one. Again, the particular fact that a given piece of wax has melted can be explained, for instance, by supposing that the sun has been shining upon it, and recalling that exposure of wax to heat regularly causes it to melt. The law also, that exposure of wax to heat regularly causes it to melt, can be explained, although the explanation of it would be more esoteric. Without attempting to give it here, we can say that it would consist of a statement that the structure of wax is molecular, and of a description of heat and of melting in terms of molecular behavior.

We may be told, however, that when the explanations offered in these or any other cases are examined, they are found to consist only of descriptions of the explicandum in more general terms. But to say this is obviously to abandon the claim that science does not explain but only describes, and to substitute for it the admission that science does explain, together with the claim that explanation consists of description in more general terms. Even this claim, however, is hardly admissible. To explain the fact that a given piece of wax melted by saying that it was exposed to heat is not to describe in more general terms its having melted; it is to assert the antecedent occurrence of a particular event of another kind, already known to be capable of causing wax to melt. Again, to explain in terms of molecular changes the law that exposure of wax to heat regularly causes it to melt, is to define and postulate a respect of identity between being heated and melting, and to do this could only very elliptically be called describing that law in more general terms.

The essential nature of explanation is much rather that, given an explicandum Q, an explanation of it always has the form: Because P, and if P, then Q. That is, the explicans of a given explicandum always consists of the major and minor premises of some hypothetical syllogism in the modus ponens, having the explicandum as conclusion.{3}

4. No Conjecture Really Explanatory if It Lacks "Predictiveness." -- To be really and not only apparently explanatory, however, a conjecture must imply some facts additional to the facts (particular or general) which it was devised to explain, for otherwise the implicans and the implicate are exactly equipollent, and what is offered as explanation is only a disguised assertion that there is some explanation, plus a mere name by which to refer to that still unknown explanation. And obviously, to give a name to what one is ignorant of does not in the least replace the ignorance by knowledge. Examples of such pseudo-explanation would be that a watch ticks because there is a "ticker" in it, that material objects attract one another because of "gravitation," or that opium makes people sleep because of its "soporific power." The requirement that, if a conjecture is to be really explanatory, it must imply something additional to the explicandum, may be stated otherwise by saying that the conjecture must have some predictive capacity. The question whether the predictions it makes turn out to be true or false is another matter, which determines not whether it is explanatory in kind, but whether the particular explanation it advances is a tenable or untenable one.

The requirement of predictive capacity holds whether the explicandum be a particular fact or a general fact (a law). But predictiveness, in the sense which the word has here, may be equally of past, present, or future events, or of known as well as of yet unknown laws. For to speak of a conjecture as predictive of a fact F means only that F was not one of the facts the conjecture was devised to explain; that, so far as could be seen independently of the conjecture, F was unconnected with these facts; and that F can be deduced from the conjecture.

5. Theory as Conceptually (vs. Causally) Explanatory Conjecture. -- The next thing to consider is the important difference between conjectures explanatory of laws and conjectures explanatory of particular events. The latter are conjectures as to some other particular event. For example, the particular event that this wax has melted is tentatively explained by the conjecture that the wax was exposed to heat, and by mention of the empirically known law that exposure of wax to heat causes it to melt. But a law, for instance the one just mentioned, is not an event, and since only an event, viz., a change or a "non-change," can strictly speaking be a cause or an effect, the conjecture explanatory of a law cannot, as with an event, be that a certain event occurred, which stood to that law as cause to effect.{4} Rather, what explains a law is always something standing to it in the relation of conceptual implicans to implicate; and a theory, in the sense we are essentially concerned with here, is always something standing in that relation to what it explains. The nature of that relation may be clarified as follows.

If we take as explicandum not a law but a particular event, e.g., that this wax has melted, what we offer as explanation of it, e.g., that exposure to heat regularly causes wax to melt and that this wax was exposed to heat, does imply the explicandum but in such a case the implication is not conceptual (rational, theoretical) but causal (empirical); that is, it rests on a law (a property of wax) inductively discovered; and contradiction of it would be contradiction of a law of nature. In the cases where the explicandum is a law, on the other hand, the implication is conceptual in the sense that it rests on a tentative definition -- a tentative stipulation as to what the sort of perceived phenomenon called by a certain name shall be conceived to consist in essentially; so that a contradiction of the tentative explicans would be contradiction in terms.{5} A definition, however, is always an equation -- the expression of an identity -- so that, as Meyerson has emphasized, to explain, in the sciences, is essentially to discover some way of conceiving as identical certain phenomena that are perceived as different.{6} For instance, in the example of the wax, increase of temperature and liquefaction are both conceived as increase of molecular motion.{7}

6. Structure of the Theories Explanatory of Laws. -- The question arises, however, as to how the invention of concepts, through prescriptive definitions, can imply a law of nature, which is a relation not between invented concepts but between kinds of natural events (our concepts of which, when we have any, are empirical, i.e., are not invented by us but dictated to us by inductive observation).

The answer is that a theory explanatory of empirical laws does not consist solely of a set of definitions and postulates creative of certain concepts, but includes also, and indispensably, a method for the identification of the empirical entities that are to be regarded as exemplifying (or as nearly enough, exemplifying) those concepts. That is, the theory includes either a prescription that, or a prescription for deciding whether or not (for purposes of explanation and prediction of the given empirical laws), a given invented concept and a given empirical concept are to be treated as if they were identical, i e, the exemplifications of the latter regarded as exemplifications of the former.{8}

These two parts of any theory explanatory of laws -- the definitions or other stipulations creative of concepts and the operation or method prescribed for deciding what empirical entities shall be regarded as exemplifying the created concepts -- have been called by Norman Campbell respectively the "hypothesis" and the "dictionary" of the theory; by Bridgman (when the theory is mathematical) the "equations" and the "text"; and by more recent writers the "syntax" and the "semantics" of the theory. The second of these two parts is, I believe, what F. S. C. Northrop has in mind when he speaks of "epistemic correlations."{9}

7. Grounds for Choice between Rival Theories. -- If the laws which one theory attempts to explain are incompatible with those which another theory attempts to explain, what we then have is a conflict of data rather than of theories; and the task we immediately confront is not to decide which theory is the better, but which data are erroneous. If, however, the laws which two theories attempt to explain are the same, then the questions in the light of which one of the theories is to be preferred to the other are as follows:

a) Whether one but not the other implies all the laws that were to be explained;

b) Whether, if both do, one but nor the other has predictive capacity, i.e., implies some laws additional to those that were to be explained;

c) Whether, if both have predictive capacity and any of their predictions conflict, observation verifies the predictions of one but confutes some prediction of the other;

d) Whether, if observation bears out the predictions of both, one predicts everything the other predicts, but something more also;

e) Whether, if both are equal in the foregoing respects so far as tested, one is psychologically simpler, i.e., more convenient to use than the other.

If one theory predicts certain laws that observation verifies and that the other theory is not able to predict, and conversely, then we are not called upon to choose between them but, for the time being, we use each for what it alone is able to do, and use either one indifferently for what both alike are able to do. But in such a case the desire for integration of our knowledge, which moves us to the construction of theories, is not satisfied until we succeed in devising some theory which predicts everything each of the others separately predicts.

8. The Facts Which a Given Theory Seeks to Explain Often Derivative. -- In the preceding discussion, the laws which a theory attempts to explain and predict have been described as empirical laws, obtained inductively from examination of some of the primitive facts of the given field of inquiry. It should be clear, however, that the laws to be explained may in a given case be more or less remotely derivative from these instead of obtained thus directly from primitive facts. The structure of a theory -- as in essence consisting of a definition of one or more terms predicated in the given laws and of a method for determining whether any given entity is or is not to be accepted as a case of the definiens -- this structure, and likewise the explanatory and heuristic powers it possesses if it meets the tests of validity described, remain the same no matter how the laws given as explicanda in a particular case may have been obtained.

Moreover, in view of the tendency already pointed out that derivative facts will bulk larger than primitives in the picture of an inquiry as it develops, we may expect the laws with which most of the theories in a given field concern themselves to be more or less remote derivatives of that field; and in the statements of these, no explicit mention of the primitives will occur. This will be true in philosophy as well as in other sciences, and will mean that although appraisals are the primitive facts of philosophy, the majority of the terms for which philosophy has to seek valid definitions will not be terms of appraisal. They will be terms standing not for primitive philosophical facts but for facts which are philosophical only because implicit in the philosophical primitives.

When the facts -- whether philosophical or other -- which a theory attempts to explain are not laws directly obtained by induction from the primitives of the given field, but are derivatives from these, they can be described as empirical only in the sense that, no matter how abstract they are, their factuality has nevertheless indirectly been put to empirical test. Accordingly, the contrast between a theory and what it is about is better described as one between quaesitum explicans and data explicanda than as one between reason or theory on the one hand, and observation or experience on the other. As Whewell has pointed out, once we have accepted a theory, we describe our observations in terms of the concepts of it as a matter of course; and yesterday's successful theories thus tacitly permeate today's descriptions of empirical facts.{10}

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{1} Failure to distinguish between qualities and properties breeds endless difficulties. For this reason, it is important to bear in mind that a property is the sort of attribute that always has the form of a law. Thus in the case of properties of the entitles of nature, to say that entity O has property P is to say that O is such that if a change of kind A occurs in environment of kind E of 0, a change of kind B regularly occurs in O. Cf. Emile Meyerson, Identiti et realite, pp. 33 f. Or in some cases, to say that O has property P is to say that O is such that whenever O has property Q it has also property R (and sometimes also that whenever it has R it has Q.) In the case of a mathematical entity, e. g., the number 17, to say that it has the property of being "prime" is to say that it is such that if the arithmetical operation called division is performed upon 17 then the remainder is 0 when and only when the divisor is either 17 or 1. Opinions, beliefs, dispositions, habits are similarly properties of the minds that have them, in the sense of being laws of these minds: being Republican is a property of the mind of Herbert Hoover in exactly the same sense of "property" as that in which being malleable is a property of certain pieces of steel. Cf. the writer's "On the Attributes of Material Things," Jour. of Phil., XXXI, No. 3 (Feb. 1934).[Back]

{2} Essai sur la classification des sciences (1898), chap. ii, p. 27. [Back]

{3} The major premise of the hypothetical syllogism must consist of some law of connection, whether causal or conceptual. That is, no basis for explanation is provided by a law of mere joint incidence. For example, that giraffes have cloven hoofs is not explained by the fact that giraffes are ruminants and the conjecture that all ruminants have cloven hoofs. [Back]

{4}The two notions of "cause" and "agent" are often not discriminated. For instance, we say loosely that a given person caused a certain accident, but strictly speaking it was an act of a volition of that person, i. e., an event, which, under the circumstances existing at the time, caused the accident. An agent -- a doer - is a being, a certain change in whom (or in which) causes a certain change in something else. If desire for the latter change was the cause of the change in the agent which itself caused the change in the other entity, then the agent is a purposive agent and the causation is teleological. Another use of the word "cause" is that of Meyerson. By "cause" he means the "sufficient reasons" of a law, not the "sufficient reason" of an event. This usage although deliberate, is unfortunate because it clashes with the sense in which the word is ordinarily used. But Meyerson would agree -- indeed insist -- that what explains a law (whether or not it be called the "cause" of the law) is not an event. [Back]

{5} Cf. Hume's distinction between denial of assertions as to matters of fact and of assertions as to relations of ideas (Inquiry Concerning Human Understanding, Part I, sec. iv) and Carnap's distinction between the P-rules and the L-rules of language (P. L. S., pp. 50 f.). [Back]

{6} Meyerson, op. cit. The principle of "causality" i. e., as he uses the term, the principle of explanation, "is but the principle of identity applied to the existence of objects in time" (p. 38), and "where we employ it, the phenomenon becomes rational, adequate to our reason: we understand it and are able to explain it" (p. 35). This statement of Meyerson's, however, applies only to explanation of laws. But there is also such a thing as explanation of particular events, and in their case explanation consists not in conceiving as in some way identical two things perceived as different, but in suggesting an adequate cause-event. [Back]

{7} In the case of a particular event it seems possible to ask both for a conceptual (rational, theoretical) and for a causal (empirical) explanation. To ask for the latter is to ask what other particular event probably caused the given one. The particular event which was the cause explains no other particular event of the same kind. It therefore explains a strictly unique particular. But to ask for a conceptual explanation of a given particular event is to speak elliptically, for strictly it is to ask how any event of its kind (and therefore also itself) must be conceived in order to account for the laws of occurrence of events of that kind. And explanation in this sense is not explanation of, uniquely, the given particular event. [Back]

{8} Kant's contention that the pure categories of the understanding are heterogeneous to empirical intuitions, and that, to render the former applicable to the latter, or the latter recognizable in the former, there must be available a third thing, homogeneous with both, viz., the "transcendental schema" of the understanding. [Back]

{9} Campbell, op. cit., p. 122; Bridgman, op. cit., p. 59; J. H. Woodger, The Technique of Theory Construction, p. 6. It is from Whewell, however, that the writer first gained the general idea of the structure of theories. Cf. in particular the following passage from the Novum Organum Renovatum (Bk. II, chap. ii, sec. ii, art. 7): "It is very important for us to observe that these controversies [about the right definition of certain terms in science] have never been questions of insulated and arbitrary definitions, as men seem often tempted to suppose them to have been. In all cases there is a tacit assumption of some Proposition which is to be expressed by means of the Definition, and which gives it its importance. The dispute concerning the Definition thus acquires a real value, and becomes a question concerning true and false."

Campbell points out that a theory cannot be said to explain a law merely if the theory is such that the law can be deduced from it. In addition, he believes, the proposition of the "hypothesis" of the theory must display an analogy -- be similar in form -- to the laws the theory is to explain. But he does not specify how we can tell whether such analogy is present, or present in sufficient degree, or in relevant respects. And in the absence of specification of this, one may say that some analogy can, with sufficient ingenuity, always be exhibited. It seems to me that the only test of the relevance and sufficiency of any analogy exhibited by the "hypothesis" of a theory is whether the theory possesses predictive capacity in the sense already stated, and therefore that if this requirement is satisfied, that of analogy is superfluous. [Back]

{10} See, e. g., Nov. Org. Renov., Bk II, chap. v, sec. i, art. 4. In general, Whewell's account of scientific method anticipated modern views of the subject much more closely than did J. S. Mill's, which overshadowed Whewell's in its time. [Back]

[Table of Contents] [Chapter 12]