Jacques Maritain Center :
Theories of Knowledge / by Leslie J. Walker, S.J.§ 287. The third problem of the theory of knowledge, the problem of validity, is so intimately bound up with the second problem, the conditions of knowledge, that it is impossible to keep the two distinct. This will become more and more apparent as we proceed. We shall find that Absolutism, because it is Absolutism, has an Absolute theory of truth, a theory in which truth is regarded as an ideal whole, embracing interdependent parts, none of which are true in abstraction from the rest. In Absolutism the doctrine of reality is prior to the doctrine of truth, and both the nature and the criteria of the latter presuppose and are determined by the metaphysical conditions of knowledge. Pragmatism, on the other hand, starts with tbe criteria of truth, and hence infers, first its nature and then its metaphysical conditions. Consequently, in treating of the philosophy of Pure Experience before we treated of tbe pragmatic doctrine of truth, we have really been considering the conclusion -- at any rate, in the case of Professor James -- before we examined the premises. This was necessary owing to the general method we adopted in the beginning, and I do not think it should lead to misunderstanding; for although every theory of knowledge, if it is to be complete, must treat of psychological, metaphysical, as well as epistemological problems, a man may be a pragmatist in method without being a pragmatist in metaphysics.
The strictly epistemological aspect of Realism is no less essentially connected with its metaphysics than is that of Absolutism. The Causal theory, the theory which maintains that all knowledge, in so far as it is in truth knowledge, is determined by its object, is characteristic of Aristotelian Realism from whatever point of view we regard it. Primarily, it is a metaphysical theory; but it pervades also the realist's doctrine of truth. and it characterises also his psychology, whenever the latter is explanatory and not merely descriptive. Nay, even in descriptive psychology we find traces of causality, for causality, as I have already pointed out, seems to be directly revealed in many of the processes of our active conscious life.
§ 288. Having discussed, then, the various theories at present current in regard to the metaphysical conditions of knowledge, we must now proceed to examine how far these theories affect the validity and significance of knowledge, and, incidentally, how far preconceived views in regard to the validity of knowledge have reacted upon and determined metaphysics. It would, however, be sheer waste of time to discuss the validity of knowledge and the criteria of truth, if knowledge itself be a nonentity and truth an unattainable ideal. It would be useless to try to distinguish what is true from what is false, if everything is false and nothing true, Unless we have some knowledge and some truth it is absurd to talk of knowledge and truth at all. This, in general, is admitted by every philosopher, and is presupposed by the fact that he is a philosopher. Yet, though no philosopher nowadays is guilty of so glaring a self-contradiction as to profess to be an out-and-out sceptic, some philosophers seem to approach dangerously near to this fatal inconsistency and their philosophies to be impregnated, in consequence, with a suicidal tendency. No philosopher professes to know that knowledge is impossible, nor does he declare in so many words that so far we know nothing at all for certain; yet this is the logical conclusion which seems to follow from current theories as to the effect of development in knowledge upon its validity, just as it follows from current theories as to the conditions and ultimate origin of knowledge. To this conclusion I cannot give my assent, for it seems to destroy knowledge altogether and to land us at least in negative, if not in positive, scepticism. I argue, therefore, that as the conclusion is false there must be something wrong with the premises. This I have already endeavoured to show so far as concerns the origin and conditions of knowledge, and have also stated in outline an alternative theory which does not lead to this undesirable conclusion. In the present chapter I propose to discuss the question of development in knowledge, and to show that development and validity are not incompatible.
§ 289. Development, we are told, implies an intrinsic and essential modification in knowledge of so radical a nature that what appears to be knowledge may not really be knowledge at all. This view of the development of knowledge may be derived from two sources, either by inference from a theory as to the nature of development in knowledge, or from a study of alleged facts in regard to developments which have actually taken place. In either case the result is the same knowledge is a fraud and an illusion. But while both the absolutist and the pragmatist seem to adopt this sceptical attitude the absolutist does so because it is the logical outcome of his theory that all knowledge is a 'reconciliation of antitheses in a higher synthesis,' the pragmatist because he thinks that, knowledge having undergone so many trausmutations in the past, there is no reason to suppose that our present knowledge will not be subject to a like corruption. Neither of these methods of establishing the invalidity of human knowledge seem to me themselves to be valid. But while it is comparatively easy to show that the argument of the absolutist is fallacious because it is based on a misconception of the nature of 'reconciliation'; it is a very different matter to attempt to answer the arguments adduced by the pragmatist. Indeed, to do so would involve a careful study of the history of every branch of human knowledge. This of course is impossible here, much as such a study is needed. Yet as the pragmatist contents himself with general statements, and as a particular negative is the contradictory of a universal affirmative, I shall be content if I can show that some propositions, and some general laws, and some branches of knowledge have not undergone a change which is radical enough to render them unreliable and uncertain.
§290. The principle of 'reconciliation of antitheses in a higher synthesis' defined by Dr. Caird as "a solution of the antinomy between opposing principles which seem to have an equal or similar claim to our acceptance, by means of a regress upon the ultimate conditions of knowledge or thought-conditions which are presupposed in the controversy itself." So much for the general principle of a 'critical regress.' It is applied, however, not only to divergences in philosophical principles, but also to every kind of divergence and every kind of difference, whether ontological or logical, whether pertaining to categories, propositions, or theories. The doctrine of Unity in Difference and the Dialectic method of reasoning from thesis through antithesis to a higher synthesis is characteristic of every aspect of Kantian and Hegelian philosophy. We have seen how this principle is applied by Kant. The opposition between physical science and philosophical theory is solved by a distinction of the sphere of the practical from that of the speculative Reason. Materialism and Spiritualism are reconciled by Faith; while the opposition between the speculative and the practical Reason is itself solved in the Critique of Judgment, where the universe is regarded teleologically as the manifestation of Divine Reason. It is in the third Critique that the 'principle of reconciliation' is especially prominent; but it is by no means confined to that Critique. It appears in the Kantian categories, which are arranged in sets of three, the 'third' category in each set being the synthesis of the second with the first. Thus totality is plurality regarded as unity. Again, Kant defines judgment as "simply the way in which given ideas are brought together under the unity of apperception." Thus we have (1) the thesis or simple assertion of a thing (2) the antithesis or determination of it by distinguishing it from other things -- 'omnis determinatio est negatio;' and (3) the synthesis or "redintegration of the elements thus differentiated and related." That is to say, objects are "first determined as things in themselves, then as related one to another; and finally as a system of distinct yet inter-related parts within the unity of thought as their centre." Judgment, therefore, may again be defined as "at once the distinction of objects from and their relation to each other, and their distinction from and relation to the thought for which they are."{1}
§ 291. Psychologically, the principle of a synthetic reconciliation of differences is well known under the name of Apperception; and is admitted on all sides. Knowledge is a growth. It develops by differentiation and integration rather than by mere accretion, for a new truth usually modifies to some extent our previous knowledge of the subject to which it pertains. Professor James thus describes the process by which an individual settles into new opinions:
The individual has a stock of old opinions already, but he meets a new experience that puts them to the strain. Somebody contradicts them; or in a reflective moment he discovers that they contradict each other; or he hears of facts with which they are incompatible; or desires arise in him which they cease to satisfy. The result is inward trouhle to which his mind had hitherto been a stranger, and from which he seeks to escape by modifying his previous mass of opinions.{2}
Or, again, in more characteristic language
Our past apperceiver and co-operates; and in the new equilibrium in which each step forward in the process of learning terminates, it happens relatively seldom that the new fact is added raw. More usually it is embedded cooked, as one might say, or stewed down in the sauce of the old . . . New truths are thus the resultants of new experiences and of old truths combined and mutually modifying one another.{3}
Le Roy expresses a similar idea, when he says "Progress is a conquest of the obscure, of the unintelligible, almost of the contradictory." And Blondel, "Action is a continuous state of unstable equilibrium, and . . . each attempt to satisfy an actual need reveals further needs qui s'imposent moralement l'action."
Both Pragmatism and Criticism, then, accept this principle of development as a psychological law; and Hegel in his History of Philosophy has applied it to the growth of the mind of humanity in general. But when we examine this principle more in detail, and try to explain its working and to apply it to the theory of knowledge, we find at once a divergence of opinion.
Pragmatism insists that some new idea must "mediate between the stock and the new experience." Its function is "to preserve the older stock of truths with a minimum of modification."{4} "Our minds grow in spots; and like grease-spots, the spots spread. But we let them spread as little as possible we keep unaltered as much of our old knowledge as we can."{5} Hence, for the pragmatist, the 'mediating idea' does not necessarily lead to a 'higher synthesis.' On the contrary, we prefer usually to 'patch and timber' old prejudices and old beliefs, so as to admit the novelty which is forced upon us. Moreover, these ideas through whose mediation old truth grows, are 'new' ideas; we make them; they did not exist before; they are additions to our former stock. And they are true ideas precisely in so far as they perform satisfactorily their function of mediation. "Our thoughts become true in proportion as they successfully exert their go-between function."{6}
§ 292. The pragmatist, then, explains the growth of knowledge by the mediation of new ideas or Denkmittel; the Hegelian by the modification and higher synthesis of the old. Let us illustrate this by an example. The idea of radium "paying heat away indefinitely out of its own pocket," seemed, says Professor James, to violate the law of Conservation of Energy. The contradiction was avoided, however, by supposing that "the radiations were nothing but an escape of unsuspected potential energy, pre-existent inside of the atoms" -- an hypothesis which was confirmed by the discovery of helium. The new idea -- or, in the language of Avenarius, the beibegriff -- which mediates here, is the escape of unsuspected potential energy. The Hegelians may object, however, that this is no new idea, for 'potential energy ' was already known, and all we do now is to suppose that it can, as Professor James puts it, 'escape;' and to this the pragmatist might reply that at any rate the 'possibility' of its escape is a new idea, and that in this way we have come to know a difference of energy, of which we were formerly ignorant. Certainly the idea of potential energy 'escaping' is new, though, on the other hand, we already had ideas of 'potential energy' and of 'escapings.' Let us, however, substitute for Professor James' picturesque account of radio-activity the scientific explanation, and see what kind of modification it has introduced into previous theories.
Radio-activity is supposed to be due -- so I understand -- to the disintegration of the relatively complex atom of radium into the less complex atom of helium, in which process the internal energy of the former is transformed into electrical and thermal energy; hence the 'waves' and the rise of temperature. The argument is one from experienced effects (electrical, photographic, luminescent, chemical, and even physiological) to presupposition or cause (internal disintegration of the atoms) -- a type of argument that we have met with before. But the question which is of interest for us is whether the Electron theory -- for it is this which has been modified, if any -- has been so modified by this postulated disintegration of the atom of radium as to render previous accounts of it not only inadequate but false. It would not matter much, perhaps, if this were so, since the atomic structure of material substances is a hypothesis and not an established truth. But, as a matter of fact, it is not so. The idea of atomic disintegration is not only compatible with, but, according to Sir Oliver Lodge, was already potentially contained in the theory of Lorentz, Larmor, and J. J. Thomson, which affirms that the atom is a positively charged nucleus around which are grouped relatively small and negatively charged electrons. Whether the doctrine of Conservation is saved by this 'regress' will depend, of course, upon the validity of the Electron theory. But, at any rate, we have here a regress which reconciles pro tem pore an apparent contradiction, not by showing that both the antitheses were false and reuniting them in higher synthesis, but by denying one of them altogether (viz., the assertion that in radioactivity energy is lost) and re-affirming the other.
§ 293. This kind of reconciliation is typical of the way in which theories develop. The growth of knowledge does not necessarily involve the negation of a previous thesis, but rather its amplification and when this is the case, as it often is, I can find no sense in which the reconciliation effected can be called a 'higher' synthesis, unless all syntheses are to be called 'higher' which make knowledge fuller and more complete.
The 'higher synthesis' of the Hegelian, however, means more than this. It means a synthesis in which all the differences remain and yet are intrinsically changed in some mysterious manner by the synthesis. Unfortunately, the Hegelian is not fond of illustrating his doctrine of 'reconciliation in a higher synthesis,' and perhaps I have misinterpreted its meaning in my application of it to the above example of a scientific regress. But I do not think that I have. The general doctrine and its consequences seem to be clear enough; and though it is applied primarily to the universe as a whole, we know that for the Hegelian thought and reality are one. In all forms of Absolutism, the endeavour of human thought is to equate itself with reality, and when this has been accomplished the logical principle of 'reconciliation in a higher synthesis' will be identical with the ontological principle of Unity in Difference. The function of reason, according to Kant, is to guide the understanding in its search for a full and adequate knowledge, of which the final aim is an "absolute totality of syntheses on the side of conditions." And Fichte, starting with the ultimate condition of conditions, the Ego, obtained by a process of analysis and synthesis a logic and a phenomenology or pragmatic (sic) history of consciousness. The rational procedure of the human intellect was thus interpreted, by Fichte statically and by Hegel dynamically, as revealing the inner structure of the universe. And this as a general principle is still characteristic of the attitude of the absolutist. Hence, whatever can be predicated of the inner structure and processes of the universe can be predicated of the structure and processes of thought. As, therefore, the differences which are somehow reconciled in the Absolute undergo an essential modification in the process, it follows that in the synthetic reconciliations which will have to take place in human thought before it is completely identical with the universe, modifications of the most wholesale, radical and indefinite kind will surely occur. Hence the conclusion that human knowledge, which at present is certainly far from adequate or complete, is not strictly knowledge at all, but a construction in which truth and error are inseparably blended and mixed.
The significance of this doctrine will be clearer when we come to treat of Absolute truth, but its sceptical tendency is evident. If human knowledge contains an element of truth, but an element which cannot be distinguished from error, we might as well be without truth altogether, for to possess truth and yet to be ignorant of what it is, is certainly not what we mean by possessing truth. To affirm that all and every part of human knowledge is liable to modification is to affirm that we cannot be certain of anything; and if this is not scepticism, it is something very like it. The Hegelian theory of the development of knowledge follows logically from its metaphysical theory of the universe; and just as the metaphysical theory is inconsistent with facts, so also is the epistemological theory, as we shall see presently. But first I wish to point out that the pragmatist, though approaching the matter from a different point of view, has arrived at the same sceptical conclusion.
§ 294. In Baldwin's Dictionary of Philosophy,{7} we are informed by Mr. C. S. Peirce that Pragmatism is part of a larger doctrine which he calls Synechism. Synechism is "that tendency of philosophic thought which insists upon the idea of continuity as of prime importance in philosophy."{8} "Metaphysically" -- though Synechism professes not to be metaphysical -- "a continuum is something whose possibilities of determination no multitude of individuals can exhaust," while epistemologically it is a conception of the universe of thinking beings as gradually approximating to, but never attaining systematic truth. Man is ever striving toward a more rational and more complete interpretation of the universe, but his knowledge at present is so incomplete and so disjointed that he can never tell how far any one of his theories or even of his propositions about reality may have to be modified in the future. Gradually, however, through the intercourse of many minds, his knowledge is becoming more coherent, and, perhaps, more adequate, and "the becoming continuous, the becoming governed by laws, the becoming instinct with general ideas, are but phases of one and the same process, the growth of reasonableness."{9} All hypotheses must be regarded as 'continuous,' i.e., as subject to further determination, which for us can never be exhausted.{10} Truth grows and will continue to grow. It has had a 'career,' and therefore is going to have a career in the future.
This is obvious enough; but the problem is as to how far future truths have "the power of retrospective legislation." How far will our theories, physical and metaphysical, be modified? How far our axioms ? Will it be beyond all recognition? And will the modification be so radical as to extend even to our 'truest formulae'? Pragmatism, in spite of its admission that we strive to retain old theories with a minimum of change, thinks that it may be so; and Absolutism, in the person of Mr. Joachim, is of the same opinion. Professor James writes
The enormously rapid multiplication of theories in these latter days has well-nigh upset the notion of any one of them being a more literally objective kind of thing than another. There are so many geometries, so many logics, so many physical and chemical hypotheses, so many classifications, each one of them good for so much and yet not good for everything, that the notion that even the truest formulae may be a human device and not a literal transcript has dawned upon us.{11}
Nay, has more than 'dawned upon us,' has led Pragmatism to adopt as a fundamental tenet that our solutions must be imperfect, and that human knowledge is throughout only an approximation to truth.{12} And this must be so, if thought and action are really one, and if our only justification for admitting a proposition or a theory is that it enables us to 'think clearly and act efficiently.'{13}
§ 295. Professor James, indeed, seems at times to be struggling against this sceptical current in the pragmatic stream. He speaks of relations between our ideas, which are irreversible, and of questions to which there can only be one answer.{14} He acknowledges, too, that it is Dr. Schiller who leads the way in this genetic view of truth, though, at the same time, he declares himself a staunch supporter of the English leader.
Surely Professor James has need to hesitate before adopting an attitude so avowedly sceptical. A cursory view of current philosophy and current science may suggest a hopeless confusion; but to a more careful observer there will appear much harmony amid the strife, and much that is true amid what is erroneous or doubtful. There may be two geometries; but meta-geometry is confessedly based on the denial of a postulate which the three-dimensional world of our experience necessitates. There may be several logics; but the logic of Hegel should rather be classed as a metaphysic, and the logic of Pragmatism as a very one-sided aspect of psychology. There may be many hypotheses, chemical and physical; but most do not conflict, and of those which do the majority are based on theories so well-established that upon them further speculation rests as upon an accepted fact. And as for classifications, these are confessedly pragmatic, having utility as their end, and seldom claiming to be more than provisional. Let us, however, examine the matter a little more closely and see whether development does involve a radical change in past belief; whether our knowledge, such as it is, does contradict the claims to truth our ancestors asserted; or whether it is not rather that development adds to truth, enriches it. renders it more adequate and more complete.
§ 296. By far the most important sphere of knowledge which it is necessary to rescue from the corrosive influence of Scepticism is that body of common-sense truths, which, as M. Duhem remarks, are "in the last analysis the source whence flows all truth and all scientific certitude."{15} These truths are not static; they develop. They are not a treasure buried in the ground, but a treasure which everyone shares, which he needs in order to perform the actions of his daily life, and to which he is ever adding by fresh discovery and research. The truths of common-sense grow, and in growing are modified. But the question is whether these modifications affect the main body of truth or only its excrescences. Certainly, if we exclude interpretations of a theoretical kind, legendary stories and local traditions as to the nature and number of the gods, the identification of tribal heroes on account of prodigies long since forgotten and in consequence exaggerated, and the superstitious attributing of natural events to unseen spirits of a superhuman or diabolical character, there remains a vast number of truths which men believe in now and always have believed in. Our environment is much the same as it was two thousand years ago; and the events which occur in that environment are perceived in much the same way and under almost precisely the same categories as they were in bygone ages. We understand perfectly what Herodotus means when he says of the Borysthenes (Dnieper) that
It has upon its banks the loveliest and most excellent pasturages for cattle; it contains abundance of the most delicious fish; its water is most pleasant to the taste its stream is limpid, while all the other rivers near it are muddy; the richest harvests spring up along its course, and where the ground is not sown, the heaviest crops of grass; while salt forms in great plenty about its mouth and large fish are taken in it of the sort called Antacei (sturgeon) without any prickly bones, and good for pickling.{16}
Moreover, Herodotus' account of the general features of Scythia is remarkably accurate; so much so that
it might pass [says Rawlinson] for an account of the same country at the present day. The rivers are still as large as before, and their fish are still abundant. The sturgeon of the Dnieper are still celebrated and the natural salt which is found near its mouth is still of the greatest value. Again, the steppes through which the Dnieper flows are still a corn-growing country, while to the east cattle are even now produced in great abundance.{17}
The knowledge our forefathers possessed of the general sequence of events and of the results which inevitably follow from certain lines of action also was reliable; though, owing to the lack of detailed information, and the absence of any scientific method of induction, they were unable to distinguish the real causes of the sequences they observed, and of their unscientific surmises Herodotus gives us innumerable examples.
§ 297. But perhaps it will be said that I have no right to exclude all that we now call superstition and rash theoretical speculation from the general head of knowledge and then to claim that common-sense truths have developed without any essential or intrinsic change. For it may be contended, in the first place, that the residue is 'mere fact,' and that facts are not knowledge; and, in the second place, that the beliefs of our ancestors, though superstitions, were none the less 'beliefs,' and therefore claims to knowledge.{18}
I have already given reasons for the inclusion of facts under the head of knowledge. Everybody does call acquaintance with facts real knowledge and whatever else facts are they are certainly not 'pure experiences,' for in that case it would be absurd to talk of their getting 'made ' and 're-made.' Facts imply to some extent interpretation; but they differ from theoretical interpretations in that they are more direct, more vague, more haphazard, and at the outset are neither systematised nor co-ordinated. Yet facts do claim to belong to what is generally understood by the term knowledge; while, on the other hand, beliefs of a religious character, as a rule, do not. The superstitious and contradictory beliefs of the ancients were not inferences based upon the data of experience, but were due to ignorance, tradition, or blind and unreasoning faith. Moreover, they have no claim whatsoever to be called common-sense truths, for they were not common to humanity at large, but varied from tribe to tribe; and were frequently looked upon with considerable suspicion by thinking men. The great variety of opinions and beliefs which existed among the Greeks and Romans in regard to the nature, the number, the character and the legendary history of the 'gods,' and the sceptical view of these myths which was taken by Socrates and other philosophers, needs no comment. But observe, too, how in the interpretation even of natural events opinion was tentative, uncertain and varied. Take, for instance, the causes which were suggested in order to account for the madness and death of Cleomenes.
The Argives [says Herodotus]{19} declare that Cleomenes lost his senses and died so miserably on account of these doings (sacrilege and massacre). But his own countrymen say that his madness arose, not from any supernatural cause at all, hut from the habit of drinking wine unmixed with water, a habit which he learned from the Scythians; . . . while, for my own part, I believe that his death was a judgment on him for wronging Demaratus.
Observe, again, how cautious Herodotus is in accepting the legendary histories of tribal heroes and gods; how, for example, while not rejecting altogether the story of Zelmodis, he does not put "entire faith in it, and even doubts whether there ever really was a man of that name;"{20} and, lastly, how when himself endeavouring to account for natural phenomena by natural causes, he seldom claims positive knowledge; but uses, again and again, some such expression as dokeei de moi.
I maintain, then, that the reversals which have occurred as common-sense knowledge has developed, have for the most part affected only (1) traditional and irrational beliefs which were by no means universal, and (2) hypothetical interpretations of natural events which were little more, and as a rule claimed to be little more, than rough guesses. The complexus of common-sense truths has grown rather by increment than by higher syntheses, and the main body of such truths is still left intact. Modern research confirms instead of invalidating the general knowledge which our forefathers possessed of the geographical features of the countries in which they lived, of the periodicity of the seasons, the phases of the moon and the tides, of the species of plants and animals of which no less than five hundred are enumerated by Aristotle in his 'Researches,' of minerals and some of their properties, of the habits and characteristics of man: in a word, of the co-existences and sequences which in general characterised their environment. Nay, further, their very belief in supernatural agencies testifies to their recognition of the principle of causality while the ready credence which they gave to the existence of a region of preternatural phenomena is not without foundation, if we may credit the accounts which are given of that region in the Proceedings of the Society for Psychical Research.
§ 298. The general impression which one gets from a study of knowledge is adverse, therefore, to the sceptical view of development. Can we say the same in regard to theory? In discussing this question, we must remember that theory is at present, owing to the stupendous advance which has been made in scientific appliances, instruments and methods, on quite a different footing from what it was three hundred years ago. The telescope and the microscope alone have revealed a vast complexus of data of which our ancestors never dreamt, and, thanks to modern metrical instruments, measurement and detail is incomparably more exact than ever it was in the past. The Greeks and Romans, the Schoolmen, the astrologers and the alchemists of the Middle Ages had no data upon which to build a scientific theory worthy of the name. Hence, that reversals should have occurred in the realm of theoretical speculation is not surprising. Indeed, the possibility of it was recognised by theorists themselves much more fully, I think, than we are apt to imagine. They appear, moreover, to have distinguished between different parts in a theory, some of which they regarded as of greater probability than others. Thus, according to Aquinas,
there are two ways of arguing. The first way is to bring forward reasons in order sufficiently to prove a certain principle; as in natural science reasons are given sufficient to prove that the motion of celestial bodies is of uniform velocity. The second way is to bring forward reasons which do not sufficiently prove a principle, but which show that with a principle already postulated the consequent effects agree; as in Astronomy the principle of eccentrics and epicycles is postulated in order that on this hypothesis sensible appearances{21} in regard to celestial motions may he saved; but this reason is not sufficient proof, because it may be that on some other hypothesis they can be saved.{22}
The difference between a verified truth and a mere 'claim to truth' was recognised, then, even by one who is generally regarded as a typical dogmatist. And the fact that such a distinction should have been made by the theorists of former ages is of considerable import in the problem of development and validity; for, as a rule, it is in the less essential parts of a theory or system that reversals occur.
§ 299. The one striking exception to this rule in the sphere of scientific research is the Copernican revolution in Astronomy, in which the Ptolemaic system was literally turned inside out by the denial of its fundamental hypothesis. I do not intend to attempt to explain this reversal away, for although Aquinas apparently suspected that there was something wrong somewhere, it can hardly be doubted that most astronomers believed that the heavens really moved round the earth. Being led astray by appearances, they came gradually to regard as a fact what was really an interpretation of a fact, and an interpretation which was not the only one possible, as even the ancients might have inferred from their knowledge that motion through space is relative. The Copernican revolution, therefore, was unquestionably a reversal of an essential principle in previous theory.
In saying this, however, we must bear in mind that this reversal by no means invalidated all the astronomical knowledge that had hitherto been acquired. The precession of the equinox and many other truths were left intact. And it is curious, too, that the principle of uniform 'velocity' mentioned by Aquinas as 'sufficiently proved' should have reappeared in a somewhat different form in the 'first law of motion.'{23} Moreover, the Ptolemaic system, as a system, can hardly have been regarded as proved, for its explanations were inadequate and hard to reconcile with facts. Indeed, the epicycles and eccentrics which are essential to it, were, as we have seen, regarded only as probable and tentative by Aquinas. Lastly, the reversal introduced by Copernicus, Kepler and Galileo, was not a 'higher synthesis of previous hypotheses,' but a fiat contradiction of what had hitherto been regarded as a fact.
§300. The negative element in Newton's theory of Gravitation is much less prominent. The law of inverse squares was not previously known; but that heavy bodies tend towards a centre of gravity had already been asserted by the Greeks, notably by Aristotle, and was, in fact, generally held; though as to the nature of gravity, again, there was no commonly accepted theory and no certain knowledge. Consequently, Newton's discovery was not a reversal of established truths, but rather a new truth which at once supplemented and systematised the old.
§ 301. The theory of chemical elements, on the other hand, as at present held, seems directly to contradict the more ancient theory that the elements were four, if we take that theory to be a bare statement that fire, air, earth and water are the ultimate constituents of all material things. But this is not what was meant. For, in the first place, the four so-called elements were not regarded, by Aristotle at any rate, as ultimate; but as due to the combination of an active hot-cold principle with a passive wet-dry principle. And, secondly, the essence of Aristotle's theory lay not in his assertion that the ultimate principles were 'hot-cold' and 'wet-dry' -- an error which was due to the almost complete absence of scientific data -- but in his assertion that the principles were active and passive, for this he deduced a priori from his metaphysics. Now, that the ultimate principles of things are active and passive, positive and negative, actual and potential, is a doctrine which is fundamental in modern theories of the nature of matter. Again, that there are "solid massy, hard, impenetrable, moveable particles of such size and figure and with such and such properties," is a view held not only by Newton and Dalton in modern times, and by Democritus and Leucippus of old, but still held and indeed widely recognised as true, though 'atoms' are no longer regarded as ultimate and indivisible. Indeed, the transmutation of the elements, which was a belief that prompted so much research in mediaeval times, does not seem so utterly impossible now that radium converts itself into helium. Looking back, therefore, upon the various theories which have been held in regard to the constitution of matter, so far from finding grounds for scepticism, we seem, on the contrary, to find good reason to trust that knowledge is gradually advancing, and that in its advance what was essential and fundamental in past theories will be preserved, the accidental and the subsidiary alone being sacrificed.
§ 302. Modern theories of light and heat do not tend to destroy this optimistic view. Many physicists ave given up the Emission theory. Its minute corpuscles and the transmitted species of the Greeks have been interpreted as motions in the ether. But that light is a something which is propagated by vibration in luminous bodies, that its propagation is rectilinear, and that it comes to us through a medium which reminds one forcibly of the media so characteristic of Aristotelian Physics is still mainained. The theory that heat is a 'caloric' or highly elastic fluid permeating the interstices of substances has also been abandoned; but we still believe with the Greeks that it may be due to the highly repellant and rapid movements of particles, and with the Calorics that it is connected with an entity which is elastic and which interpenetrates all material things, though this entity is now regarded the medium for the propagation of heat and not its source.
§ 303. One more point, and I have finished this brief review of the effect of development on validity. Has the older geometry of Euclid been invalidated by meta-geometries and the geometry of a fourth dimension? Dr. Schiller thinks that it is nonsense to enquire whether our space is Euclidian or not. Conceptual space is valid, he says, in so far as it is useful, but it is never real.{24} But can this assertion be proved? The notion of space seems to be valid, not merely because it is useful, but because it has a fundamentum in re, because the ideas and relations of which it is made up are derived directly from the data of objective experience; and because they adequately express the relations which hold between the configurations of objects in the real world, in so far as those configurations conform to the precise notions of geometry, which they do approximately. The idea of a fourth dimension may be got at in several ways, but it seems to me that it owes its origin really to the algebraical theory of indices. As, however, it is generally admitted that our space has only three dimensions, and as I have already given one reason for thinking that this is so, I shall not say more on this matter. In fact, if we are mistaken here, the error is negative, not positive; so that it is of no consequence from our present point of view.
§ 304. On the other hand, the meta-geometries of Riemann and Lowatchewski are of consequence, for at first sight they seem to contradict the Geometry of Euclid, and also to contradict one another; and yet in spite of this to be each of them self-consistent. Both Lowatchewski and Riemann deny Euclid's assumption that a straight line is determined by any two points, and both deny Euclid's axiom that through a given point in the same plane one, and only one, straight line can be drawn parallel to a given straight line; but while Riemann postulates that through a given point in the same plane no line can be drawn such that it will never meet a given line, Lowatchewski postulates that not one but an indefinite number of such lines can be drawn. Similarly, the sum of the angles of a triangle for Euclid is equal to two right angles, for Riemann greater than two right angles, and for Lowatchewski less than two right angles. Now, if you imagine straight lines and parallels and triangles to be drawn, not on an Euclidian plane, but on the outside surface of an immense sphere, you have straight lines which are not determined by two points, parallels all of which must meet, and triangles the angles of which are greater than two right angles. In other words, your space is spherical and your plane has a positive curvature. And if now you could imagine the contradictory opposite of all this -- which I confess I cannot do, for the inside of a spherical or ellipsoidal surface is obviously not what is needed-you would have planes with a negative curvature upon which you might construct the geometrical figures of Lowatchewski. What has really happened, then, is this: both Riemann and Lowatchewski have been working with spaces and planes which are not Euclidian spaces and planes, but imaginary entities constructed by themselves. In place of the Euclidian notion of a straight line they have substituted notions of their own. It is impossible to prove the validity of Euclid's notion of a straight line having invariable direction, for the notion is, as I have said, ultimate. Nevertheless, we have such a notion and know what it means; whereas a solid body in which straight lines are not straight lines at all, but positive or negative curves, is inconceivable.
Modern meta-geometries, therefore, do not contradict Euclidian geometry. On the contrary, they presuppose it; for they are in reality an Euclidian spherical geometry or its inverse conceived as a pseudo-plane geometry of two dimensions. That this is so is proved by the fact that the theorems of Riemann and Lowatchewski may be translated into Euclidian theorems by the aid of analytical geometry. While that the Euclidian notion of a straight line alone is valid, is, at any rate, confirmed by the fact that, when applied in the concrete, meta-geometries will not work.
§ 305. Our conclusion is, therefore, that neither a study of the changes that have actually taken place as knowledge has developed, nor a study of the principles which have governed those changes justifies us in adopting a sceptical attitude in regard to present knowledge, whether theoretical or factual. In the realm of facts there have been but few reversals. Our knowledge of facts grows not by intrinsic modifications, but by an increase in the number, the detail, and the accuracy of our observations. In the realm of theory, on the other hand, there have been many reversals; yet these have seldom, if ever, entirely destroyed the validity of those interpretations we now stigmatise as false. On the contrary, the tendency has been to distinguish in previous theories principles which have led to error from those which led to truth, and while rejecting the former to retain the latter and embody them in a more adequate theory. Moreover, the principes which have been retained are in general those which were most essential in previous theories and which were recognised as such at the time that those theories were framed. Apperception by the individual and apperception, if I may so call it, by the race adds to the old stock of truths, and at the same time gives them a fuller significance but it does not destroy either the facts or the more fundamental principles upon which those truths were based. Our conception of things and their relations grows more and more systematic; but the facts upon which it is based and the principles which guide us in the search for truth alike remain constant throughout.
§ 306. The Hegelian theory of Apperception likewise affords no ground for scepticism. In the theoretical developments, briefly outlined above, I can find no trace of reconciliation by higher syntheses in the Hegelian sense of that term. Rather, development has consisted in the explicit negation of certain principles in a previous theory and the reassertion of others supplemented by an element which was new. There is some truth in the statement that development is a sort of critical regress in which the universal implicit in divergent views is analysed out and reasserted. But the differences between divergent views are seldom reconciled in a 'higher' synthesis. In fact, often enough they are not reconciled at all, but one is denied and the other established. And if a reconciliation is effected, it is effected by a distinction in the differences rather than by a synthesis of them wholesale and vago modo. The result of the regress in this case is that the differences are taken in analysis and some part of one or both rejected. For so long as either of the antitheses contains positive error, a synthesis is impossible. The error must first be removed, and then, since all theories, however divergent, contain an element of truth, they may be combined to form a system of truth more adequate, and in this sense higher than before. This kind of synthesis, indeed, it is the aim of the French philosophy of Immanence to bring about. Led by the author of L'Action it seeks to reconcile conflicting opinions in religious matters by a regress which shall draw forth from error the truth that is immanent within it. No need is more urgent than the need of getting rid of contradictions. It is felt alike by pragmatist, absolutist, and realist. But while the pragmatist says 'take your choice of either alternative according as you feel yourself prompted by emotional desires;' and the absolutist says, 'No, don't choose, but wait, the antitheses will some day be reconciled in higher but misty synthesis;' the realist of the Scholastic frame of mind says, 'First distinguish, then choose; but choose on rational, not on emotional, grounds; and thus by separating truth from error, you will be able, without waiting long, to obtain a synthesis which shall include past truths, and at the same time be a basis from which to proceed to further truth.' And the latter, it seems to me, is the best answer of the three.
{1} Critical Philosophy of Kant, pp. 460-462.
{2} Pragmatism, pp. 59, 60.
{3} Ibid., p. 569. (italics mine.) Annales de phil. chrétienne, 1906, p. 234.
{4} Pragmatism, p. 60.
{5} Ibid., p. 168.
{6} Ibid., p. 66.
{7} Baldwin's Dictionary of Philosophy, article, "Pragmatism."
{8} Ibid., article. "Synechism."
{9} Ibid., article, "Pragmatism."
{10} cf. Studies in Humanism, p.
{11} The Meaning of Truth, p. 58. (Italics mine.)
{12} Riddles of the Sphinx, p. 9.
{13} cf. Albée, "Methodological Principles," Amer. Phil. Review, 1906.
{14} Pragmatism, pp. 244, 245, and The Meaning of Truth, p. 69,
{15} La Theéorie Physique, chap. vii., 5,
{16} History, chap. iv., § 53 (Rawlinson's trans., vol. iii., p. 40).
{17} Rawlinson's Herodotus, iii., pp. 171, 172, and cf. p. 40.
{18} Studies in Humanism, p. 189.
{19} History, Book vi., § 84.
{20} Ibid., iv., § 95.
{21} v.g. the apparent increase of speed when the sun and earth approach.
{22} I. q. 32, a. and 2. "Ad secundum dicendum, quod ad aliquam rem dupliciter inducitur ratio; uno modo ad probandum sufficienter aliquam radicem; sicut in scientia naturali inducitur ratio sufficiens ad probandum quod motus coeli semper sit uniformis velocitatis. Alio modo inducitur ratio non quae sufficienter probet radicem, sed quae radici jam positae ostendat congruere consequentes effectus; sicut in astrologia ponitur ratio excentricorum et epicyclorum ex hoc quod hac positione facta possunt salvari apparentia sensibilia circa motus coelestes; non tamen ratio haec est sufficienter probans, quia etiam forte alia positione facta salvari possent"
{23} 'Uniform velocity' in the Ptolemaic system is supposed actually to exist; in the Newtonian theory it is a tendency. In the Ptolemaic system bodies move in a circular orbit; according to Newton's law they tend to move in a straight line.
{24} 'Axioms as Postutates,' p. 115.