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The Passage From The Abstract To The Concrete

110. THE recognition of the fact that Science is in no respect a plain transcript of Reality, in no respect a picture of the External Order, but wholly an ideal construction in which the manifold relations of Reals are taken up and assimilated by the mind, and there transformed into relations of ideas, so that the world of Sense is changed into the world of Thought, — this fact leads to the deeply interesting question, How can Science avail in our search after the External Order, and explain the real relations of Things ? Its own domain is exclusively ideal. Yet it seeks to reveal the processes of Reals, the Laws of Things, that thereby we may so modify the con-junctures of events as to render events our servants ; or so modify our attitude towards events as to reconcile us to the fatalities we cannot alter. Its vision is directed to processes rather than to objects, and it regards objects solely in the light of necessary materials for the construction of general conceptions which are to guide action. This comparative disregard of the concrete in favor of the abstract, this transformation of the particular into the general, of the sensible into the intelligible, is the necessary consequence of our mental limitation. Every Real is the complex of so many relations, a conjuncture of so many events, a synthesis of so many sensations, that to know one Real thoroughly would only be possible through an intuition embracing the universe. This being impossible, we can only approach a knowledge of an object by separately studying its several relations, so far as each can be laid hold of by itself, i. e. by Abstraction. The nature of our organism prevents our having more than one aspect of an object at each instant present to Consciousness ; so that relations which are objectively simultaneous are by us perceived successively. In succession we feel that a thing is visible, tangible, resistant, etc., and such successions are condensed into a single perception. Any one element of this group becomes the sign of all the rest. Every perception is also an act of judgment which classes the present feeling with past feelings, and assumes the presence of unfelt relations. The validity of the perception is the possibility of converting the unfelt into felt relations. A scientific conception differs from the simple perception mainly in its higher degree of abstraction and generality. It has constructed general formulas of the relations of visibility, tangibility, etc., which it extends to all similar cases, real or imaginary, and thus is furnished with the Law or condensed synthesis of experiences.

The Laws of Light, of Vision, of Motion, of Muscular Sensation, of Quantity, of Combination, etc., are all separately studied, — are abstractions from the processes 'actually observed. The mathematician keeps to Quantity, never allowing himself to be perplexed by considerations of Quality. The astronomer fixes attention on the movements of the planets without regarding the structure and composition of these masses. The physicist and chemist separate the molecular relations from all the phenomena of Life, and the .biologist studies the phenomena of life apart from historical and social relations. In every science the concrete Real is stripped of all its qualities except those which the science specially needs for its construction. The actual sensible thing is set aside. Nor is this all. The substitution of an ideal object for a sensible object, an abstract for a concrete, is the substitution of a general relation for a particular relation. The relation of weight in this mass is the relation which will, exist in all similar masses similarly placed; the resistance recognized in this body is seen to belong to all bodies. To the geometer a circle is not the round figure visible by his eye, but a figure visible by his mind, in which all the radii from the centre are absolutely equal; it is not this particular sensible circle, it is the ideal circle To the physicist .Heat is not a sensation, but a vibration of molecules ; to the physiologist it is not a vibration of molecules, but. an affection of a sensory nerve. The sciences of Thermotics and Acoustics are not records of the actual phenomena observed in thermal and sonorous events, but general relations detached from them. The first effort of the physicist is not to enumerate all the facts, but to reduce the multiplicity to certain elementary relations of a mechanical kind ; these are then translated into mathematical formulas, which are operated on as if they were Heat and Sound.

111. -The universe presented to us is constituted by Elements, Groups of Elements, and Groups of Groups. The combinations being practically infinite we can never know them all, and being complex, we can only approximate to the knowledge of any. Imperfect as our knowledge is, it may be absolutely certain, to the extent of its own reach ; and this certainty is secured whenever the boundaries are not overstepped. A particular relation is absolutely certain under the particular conditions ; if we generalize it we must at the same time generalize the conditions, or else we are substituting a new proposition in place of the old one. " That I feel warm at this moment," is an irresistible truth, though not one valuable to science. " That I shall always feel warm," is equally certain, if I generalize the present conditions: but if I simply assert that I shall always feel warm irrespective of any change whatever in the conditions, it is" clear that I violate the first principle of rational judgment, unless I have previously established the fact that warmth is wholly independent of conditions.

112. Now the power of Science consists in this : having seized upon the relations that are uniform amid the relations that are various, and having formulated the conditions under which phenomena occur, it is enabled to generalize these, and say " whenever such conditions are present such phenomena must be present," no matter how various may be the accompaniments. And observation having disclosed that some conditions are very general, others universal, these are formulated as Laws of Phenomena. But as all these must be first disclosed by observation before they are generalized, — as all deductions rest on inductions, and all inductions on sensible experiences,—Science, which seems to depart from Experience in its pursuit of abstractions, is only a reproduction of Experience, — a translation of the heterogeneous facts observed, into the homogeneous relations thought, — and it errs whenever its abstractions admit any elements not given in the concretes.

113. The passage from the abstract to the concrete can only be the inverse of the passage from the concrete to the abstract. What was dropped out of sight in establishing the ideal — namely, all the details which particularized the particular phenomena — must be restored in each particular case. The law of uniform Motion was reached by abstracting it from all the variations to which every moving body is subject; in applying this ideal law to any real, case we must compound it with the observed variations. That all bodies fall to the earth in equal times is ideally true, but really false ; to make it accord with fact, we must abstract the resistance of the air, which, inappreciable in the fall of condensed masses, is appreciable in the fall of niasses with surfaces which are broad compared with their thickness. And so with all other laws. Applied Mechanics presents us with the best illustration of ideal laws, true in their generality yet falsified in every particular case, which are nevertheless because of their ideal truth the most invaluable guides in practice.

( Originally Published 1874 )

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Ideal Construction In Science

What Are Laws Of Nature?

The Use And Abuse Of Hypothesis

The Passage From The Abstract To The Concrete

Ideal Construction In Metaphysics

The Search After Causes

Intuition And Demonstration

Axioms And Their Validity

Necessary Truths

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