Physics

The Timaeus offers an account of the visible world as the work of a divine craftsman who fashions matter after the pattern of the eternal forms. The cosmos is orderly, on this view, because it is a copy, and the order it displays is mathematical. The four elements are constructed out of geometrical solids, and the revolutions of the heavens are numbered. It is for a related reason that Plato conceives astronomy as dealing with the possible forms of the motions of solids rather than with the observed motions of the heavenly bodies, and associates it with geometry, as he associates music divorced from audible harmonies with arithmetic. Whether such a science remains a physics at all is a question Aristotle would afterward press.

Plato distinguishes the standing of any account of becoming from that of mathematics and dialectic. Since the sensible world comes to be and passes away, the physicist who tries to give an account of it can, in Timaeus' phrase, do no better than adduce probabilities as likely as any others. Knowledge in the strict sense belongs to the immutable, and the study of the immutable belongs to mathematics and to dialectic. The relation of certain knowledge to opinion and probability is treated more fully under the ideas of Knowledge and of Opinion.

Two consequences may be drawn from this position, and they pull in different directions. If nature is mathematically ordered, then measurement and number are the fitting instruments for investigating it, and the mathematical physics of later centuries has a warrant. But if all such investigation yields probability only, then physics is a lesser employment of the mind. Timaeus himself treats the discourse on natural things as a wise and moderate pastime, a recreation from meditation upon eternal things. In the traditional estimate of the dignity and value of physics, this appears to be one extreme.

The tradition divides on both halves of Plato's position. Aristotle holds that physics is a science in the strict sense, and criticizes the discussion of becoming in the Timaeus for substituting mathematical for physical terms. Hume, at the other end, allows physics no more than probability, yet unlike Plato finds no depreciation in that. Newton and his successors, meanwhile, take the mathematical order of nature as the very ground of their method. The question of what the physical world is a copy or an image of is pursued further under the ideas of Being and Eternity.

Aristotle takes as the object of physics whatever has in itself a principle of motion and rest. The realm of nature is the realm of change, and the physicist is the man who studies what neither exists nor can be conceived apart from matter and motion. So understood, physics is a part of speculative philosophy, distinct from mathematics and from that first philosophy which comes after it. Its proper principles are matter, form, and privation, the three that any change requires: a substratum which changes, and the contraries from which and to which the change occurs. The deeper analysis of matter and form in terms of potentiality and actuality is left to metaphysics, on which physics depends for the establishment of its principles though not for its subject matter.

The Physics undertakes rather more than a doctrine of principles. It defines change and classifies its types, separating coming to be and passing away simply from change in quality, quantity, and place. It distinguishes what happens by chance from what happens of necessity, and natural from violent motion. It considers the relation of mover to moved, the continuity and divisibility of motion, place and time as conditions of motion, and the questions of the infinite and of the eternity of motion. On these matters the reader is referred to the chapters on Change, Cause, Chance, Infinity, Space, and Time.

Explanation in this physics is by the four causes: the material, the formal, the efficient, and the final. Aristotle proceeds without experiment, though not without induction from experience, and without measurement, though not without observation. Where Newton and Fourier would afterward seek to reduce the variety of nature to a few laws of maximum generality, Aristotle tends to insist upon an irreducible variety of kinds of matter, types of motion, and causes of change. By his criteria of physical inquiry the biological treatises, and even the short works on sensation, memory, and dreams, fall within the domain of physics.

Aquinas receives this physics and sets it within a Christian account of creation. Bacon and Kant agree with Aristotle in separating physics from mathematics, though they differ from him and from each other about its scope. The experimentalists depart on both counts, holding that principles are to be sought in mathematics and settled by contrived experiment. Whether the two enterprises are in conflict or represent a division of labor, each dealing according to its method with different problems, is a question the tradition has not closed. It is treated further under Philosophy and Science.

Lucretius expounds in verse the physics of the Epicureans, according to which nature as it exists by itself is founded on two things only, bodies and the void in which they move. The atoms are indivisible and imperceptible; they neither come to be out of nothing nor pass away into nothing. Everything else, from the weather to the growth of crops, follows from their combination and separation. Of the third use to which the study of nature may be put, Lucretius leaves no doubt: men fear what they cannot explain, and an account of the causes of things is offered as a release from that fear. The gods, on this view, exist without concern for human affairs.

The atomic hypothesis proposes a mode of explanation different from Plato's and from Aristotle's alike. Where Plato looks to mathematical patterns and Aristotle to natures and ends, Lucretius appeals to the shapes, sizes, weights, and motions of particles. Color, sound, and taste accordingly belong not to things but to the encounter of atoms with the organs of sense. The distinction between what belongs to bodies and what arises in the perceiver is treated at greater length under the ideas of Quality and Sense.

To the straight fall of the atoms Lucretius adds the swerve, a slight and uncaused declination at no fixed time or place. Two offices are assigned to it. Without the swerve the atoms would fall forever in parallel and nothing would ever meet or combine; and without it the motions of the mind would be bound in an unbroken chain of antecedent causes, leaving no room for the will. Whether an uncaused motion can be admitted into a physics that begins by denying that anything comes from nothing has been questioned since antiquity. The issue belongs to the chapters on Cause, Chance, and Will.

Little read in the medieval centuries, the poem was recovered in the Renaissance, and in the seventeenth century Gassendi and others found in atomism an alternative to the physics of the schools. The mechanical philosophy which followed retains the atoms and the void while abandoning the swerve, and Newton's conjecture that the phenomena of nature may all depend on forces by which the particles of bodies are mutually impelled or repelled stands in the same line of speculation. What is common to these positions, and what divides them, is considered under the ideas of Element, Matter, and Mechanics.

Aquinas takes over the Aristotelian division of the speculative sciences and states it in terms of the manner in which each abstracts from matter. Natural science treats of things which depend on matter both for their being and for their being known; its object is mobile being, that is, things considered as subject to motion. It is a science in the strict sense, proceeding by demonstration from principles, and it is not deprived of that character by standing below metaphysics and sacred doctrine in the order of the sciences. What distinguishes the sciences from one another, on this account, is not the things they treat but the formal aspect under which they treat them.

The order among the sciences bears on the questions physics may be asked to settle. That natural things have causes, and what those causes are, is a matter for the philosopher of nature. That nature exists at all is not. Creation, as Aquinas understands it, is not a change and has no subject undergoing it, and therefore falls outside a science whose whole business is with change. Whether the world had a beginning in time he holds to be undemonstrable by natural reason, a position which separates him both from those who would prove the world eternal and from those who would prove it created in time. The argument is set out under Eternity and World.

The same doctrine of formal aspects governs the relation of physics to mathematics. The natural philosopher considers bodies as subjects of motion; the mathematician considers their quantity apart from motion, though the surfaces and volumes he studies exist only in physical bodies. Sciences such as optics and harmonics, which apply mathematical demonstration to natural phenomena, are on this view mixed rather than pure, and their existence is taken to confirm the distinction rather than to erase it.

The dependence of physics upon metaphysics for the elucidation of its principles is what Bacon, Galileo, and Newton set aside, each proposing that the principles of natural philosophy be drawn instead from experiment or from mathematics. Yet the question Aquinas raises does not disappear with the hierarchy he defends. Where the experimentalist employs physical rather than mathematical principles, as Galileo does in distinguishing natural from violent motion, he may still have to derive them from some philosophy of nature. Kant's rational physics, though it reaches a different conclusion, addresses the same difficulty. See also Metaphysics and Science.

Bacon holds the natural philosophy he inherits to have been corrupted from two directions, by logic in the school of Aristotle and by mathematics in the school of Plato. The sciences so formed rest, in his account, on generalizations made in haste from ordinary experience and afterward defended by disputation rather than by any fresh consultation of nature. He does not deny the use of mathematics in physics, and observes elsewhere that the investigation of nature is best conducted when mathematics is applied to it. His objection is to those who would have their science preside over physics; mathematics should terminate natural philosophy rather than generate it, serving as an appendage or auxiliary.

The reform proposed is one of method. Ordinary experience is to be replaced by experiment, in which nature is put under constraint and vexed so that what lies hidden in her may appear. The results are to be collected in tables of presence, absence, and degree, and from these the form, or operative law, of a nature is to be drawn by an induction that proceeds by successive exclusions rather than by simple enumeration. Of the four causes, Bacon assigns the material and efficient to physics and reserves the formal and final to what he calls metaphysics, a division which leaves both parts of natural philosophy open to experimental treatment.

Two ends are set before the whole inquiry. The first is that human knowledge and human power meet in one, so that what is discovered as a cause in speculation may be produced as an effect in operation. The second is the relief of man's estate through the useful arts. Bacon accordingly ranks the practical fruits of physics, in mechanics and in what he calls magic, alongside its speculative parts, and the utility of physics has since been argued on the terms he set. The matter is pursued under Art, Knowledge, and Progress.

The tables Bacon devised were little used, and his doctrine of forms retains more of the scholastic vocabulary than his polemic against the schools would suggest. The physics that answered his demand for universal laws drawn from phenomena was Newton's, which reached them by mathematical demonstration confirmed at every point by experiment rather than by inductive exclusion. Yet the insistence that the philosopher must go to nature under conditions of his own contriving, and that knowledge is tested by what it enables men to do, passes into the tradition of experimental science and is repeated by Lavoisier and Faraday in nearly Bacon's words. See Experience, Induction, and Science.

Newton calls his work a philosophy of nature, and also an experimental philosophy, the second term distinguishing it from the natural philosophy of those who did not experiment. The principles he lays down in the first two books he describes as principles not philosophical but mathematical, laws and conditions of certain motions and of powers or forces, upon which reasonings in philosophical inquiries may be built. From these, in the third book, he undertakes to demonstrate the frame of the system of the world, deriving from the celestial phenomena the forces of gravity, and from these forces the motions of the planets, the comets, the moon, and the sea. Method here runs in both directions: analysis by experiment and induction is to precede composition, in which the principles assumed are used to explain the phenomena and the explanations are proved.

Two convictions govern the whole. The first is that nature is pleased with simplicity and affects not the pomp of superfluous causes, so that the laws sought should be as few and as general as the phenomena permit. The second is that they should be capable of mathematical statement. Newton does not claim to have reached the end of such an inquiry. He wishes the rest of the phenomena of nature might be derived by the same kind of reasoning, suspecting that they may all depend on forces by which the particles of bodies are mutually impelled or repelled by causes hitherto unknown.

The refusal to frame hypotheses concerns the cause of gravity, not gravity itself. That bodies attract one another according to a determinate law is deduced from the phenomena; why they should do so is left undetermined, and whatever is not deduced from the phenomena Newton is willing to call hypothesis and to exclude from experimental philosophy. The four Rules of Reasoning which open the third book set out the accompanying maxims of parsimony and of the uniformity of nature. Whether a physics so restricted describes nature or merely calculates it is a question taken up under Cause and Hypothesis.

Fourier, writing between Newton and Einstein, testifies that the successors of Newton and Galileo have taught that the most diverse phenomena are subject to a small number of universal laws reproduced in all the acts of nature. The unified equations sought in the following century pursue the same ideal. In philosophy the effect is different: Hume and Kant both take the Newtonian laws as the clearest case of scientific knowledge and ask on what their universality and necessity can rest. Newton's own answer, that they are deduced from the phenomena, is what each of them finds insufficient, though for opposite reasons.

Lavoisier applies to the phenomena of chemical change the standard of measurement that Newton had brought to the phenomena of motion. We ought never, he writes, to search for truth but by the natural road of experiment and observation, and his Elements of Chemistry of 1789 proceeds accordingly. The balance is the instrument on which the argument turns. Every substance entering an operation and every substance issuing from it is weighed, and the sums are compared. From such comparisons Lavoisier concludes that combustion is not the escape of phlogiston from a burning body but the combination of that body with a portion of the air, and the theory which had organized chemistry for a century is set aside.

The principle assumed throughout is that nothing is created in the operations either of art or of nature, and that an equal quantity of matter exists before and after every operation. Something like this had been asserted by the atomists in antiquity, but as a speculative axiom rather than as a rule of laboratory practice. In Lavoisier's hands it becomes the condition under which an experiment counts as complete, since any discrepancy in the weights is taken to indicate that some substance has escaped notice. The character of such principles, which are presupposed by experiments rather than established by them, belongs to the discussion of Element and Matter.

Lavoisier also undertakes a reform of chemical language, replacing the vocabulary of the alchemists with names formed from the composition of the substances they denote. His view is that a science cannot be improved without improving its language, since the words in which the facts are recorded govern the reasoning conducted upon them. The relation of naming to knowing is treated more fully under Definition, Language, and Sign and Symbol.

The extension of exact measurement from motion to matter brought chemistry within the group of sciences that Newton's example had defined, and it sharpened a difficulty that Hume had already raised. The conservation of matter is not the conclusion of any one experiment; it is what every experiment must assume before its result can be interpreted. Whether a proposition of that kind can be confirmed by experience, or must be brought to experience beforehand, is the question Kant would place at the center of his account of nature. The permanence of substance figures there as one of the Analogies of Experience.

Hume examines the reasoning by which the physicist passes from what has been observed to what has not. Such reasoning, he holds, turns on the relation of cause and effect, and that relation cannot be established by any analysis of the ideas involved, since there is no contradiction in supposing that any cause might be followed by any effect whatever. Nor can it be established by experience, for experience acquaints us only with what has occurred, and the inference from the observed to the unobserved presupposes that nature will continue uniform, which is the very point at issue. Argument from past experience to that uniformity would move in a circle.

The conclusion drawn is that the inference rests on custom rather than on reasoning. Having found one sort of event constantly attended by another, the mind is determined by habit to expect the second upon the appearance of the first, and it is this determination of the mind, and not anything discovered in the objects, that we express when we speak of necessary connection. Looking outward upon bodies, Hume maintains, we never in a single instance perceive any power by which one produces another. What is treated here as a question about physics is thus also a question about the mind, and the argument is carried further under Cause, Induction, and Necessity and Contingency.

The result is not that physics should be abandoned. Experimental reasoning about matters of fact remains for Hume the whole of our knowledge of reality, and questions about nature which physics cannot answer cannot be answered scientifically at all. Its conclusions are at best probable, but Hume, unlike Plato, draws no depreciation from that. He does not think the probability of physics detracts from its utility, and in this he stands nearer to Bacon than to those who would reserve the name of knowledge for what is certain.

Two consequences of Hume's position have been much discussed. The first concerns metaphysics, which on his account yields no knowledge, so that natural science, restricted to experimental reasoning about matters of fact, is left as the only knowledge of reality; a primacy of physics is thus reached by a different route from Hobbes', who reaches it by holding that nothing exists but bodies in motion. The second is Kant's, who accepts the argument that experience cannot supply necessity and looks elsewhere for the ground of the universality which Newton's laws appear to possess.

Kant asks how a pure natural science is possible, taking the Newtonian laws as propositions which claim to hold universally and without exception. Hume's argument he accepts so far as it goes: no accumulation of observations can yield necessity, and experience informs us what has been the case but never what must be. If the propositions of physics carry necessity, the ground of it lies elsewhere. The alternative Kant proposes is that the understanding does not derive its laws from nature but prescribes them to it, so that what appears as the lawfulness of nature is the form which anything must have if it is to become an object of experience at all.

On this view the categories of substance, causality, and reciprocity are not generalizations drawn from what we have observed but conditions under which observation of an objective order is possible. That every event follows upon something according to a rule is not learned from the succession of events; it is what allows a succession to be judged as objective rather than as a mere sequence of impressions. The doctrine is developed in the Principles of Pure Understanding, where the Axioms of Intuition provide that all appearances have extensive magnitude and so admit of measurement, the Anticipations of Perception that sensation has degree, and the Analogies that appearances stand in determinate relations of permanence, succession, and coexistence.

Kant distinguishes this rational or pure physics from the empirical science built upon it. The whole body of theoretical knowledge which is a priori he calls the metaphysic of nature, of which the metaphysic of corporeal nature, or rational physic, is one part and rational psychology the other. Rational physics he holds to be entirely separate from mathematics, and in this separation he stands with Aristotle and Bacon, though his conception of physics as a priori knowledge of nature agrees with neither. What is a priori supplies the form of natural science; its particular laws must still be found by observation and experiment.

The position offers terms on which the claims of the experimentalists and of the philosophers of nature might both be allowed, the one furnishing the content of physics and the other its form. Whether the settlement holds has been disputed since, and the geometries and mechanics of the last century have been urged against the particular framework Kant took to be necessary. The question he put, on what ground a science of nature is possible at all, is nevertheless the question that the whole tradition from Aristotle onward has been answering in various ways. It is pursued under Metaphysics, Nature, and Science.