Chapter IX: Of the Classification of Sciences

1. THE Classification of Sciences has its chief use in pointing out to us the extent of our powers of arriving at truth, and the analogies which may obtain between those certain and lucid portions of knowledge with which we are here concerned, and those other portions, of a very different interest and evidence, which we here purposely abstain to touch upon. The classification of human knowledge will, therefore, have a more peculiar importance when we can include in it the moral, political, and metaphysical, as well as the physical portions of our knowledge. But such a survey does not belong to our present undertaking: and a general view of the connexion and order of the branches of sciences which our review has hitherto included, will even now possess some interest; and may serve hereafter as an introduction to a more complete scheme of the general body of human knowledge.

2. In this, as in any other case, a sound classification must be the result, not of any assumed principles imperatively applied to the subject, but of an examination of the objects to be classified;--of an analysis of them into the principles in which they agree and differ. The Classification of Sciences must result from the consideration of their nature and contents. Accordingly, that review of the Sciences in which the _History_ of the Sciences engaged us, led to a Classification, of which the main features are indicated in that work. The Classification thus obtained, depends neither upon the faculties of the mind to which the separate parts of our knowledge owe their origin, nor upon the objects which each science contemplates; but upon a more {137} natural and fundamental element;--namely, the _Ideas_ which each science involves. The Ideas regulate and connect the facts, and are the foundations of the reasoning, in each science: and having in another work more fully examined these _Ideas_, we are now prepared to state here the classification to which they lead. If we have rightly traced each science to the Conceptions which are really fundamental _with regard to it_, and which give rise to the first principles on which it depends, it is not necessary for our purpose that we should decide whether these Conceptions are absolutely ultimate principles of thought, or whether, on the contrary, they can be further resolved into other Fundamental Ideas. We need not now suppose it determined whether or not _Number_ is a mere modification of the Idea of Time, and _Force_ a mere modification of the Idea of Cause: for however this may be, our Conception of Number is the foundation of Arithmetic, and our Conception of Force is the foundation of Mechanics. It is to be observed also that in our classification, each Science may involve, not only the Ideas or Conceptions which are placed opposite to it in the list, but also all which _precede_ it. Thus Formal Astronomy involves not only the Conception of Motion, but also those which are the foundation of Arithmetic and Geometry. In like manner. Physical Astronomy employs the Sciences of Statics and Dynamics, and thus, rests on their foundations; and they, in turn, depend upon the Ideas of Space and of Time, as well as of Cause.

3. We may further observe, that this arrangement of Sciences according to the Fundamental Ideas which they involve, points out the transition from those parts of human knowledge which have been included in our History and Philosophy, to other regions of speculation into which we have not entered. We have repeatedly found ourselves upon the borders of inquiries of a psychological, or moral, or theological nature. Thus the History of Physiology[28\2] led us to the consideration {138} of Life, Sensation, and Volition; and at these Ideas we stopped, that we might not transgress the boundaries of our subject as then predetermined. It is plain that the pursuit of such conceptions and their consequences, would lead us to the sciences (if we are allowed to call them sciences) which contemplate not only animal, but human principles of action, to Anthropology, and Psychology. In other ways, too, the Ideas which we hare examined, although manifestly the foundations of sciences such as we have here treated of also plainly pointed to speculations of a different order; thus the Idea of a Final Cause is an indispensable guide in Biology, as we have seen; but the conception of Design as directing the order of nature, once admitted, soon carries us to higher contemplations. Again, the Class of Palætiological Sciences which we were in the _History_ led to construct, although we there admitted only one example of the Class, namely Geology, does in reality include many vast lines of research; as the history and causes of the division of plants and animals, the history of languages, arts, and consequently of civilization. Along with these researches, comes the question how far these histories point backwards to a natural or a supernatural origin; and the Idea of a First Cause is thus brought under our consideration. Finally, it is not difficult to see that as the Physical Sciences have their peculiar governing Ideas, which support and shape them, so the Moral and Political Sciences also must similarly have their fundamental and formative Ideas, the source of universal and certain truths, each of their proper kind. But to follow out the traces of this analogy, and to verify the existence of those Fundamental Ideas in Morals and Politics, is a task quite out of the sphere of the work in which we are here engaged.

[Note 28\2: _Hist. Ind. Sc._ b. xvii. c. v. sect. 2.]

4. We may now place before the reader our Classification of the Sciences. I have added to the list of Sciences, a few not belonging to our present subject, that the nature of the transition by which we are to extend our philosophy into a wider and higher region may be in some measure perceived. {139}

The Classification of the Sciences is given over leaf.

A few remarks upon it offer themselves.

The _Pure_ Mathematical Sciences can hardly be called _Inductive_ Sciences. Their principles are not obtained by Induction from Facts, but are necessarily assumed in reasoning upon the subject matter which those sciences involve.

The Astronomy of the Ancients aimed only at explaining the motions of the heavenly bodies, as a _mechanism_. Modern Astronomy, explains these motions on the principles of Mechanics.

The term _Physics_, when confined to a peculiar class of Sciences, is usually understood to exclude the Mechanical Sciences on the one side, and Chemistry on the other; and thus embraces the Secondary Mechanical and Analytico-Mechanical Sciences. But the adjective _Physical_ applied to any science and opposed to _Formal_, as in Astronomy and Optics, implies those speculations in which we consider not only the Laws of Phenomena but their Causes; and generally, as in those cases, their Mechanical Causes.

The term _Metaphysics_ is applied to subjects in which the Facts examined are emotions, thoughts and mental conditions; subjects not included in our present survey. {140}

Fundamental Ideas or Sciences. Classification.
Conceptions.

Space Geometry ) Time ) Pure Mathematical _Number_ Arithmetic } Sign Algebra ) Sciences. Limit Differentials ) _Motion_ Pure Mechanism } Pure Motional Formal Astronomy } Sciences.

Cause _Force_ Statics ) _Matter_ Dynamics ) Mechanical _Inertia _ Hydrostatics } _Fluid Pressure_ Hydrodynamics ) Sciences. Physical Astronomy )

Outness Medium _of Sensation_ Acoustics ) Intensity _of Qualities_ Formal Optics ) Secondary _Scales of Qualities_ Physical Optics } Mechanical Thermotics ) Sciences. Atmology ) (_Physics_.) Polarity Electricity ) Analytico-Mecha- Magnetism } nical Sciences. Galvanism ) (_Physics_.)

Element (_Composition_) _Chemical_ Affinity Substance (_Atoms_) Chemistry Analytical Science. Symmetry Crystallography } Analytico-Classifi- Likeness Systematic Mineralogy } catory Sciences. _Degrees of Likeness_ Systematic Botany ) Systematic Zoology } Classificatory _Natural_ Affinity Comparative Anatomy ) Sciences. (_Vital Powers_) Assimilation Irritability (_Organization_) Biology Organical Sciences. Final Cause Instinct Emotion Psychology (_Metaphysics_.) Thought Historical Causation Geology ) Distribution of ) Palætiological Plants and Animals } Sciences. Glossology ) Ethnography ) First Cause Natural Theology.

[*Transcriber's Note: The two following tables were inserted on separate sheets at this point. They were structured as trees, but have here been converted into a diagram to be read from left to right, and an associated key. Arrows have replaced the brackets Whewell used. In the original, the names of discoverers and comments about inadequate explanations were printed in red.]

INDUCTIVE TABLE OF ASTRONOMY

a r ) { )
) { )
b → j s ) { J )
) → z { )
c → k ) { )
) )
d → l t ) )
)
e → m ) ) { b1 → c1 → m1 )
u ) → A E → H ) → M { N → Q → W )
f → n ) ) { b1 → d1 → n1 ) )
) ) )
) { R → X b1 → e1 ) ) )
g → o v → B F → I K ) { ) ) )
) { O S → Y b1 → f1 )→ o1 ) )
) { ) ) )
) { S → Z b1 → g1 ) ) )→ u1
h → p w → C G L ) )→ t1 )
P T b1 → h1 → p1 ) )
) )
q x → D b1 i1 → q1 ) )
) )
i y b1 j1 → r1 ) )
) )
U → a1 b1 k1 → s1 ) )
) )
V b1 → l1 ) )

a = THE EARTH appears to be immovable. b = THE STARS keep their relative places in the vault of the sky, and with the Sun and Moon, rise, move, and set. c = THE MOON'S bright part is of the shape of a ball enlightened by the Sun. d = THE MOON'S ECLIPSES occur when she is full. e = ECLIPSES OF THE SUN AND MOON often occur. f = THE MOON rises and sets at different times and places. Her course among the Stars varies. g = THE PLANETS are morning and evening Stars: are direct, stationary, and retrograde. h = THE SUN rises, culminates, and sets in different times and places at different seasons: different CONSTELLATIONS are visible at night. i = THE TIDES ebb and flow. j = Chald^ns. _The Sphere of the Heavens appears to make a Diurnal Revolution._ k = Greeks. The Moon receives her light _from the Sun_. l = Greeks. The Moon's Eclipses are caused by the _Earth's shadow._ m = Chald^ns. The Moon's Eclipses follow certain cycles. n = Greeks. The Moon appears to revolve monthly in an _oblique orbit_, which has _Nodes_ and an _Apogee_. o = Chaldeans. The Planets have proper motions and certain _Cycles_. p = Pythagoras. The Sun appears to move annually in an _Ecliptic_ oblique to the diurnal motion. q = The places of Stars are determined by their Longitude measured from the Equinox. r = The forms and dist^s of known parts of the earth are such as fit a convex surface. s = The visible Pole of the Heavens rises or drops as we travel N. or S. t = The boundary of the Earth's shadow is always circular. u = By observations of Eclipses, the Moon's Nodes and Apogee revolve, and her motion is unequal according to certain laws. v = By observations of the Planets, their progressions, stations, and retrogradations. w = By observations of the Sun, his motion is unequal according to certain laws. x = By observations, Longitudes of Stars increase. y = By observations, the Tides depend on the Moon and Sun. z = Aristotle? The Earth is a _Globe_, about which the Sphere of the Heavens performs a _Diurnal Revolution_. A = Hipparchus. The Moon appears to move in an _Epicycle_ carried by a Deferent: the _Velocity of Apogee_ and _Nodes_ determined. B = Eudoxus. The Planets appear to move in Epicycles carried by _Deferents_. C = Hipparchus. The Sun appears to move in an _Eccentric_, his _Apogee_ being fixed. D = Hippar. There is a _Precession of the Equinoxes_. E = By additional observations, the Moon's motion has another inequality. Evection. F = By additional observations, the Planets' motions in their Epicycles are unequal according to certain laws. G = By additional observations, the Sun's Apogee moves. Albategnius. H = Ptolemy. The Moon appears to move in an _Epicycle_ carried by an _Eccentric_. I = Ptolemy. The Planets appear to move in _Epicycles_ carried by _Eccentrics_. J = * _By the nature of motion_, the apparent motion is the same whether the Heavens or the Earth have a diurnal revolution: the latter is _simpler_. K = * _By the nature of motion_, the apparent motion is the same if the Planets revolve about the Sun: this is _simpler_. L = * _By the nature of motion_, the apparent motion of the Sun is the same if the Earth revolve round the Sun: this is _simpler_. M = * Copernicus. The Earth and Planets revolve about the Sun as a center in Orbits nearly circular. The Earth revolves about its axis inclined to the Ecliptic in a constant position, and the Moon revolves about the Earth. The _Heliocentric Theory_ governs subsequent speculations. N = Retaining Moon's Eccentric and Epicycle; By additional observations, the Moon's motion has other inequalities. O = Retaining but referring to the Sun as center the Planets' Epicycles and Eccentrics and the annual Orbit; P = Retaining obs^ns. Earth's Aphelion revolves. Q = Tycho. Moon's _Variation_; _Unequal Motion of Node_; _Change of Inclination_. R = By calc^ns. of the periodic times and distances. S = By additional observations and calculations. T = Planets' Aphelia revolve. Jupiter and Saturn's motions have an inequality dep^g. on their mutual positions. U = THE WEIGHT of bodies dimin^s in going towards the Equator. V = THE SATELLITES of Jupiter and Saturn revolve according to Kepler's Laws. W = Horrox. Halley. The Moon moves in an _Ellipse_ with variable _axis_ and _eccentricity_. X = Kepler. Distances cubed are as times squared. Y = Kepler. Areas as described by Planets are as times. Z = Kepler. Curves described by Planets are as ellipses. a1 = Newton. Earth is oblate. b1 = * By Mechanics. c1 = * Newton. Moon is attracted by the Earth. Fall of heavy bodies. d1 = * Newton. Moon's inequalities produced by attraction of Sun. e1 = * Newton. Wren. Hooke. Sun's force on different Planets is invers. as square of distance. f1 = * Newton. Planets are attracted by the Sun. g1 = * Newton. Sun attracts Planets invers. as square of distance. h1 = * Newton. These inequalities are produced by mutual attraction of the Planets. i1 = Precession of Equinoxes is produced by attraction of Moon and Sun on oblate Earth. j1 = Tides are produced by attraction of Moon and Sun on Sea. Explanation imperfect. k1 = Diminution of gravity and oblateness of Earth arise from attractions of parts. l1 = * Newton. Jupiter and Saturn attract their Satellites inversely as the square of the distance, and the Sun attracts Planets and Satellites alike. m1 = Newton. Earth attracts Moon invers. as square of distance. n1 = Newton. Sun attracts Moon. o1 = Newton. Sun attracts Planets inversely as the square of the distance. p1 = Newton. Planets attract each other. q1 = * Newton. Moon and Sun attract parts of the Earth. r1 = * Newton. Moon and Sun attract the Ocean. s1 = * Newton. Parts of the Earth attract each other. t1 = Newton. All parts of the Earth, Sun, Moon. and Planets attract _each other_ with Forces inversely as the square of the distance. u1 = Newton. THE THEORY OF UNIVERSAL GRAVITATION. (All bodies attract each other with a Force of _Gravity_ which is inversely as the squares of the distances.)

INDUCTIVE TABLE OF OPTICS

First Facts. The common and obvious Phænomena of Light and Vision.

By the _Idea of a Medium_ Light and Vision take place by means of something intermediate.

First Law of Phænomena. The effects take place in straight lines denoted by the Term _Rays_.

Facts of

a → m h1 ) ( ) )
) ( ) )
b → n ) ) i1 ) ( ) )
)→ r ) ) ( C1 ) )
c o ) )→ K ) ) ( ) → F1 )
) ) j1 )→ x1 ( ) )
d p ) L S ) ) ( ) )
) ) )
e s → M ) T h1 ) D1 ) ) ) → H1 )
)→ ) ) ) )
f t ) U k1 ) ( ) → G1 ) )
( E1 ) ) )
g ) ( u → W l1 ) ( ) ) )
) ( ) ) )
) ( v → X l1 )→ y1 ) )
)→ q ( ) ) )
) ( w → Y j1 ) ) )
) ( )
) ( x → Z ) ) ) )
( ) m1 ) ) )
( y → a1 ) ) ) )
( ) ) → I1 )
( z n1 )→ z1 ) )
( ) ) ) → K1
( A N b1 o1 ) ) )
q ←( ) ) )
( B O p1 ) ) )
( )
( C ) c1 q1 ) ) )
( ) V ) ) )
( D ) d1 q1 ) ) )
( ) ) )
( E j1 )→ A1 ) )
( ) ) )
( F P e1 ) ) ) )
( ) r1 ) ) )
( G f1 ) ) ) )
( ) → J1 )
( H Q s1 )
)
h ( R g1 t1 ) )
( ) )
i ( I u1 ) )
( ) )
j ( v1 )→ B1 )
) )
k ( w1 ) )
( J ) )
l ( w1 ) )

a = Rays falling on water, specula, &c. b = Rays passing through water, glass, &c. Measures. Ptolemy. c = Colours seen by prisms, in rainbow, &c. d = Colours in diff. transp. Substances. Optical instrum^ts. e = Two Images in Rhomb. of Calcspar. f = Two Images in other crystals. g = Two Rhombs of Calcspar make 4 images alternately appear and disappear. h = Fringes of shadows. Grimaldi. Hook. Newton. i = Spectra of gratings. Fraunhofer. j = Colours of striated surfaces. Coventry's Micromet^r. Barton's Buttons. Young. k = Colours of _thick Plates_. Newton. l = Colours of _thin Plates_. Hook. Newton. m = Euclid. Ang. Inc. equals Ang. Reflection. n = Snell. Sin. Refr. to Sin. Inc. in giv. _Ratio_ in same med. o = By measures of Refraction. p = Dispersion of colours is same when Refr. is diff. Measures. Dollond. q = Huyghens. Rays of light have four Sides with regard to which their properties alternate. Newton. Idea of _Polarization_ introduced, which governs subsequent observations. _Dipolarization_ with Colours. r = Newt. Refr. R^o. is diff. for diff. colours, but in same med. is const. for each colour. s = Measures. Huyghens. t = Double Refr. in biaxal crystals. Brewster. u = Rays are polarized by Calcspar, Quartz, &c. v = Rays are polarized by biaxal crystals. w = Rays are polarized by Tourmaline, Agate, &c. x = Rays are polarised by Refl. at glass. y = Rays are polarized by transmission through glass. z = Variable q^y. of pol. refl. light paral. plane of Refl. Arago. A = Variable q^y. of pol. refl. light perp. plane of Refl. B = Whole light reflected by internal Refl. C = Pol. Rays through uniaxal crystals give colours. Rings. Wollaston. D = Pol. Rays through biaxal crystals give colours. Arago. E = Pol. Rays. through imperf. crystallized bodies give colours. (Glass strained, jellies prest.) Brewster. F = Pol. Rays in axis of Quartz give a peculiar set of colours. Plane of Pol^n twisted diff^ly. for diff. colours. Biot. Arago. G = Pol. Rays oblique in Quartz give peculiar rings, &c. H = Pol. Rays through certain liquids give a peculiar set of colours. I = The Laws of these Phænomena were never discovered till Theory had indicated them. J = _Newton's Scale of Colours._ _Fits_ of Rays. Newton. K = Dollond. L = Prop^n of Ref. R^s is diff. in diff. med. _Achromatism_. M = Huygh^s. Law of Double Ref. exp. by a spheroid. N = Change of plane of pol. by Refl. Arago O = Light is _circularly pol._ by 2 Refl. in _Fresnel's Rhomb._ Fresnel. P = + in dir^n of plagihedral faces. J. Herschel. Q = Plane of Pol^n. twisted. Biot R = Fringes obliterated by stopping light from one edge or interposing a glass. Young. Arago. S = Ratios not reconcilable. _Irrationality_. Blair. T = Fresnel. U = Law exp. by surface of 4 dim^s. V = Optical classification of crystals. Brewster. W = Newt. Malus. Ray pol. in _principal plane_ of Rhomb.; and perp. to it. X = Brews. Biot. Ray pol. in plane bisecting ang. at axis; and perp. to it. Y = Brews. Ray pol. paral. to axis. Z = Malus. Ray pol. in plane of Refl. for _given angle_. a1 = Malus. Ray partially pol. in plane perp. to plane of Reflection. b1 = None Refl^d. if tan. ang. equal Refr. R^o. Brewster. c1 = Tint is as sq. of sin. Biot. d1 = Tint is as sin. α sin. β. Brewster. Biot. Lemniscates. J. Herschel. e1 = * By interf. of resolved undul^ns. of 2 rays circularly pol^d. in opp. directions. * Fresnel. f1 = * By interf. of resolved undul^ns. of 2 rays elliptically pol^d. in opp. directions. * Airy. g1 = * By interf. of rays from edges. Young. h1 = * Refl. produced by spherical undul^ns. i1 = * Refr. produced by spherical undul^ns. of diff. vel. for diff. colour. j1 = † Explanation imperfect. k1 = * Refr. produced by curved surf. undul^ns. l1 = * Pol^n. being prod. by resolution of transv^e undul^ns. m1 = * Polarization being produced by resolution of transverse undulations. n1 = * Undul^ns. being com^d. acc. to laws of elastic bodies. o1 = * Undul^ns. being com^d. acc. to a certain hypothesis. p1 = * Impossible formulæ being interpreted by analogy. q1 = * By interf. of resolved parts of transverse undul^ns. r1 = * Same hypothesis explains separation of rays in axis and oblique. † Explanation imperfect. * Maccullagh. s1 = † Explan. wanting. t1 = * By interf. of rays from all parts. * Young. * Fresnel. u1 = * By interf. of undul^ns. from all parts. * Fraunhofer. v1 = * By interf. of rays from striæ. * Young. w1 = * By interf. of undul^ns. from two surfaces. * Young. x1 = * Huyghens. Reflection and Refraction are propagation of undulations. y1 = * Young. * Fresnel. Polarization in crystals is transverse undulations. z1 = * Fresnel. Polarization in Reflection and Refraction is transverse undulations. A1 = * Fresnel. * Arago. Dipolarized Colours are produced by interference of Rays polarized in same plane; length of undulation being different for different colours. B1 = * Young. * Fresnel. Colours of Fringes, Gratings, Striæ, thick Plates, thin Plates &c. are produced by interference of undulations; length of undulation being different for different colours. C1 = * Undulations being propagated by the uniform elasticity of each medium. D1 = * Undul^ns. prop. by el^y. of medium diff. in 2 diff. dir^ns, (_axis of crystal._) E1 = * Undul^ns. being prop. by elasticity of med. diff. in 3 diff. directions (_axes_). F1 = Young. Reflection and double Refraction are propagation of undulations by crystalline elasticity. G1 = * Fresnel. Double Refr. and Pol. arise from same cause. H1 = Young. Fresnel. Light is transverse undulations propagated in media by elasticity dependent on axis, when crystalline. I1 = Fresnel. Light is transverse undul^ns. transmitted from one med. to another according to probable hypotheses. J1 = Young. Fresnel. Colours result from interferences, the lengths of undulation being different for different colours. K1 = THE UNDULATORY THEORY OF LIGHT.

{{141}} NOVUM ORGANON RENOVATUM.