INDEX

Abraham, M.: correspondence with Einstein, 302 acceleration: see motion Achinstein, Peter: model-theory, 15 (see also models) aether: theory of, Newtonian, 269, 270, 271 analysis: Leibnizian, defmed, 200-201 anima mundi: Cambridge Platonists' answer to materialism, 133 Archimedes: hydrostatics, 24, 33; On Floating Bodies, 24; hydrostatic model, used by

Galileo, 53 architectonic: see verities, eternal, Cartesian ars iudicandi: Leibnizian, part of scientific model, 178 Aristotle: mechanics, compared with medieval theory of impetus, 18; on lightness con­

cept, as inherent property, 53;Mechanical Questions, model of lever in, 53;Physica, 54, 73, 80, 81,83,115,117; motion, concept of, 61; extension, concept of, 80-83; Metaphysica, 80, 114; potential infmite, doctrine of, 82, 115; quantity, theory of, 108-109; influence on 17th century natural philosophy, 113; rejection of actual infmite, 117; scholasticism, metaphysical principles in, 204

atomism: as source of Newtonian concept of infinite extension, 70; Renaissance version of, 120; Democritean, conflated with Cartesianism, 133

attraction: Kantian, as empirically determined force, 252

Baliani, G.: De motu gravium, gravity as active agent, 56 Belaval, Y.: Leibniz: Critique de Descartes, 215 Bernoulli, J.: theory of living force, 229; Laws of the Communication of Motion, 233;

On the True Concept of Living Forces, 233 Bohr, N.: model of atom, theoretical, 16 Bolzano, B.: mathematical classes, introduction of, 142; ideal of mathemati~ation,

291; Die drey Probleme der Rectification, der Complanation und der Cubirung, 291; Wissenschaftslehre, 291; rejection of Kantian mathematical theory, 292-293

calculus: infmitesimal, Leibniz as one of inventors of, 179, 184 Cambridge Platonists: 132; indictment of Cartesianism, 133; rivalry with Hobbes, on

infmity, 133 Camap, R.: as philosopher of science, 4-6 causality: Kantian principle of, 244 classes: infmite, Cartesian, 142; mathematical, introduced by Bolzano and Dedekind,

142 Cohen, I. B.: history of science methodology, 4; explication of Newton on deduction,

12; criticism of Salisbury's interpretation of Galileo, 13 completeness: idea of, Leibnizian, 168; idea of, Cartesian, constructured, 171 comprehending: as distinct from understanding, 96-97

319

320 INDEX

conceivability: Cartesian notion of, 88-89 Conring, H.: correspondence with Leibniz, 204 conspiration universelle: Leibnizian, as account of mathematical order of universe, 178,

179, 186; rejection of, entailed by Cartesian rejection of fmal causes, 222 continuity: law of, Leibnizian, 233, 234 contradiction: principle of, in Leibniz, 161,165,171,199,200,201 creation: theories of, in capsule, 119-121 Cusanus, Nicholas ofCusa: Opera Omnia, 111 n8; Descartes' debt to, 119

Dedekind, R.: introduction of mathematical classes, 142 (see also classes) deduction: systems of, Cartesian and Leibnizian, as fmitely axiomatizable, 162-163,

201; related to Leibnizian sufficient reason, 168; Cartesian, 197-198,206,220 derivability: Bolzanian theory of, 294-297 Descartes, Rene: interpretation of Galilean dynamics, 9; Principles of Philosophy, 9,

71,87,91, 125, 127, 128; criticism of Galilean method, 52; doctrince of material extension, 69, 71, 87; representative character of knowledge, 70; Objections and Replies, 70, 76, 98, 216; natural philosophy, 70; Meditations on First Principles, 70, 71, 76, 78, 95, 98, 132; divine being, notion of, 88,95,122,216-217,221; debt to Cusanus on infinite, 119; LeMonde, 125; on perfection, relative to Newton, 125; on infmite classes, 142; intuition, statements of, 152; scientific method, 156,166,170; Discourse on Method, 197,198,200; eternal verities, 200; hypo­thetical system, 206; hypothesis, doctrine of,justified, 212; refutation of skepticism, 218; refuation of final causes, 221

divine being: Henry More's conception of, 70; Newtonian conception of, in relation to space, 70; as independent of understanding, 71; as only infmity, 88,122,221; ontology of, 93; relation to extension and space, 94,95,128; Cartesian apprehen­sion of, 95, 96; Lockian conception of, 137-139; as efficient cause of eternal verities, 216-218; Thomist understanding of essence of, 217-218; will of, as foundation of physics, 221

dynamics: Galilean, 6, 7, 8; Cartesian, distinguished from Galilean, 9; John Wallis' contribution to, 9; Leibnizian, 206,232,241; relation to mechanics, as foundation of, 261

Ehrenfest, P.: correspondence with Einstein, 304 Einstein, A.: development of gravitation theory, 299-314; "Relativity and Gravitation:

Reply to Abraham's Remarks", 303 epistemology, of space:

- Cartesian: representative nature of knowledge, 70; negative formulation of in­finitude, 72; influence on Newtonian, 76-78; conceivability, 89; distinction between comprehendo and intelligo, 125-126; relation to Newtonian, 132

- Newtonian: 70, 108, 109; divergence from Cartesian, 71; distinction between understanding and imagination, 72, 73, 76, 131 (see also imagination and under­standing); relation to Cartesian, 87, 13 2

electrical arc: Petrov's 279 equivalence: principle of, Einsteinian, 299,300,301,304,306,309,312,313 essences: Cartesian notion of, as discrete, therefore created, 218 Euclid: Elements, 28,29,31,32,51,81,291,297

INDEX 321

Euler, Leonhard: mathematics of inimitude, 143; distinction of force and inertia, 229, 238; The Force of Impact and Its True Measure, 234; On the Origin of Forces, 238; Letters to a German Princess, 239

evidence: Cartesian, as indubitability, 220 extension: Cambridge Platonists' version of, as inimite spirit, 133 (see anima mundi);

- Cartesian: indefmite and material, 69,71,87,91,97,99,127, 129-130; negative formulation of, 72; character of, 76, 93, 94; conceivable, 89; created, 98, 99; imaginable, 107; undifferentiated, 109; related to concept of divine being, 128

- Newtonian: infmite but geometrizable, 69,100-104; as object of understanding, 70; as inimite, 71,72,73,74,76,79,96; as coeval with divine being, 99-100; as infinite but compositional, 110

Feyerabend, Paul: relativistic approach to history of science, 17, 18 finite, the: as negation of being, 122 fmiteness: necessary defect of created entities, 99 first principles, primitive truths: as fust tenet of Rationalism, 152, 153 (see also intui­

tion, Cartesian judgement by) force: Newtonian, 11; Cartesian measure of, as quantity of motion, 231; problems in

measurement of, 231; as physical entity, 232; Kantian, distinction between mathe­matics of an ontological status of, 235; related to intertia, 237; related to im­penetrability, 238; as ontologically prior to impenetrability, 240; Leibnizian, as constitutive of matter, 256

forces: Leibnizian, as derivative, 232; Kantian, as defming properties of matter, 240; of attraction and repulsion, 242; original-constitutive and impressed, 259-261; metaphysical, 274; mechanical, 274

Galileo Galilei: 3,6,7; Discourses Concerning Two New Sciences, 7,8,9,12,25,46, 47, 51, 54, 55, 56, 57, 61, 62, 63,64; Letters on the Sunspots, 8; dynarnicallaws, relation to Newtonian physics, 10; Dialogues on the Two Chief World Systems, 12, 37,54, 56, 61, 62, 63, 65; as creator of new discourse about nature, 23; Le Meccaniche, 26; geometrization of naturally accelerated motion, 35-46; De Motu, 53,55,56

galvinism: 280 Gassendi, P.: on epistemology of inimitude, 126 geometrization: of empirical truths, Leibnizian, 209 gravitation: Kant's inverse square law for, 252; relativistic theory of, 299,305, 309;

tensor-geometrical conception of, 299,303,305,306,308,309,311,312,313,314 gravity: Galilean, 22; as agent of cosmological ordering, 24; Galilean geometrization

of, 24; as natural motive force, cause of accelerated motion, 24, 25, 26,45, 52, 55, 56

Grossman, M.: collaboration with Einstein, 308-311

Harriott, Thomas: Atomism, Renaissance version of, 120; rejection of creation ex nihilo, 120

Hobbes, Thomas: on inimity, rivalry with Cambridge Platonists, 133 hylozoism: Kantian concept of, in mechanical theory, 245, 263

322 INDEX

ideas: Lockian, positive, 136; innate, Cartesian, 157-158; innate, Cartesian, relation to simple natures, 200; innate, Leibnizian, 158-159,199,201; innate, Newtonian, 134; innate, in Rationalist doctrine, 152

imagination: Newtonian, as distinct from understanding, 69,70,72,73,76-79,131; inadequate in grasping inrmity, 71,87; Cartesian, limits of, 78-79

impenetrability: Eulerian, relation to force, 238, 239; Newtonian, as absolute universal quality of matter, 238; Kantian, as relative, 242

impetus: medieval theory of, 18; relative to gravity, 55,56 indivisibles: method of, Galilean use of, in geometrizing accelerated motion, 41 inertia: Galilean, as case study of relationship of history and philosophy of science,

6-14; coining of term, 7; principle of, compared with medieval theory of gravity, 18; Newtonian, as universal quality of matter, 238; force of, as contradiction in terms, 253-254; Kantian, as non-dynamical property, 263; Eulerian concept of, as contrasted with Kantian, 264-266; Mach conception of, 303,306,307

infinitesimals: Leibnizian, 232 infinitude: Galilean concept of, 63,64; Newtonian, 69,95; as second level attribute,

70, 75,94; spatial, as completeness of being, 73; mathematization of, 85; positive and negative, 88, 123; Cartesian, of divine essence, 92,93,96,97; actual, cate­gories of, 102-103, 134; geometrizable, 107; Aristotelian concept of, 113-115; 17th century modification of Aristotelian, 113, 118; distinction of potential and actual, 115-117; Cartesian, indefinite, 118; philosophers of, in capsule, 120-121; of human will, 131; Lockian concept of, 134,135, 136, 140

intension: Kantian, 235 intuition, Cartesian: 152, 153,154,155; distinguished from Leibnizian, 155; limits of,

in demonstration process, 211

Kant, I.: First Antimony, adoption of Lockian distinction of space inrmite and infinity of space, 135; Metaphysical Foundations of Natural Science, 229, 230, 239, 240, 241,244,245,246, 251, 255,257,259,261,262,266,272,273,274;Thoughuon the True Estimation of Living Forces, 231, 235, 236, 237, 240, 244, 258; force, living and dead distinction rejected, 234; intension, 235-236; monads, theory of, Wolffian as opposed to Leibnizian influences on, 236; Physical Monadology, 236, 237, 240, 245, 258, 259, 261; force, restructuring of relation with inertia, 237; impenetrability, inversion of Euler's linking of force with, 239; material substance, derming properties of, 239; Critique of Pure Reoson, 239,244,272,274; gravity, justification of possibility of concept of, 243; matter, metaphysico-dynarnical ex­plication of, 243-244; mechanics, three laws of, in relation to Newton's three laws of motion, 244, 251, 254, 262; critical philosophy, relation to Newtonian mechan­ics, 255

Kepler, J.: coining of term 'inertia', 7 Kneale, W.: Probability and Induction, explication of Newton on deduction, 11 Koyre, A.: philosophical contribution to history of science, 4 Kuhn, T.: contribution to history of science, 4, 17, 18

Lakatos, I.: 300 LaPlace, H.: Systeme duMonde, 272 lawlikeness: Kantian and Newtonian concepts of, compared, 251; Kantian, 262,263

INDEX 323

Leibniz, G. W.: inf'mitude, mathematics of, 135-136; critique of Hobbes, 143; primit­ive truths, 153, 166; Meditationes de Cognitione, Veritate et Ideis, 154,198,205; scientific method, 157; contradiction, principle of, 161,165,171; ars inveniendi, 177; an iudicandi, 178; calculus, inf'mitesimal, as one of inventors of, 179, 184; New Physical Hypothesis, 197,205; dynamics, formulation of original principles of, 197; Discourse on Metaphysics, 198,205,218,221; IntroductioadEncyclopaediam arcanum, 199; analysis, method of, def'med, 200; hypothesis, notion of, 204, 205, 206, 209, 210; demonstration, theory of, 204,211; Animadversiones in partem generalem Principiorem Cartesianorum, 208, 219; Cartesianism, critique of, 211-219; causation, f'mal, restoration of, 221; Theoria motus abstracti, 221; Specimen dynamicorum, 232; New Essays Concerning Human Understanding, 295,297

lightness: Aristotelian principle of, contradictory reintroduction of, by Galileo, 53 Locke, J.: Essay Concerning Human Understanding, 84,121,122,134,136,137,138,

140; ideas, positive, 84, 136; inf'mity, 84-87,132,134,139,140; Cambridge Platonists, point of agreement with, 134; divine being, on nature of, 137; quantity, distinction between notions of, 142

Lukasiewicz, J.: four axioms of assertion, axiom of rejection, 176

mathematization: of infinity, 85; Cartesian and Leibnizian ideal of, 197; limits of, 258; Leibnizian, as modified by Bolzano, 292

matter, theory of: mathematical/mechanical vs. metaphysical/dynamical, 256-257; Kantian, 262

maximization, principle of: 178-186,203 Maxwell, J. C.: representational model of electric field, 15, 17 mechanica: Eulerian and Kantian use of term, 241 mechanics: Kant's second law of, 244 Mersenne, M.: 52,56 metaphysics: Kantian, of nature, 231, as foundations of mathematics, 258-259 mind: ontology of, Cartesian, 77,78 (see also imagination and understanding) minimization, principle of: Leibnizian, 178, 186, 203 Minkowski, H.: 305 mede1s: rationalizing, 6; Achinstein's three kinds, 15-17; Maxwell's, of electric field,

15; Bohr's theoretical, 16; Poincare's, of non-Euclidean world, 16; Cartesian development and use of, 206; Leibnizian, treatment of, 207

monads: hierarchical order of, 134n, 192; Kantian, 236; Leibnizian, as centers of metaphysical force, 257

more geometrico: Cartesian and Leibnizian, distinguished, 159-166; Leibnizian, applied to all science, 169,201- 204

More, H.: conception of God, 70; influence on Newtonian doctrine of space, 70,89; Injinitie of Worlds, 132; Divine Dialogues, 133

motion: law of, Newton's second, as case-study of relation of history and philosophy of science, 6-13; as ungeometrizable process, 25; acquired, conservation of, 27; as uniform, geometrizable, 27-32; accelerated, naturally, underivable from Archimedean hydrostatics, 33; geometrization of, 35; Galilean, difficulties in representing, 445; accelerated, uniform, reduced to uniform, 45,46, 57,58,61,62; Aristotelian notion of, 61; laws of, Newtonian, in relation to Kantian dynamics, 244-245; uniform, rectilinear, 253'

324 INDEX

necessity: as physical law, 65 Newton, I.: Mathematical Principles of Natural Philosophy, 9,10,237,238,253,269,

272; Galilean physics, interpretation of, 10; De Gravitatione, 69, 71, 72,75,76, 77,80,86,90,92,94,100,102,103,104,105,106,122,141, 171; epistemology, 70; Questiones, 70,71,76,78,90, 106; extension, infmity of, 71,74,86; inrmity mathematization of, 85; Locus et Tempus, 100,102,103,104; Cartesian epistem­ology of infmitude, assessment of, 130; motion, three laws of, related to Kant's three laws of mechanics, 244,245, 251, 252-254; inertia, force of, 253; Optics, 270

non-contradiction, principle of: Cartesian, 217

Pascal, B.: Rationalist doctrine, 152 perception: Cartesian and Newtonian notions of, 79,123 Petrov, Vasily Vladimirovich: experiments in electricity, 279 phoronomia: Kantian and Leibnizian uses of term, 241 physics: moods of, Cartesian and Leibnizian, 202-203; mathematical, relation to

metaphysics, 258-259; mathematical, limitations of, 260 Poincare, H.: non-Euclidean world, model of (see also models) proportionality: of space and time, 62

quantity: Aristotelian notion of, 74, 75, 80-83, 106, 108-109; related to idea of infinitude, 86,122,142, Lockian notion of, 134

quantum: Newtonian conception of, 75; mechanics, 299

Raleigh, Sir W.: History of the World, 120; heresy trial, 120 Rationalism: of 17th and 18th centuries, 151-152 reasoning: mathematical, 172-174,177 relativity: general theory of, 299; special theory of, 300,301,302,305,306,313 representation: role in Cartesian and Newtonian epistemology, 70,77, 78 Rescher, N.: basis of Leibnizian system, 222-223 Rocco, A.: Esercitazioni Filosofiche, 54

science: history of, 3, 5,4-13, 23, 52; philosophy of, 3, 13-19; rationalized, 5, opposed to religion, 272

skepticism: Cartesian refutation of, 218,219 space: Newtonian, complete, 75, 105-106; Cartesian notion of, 105-106; Lockian,

the infmity of, vs. the infinite, 135; relation to motion theory, 254; Kantian relativity of, 254-255

speed: Galilean concept of, 30,31,32,41,51,53,55,57,61,62; relation to time, 32; relation to density of medium, 34, 35; instantaneous, 36,56,62; of uniform motion, 62; of light, 301, 302

Spinoza, B.: Rationalist doctrine, 152 Stanley, T.: History of Philosophy, 73 Suarez, F.: Disputationes Metaphysicae, 216 sufficient reason: Leibnizian concept of, 166-168,204; analytic rendering of, 202 syllogism: modes of, 155 syllogistics: Leibnizian application of, 174-176

INDEX 325

synthetic ideas: Lockian idea of infinity, 134

Themistius: paraphrase of Aristotie'sPhysics, 54 truth criteria: Cartesian and Leibnizian, distinguished, 154,155,198,199,200

understanding: as distinct from imagination, 69, 70, 72, 73, 76,77,78,79,107, 131, 132; as conceiver ofinfmity, 70,87; as distinct from comprehending, 96-97

validation criteria: 209,210,211; BoIzanian, 293 verities, eternal: Leibnizian, increate, 216; Cartesian, created, 217-218,220

Wallis, J.: Mechanica, 9; dynamical theory, 9; Arithmetica Infinitorum, influence on Newton, 85

will: Cartesian infinity of, 131 Wolff, C.: Rationalist doctrine, 152

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