Philosophy and Unified Science

by TALBOTT GEORGE

• ISBN13: 9780941524186
• ISBN10: 0941524183
• Format: Hardcover
• Copyright: 1999-06-01
• Publisher: Lotus Pr

Table of Contents

Acknowledgments	xvii
Introduction	xxi
David Lee Hilliker
Foreword: What This Book is About	xxxi
Prologue: A Working Definition of Philosophy	xxxv
Preface: The Philosophy of Science	xliii
Introductory Essay: Science, Philosophy and the Analysis of Formal Structure	1	(19)
A Formal Schematization: The Ontological Network	20	(17)
Biophysical Foundations: The Homeostatic Calculus	37	(7)
A Formalization of Epistemology: The Truth Relation	44	(6)
Development of the Formal Operator: Symbolic Logic	50	(10)
Mathematics: Functions and Identities	60	(971)
elementary geometrical inference in astronomy	62	(2)
Euclidean and Non-Euclidean space	64	(3)
trigonometric identities	67	(2)
quadratic equations, completing the square	69	(1)
test for distinguishing functions and identities	70	(1)
analytic geometry (algebraic geometry)	71	(2)
differentiation	73	(6)
interpretations of derivatives	79	(2)
integration	81	(2)
interpretations of the integral	83	(2)
multiple integration in potential theory	85	(3)
volume integrals	88	(8)
trigonometric substitutions	96	(3)
partial differentiation	99	(560)
Development of the Contental Operand: General Science
Chemical Foundations: Thermodynamics and the Molecule	656	(3)
Physics of the Interface: Thermodynamics	659	(6)
first law of thermodynamics	665	(1)
work	666	(1)
gas laws	667	(1)
molar gas constant	668	(1)
temperature scale conversions	669	(2)
enthalpy	671	(2)
specific heat and gas constant	673	(3)
adiabatic processes	676	(1)
Carnot cycle	677	(7)
entropy	684	(2)
absolute zero	686	(2)
Caratheodory's principle	688	(6)
Gibbs' free energy and Helmholtz's work function	694	(1)
entropy and isentropic processes	695	(1)
adiabatic processes	696	(3)
isothermal processes	699	(2)
isobaric processes	701	(1)
isometric processes	702	(2)
process summary	704	(3)
isobaric and isothermal processes	707	(3)
chemical thermodynamics	710	(3)
chemical entropy	713	(2)
free energy calculations	715	(5)
electrochemical cells	720	(3)
isobaric and isometric processes	723	(1)
reversible, isothermal processes	724	(1)
van't Hoff's isotherm	725	(3)
Nernst's equation	728	(3)
rate constants and kinetics	731	(2)
Gibbs-Helmholtz equations	733	(2)
van't Hoff equation	735	(1)
Arrhenius equation	736	(3)
chemical kinetics, basic ideas of	739	(2)
first order reaction	741	(1)
second order reaction	742	(3)
consecutive reactions	745	(3)
periodic kinetics	748	(6)
statistics mechanics	754	(1)
Chemical Foundations: Thermodynamics and the Molecule (Continued)
derivation of Boltzmann-Maxwell formula	754	(6)
derivation of Fermi-Dirac distribution	760	(1)
derivation of Bose-Einstein distribution	761	(3)
Planck's distribution	764	(1)
derivation of Stefan-Boltzmann law	764	(4)
Fluid Mechanics of Incompressible and Compressible Flow	768	(1)
continuity equation	769	(1)
Bernoulli`s law	770	(3)
pressure loss	773	(2)
Toricelli's law, example	775	(1)
Poiseuille's equation	776	(3)
surface tension and capillarity	779	(2)
wetting and adhesion	781	(3)
Nuclear Heat: Thermal Transfer and Nuclear Energy	784	(1)
time constants and radioactivity	784	(4)
radiocarbon dating	788	(2)
binding energy, mass defect, nuclear energy	790	(6)
thermal energy and transfer	796	(3)
radiation and photochemistry	799	(2)
Einstein's equation and mass defect	801	(1)
critical ratio	802	(1)
cyclotron summary	803	(1)
Molecular Bond Energy: The Orbital	804	(1)
light scatter	804	(4)
infrared absorption	808	(1)
nuclear magnetic resonance	809	(2)
molecular orbital calculations	811	(1)
position eigenfunctions	812	(1)
momentum eigenfunctions	813	(1)
energy eigenfunctions	813	(2)
orthogonality	815	(1)
normalization	815	(2)
Heisenberg's ``indeterminacy''	817	(1)
linear combinations of atomic orbitals	818	(6)
LCAO, for hydrogen molecule-ion	824	(2)
LCAO, for butadiene molecule	826	(5)
Interactions between Radiation and Matter	831	(2)
spectral analysis	833	(1)
environmental simulation	834	(4)
cross section and absorption coefficients	838	(21)
six effects of absorbed radiation	859	(1)
photoelectric effect	859	(1)
Compton scatter	859	(1)
derivation of Compton's equation	860	(6)
pair production	866	(1)
nuclear transformations	866	(1)
chemical transformations	866	(1)
thermal effects	867	(1)
shield design	867	(5)
shield design program	872	(6)
complete example	878	(7)
Biological Foundations: Polymer, Crystal and Cell	885	(1)
unity of science, discussion	885	(2)
debunkers and fashions	887	(1)
organism tensor	888	(1)
historical summary	889	(3)
characteristics of biology	892	(1)
homeostasis	893	(2)
physiological function, in outline	895	(3)
immunological behavior	898	(3)
servo-systems and homeostasis	901	(2)
biological motion	903	(2)
psychology and psychiatry	905	(4)
topological and vector psychology	909	(2)
topological representation	911	(1)
life space, Lewin's	912	(1)
reality differentiation	913	(3)
networks in psychology	916	(3)
network examples and techniques	919	(1)
networks and matrices	919	(2)
minimum span tree	921	(1)
minimum distance in networks	922	(1)
PERT networks	923	(2)
tensors in psychology	925	(4)
tensors and ophthalmic centers	929	(1)
Rorschach's test	930	(6)
Rorschach summary and quantification	936	(2)
Rorschach scoring formulas	938	(1)
Rorschach scoring computer	939	(7)
statistics philosophy	946	(1)
statistics mean and variance	947	(1)
statistics mean deviation	948	(3)
statistics expectation	951	(1)
statistics, standard error derived	952	(2)
statistics and probability	954	(1)
statistics, normal distribution	955	(2)
statistics, Poisson distribution	957	(3)
statistics estimation	960	(2)
statistics sample size	962	(2)
statistics ``tailed'' tests	964	(4)
statistics, chi square	968	(3)
statistics correlation	971	(2)
statistics, Scoremaster program	973	(4)
statistics, Chi Square program	977	(2)
statistics, linear regression	979	(1)
statistics, correlation coefficients	980	(1)
statistics, multiple variate analysis	981	(2)
Statistics, factor analysis	983	(4)
Statistics, factor analysis example	987	(6)
statistics, factor analysis program	993	(6)
statistics, formula summary	999	(10)
statistics, examples	1009	(8)
statistics, gambling and dice	1017	(3)
statistics; probability calculations	1020	(1)
statistics, Bayes' theorem illustrated	1020	(6)
statistics, Bernoulli's theorem illustrated	1026	(5)
Conclusion and Integrative Summary: The Continuum of Applied Logic from Measurement to Aesthetic Construction	1031	(14)
Summary of the Thesis: A Formal Synopsis	1045	(24)
Postscript: Leibniz and the Philosophy of Science	1047	(22)
Bibliographical List: Ideas and Techniques	1069	(359)
TECHNICAL APPENDIX
Mathematical Summary of Godel's Proof
arithmetization of propositional calculus	1120	(7)
arithmetically derived tautologies	1127	(8)
codification of symbolic logic	1135	(5)
Godel's proof, discussion	1140	(1)
recursive definition, example	1141	(2)
Units; Dimensions and Dimensional Analysis
unit ratios	1143	(1)
unit conversion example	1144	(4)
force and mass unit example	1148	(3)
units, dimensions and conversions in mechanics	1151	(5)
The Curvature Tensor and a Four Dimensional World
curvilinear coordinates	1156	(1)
unit tangent and unit normal	1157	(1)
contravariance and covariance	1158	(1)
reciprocal vector systems	1158	(1)
arc length	1159	(2)
contravariant transformation	1161	(4)
covariant transformation	1165	(4)
velocity as a contravariant tensor	1169	(1)
rotational transformation in tensor form	1169	(2)
summation convention	1171	(1)
matrix representation	1172	(2)
mixed tensors	1174	(1)
sums of tensors	1175	(1)
outer multiplication of tensors	1176	(1)
contraction of tensors	1176	(1)
inner multiplication of tensors	1177	(1)
conjugate tensors	1177	(1)
associated tensors	1177	(1)
Christoffel symbols	1178	(1)
geodesics, derivation of	1178	(7)
geodesics in Euclidean space	1185	(2)
covariant differentiation	1187	(1)
curvature tensor; derivation of	1188	(2)
Einstein's law of gravity	1190	(2)
Group Theory in Modern Physics
molecular isomers	1192	(3)
optical antipodes	1195	(1)
diastereoisomers	1195	(1)
symmetry operations	1196	(1)
groups, mathematical	1196	(1)
symmetry groups	1197	(1)
matrices and symmetry groups	1198	(1)
group theory, and wave functions	1199	(3)
Mathematical Ideas of Quantum Theory
Hamiltonian operator explained	1202	(4)
Lagrange equation	1206	(5)
Lagrangian analysis of pendulum	1211	(2)
Hamiltonian and Lagrangian expressions related	1213	(2)
calculus of variations	1215	(8)
Hamilton's integral applied	1223	(1)
catenary equation	1224	(3)
brachistochrone problem	1227	(7)
Laplace equation	1234	(1)
heat flow	1234	(2)
gravitation	1236	(3)
vector generalization	1239	(2)
Bessel's equation and Laplace's equation	1241	(2)
Schrodinger equation and rotating dipoles	1243	(11)
The Computer and its Program
computers, impact on science and philosophy	1254	(8)
mathematical analysis with computers	1262	(5)
program for investigating a function	1267	(4)
mathematical applications	1271	(2)
differential equation algorithm	1273	(3)
Euler solution	1276	(4)
nonlinear differential equation	1280	(1)
Riemann integration algorithm	1281	(7)
Lebesgue integration algorithm, numerical	1288	(2)
Lebesgue integration, general	1290	(3)
Stieltjes integration algorithm	1293	(3)
series representation	1296	(1)
Fourier analysis program	1297	(2)
Fourier synthesis program	1299	(4)
failure rate program example	1303	(3)
machine language expression	1306	(2)
Fortran expression	1308	(1)
source languages	1309	(3)
machine language	1312	(1)
assembler language	1312	(1)
Fortran IV	1312	(1)
COBOL	1313	(1)
PL/1	1314	(2)
assembler program example	1316	(1)
square root algorithm	1317	(5)
Monte Carlo integration	1322	(5)
Laplace Transform algorithm	1327	(4)
algorithm organization chart	1331	(2)
radiation program, shields	1333	(8)
personnel coding algorithm	1341	(14)
stock market averages program	1355	(2)
mathematics of finance	1357	(3)
amortization schedules	1360	(5)
economics, mathematics of	1365	(1)
monopoly and perfect competition	1365	(5)
economics problems and solutions	1370	(8)
operations research problems	1378	(9)
cost, volume, income analysis	1387	(1)
economics of curriculum planning	1388	(2)
learning curve mathematics	1390	(2)
Markov analysis and market share prediction	1392	(3)
faculty planning and Markov analysis	1395	(1)
faculty planning and queue analysis	1396	(2)
networking techniques and curriculum	1398	(6)
linear programming, demonstrated	1404	(5)
simplex tableau, demonstrated	1409	(7)
symbolic logic and arithmetic	1416	(1)
number bases in counting	1417	(1)
logic circuit example	1418	(2)
the half-adder	1420	(1)
the full adder	1421	(2)
analogue feedback loop	1423	(2)
analogue addition	1425	(1)
analogue differentiation	1426	(1)
analogue integration	1427	(1)
analogue solution of differential equation	1427	(1)
concluding remarks	1428