CONTENTS. V 



CHAPTER XXII. Of Uniformities of Co-existence not 

 dependent upon Causation. 



PAGE 



1. The uniformities of co-existence which result from laws of 



sequence . . . . .120 



2. The properties of Kinds are uniformities of co-existence . 121 



3. Some are derivative, others ultimate . . . 124 



4. No universal axiom of co-existence . . .126 



5. The evidence of uniformities of co-existence, how measured 128 



6. When derivative, their evidence is that of empirical laws . J 29 



7. So also when ultimate . . . .131 



8. The evidence st longer in proportion as the law is more 



general. ..... 132 



9. Every distinct Kind must be examined . . 134 



CHAPTER XXIIL Of Approximate Generalixations, and 

 Probable Evidence. 



1. The inferences called probable, rest upon approximate 



generalizations . . . . .137 



2. Approximate generalizations less useful in science than 



in life . . . . . . 138 



3. In what cases they must be resorted to . .139 



4. In what manner proved . . . .141 



5. With what precautions employed . . . 145 



6. The two modes of combining probabilities . .146 



7. How approximate generalizations may be converted into 



accurate generalizations equivalent to them . .150 



CHAPTER XXIV. Of the Remaining Laws of Nature. 



1. Propositions which assert mere existence . .154 



2. Resemblance, considered as a subject of science . .156 



3. The axioms and theorems of mathematics comprise the prin- 



cipal laws of resemblance .... 159 



4. and those of order in place, and rest upon induction by 



simple enumeration . . . .164 



5. The propositions of arithmetic affirm the modes of forma- 



tion of some given number . . .166 



6. Those of algebra affirm the equivalence of different modes 



of formation of numbers generally . . .168 



7. The propositions of geometry are laws of outward nature . 172 



8. Why geometry is almost entirely deductive . .176 



9. Function of mathematical truths in the other sciences, and 



limits of that function . . . .178 



VOL. ii. a 3 



