Vlll .CONTENTS. 



CHAPTER XXIV. Of the Remaining Laws of Nature. 



PAGB 



1. Propositions which assert mere existence . . 139 



2. Resemblance, considered as a subject of science . . 141 



3. The axioms and theorems of mathematics comprise the 



principal laws of resemblance .... 143 



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



simple enumeration ..... 145 



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



tion of some given number . . . . 146 



6. Those of algebra affirm the equivalence of different modes 



of formation of numbers generally . . .151 



7. The propositions of geometry are laws of outward nature 154 



8. Why geometry is almost entirely deductive . .156 



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



limits of that function . . . . .158 



CHAPTER XXV. Of the Grounds of Disbelief. 



1. Improbability and impossibility .... 161 



2. Examination of Hume's doctrine of miracles . . 162 



3. The degrees of improbability correspond to differences in 



the nature of the generalization with which an assertion 

 conflicts . . . . . . .166 



4. A fact is not incredible because the chances are against it 170 



5. Are coincidences less credible than other facts? . .172 



6. An opinion of Laplace examined . . . .175 



BOOK IV. 



OF OPERATIONS SUBSIDIARY TO INDUCTION. 



CHAPTER I. Of Observation and Description. 



1. Observation, how far a subject of logic . . .183 



2. A great part of what, seems observation is really inference 184 



3. The description of an observation affirms more than is 



contained in the observation .... 187 



4. namely an agreement among phenomena ; and the com- 



parison of phenomena to ascertain such agreements is a 

 preliminary to induction . . 190 



