146 MEMOIR OF AUGUSTUS DE MORGAN. 



18-42. I f r gt m y hieroglyphic of Uranus ; I told you, I think, that 



the baronetage draws Mars instead of Uranus in your shield. 



I pointed out the mistake of latitude to Charles Knight's 

 people to-day. They told me they were partly aware of it 

 already. What is meant by being partly aware of the pole-star 

 not being exactly on the pole ? 



'In order to be sure that a general proposition is true we 

 must be sure that all its particular applications are true.' If ' in 

 order ' means previously I deny the assertion. Certainly, to be 

 sure that a general proposition is true we must be sure that all 

 its particular cases are true, for a general proposition =S (par- 

 ticular case). 



I suppose it is meant that there is no surety without exami- 

 nation of all the particular cases ; this I admit too, but I suppose 

 it is farther meant that there is no surety without enumeration 

 of the particular cases : if so, this I deny. 



For example, the angles at the base of an isosceles triangle 

 are equal. In the proof I have moral certainty that I examine 

 every isosceles triangle ; any one 'whatsoever is every one. Ab- 

 straction and rejection of all that distinguishes one particular 

 case from another is the mode of induction, if people like to call 

 it so, which general reasoning employs. 



' Consequently it is reasoning in a circle to include the truth 

 of the particular from that of the general.' I deny the conse- 

 quence. If any one likes to say, on the preceding view, that 

 general reasoning is induction of particular cases, which I do not 

 in a certain sense deny, he must not say that I conclude or infer, 

 but only that I go to a drawer in which I have laid up all the 

 cases ready for use, for this must be the correlative meaning of 

 inference. But shall the very man who found out that I had 

 got my drawer full be the one to deny me liberty to take out 

 the contents, because the etymology of the words I use to 

 describe such out- taking rather seems to describe making the 

 goods, as wanted, by a machine, than taking them out ready 

 made from a receptacle ? No, if he goes and alters my words of 

 first process, he must allow me either to resist or to alter the 

 words of second process to match. 



Again, how dares any one say, ' To be sure of the general, we 

 must be sure of all the particulars ' ? Epimenides said all the 

 Cretans are always liars. Now Epimenides was a Cretan him- 

 self ; how could he establish his proposition ? If it were true, it 

 was therefore false. 



