394 PROFESSOR DE MORGAN, ON THE STRUCTURE OF THE SYLLOGISM, 



as a man. But the simile is as inapt as the recommendation it contains is unwise; for the endeavour 

 is to hit the mark, not merely to fire a shot : and the bow which most often succeeds in doing that 

 is the best. Closely examined, this direction to dispense with authority amounts to requiring 

 us to suppose that the proposer of an argument is as often right as wrong, and wrong as right, in 

 his conclusions. But what can be the wisdom of making believe that a person tells us ten truths to 

 ten falsehoods, if we know it for a fact that he tells us nineteen truths to one falsehood ? If 

 absolute demonstration be given, no rule is necessary, for we cannot attend to authority- If some- 

 thing very near to demonstration be given, no rule is practically necessary, for we have what is called 

 moral certainty. 



But, it may be said, why not throw away authority altogether .' I answer that it is impossible : 

 and that any one who forms an undenionstrated conclusion independent of the authority of others, 

 can only do it by assuming some value for his own. All arguments, and all balance of arguments, 

 will leave three possible cases. Either one or more of the arguments for the conclusion will prove 

 it, or one or more of the arguments against will refute it, or all the arguments are inconclusive. 

 The conclusion is proved, disproved, or left neither proved nor dis])roved. But it is not one of the 

 three, true, false, or neither true nor false: it must be either true or false. And the mind must 

 come to some conclusion upon this point : it must, so to speak, distribute the inconclusivene.ss of 

 the arguments, in some way or other, between belief and disbelief. In whatever way this is done, it 

 amounts, as we shall see, to some assumption as to the authority either of the proposer or of 

 the receiver, or of some third person, or of all together. 



There is but one way in which we can really deprive the proposer of an argument of any 

 authority ; and that is, by depriving him of any peculiar authority. If Newton propose an 

 argument, to the conclusion of which Halley assents without knowledge of the argument, we have a 

 right to allow it to be reasonable that the argument should lend the same force to the conclusion as if 

 Halley had proposed it, and Newton had assented, also without knowledge. Admit this, so far 

 as the premises do not depend on the authority of the proposer, and we admit all the separation of 

 argument and authority which is practicable. 



A conclusion is usually opposed, in argument, to what logicians call the contradictory, which 

 must be true if the conclusion be false, and vice versa. It is not often that it is opposed to 

 the contrary, which must be false when it is true, but not vice versa. I shall first consider the 

 proposition and its contradictory, as to authority, as to argument, and then as to the two in 

 combination. 



Prob. 1. Required the joint value of authorities the separate values of which are given. 



Let the first authority be one of the testimony /u, or of m truths to n errors, yu being 

 TO -;- (m + «). Let //, m\ n, take the place of m> in, n in the second authority : and so on. Now 

 since the conclusion asserted cannot be true on one authority and false on another, our position with 

 respect to the conclusion is as follows : We have an urn of m white and n black balls, another of 

 m white and «' black, &c. from each of which we have to draw. The balls however are not free, 

 but are connected by such mechanism that no ball will leave its urn unless a simultaneous effort be 

 made upon one of the same colour in every urn. Now the number of ways of choosing one white ball 

 out of each urn is hi ni m" ... ; and of choosing one black ball n n' n" ... . Hence the united testi- 

 mony for the conclusion is 



and against it 



and 



fJLM.'/i"... +{l - m) (1 -m')(1 - n")... t^ix'^".-. +(!-«) (I -(ii')(l -fi")... ' 



If a = 2|ii — 1, Sec. we have for the joint authority expressed in terms of the separate 

 authorities. 



