200 PROFESSOR WHEWELL's DEMONSTRATION 



deduced from the axioms, their truth also becomes evident, and the contrary 

 becomes inconceivable. When a person has familiarized himself with the 

 first twenty-six propositions of Euclid, and not till then, it becomes evident 

 to him, that parallelograms on the same base and between the same parallels 

 are equal ; and he cannot even conceive the contrary. When he has a little 

 further cultivated his geometrical powers, the equality of the square on the 

 hypothenuse of a right-angled triangle to the squares on the sides, becomes 

 also evident ; the steps by Avhich it is demonstrated being so familiar to the 

 mind as to be apprehended without a conscious act. And thus, the contrary 

 of a necessary truth cannot be distinctly conceived ; but the incapacity of 

 forming such a conception is a condition which depends upon cultivation, 

 being intimately connected with the power of rapidly and clearly perceiving 

 the connection of the necessary truth under consideration with the elemen- 

 tary principles on which it depends. And thus, again, it may be that there 

 is an absolute impossibility of conceiving matter without weight ; but then, 

 this impossibility may not be apparent, till we have traced our fundamental 

 conceptions of matter into some of their consequences. 



The question then occurs, whether we can, by any steps of reasoning, 

 point out an inconsistency in the conception of matter without weight. 

 This I conceive we may do, and this I shall attempt to shew. 



The general mode of stating the argument is this : — the quantity of 

 matter is measured by those sensible properties of matter which undergo 

 quantitative addition, subtraction and division, as the matter is added, sub- 

 tracted and divided. The quantity of matter cannot be known in any other 

 way. But this mode of measuring the quantity of matter, in order to be 

 true at all, must be universally true. If it were only partially true, the 

 limits within which it is to be applied would be arbitrary ; and therefore 

 the whole procedure would be arbitrary, and, as a method of obtaining 

 philosophical truth, altogether futile. 



We may unfold this argument further. Let the contrary be sup- 

 posed, of that which we assert to be true : namely, let it be supposed that 

 while all other kinds of matter are heavy, (and of course heavy in propor- 

 tion to the quantity of matter) there is one kind of matter which is abso- 

 lutely destitute of weight; as, for instance, phlogiston, or any other element. 



