176 dk. whewell, on the fundamental antithesis of philosophy. 



ideas leads us to believe a connexion of the things : but they have never told us that this association 

 gave us the power of forming the ideas. Association may determine belief, but it cannot determine the 

 possibility of our conceptions. The African i<ing did not believe that water could become solid, because 

 he had never seen it in that state. But that accident did not make it impossible to conceive it so, 

 any more than it is impossible for us to conceive frozen quicksilver, or melted diamond, or liquefied 

 air ; which we may never have seen, but have no difficulty in conceiving. If there were a tropical 

 philosopher really incapable of conceiving water solidified, he must have been brought into that 

 mental condition by abstruse speculations on the necessary relations of solidity and fluidity, not by 

 the association of ideas. 



18. To return to the results of the nature of the Fundamental Antithesis. As by assuming 

 universal and indissoluble connexion of ideas with perceptions, of knowledge with experience, as an 

 evidence of derivation, we may assert the former to be derived from the latter, so might we, on the 

 same ground, assert the latter to be derived from the former. We see all forms in space ; and we 

 might hence assert all forms to be mere modifications of our idea of space. AVe see all events 

 happen in time ; and we might hence assert all events to be merely limitations and boundary-marks 

 of our idea of time. AVe conceive all collections of things as two or three, or some other number : 

 it might hence be asserted that we have an original idea of number, which is reflected in external 

 things. In this case, as in the other, we are met at once by the impossibility of this being a complete 

 account of our knowledge. Our ideas of space, of time, of number, however distinctly reflected to 

 us with limitations and modifications, must be reflected, limited and modified by something different 

 from themselves. We must have visible or tangible forms to limit space, perceived events to mark 

 time, distinguishable objects to exemplify number. But still, in forms, and events, and objects, we 

 have a knowledge which they themselves cannot give us. For we know, without attending to them, 

 that whatever they are, they will conform and must conform to the truths of geometry and arith- 

 metic. There is an ideal portion in all our knowledge of the external world ; and if we were 

 resolved to reduce all our knowledge to one of its two antithetical elements, we might say that all 

 our knowledge consists in the relation of our ideas. Wherever there is necessary truth, there must 

 be something more than sensation can supply : and the necessary truths of geometry and arithmetic 

 show us that our knowledge of objects in space and time depends upon necessary relations of ideas, 

 whatever other element it may involve. 



19. This remark may be carried much further than the domain of geometry and arithmetic. 

 Our knowledge of matter may at first sight appear to be altogether derived from the senses. Yet 

 we cannot derive from the senses our knowledge of a truth which we accept as universally certain ; — 

 namely, that we cannot by any process add to or diminish the quantity of matter in the world. 

 This truth neither is nor can be derived from experience; for the experiments which we make to 

 verify it pre-suppose its truth. When the philosopher was asked what was the weight of smoke, 

 he bade the inquirer subtract the weight of the ashes from the weight of the fuel. Every one who 

 thinks clearly of the changes which take place in matter, assents to the justice of this reply : and 

 this, not because any one had found by trial that such was the weight of the smoke produced in 

 combustion, but because the weight lost was assumed to have gone into some other form of matter, 

 not to have been destroyed. When men began to use the balance in chemical analysis, they did no; 

 prove by trial, but took for granted, as self-evident, that the weight of the whole must be found in 

 the aggregate weight of the elements. Thus it is involved in the idea of matter that its amount 

 continues unchanged in all changes which takes place in its consistence. This is a necessary truth : and 

 thus our knowledge of matter, as collected from chemical experiments, is also a modification of our 

 idea of matter as the material of the world incapable of addition or diminution. 



20. A similar remark may be made with regard to the mechanical properties of matter. Our 

 knowledge of these is reduced, in our reasonings, to principles which we call the laws of motion. 



