96 dk whewell, on the Platonic theory of ideas. 



was, the desire of solving the Problem, " How is it possible that man should apprehend 

 necessary and eternal truths?" That the truths are necessary, makes them eternal, for 

 they do not depend on time; and that they are eternal, gives them at once a theological 

 bearing. 



That Plato, in attempting to explain the nature and possibility of real knowledge, had in 

 his mind geometrical truths, as examples of such knowledge, is, I think, evident from the 

 general purport of his discourses on such subjects. The advance of Greek geometry into a 

 conspicuous position, at the time when the Heraclitean sect were proving that nothing could 

 be proved and nothing could be known, naturally suggested mathematical truth as the refu- 

 tation of the skepticism of mere sensation. On the one side it was said, we can know nothing 

 except by our sensations; and that which we observe with our senses is constantly changing; 

 or at any rate, may change at any moment. On the other hand it was said, we do know 

 geometrical truths, and as truly as we know them, we know that they cannot change. Plato 

 was quite alive to the lesson, and to the importance of this kind of truths. In the Meno 

 and in the Phcedo he refers to them, as illustrating the nature of the human mind : in the 

 Republic and the Timceus he again speaks of truths which far transcend anything which the 

 senses can teach, or even adequately exemplify. The senses, he argues in the ThecBtetus, 

 cannot give us the knowledge which we have; the source of it must therefore be in the mind 

 itself; in the Ideas which it possesses. The impressions of sense are constantly varying, and 

 incapable of giving any certainty: but the Ideas on which real truth depends are constant and 

 invariable, and the certainty which arises from these is firm and indestructible. Ideas are the 

 permanent, perfect objects, with which the mind deals when it contemplates necessary and 

 eternal truths. They belong to a region superior to the material world, the world of sense. 

 They are the objects which make up the furniture of the Intelligible World: with which the 

 Reason deals, as the Senses deal each with its appropriate Sensation. 



But, it will naturally be asked, what is the Relation of Ideas to the Objects of Sense ? 

 Some connexion, or relation, it is plain, there must be. The objects of sense can suggest, 

 and can illustrate real truths. Though these truths of geometry cannot be proved, cannot 

 even be exactly exemplified, by drawing diagrams, yet diagrams are of use in helping ordinary 

 minds to see the proof; and to all minds, may represent and illustrate it. And though our 

 conclusions with regard to objects of sense may be insecure and imperfect, they have some 

 shew of truth, and therefore some resemblance to truth. What does this arise from.!" How 

 is it explained, if there is no truth except concerning Ideas? 



To this the Platonist replied, that the phenomena which present themselves to the senses 

 partake, in a certain manner, of Ideas, and thus include so much of the nature of Ideas, 

 that they include also an element of Truth. The geometrical diagram of Triangles and 

 Squares which is drawn in the sand of the floor of the Gymnasium, partakes of the nature of 

 the true Ideal Triangles and Squares, so that it presents an imitation and suggestion of the 

 truths which are true of them. The real triangles and squares are in the mind: they are, as 

 we have said, objects, not in the Visible, but in the Intelligible World. But the Visible 

 Triangles and Squares make us call to mind the Intelligible; and thus the objects of sense 

 suggest, and, in a way, exemplify the eternal truths. 



