ragraph, he believed that you could learn more through contemplation, then actual experimentation. Plato deduced that math could not possibly exist in the material world, the sensory world of objects. Consider that no triangle that we see is exactly a triangle but an approximation of one. The only "real" triangle, perfect triangle, would be the triangle that the pythagorean theorum creates, which only exists in the world of forms or ideas, the other world in his two world theory. Our visual world is merely an illusion based on the world of ideas, what I mean by this is that the exterior appearance means nothing, it is inconsequential with respect to the world of ideas. Take for instance this example, a pig and the idea of a pig, only the latter is "real".Plato thought a theory of forms was necessary in order to account for the possibility of wisdom. Plato proposed that because wisdom is static, "eternal" (whereas physical objects are subject to constant change) it is proper to posit eternal ideals are grasped by the intelligence but not the senses. The senses are defective because they can only percieve imperfect instances of what "pure thought" grasps in an unadulterated state. The best part sensory perception can play in "understanding forms" is to remind the "soul" of the forms the soul has already grasped independently of, and prior to, the senses. Plato discusses his ideas of these two worlds in the "Allegory of the cave". The prisoner is finally released from his shackles and let free into the world, ".his instructor is pointing to the objects as they pass and requiring him to name them, -- will he not be perplexed? Will he not fancy that the shadows which he formerly saw are truer than the objects which are now shown to him?" (Book 7 Republic 515d) This just shows that perception has no meaning, Life in the cave symbolises the material world, where the shadows and noises heard with in are only images and sounds of the true objec...
