Deficiency of _understanding_ we call _stupidity_: deficiency in the application of _reason_ to practice we shall recognise later as _foolishness_: deficiency of judgment as _silliness_, and lastly, partial or entire deficiency of _memory_ as _madness_. But each of these will be considered in its own place. That which is correctly known by _reason_ is _truth_, that is, an abstract judgment on sufficient grounds (Essay on the Principle of Sufficient Reason, § 29 and following paragraphs); that which is correctly known by _understanding_ is _reality_, that is correct inference from effect on the immediate object to its cause. _Error_ is opposed to _truth_, as deception of the _reason_: _illusion_ is opposed to _reality_, as deception of the _understanding_. The full discussion of all this will be found in the first chapter of my essay on Light and Colour. Illusion takes place when the same effect may be attributed to two causes, of which one occurs very frequently, the other very seldom; the understanding having no data to decide which of these two causes operates in any particular case,—for their effects are exactly alike,—always assumes the presence of the commoner cause, and as the activity of the understanding is not reflective and discursive, but direct and immediate, this false cause appears before us as a perceived object, whereas it is merely illusion. I have explained in the essay referred to, how in this way double sight and double feeling take place if the organs of sense are brought into an unusual position; and have thus given an incontrovertible proof that perception exists only through and for the understanding. As additional examples of such illusions or deceptions of the understanding, we may mention the broken appearance of a stick dipped in water; the reflections in spherical mirrors, which, when the surface is convex appear somewhat behind it, and when the surface is concave appear a long way in front of it. To this class also belongs the apparently greater extension of the moon at the horizon than at the zenith. This appearance is not optical, for as the micrometre proves, the eye receives the image of the moon at the zenith, at an even greater angle of vision than at the horizon. The mistake is due to the understanding, which assumes that the cause of the feebler light of the moon and of all stars at the horizon is that they are further off, thus treating them as earthly objects, according to the laws of atmospheric perspective, and therefore it takes the moon to be much larger at the horizon than at the zenith, and also regards the vault of heaven as more extended or flattened out at the horizon. The same false application of the laws of atmospheric perspective leads us to suppose that very high mountains, whose summits alone are visible in pure transparent air, are much nearer than they really are, and therefore not so high as they are; for example, Mont Blanc seen from Salenche.