(3) Another limit to explanation lies in the infinite character of every particular fact; so that we may know the laws of many of its properties and yet come far short of understanding it as a whole.  A lump of sandstone in the road:  we may know a good deal about its specific gravity, temperature, chemical composition, geological conditions; but if we inquire the causes of the particular modifications it exhibits of these properties, and further why it is just so big, containing so many molecules, neither more nor less, disposed in just such relations to one another as to give it this particular figure, why it lies exactly there rather than a yard off, and so forth, we shall get no explanation of all this.  The causes determining each particular phenomenon are infinite, and can never be computed; and, therefore, it can never be fully explained.

Sec. 8.  Analogy is used in two senses:  (1) for the resemblance of relations between terms that have little or no resemblance—­as The wind drives the clouds as a shepherd drives his sheep—­where wind and shepherd, clouds and sheep are totally unlike.  Such analogies are a favourite figure in poetry and rhetoric, but cannot prove anything.  For valid reasoning there must be parallel cases, according to substance and attribute, or cause and effect, or proportion:  e.g. As cattle and deer are to herbivorousness, so are camels; As bodies near the earth fall toward it, so does the moon; As 2 is to 3 so is 4 to 6.

(2) Analogy is discussed in Logic as a kind of probable proof based upon imperfect similarity (as the best that can be discovered) between the data of comparison and the subject of our inference.  Like Deduction and Induction, it assumes that things which are alike in some respects are also alike in others; but it differs from them in not appealing to a definite general law assigning the essential points of resemblance upon which the argument relies.  In Deductive proof, this is done by the major premise of every syllogism:  if the major says that ’All fat men are humorists,’ and we can establish the minor, ‘X is a fat man,’ we have secured the essential resemblance that carries the conclusion.  In induction, the Law of Causation and its representatives, the Canons, serve the same purpose, specifying the essential marks of a cause.  But, in Analogy, the resemblance relied on cannot be stated categorically.

If we argue that Mars is inhabited because it resembles the datum, our Earth, (1) in being a planet, (2) neither too hot nor too cold for life, (3) having an atmosphere, (4) land and water, etc., we are not prepared to say that ’All planets having these characteristics are inhabited.’  It is, therefore, not a deduction; and since we do not know the original causes of life on the Earth, we certainly cannot show by induction that adequate causes exist in Mars.  We rely, then, upon some such vague notion of Uniformity as that ’Things alike in some points are alike in others’; which, plainly, is either false or nugatory.  But if the linear markings upon the surface of Mars indicate a system of canals, the inference that he has intelligent inhabitants is no longer analogical, since canals can have no other cause.