(1) We are not concerned to know only what statements may be made on the basis of certain other statements.  We want to know what is true and what is false.  We must ask:  Has a man the right to set up these particular statements and to reason from them?  That some men accept as true premises which are repudiated by others is an undoubted fact.  Thus, it is maintained by certain philosophers that we may assume that any view of the universe which is repellant to our nature cannot be true.  Shall we allow this to pass unchallenged?  And in ethics, some have held that it is under all circumstances wrong to lie; others have denied this, and have held that in certain cases—­for example, to save life or to prevent great and unmerited suffering—­lying is permissible.  Shall we interest ourselves only in the deductions that each man makes from his assumed premises, and pay no attention to the truth of the premises themselves?

(2) Again.  The vast mass of the reasonings that interest men are expressed in the language that we all use and not in special symbols.  But language is a very imperfect instrument, and all sorts of misunderstandings are possible to those who express their thoughts in it.

Few men know exactly how much is implied in what they are saying.  If I say:  All men are mortal, and an angel is not a man; therefore, an angel is not mortal; it is not at once apparent to every one in what respect my argument is defective.  He who argues:  Feathers are light; light is contrary to darkness; hence, feathers are contrary to darkness; is convicted of error without difficulty.  But arguments of the same kind, and quite as bad, are to be found in learned works on matters less familiar to us, and we often fail to detect the fallacy.

Thus, Herbert Spencer argues, in effect, in the fourth and fifth chapters of his “First Principles,” as follows:—­

  We are conscious of the Unknowable,
  The Unknowable lies behind the veil of phenomena,
  Hence, we are conscious of what lies behind the veil of phenomena.

It is only the critical reader who notices that the Unknowable in the first line is the “raw material of consciousness,” and the Unknowable in the second is something not in consciousness at all.  The two senses of the word “light” are not more different from one another.  Such apparent arguments abound, and it often requires much acuteness to be able to detect their fallacious character.

When we take into consideration the two points indicated above, we see that the logician is at every turn forced to reflect upon our knowledge as men do not ordinarily reflect.  He is led to ask:  What is truth?  He cannot accept uncritically the assumptions which men make; and he must endeavor to become very clearly conscious of the real meaning and the whole meaning of statements expressed in words.  Even in the simple logic with which we usually begin our studies, we learn to scrutinize statements in a reflective way; and when we go deeper, we are at once in contact with philosophical problems.  It is evidently our task to attain to a clearer insight into the nature of our experience and the meaning of proof than is attainable by the unreflective.