Sec. 3.  Connotative Subalternation.—­We have seen (chap. iv.  Sec. 6) that if the connotation of one term is only part of another’s its denotation is greater and includes that other’s.  Hence genus and species stand in subaltern relation, and whatever is true of the genus is true of the species:  If All animal life is dependent on vegetation, All human life is dependent on vegetation.  On the other hand, whatever is not true of the species or narrower term, cannot be true of the whole genus:  If it is false that ‘All human life is happy,’ it is false that ’All animal life is happy.’

Similar inferences may be drawn from the subaltern relation of predicates; affirming the species we affirm the genus.  To take Mill’s example, if Socrates is a man, Socrates is a living creature.  On the other hand, denying the genus we deny the species:  if Socrates is not vicious, Socrates is not drunken.

Such cases as these are recognised by Mill and Bain as immediate inferences under the principle of Identity.  But some Logicians might treat them as imperfect syllogisms, requiring another premise to legitimate the conclusion, thus: 

      All animal life is dependent on vegetation;
      All human life is animal life;
    .’.  All human life is dependent on vegetation.

Or again: 

      All men are living creatures;
      Socrates is a man;
    .’.  Socrates is a living creature.

The decision of this issue turns upon the question (cf. chap. vi.  Sec. 3) how far a Logician is entitled to assume that the terms he uses are understood, and that the identities involved in their meanings will be recognised.  And to this question, for the sake of consistency, one of two answers is required; failing which, there remains the rule of thumb.  First, it may be held that no terms are understood except those that are defined in expounding the science, such as ‘genus’ and ‘species,’ ‘connotation’ and ‘denotation.’  But very few Logicians observe this limitation; few would hesitate to substitute ‘not wise’ for ‘foolish.’  Yet by what right?  Malvolio being foolish, to prove that he is not-wise, we may construct the following syllogism: 

      Foolish is not-wise;
      Malvolio is foolish;
    .’.  Malvolio is not-wise.

Is this necessary?  Why not?

Secondly, it may be held that all terms may be assumed as understood unless a definition is challenged.  This principle will justify the substitution of ‘not-wise’ for ‘foolish’; but it will also legitimate the above cases (concerning ‘human life’ and ‘Socrates’) as immediate inferences, with innumerable others that might be based upon the doctrine of relative terms:  for example, The hunter missed his aim:  therefore, The prey escaped.  And from this principle it will further follow that all apparent syllogisms, having one premise a verbal proposition, are immediate inferences (cf. chap. ix.  Sec. 4).