VI. LAWS OF THOUGHT ON WHICH THE SYLLOGISM DEPENDS.
_Statement._--There are certain universal laws of thought on which all reasoning, and, of course, all syllogisms, depend. These laws, according to Hamilton, are the principles of _identity_, of _contradiction_, and of _excluded middle_; from which primary laws results a fourth, that of _reason and consequent_.
_Law of Identity, what._--The principle of _identity_ compels us to recognize the equivalence of a whole and its several parts taken together, as applied to any conception and its distinctive characters. As, for example, the sameness or equivalence of the notion man with the aggregate of qualities or characters that constitute that notion.
_Law of Contradiction, what_.--The law of contradiction is the principle that what is contradictory is unthinkable: as, for example, that A has, and yet has not, a given quality, B.
_Law of excluded Middle._--The principle of _excluded middle_ is this, that of two contradictory notions, we must think one or the other to be true; as, that A either has or has not the quality B.
_Law of Reason and Consequent._--From these primary principles results the law of _reason and consequent_. All logical inference is based on that law of our nature, that one notion shall always depend on another. This inference is of two kinds, from the whole to the parts, or from the parts to the whole, respectively called deductive and inductive, as already explained.
_Certain Points not included in the preceding Synopsis._--I have presented, as was proposed, in brief outline, a synopsis of the forms of reasoning. For a full treatment of these forms, and the laws which govern them, the treatises on logic must be consulted.
Some things usually considered essential to logical forms, as the _modality_ of propositions and syllogisms, and the _conversion_ of the other figures of the syllogism into the first, I have not included in the above outline, for the reason that the former does not properly fall within the province of logic, which has to do only with the _form_ and not with the _matter_ of a proposition or an argument, while, as to the latter, it is only an accidental, and not an essential circumstance, what may be the figure of a syllogism, and it is, therefore, of no importance to reduce the second and third figures to the first.