(10) Illustrate the difference between a complete division and an exhaustive division.
(11) Show in what ways, if any, the following divisions violate the rules of logical division.
{ 1 Memory (History) Human Learning { 2 Imagination (Poetry) (by Bacon) { 3 Reason (Philosophy) { or (the Sciences)
{ 1 Mathematics { 2 Astronomy Sciences { 3 Physics (by Comte) { 4 Chemistry { 5 Biology { 6 Sociology { 7 Morals
Judging has been defined as the process of conjoining or disjoining notions. This may be put in another way: “Judging is the process of asserting or denying the agreement between two notions.” The product of the act of judging is a judgment and when judgments are put in word-form such expressions are called logical propositions.
Definition: _A logical proposition is a judgment expressed in words._ Just as percept and concept notions are expressed by means of logical terms so judgment notions may be expressed by logical propositions.
To illustrate: The terms _the squirrel_ and _cracking a nut_ express two notions, and when an agreement between them is asserted and the product is expressed in word form, then such an expression becomes the logical proposition, “The squirrel is cracking a nut.”
The following being _expressed_ judgments are logical propositions:
(6) Some good orators are not good statesmen.
There are three kinds of logical propositions; namely, categorical, hypothetical and disjunctive.
_A categorical proposition_ is one in which the assertion is made unconditionally. _An hypothetical proposition_ is one in which the assertion depends upon a condition. _A disjunctive proposition_ is one which asserts an alternative.
(1) “Every dog has his day.” Categorical.
(2) “If you do your best, success will reward you.” Hypothetical.
(3) “He is either stupid or indolent.” Disjunctive.
(4) “All vices are reprehensible.” Categorical.
(5) “Either you are very talented or very industrious.” Disjunctive.
(6) “If capital punishment does not aid society, it should be abolished.” Hypothetical.
(7) “You may go provided your teacher is willing.” Hypothetical.
(8) “No intelligent man can ignore the practice of temperance.” Categorical.
By studying the illustrations it will be observed that the categorical propositions are direct, bold, assertive statements, whereas the hypothetical are limited by conditions which make them less forceful. In the second proposition, for example, “success will reward you,” is limited by the condition, “If you do your best.” The disjunctive may be regarded as categorical in form, but hypothetical in meaning, because in such a proposition as, “He is either, stupid or indolent,” a direct assertion is made which suggests the categorical, and yet it may be implied that, if he is stupid then he is not indolent; this is indicative of the hypothetical.