READ Copi/Cohen, 5.4, pp. 188-192
 

13. [Copi/Cohen, 188] Note the technical term "opposition." This section will describe and discuss four distinct types of opposition. The four types of opposition are deployed on a square, hence "the square of opposition." The term "opposition" might remind us of "opposites"; but the latter English term is a bit stronger than what is meant by opposition here. Each "opposed" pair on the square are "opposite" only in some one respect and thus are not always true "opposites," except for the type of opposition called contradictories.
 

14. [Copi/Cohen, 189] In contradictory opposition, the quantity and the quality of the two propositions are opposed--negative vs. affirmative and universal vs. particular--these statements are true opposites, since they are opposed in both characteristics of propositions. Thus, their characteristic called a truth value is also opposite: if one of the propositions is TRUE, then the contradictory proposition MUST be FALSE; if one of the propositions is FALSE, then the contradictory proposition MUST be TRUE. There are no exceptions or middle ground.
 

15. [Copi/Cohen, 189] In contrary opposition, only the quality of propositions is opposed. Logical or mathematical propositions occasionally do not operate the way other propositions operate. Copi/Cohen is explaining one of these differences in the last paragraph under the "Contraries" section. Please note that for purposes of our study of the Square of Opposition, the warning Copi/Cohen issues in this paragraph will not come into play.
 

16. [Copi/Cohen, 190] In subcontrary opposition, only the quality of the propositions are opposed. Copi/Cohen makes the same point about subcontraries that it did about contraries, i.e., if they are necessary because of their logical or mathematical content, then the subcontrary opposition does not hold. Again, this will not pertain to our study of the Square of Opposition.
 

17. [Copi/Cohen, 190-1] In subalternation opposition only quantity if opposed. The point made about implication in subalternation bears repeating. That is, if "All animals are cats" is true [in fact, it is not true, but this does not matter to the logical point], then it follows that "Some animals are cats" is true. However, this implication does NOT follow going in the opposite direction. Thus if "Some animals are cats" is true [which it is] then we may NOT infer that "All animals are cats" is true [if it was true, then if you had a pet dog it would vanish instantly--indeed, you would never have had a pet dog in the first place!].
 

18. [Copi/Cohen, 191-2] Regarding the distinction between mediate and immediate inference:  For now, understand inference to be IMMEDIATE when it draws an implication from a single premiss, and MEDIATE when it does so from more than one premiss, such as in a "categorical syllogism" where an inference is drawn from two premisses (see p. 182 for an example).

DO THE TRY IT! exercises for 5.4
 

19. [Copi/Cohen, 193] INSTRUCTIONS:--Do all the exercises on 193, using the (a) proposition as the premiss of an argument (immediate inference) which has first (b) as its conclusion; next, as a separate decision, use (a) as premiss with (c) as conclusion. Thus if 1(a) "All successful executives are intelligent people" is true, then you need to decide whether 1(b), "No successful executives are intelligent people," is true or false. Next, still taking 1(a) as true, ask whether 1(c) is true or false. Do all the propositions in 1-4 this way. Then start over with 1(a) by assuming that "All successful executives are intelligent people" is false and then asking what follows for 1(b), separately for 1(c), etc. Two reminders: (i) For review, all possible immediate inferences are given in the list on 229-230; (ii) "undetermined" is an appropriate answer--it means that given the formal relationship between the statements, it is not possible to draw a valid immediate inference and hence the "conclusion's" truth value is undeterminable (without further information). Keep in mind that strictly speaking "undetermined" is not a third truth value--it simply means that we cannot determine logically whether a given proposition is true or false.

ELOGIC WORKSPACE for 5.4, Exercises 5.4, PT. 1 (4.1)