Question

According to Copi's Introduction to Logic, in the square of opposition in Aristotle's Syllogistic Logic, there are four kinds of relationships between propositions:

contradictory: two propositions can't be both true, and can't be both false. (In Syllogistic Logic, this turns out to be that the propositions have the same subject term, same predicate term, and different quality and different quantity.)
contrary: two propositions can't be both true, but can be both false.(In Syllogistic Logic, this turns out to be that the propositions have the same subject term, same predicate term, and the same quantity, but different quality.)
subcontrary: two propositions can't be both false, but can be both true. (In Syllogistic Logic, this turns out to be that the propositions have the same subject term, same predicate term, and same quantity, but different quality.)
subalternation: two propositions have the same subject term and the same predicate term and the same quality (affirmative or negative), but different quantity (universal or particular).
Is it correct that contradictory, contrary and subcontrary can be generalized/defined for any other logic systems other than syllogistic logic, because their definitions don't depend on anything specific to syllogistic logic?

Does subalternation apply only to syllogistic logic, but not to other logic systems? Can subalternation be generalized/defined for other logic systems other than syllogistic logic?

Specifically, can subalternation be defined similarly to contradictory, contrary and subcontrary, in terms of whether two propositions can't be both true or can't be both false?

Answer 1

Contradictory, contrary, and subcontrary relationships are general principles that apply to various logical systems beyond Aristotelian syllogistic logic, while subalternation may seem specific to syllogistic logic but can also be understood in a broader context as it pertains to the inference from the universal to the particular, applicable to other logical systems as well.

Step-by-step explanation:

When discussing the square of opposition and its relation to different forms of logical systems beyond the framework of Aristotelian syllogistic logic, it is essential to recognize the nuanced roles that the relationships between propositions play in logical reasoning. The square of opposition contains four categorical relationships: contradictory, contrary, subcontrary, and subalternation.

The contradictory relationship is indeed a general logical principle that can apply to different logic systems. It posits that two propositions cannot be true or false simultaneously. This concept is deeply rooted in the law of noncontradiction, which plays a pivotal role in many logical systems beyond just syllogistic logic.

Similarly, the contrary relationship which holds that two propositions cannot both be true but can both be false, as well as the subcontrary relationship, asserting that two propositions cannot both be false but can be true together, are not exclusively pertinent to syllogistic logic. These relations echo normative principles of logical consistency applicable across different logical frameworks.

Subalternation, representing a relationship where two propositions with the same subject and predicate terms differ in terms of quantity (universal versus particular) but retain the same quality (affirmative or negative), may appear more specific to syllogistic logic due to its reliance on categorical sentences. However, the underlying concept of this relationship can also be generalized to other logical systems. It focuses on the inference from a universal statement to its corresponding particular statement, reflecting a more nuanced understanding of logical implication, which has analogs in other systems of logic where the generalization from universal to particular, or vice versa, is relevant.