Final answer:
Key theories in substructural logic, such as dialetheism and paraconsistent logics, address the nature of the Continuum regarding true contradictions and continuous motion.
Step-by-step explanation:
The Logical Structure in Substructural Logic and Theories of the Continuum
In the context of substructural logic and theories regarding the nature of the Continuum, the logical structure can be articulated considering paraconsistent and paracomplete viewpoints.
a) Key theories in substructural logic that address the nature of the Continuum regarding true contradictions and continuous motion are dialetheism and paraconsistent logics. Dialetheism allows for true contradictions to exist, while paraconsistent logics accept the possibility of contradictions without leading to trivial conclusions. These theories provide frameworks for exploring the nature of the Continuum in light of logical inconsistencies.
b) The dialethic/paraconsistent Continuum theory accommodates the notion of continuous motion involving true contradictions by allowing for contradictory states to coexist and change over time. It recognizes that reality can be paradoxical and embraces the idea that contradictory statements can both be true in different contexts or under different conditions.
c) In intuitionistic logic, the concept of the dual paracomplete moment relates to the understanding of the Continuum. It refers to a moment in which both the affirmation and negation of a proposition are valid and meaningful, creating a dual reality where contradictory statements coexist without violating the principle of non-contradiction.
d) Substructural logic has implications in defining sets that incorporate variations in understanding the nature of the Continuum. It allows for the exploration of different logical systems that can handle inconsistencies and paradoxes, broadening the understanding of the Continuum beyond traditional classical logic.