Final answer:
John C. Calhoun's philosophy that emphasized states' rights and sovereignty in the face of federal laws concerning slavery is best exemplified by his authorship of the South Carolina Exposition and Protest.
Step-by-step explanation:
John C. Calhoun was a fervent advocate for the Southern states and their right to maintain the institution of slavery. His philosophy, which emphasized the sovereignty of states and their ability to nullify federal laws they found unconstitutional, is exemplified by his action of authoring the South Carolina Exposition and Protest. In this document, Calhoun presented the theory that each state was sovereign and could decide the constitutionality of federal laws. This doctrine laid the groundwork for states to nullify laws they opposed, a significant step towards the concept of secession if their conditions were not met.
Calhoun's stance is seen in his proposal of a dual presidency, reflecting his belief in the distinct and divided interests of the North and South, particularly on issues surrounding slavery. This idea also underscored his belief in the United States as a union or confederacy rather than a single nation, where separate regions had the power to counteract the majority through a concurrent majority.