Final answer:
John Cotton is the Puritan writer who notably demonstrates the blend of Calvinist faith and rational legal and scientific reasoning.
Step-by-step explanation:
The Puritan writer who best illustrates the juxtaposition between faith and reason, blending a devout Calvinist perspective with legal and scientific rhetoric, is John Cotton. Influenced by the teachings of John Calvin, Cotton's works reflect the complex interplay between puritanical religious beliefs and the emerging importance of reason and rationality in the governance of society. The ideological views of Puritans like Cotton influenced the development of legal and social structures in New England, signifying a transition where law and reason began to hold significant sway within the religious community, a concept echoed by thinkers like John Locke later on.