Aristotle explores the concept of 'akrasia' or incontinence, where an individual knows the right action but fails to perform it due to a lack of self-control. Continence, or 'enkrateia', is the state of successfully resisting base desires to act in accordance with reason, representing a central struggle in his Nicomachean Ethics.

An enthymeme is a rhetorical syllogism where one of the premises or the conclusion is left unstated because it is assumed to be understood by the audience. Aristotle defined it as the 'body of persuasion' in rhetoric. Unlike a formal logical syllogism, which requires all premises to be explicit, the enthymeme relies on the audience's shared knowledge to complete the logical chain.

William Ebenstein, in his analysis of political philosophy, highlights Aristotle's conceptualization of the 'rule of law' as his greatest contribution. Aristotle argued that law should be sovereign over individuals, ensuring that governance is based on reason rather than the arbitrary will of rulers, which remains a cornerstone of modern constitutionalism.

Aristotle defined justice primarily as a form of equality, specifically 'proportional equality.' He argued that justice involves treating equals equally and unequals unequally in proportion to their relevant merits or contributions. This distributive justice ensures that rewards and burdens are allocated according to a rational standard of fairness within the political community.

Aristotle’s treatise 'De Anima' (On the Soul) serves as the foundation for his psychological inquiries. For Aristotle, psychology was not the study of the mind in the modern clinical sense, but rather the study of the 'psyche' or soul, which he defined as the formal principle or 'form' of a living body. He explored how the soul functions as the animating force that distinguishes living organisms from non-living matter.

The name Nicomachus was significant in Aristotle's life as it belonged to both his father, who was a physician to the Macedonian royal family, and his son, whom he had with Herpyllis. Aristotle dedicated his famous work, the 'Nicomachean Ethics', to his son, ensuring the name remained associated with his philosophical legacy.

Aristotle defined constitutional rule (polity) as a government that operates for the common good, follows established laws, and governs willing citizens. He believed that such a system respects the dignity of the subjects, as it involves them in the political process. Therefore, a system inconsistent with the dignity of the subjects would contradict his ideal of constitutional governance.

After the premature death of his parents, Aristotle was placed under the guardianship of Proxenus of Atarneus. Proxenus played a significant role in Aristotle's early life, providing him with the necessary support and resources to pursue his education, which eventually led him to travel to Athens to join Plato's Academy at a young age.

The 'Eudemus', also known as 'On the Soul', was one of Aristotle's early dialogues. It was written in honor of his friend Eudemus of Cyprus, who died in battle. The work explores themes of the immortality of the soul and reflects the influence of Plato's thought on the young Aristotle before he developed his own distinct philosophical system.

While Aristotle made foundational contributions to logic, ethics, and political theory, he is not primarily known for mathematics. The provided answer key suggests 'Biology' is the correct choice; however, this is historically contentious as Aristotle is often called the 'father of biology' for his extensive zoological studies. This conflict arises because his contributions to logic and political science are far more central to his legacy than his biological works.