In The Prince, Machiavelli proposes many logical arguments that applies deductive reasoning in forms of syllogisms and enthymeme. A Syllogism is an argument in which a conclusion can be inferred from two given premises, a major proposition and a minor proposition. They each share a term in the conclusion and a common term not present in the conclusion. However an enthymeme is an argument with one premises not explicitly stated. Machiavelli uses these literacy devices in order to evaluate the logical validity of his claims towards principalities.

“The principal foundations of all states must have, whether new or old or mixed, are good laws and good arms. And because good laws cannot exist where there are not good arms, and where there are good arms there should be good laws, I shall leave the reasoning of laws and I shall speak of arms” (Machiavelli 76) 

In this syllogism, the major premise would be that the principal foundations are good laws and good arms. Machiavelli is emphasizing that a prince must develop on “sound foundations” or it will lead to “grief.” He believes it is impossible to have good laws without military power. The minor premises will then be that good laws cannot exist without good arms. So this concludes that where there is good arms there should be good laws. Machiavelli clearly emphasizes the importance of laws and arms and how they coincide to make a stable state. One alone is necessary, however it is not sufficient enough to build a successful state. Having both foundations is sufficient and necessary. He uses these logical arguments that follow coherently to advise princes to focus first and mostly on military organizations which will pave the way for legal and civic institutions.

“Each Prince ought to desire to be believed compassionate and not cruel, nonetheless he must be alert not to use this compassion badly. Cesare Borgia was believed cruel; nonetheless, that cruelty of his restored Romagna, unified it, and led it back to peace and to faith.” (Machiavelli 90)

In this enthymeme, Machiavelli focuses more on cruelty rather than compassion. The major premise was to demonstrate the way in which cruelty, if used efficiently, may be seen as a virtue. In some ways cruelty can become a form of compassion when used to restore order and unify a state.  The minor premise states how a Prince desires to have a reputation for compassion however, they should be aware not to use compassion incorrectly. This then concludes with the example of Casare Borgia, whom was viewed cruel was in fact able to restore Romagna which brought peace to the people and state. So by using cruelty and public punishments, a prince can then show an act of compassion by controlling chaos.