I don't think "republic" is a category that has much standing in political theory
Plato, of course, wrote The Republic
Aristotle actually delineated SIX forms : there are three pairs of congruent governments : A state with only one ruler is either a monarchy or a tyranny A state with several rulers is either an aristocracy or an oligarchy A state in which mob rule or a democracy.
He found flaws with all of them and thus concluded that none were suitable systems of government. Aristotle largely embraced Plato's ideas and in his Politics three types (sans Timocracy) are discussed in detail. Aristotle views aristocracy to be the ideal form of government but he observes that none of the three are healthy and that states will cycle between the three forms in an abrupt and chaotic process known as the kyklos. In his Politics he lists a number of theories of how to create a stable government. One of these options is creating a government that is a mix of all three forms of government. .... The ideal of a mixed government was popularized by Polybius who saw the Roman Republic as a manifestation of Aristotle's theory. Monarchy was embodied by the consuls, the aristocracy by the Senate, and democracy by the elections and great public gatherings of the assemblies. Each institution complements and also checks the others, presumably guaranteeing stability and prosperity. Polybius also describes Sparta as an earlier manifestation of this ideal. Polybius was very influential and his ideas were embraced by Cicero. .... Cicero became extremely well regarded during the Renaissance and many of his ideas were embraced. Polybius was also rediscovered and the positive view of mixed governments became a central aspect of Renaissance political science integrated into the developing notion of republicanism. Mixed government theories became extremely popular in the Enlightenment and were discussed in detail by Hobbes, Locke, Vico, Montesquieu, Rousseau, and Kant. Apart from his contemporaries, only Montesquieu became widely acknowledged as the author of a concept of separation of powers
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The ideal of a mixed government was popularized by Polybius who saw the Roman Republic as a manifestation of Aristotle's theory. Monarchy was embodied by the consuls, the aristocracy by the Senate, and democracy by the elections and great public gatherings of the assemblies. Each institution complements and also checks the others, presumably guaranteeing stability and prosperity. Polybius also describes Sparta as an earlier manifestation of this ideal. Polybius was very influential and his ideas were embraced by Cicero.
Cicero became extremely well regarded during the Renaissance and many of his ideas were embraced. Polybius was also rediscovered and the positive view of mixed governments became a central aspect of Renaissance political science integrated into the developing notion of republicanism. Mixed government theories became extremely popular in the Enlightenment and were discussed in detail by Hobbes, Locke, Vico, Montesquieu, Rousseau, and Kant. Apart from his contemporaries, only Montesquieu became widely acknowledged as the author of a concept of separation of powers
What do you mean? Republic comes from the Latin Res Publica ('the public thing'). Plato's Republic was called
Πολιτεία/"Politeía", meaning "city-state governance")
De re publica (Latin: On the commonwealth, see below) is a dialogue on Roman politics by Cicero, written in six books between 54 and 51 BC. It is written in the format of a Socratic dialogue in which Scipio Africanus Minor (who had died a few decades before Cicero was born, several centuries after Socrates' death) takes the role of a wise old man -- an obligatory part for the genre. Cicero's treatise was politically controversial: by choosing the format of a philosophical dialogue he avoided naming his political adversaries directly. Cicero employed various speakers to raise differing opinions in an attempt to make it more difficult for these adversaries to take him to task on what he had written.
What do you mean?
Regardless,
Roman authors would also use the word res publica in the sense of the era when Rome was governed as a republic, that is the era between the Roman Kingdom and the Roman Empire. So in this case res publica does distinctly not refer to the Roman Empire, but to what is generally described as the Roman Republic.
Plato's Republic was a kind of aristocracy, and republicanism is an attempt to put a positive spin on oligarchy. It is rule by the few attempting to claim the legitimacy of rule by the many.
As for the idea of "mixed government", according to Wolin, America is a republic in the sense that there is a continuing unresolved conflict of interest between the many and the few. The way that inverted totalitarianism deals with this conflict of interest is through managed democracy. A bomb, H bomb, Minuteman / The names get more attractive / The decisions are made by NATO / The press call it British opinion -- The Three Johns