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The connection between rhetoric and logic is that logic, or logos, is a major part of the art of rhetoric. As well as this strong bong between the two, part of the aim of the study of logic is to deconstruct rhetoric and break an argument down to its bare bones. Rhetoric introduces appeals to emotion, known as pathos, and aims to convince people an argument is correct due to the perceived authority of the speaker, known as ethos. Although logic is part of the art of rhetoric, as are pathos and logos, its aim is specifically to discredit arguments formed on rhetoric alone.
Ancient Greek philosophers introduced the study of rhetoric to the world, and it is essentially the study of argumentation. As part of argumentation, students of rhetoric learn about logic, which focuses on the structure and validity of arguments. This study goes alongside learning to appeal to the emotions of the audience and create a believable and authoritative personal image. Rhetoric and logic are fundamentally linked in this way, and students of rhetoric are will make logic and essential element of their studies.
Combining the other main arts of rhetoric with logic can help people form a convincing argument. Politicians, for example, will use rhetorical techniques, such as anaphora and metaphor, alongside a logical argument to prove that their opponents' policies are foolish. This mixture of logical argument and appeal to emotion is often very effective in getting a point across to an audience. Politicians also embrace ethos by constantly trying to present themselves as charismatic and trustworthy. The relationship between rhetoric and logic is not always as harmonious as this, however.
In the formal study of logic, rhetoric receives a lot of attention. This is because the link between rhetoric and logic in the traditional study of rhetoric is somewhat contradictory. Rhetoric specially aims to convince people of an argument through methods other than the reasoning alone. Logic is specifically designed to break down an argument to its bland, logical assumptions and inferences. In doing this, the logician removes the irrelevant and misleading aspects of rhetoric and can focus on the structure of the argument itself.
Rhetoric and logic, although linked by the ancient Greek philosophers under the heading of “rhetoric,” are in some ways enemies. For example, if someone was to argue that “when people are taken to prison, it leaves their family broken and in turmoil, therefore prison is bad,” they would be intending to appeal to the emotions of the audience to convince them prison is bad. A logician’s job is to point out that the effects on the family of the accused may not be relevant to the argument about whether prison is good or bad. In this way, rhetoric and logic can be thought of as natural enemies.