Rhetoric is simply the art of speech, usually in an argumentative style. As described in the Merriam-Webster dictionary, fallacies are arguments that use false or invalid inferences and support. Although people will find many rhetorical fallacies in political speaking, they can use knowledge of fallacies to improve and make their own arguments stronger, usually by removing them. According to Christine Acker in the University of Texas Undergraduate Writing Center, there are three categories of fallacies: emotional, ethical and logical. Emotional fallacies, such as scare tactics, appeal to people's emotional reactions to what they hear or see. For example, Susannah Breslin, on TheFrisky.com, details how Gardasil commercials for women's health use the possibility of getting cancer without Gardasil's shot to instigate women to act. Ethical fallacies, like guilt by association, question the credibility of people and situations. For example, if a student steals from a teacher at school, his friends will often also be scrutinized because they associate with the culprit. Logical fallacies involve the plausibility of an argument.
According to a 2009 article in "Synthese," a logical fallacy is "any (possibly unnoticed) deductively invalid or erroneous argument with the appearance of validity or a demonstrably false conclusion from plausible reasoning." Basically, this describes an argument for which support is presented in a seemingly legitimate manner when it is actually false. Acker says logical fallacies include argument styles like begging the question, stacked evidence and faulty causality. For example, in an argument about the existence of God, a person might say God exists because the Bible says so, but if then asked how the Bible can be trusted, the person may say because God wrote it. Here, God is proving the existence of God, and that is circular thinking or begging the question.
Non sequitur and hasty generalization are two logical fallacies. Acker describes a non sequitur as an argument that does not necessarily follow logically what was said or came before. For example, someone might say, "My dog ran away today, so my car will start without a problem." The dog has no control over the car starting but is used as an argument because of a lack of any other evidence. Hasty generalization is developing an opinion on little or no evidence. For example, if the first container of yogurt a person took was punctured, he might decide that the brand is cheap and shouldn't be used again. That could have been one faulty container out of a thousand, but the person generalized the quality of the brand based on limited evidence.
Generalizing from incomplete sentences is an example of the hasty generalization logical fallacy. The person using the fallacy generalizes what the sentence means from the little evidence provided by the incomplete expression. Hasty generalization may be the only fallacy in this case, but if the person then forms her own opinion that is inconsistent with the purpose or meaning of the statement she is using as evidence, a non sequitur could also be involved.