Logical validity pertains to the relationships among the parts of a speech rather than the relationship between elements of a speech and the external world. Logical validity and factual correctness are determined differently. A speech can be logically or formally correct and yet factually or materially incorrect, or vice versa.
The syllogisms below illustrate the difference between formal or logical invalidity, and factual or material incorrectness.
(1) All poodles are dogs. Collies are dogs. Therefore collies are poodles.
(2) All poodles are purple. Rover is a poodle. Therefore Rover is purple.
(3) All dogs are quadripeds. A poodle is a quadriped. Therefore a poodle is a dog.
Syllogism (1) is formally invalid because the statement "collies are dogs" implies that some dogs are collies but not that all dogs are collies. Bad logic can lead the audience from true premises to a false conclusion. Syllogism (2) is formally valid but materially incorrect. If all dogs were purple, poodles would be purple, but dogs aren't purple. In syllogism (3), both the premises and the conclusion are true, but the syllogism is formally invalid because the conclusion does not follow from the premises; the second premise allows for quadripeds, such as cats, which are not dogs.
Fallacies are logical errors frequently encountered in speeches. Learning how to identify fallacies is considered especially important for educating students to be informed voters in democratic societies, able to judge whether political speeches contain valid arguments or not. Many common fallacies are based on deductions not following from premises. Argument ad hominem is one of the most common fallacies. Arguing ad hominem means attacking a person and inferring something about the quality of the person's argument from the aspect of the person being attacked. So, for example, someone might claim "You can't trust X's monetary policies because she embezzled from the treasury." Actually, a corrupt politician might make perfectly valid arguments about economic policy. Therefore, voters need to separate the two issues.
In teaching logic problems, most instructors begin with a summary of the general principles of inductive and deductive reasoning, then introduce fallacies, and finally have students analyze complete speeches for logical problems.