Logical Fallacies: Errors in Reasoning

The False Dilemma (or Black-and-White Fallacy) occurs when an argument presents only two extreme options as the only possibilities, ignoring the vast 'gray area' in between. In formal logic, this is a misuse of the disjunctive syllogism. If we define the world as only $A$ or $B$, and then prove that $A$ is undesirable, the audience is forced to accept $B$. This is a manipulation of logical necessity. By oversimplifying complex issues, the speaker eliminates nuance to railroad the listener into a specific conclusion.

A Slippery Slope argument claims that a relatively small first step will inevitably lead to a chain of related (and usually negative) events. The logical error here is the lack of evidence for the causal necessity of each link in the chain. If $A$ happens, the speaker asserts that $B, C, \dots$ and eventually $Z$ must happen. Mathematically, it looks like a series of conditional statements: $A \rightarrow B \rightarrow C \dots \rightarrow Z$. However, without proving that $P(B|A) \approx 1$, the entire argument collapses into speculation.

The full name is Post Hoc Ergo Propter Hoc, which translates to 'After this, therefore because of this.' This fallacy confuses correlation or temporal sequence with causation. Just because Event $B$ followed Event $A$, it does not mean $A$ caused $B$. In advanced composition, this often appears when writers try to attribute complex social shifts to single, preceding events without accounting for confounding variables. It is a failure of rigorous causal analysis.

In Circular Reasoning (Begging the Question), the conclusion is already assumed in the premises. The argument moves in a circle rather than advancing to a new point. If a thesis statement is circular, it is logically 'vacuous'—it contains no actual proof. For example, 'The law should be obeyed because it's illegal to break it.' Here, the 'proof' is just a restatement of the claim using different words. This destroys the strength of a thesis because it offers no external evidence to support the claim.