Fallacies of Distraction
A limited number of options (usually two) is given, while in reality there are more options. A false dilemma is an illegitimate use of the "or" operator. Putting issues or opinions into "black or white" terms is a common instance of this fallacy. "The fallacy of false dilemma is committed when an argument limits consideration of positions on an issue to two mutally exclusive ones, thereby setting up an apparent dilemma, when there are other positions that could be offered." (Bowell & Kemp, Critical Thinking, p. 164)
Also called argumentum ad ignorantiam, arguments of this form assume that since something has not been proven false, it is therefore true. Conversely, such an argument may assume that since something has not been proven true, it is therefore false. (This is a special case of a false dilemma, since it assumes that all propositions must either be known to be true or known to be false.) Other phrases often employed here, are "lack of proof is not proof"; "absence of evidence is not evidence of absence"; "the lack-of-knowledge inference"; and, "negative proof" or "negative evidence".
In order to show that a proposition P is unacceptable, a sequence of increasingly unacceptable events is shown to follow from P. A slippery slope is an illegitimate use of the "if-then" operator. This fallacy, a subgenre of the appeal to consequence, is also known as "The camel's nose". "In a typical slippery slope argument, an action is objected to on the grounds that once it is taken, another, and then perhaps still another, are bound to be taken, down a 'slippery slope,' until some undesirable consequence results. According to a slightly different version, whatever would justify taking the first step would also justify all the others, but since the last step isn't justified, the first isn't, either." (Kahane & Cavender, Logic and Contemporary Rhetoric, p. 84)
Two otherwise unrelated points are conjoined and treated as a single proposition. The reader is expected to accept or reject both together, when in reality one is acceptable while the other is not. A complex question is an illegitimate use of the "and" operator. "The fallacy of many questions is a common form or error, which has been variously defined as: 1) framing a question in such a way that two or more questions are asked at once, and a single answer is required; or 2) framing a question in such a way as to beg another question; or 3) framing a question which makes a false presumption; or 4) framing a complex question but demanding a simple answer." (Fischer, Historians' Fallacies, p. 8.)