1 Thin end of the wedge
People often argue against a particular measure on the grounds that a more extreme version of that measure would be unacceptable. For example, they say it’s unacceptable for patients to pay for NHS sight tests because it may lead to charges for GP appointments. This is false reasoning. Alarm bells should ring when people ask “Where do you draw the line?”. Deciding where to draw the line is part of everyday life and discussion; there is no reason to adopt an extreme position simply because more moderate positions involve line-drawing. This is particularly true for difficult and complex issues like embryo research, where the whole debate is about where to draw the line and 'thin end of the wedge' arguments are effectively a failure to engage.
2 False dichotomy
Complex issues rarely form neat choices, but people often try to persuade you that they do. Here, the phrase which should set off alarm bells is “If we do nothing …”. More often than not, doing nothing is not a choice favoured by anyone in the debate, but is introduced purely to serve as a false dichotomy. For example: “The police need greater surveillance powers to tackle drugs crime. If we do nothing, the war against drugs will be lost.” This deliberately elides the possibility of other effective measures. Or the classic example: “You’re either with us or against us.”
3 Misuse of analogy
Illustrating a point with an analogy is legitimate and often helpful, but it can be taken too far. So while it’s fine to liken a well-run company to a well-oiled engine, it isn’t necessarily fine to say that, like an engine, the oil needs changing regularly. Analogies are only for decoration, they have no logical force. You can’t deduce anything meaningful about the target of the analogy (how to run a company) by looking purely at the source of the analogy (how to maintain an engine).
4 Misuse of metaphorThis is similar to misuse of analogy but more subtle because metaphor is like an analogy with the scaffolding removed (to slightly misquote James Geary, who has written an excellent book on metaphor: I Is An Other). The same point applies, which is that you cannot prove anything about the target by drawing inferences about the source. Saying there has been a ‘flood of immigration’ is a metaphorical way of describing an influx of migrants. It is not a neutral metaphor – it strongly implies disapproval, because floods are invariably bad news. It doesn’t tell us anything factual about whether the influx of migrants has had a negative effect; it simply reveals the speaker’s attitude. If the speaker goes on to say that it’s time to ‘stem the flood’, the same caveat applies. Yes, we always want to stem real floods because they are always damaging but no, you can’t transfer that logic to a different scenario just through choice of metaphor. You need to argue the case for reducing immigration on its own terms.
This one is a staple of political debate and can be entertaining and effective, but from a rational perspective, it’s bogus. Usually, it involves deliberately side-stepping a specific point and responding instead with an exaggerated caricature of your opponent's opinions. So if speaker A argues that prisoners should be allowed to vote in general elections, speaker B may decide not to argue the pros of cons of the specific proposal but instead to mock a series of exaggeratedly liberal views on prison reform in general: that prisoners should have holidays in Disneyland, hot tubs in their cells, gourmet meals, and so on. This is a particularly insidious trick because it can make the person who sticks to the point appear po-faced.