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I have a small-claims matter pending with the courts in my state. Here, self-represented parties are required to attend an information session, which I attended today. During this session the presenter talked about mandatory settlement conferences, in which the parties both present summaries of their cases to the deputy-judge, who then tells the parties how he would rule if he were the trial judge for the matter. The courts operate these conferences to encourage settlement and reduce the number of cases that proceed to trial.

I asked one of the two presenters, "I heard that the settlement-conference deputy-judges usually press the guy with the most money to make the larger concession; is that true?"

She replied, "Well. Hm. Maybe my colleague should answer that." Her colleague answered, "Let's take that to an extreme. If that were the case, then the settlement conference deputy-judges would just look at each person's net-worth and tell the richer person that he expects him to prevail if the matter proceeds to trial." (I accepted his answer, but ultimately, the first speaker conceded that what I heard wasn't entirely inaccurate.)

I thought the second speaker misused reduction to the extreme in a manner analogous to countering the claim that there are aliens living on earth by arguing that if that were true, then there would be so many of them that we would have to stack them face-to-face toward the sky in order to fit them all on our planet.

But if I claimed that relish is a vegetable, one might argue that if that were the case then one could get half a day's worth of vegetables from several packets of relish and ketchup.

That example seems to succeed, but the prior example seems to fail. Why?

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    Do you mean reductio ad absurdum? If so, then no example in what you are saying clearly fits the bill. – virmaior Feb 7 '14 at 14:24
  • Really? To me it seems like saying: let's suppose everything is done to the extreme. That seems different than noting the absurd consequences of an argument. – Hal Feb 7 '14 at 15:17
  • All this proves is that they do not always rule that way (I suppose that the deputy judges have access to the parties' net worth). It does not prove that their is not any kind of tendency. – Baby Dragon Feb 7 '14 at 20:36
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    Reductio ad absurdum refers to taking an argument to its conclusion and showing the results are absurd. It's not quite done to the extreme. So the classic type of example is that (1) if you believe every effect has a cause, then (2) this leads to an infinite chain of causation, and this is an absurdity because it involves an actual infinite (argument made by Aristotle and then again Aquinas). Maybe there's something like that in what you're saying but I don't get it. – virmaior Feb 7 '14 at 23:35
  • Big Bang Theory (the show!) may be responsible for this misunderstanding. Here's the quote from Sheldon: "[reductio ad absurdum is] the logical fallacy of extending someone's argument to ridiculous proportions and then criticizing the result. And I do not appreciate it." – Hunan Rostomyan Feb 9 '14 at 4:40
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A proper reductio ad absurdum argument relies upon the fact that if a premise is true, an absurd conclusion would unavoidably follow. The word "unavoidably" is key; if any step is not logically forced by the previous step, the entire argument falls apart.

In the scenario at hand, the premise (that there is an illegitimate bias against "rich" defendants) could be true without the "absurd" statement (that no factors other than a defendant's wealth are even considered) being true. Consequently, the absurd statement does not follow from the premise, and the premise is in no way invalidated by the absurd statement. Indeed, the argument is so poor as to suggest the person making it might not be debating in good faith.

  • Can you source the definition? There's also a problem insofar as the word "absurd" is not a formal logical term, so it's impossible for an absurd conclusion to "unavoidably follow" – virmaior May 13 '14 at 14:47
  • The first sentence of the Wikipedia article en.wikipedia.org/wiki/Reductio_ad_absurdum defines it. While formal logic is more specific in delineating different kinds of false statements, an "absurd" conclusion is one whose falsity would be considered sufficiently obvious by any reasonable measure as to require no further proof or examination. One could further examine the false statement if one was unconvinced that it was actually false (and indeed in some faulty RAA arguments the "absurd" statement is actually true) but in a proper argument, ... – supercat May 13 '14 at 14:58
  • ...an "absurd" statement is one whose falsity could readily be proven, but whose proof would serve mainly as a distraction from the primary argument. – supercat May 13 '14 at 15:00
  • I think you are misunderstanding what I meant by "can you source the definition"? I didn't mean can you explain it to me or give me personally a source. I meant put a source in your answer. – virmaior May 13 '14 at 15:16
  • Regarding the second point, things that follow formally unavoidably follow. Things that follow depending on a judgment cannot follow unavoidably... they follow contingently on that judgment. – virmaior May 13 '14 at 15:17
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You question to the dude was, in other words, was "What is the probability that X will happen"? And the answer was, "if the probability is almost 100%, then undesirable things happen, so the probability is low".

I understand your question to be, is he justified is jamming the probability up to 100% to make his argument? I can't tell what his is argument is really, but he did claim to be "taking it to the extreme".

I had a teacher who advocated this type of argument to check your reasoning. In essence, you have some principle P which implies goodness, you assume that P is true for some domain of situations, and you choose some extreme (though maybe improbable) situation to try to see if P doesn't imply goodness. So, it's just a search for a contradiction and a check for consistency.

I don't think he had a good understanding of what principle or idea he was trying to disprove. All he did was choose an improbable situation (confusing the probability of your question with the probability of the situation he was constructing), find that his situation was undesirable, and then conclude whatever he wanted.

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