What "assumption" means

I came up with this example today while working with a private tutoring student. Consider the following argument: A equals two. B equals two. Therefore, A plus B equals four.

Sounds pretty good, right? Yeah, I think so too. But believe it or not, for LSAT purposes, something's missing. That missing piece is called an assumption.

The assumption here is something very obvious, but that's okay. The assumption is two plus two equals four.

Yes, I know that everyone knows two plus two equals four. That's beside the point. On the LSAT, every premise should be made explicit if the argument is going to hold water. Same thing with legal writing. As a 1L, I was shocked at how pedantic my Legal Writing instructor wanted my briefs to sound. I've always thought that 1) brevity is a virtue and 2) you shouldn't insult the reader by making points that are too obvious. This is not how legal writing works. Less is not more. More is more. If your case depends on the proposition that the ocean is wet, you better not leave the words "the ocean is wet" (properly cited to controlling case law, naturally) out of your brief.

Here, the proposition that two plus two equals four is both a necessary and sufficient assumption. I'll explain more about what this means in later posts, but for now, consider this:

  • "Two plus two equals four" is a necessary assumption of the argument because if it's not true, the argument loses. If I don't prove that "two plus two equals four", then my opponent might put on an expert witness who says that two plus two equals five. And if two plus two equals five, then A plus B does not equal four--it equals five, and I lose my case. (And then I lose my job, for leaving something so elementary out of my case.) Because "two plus two equals four" must be true in order for my argument to make sense, it is a necessary component of my argument. Since it was unstated, it is a necessary assumption of my argument. If the question had asked "Which one of the following is an assumption on which the argument relies," or "Which one of the following is an assumption required by the argument," then two plus two equals four would be a perfect answer.
  • "Two plus two equals four" is a sufficient assumption of the argument because if it is true, then my argument wins. There are no other holes in the argument: If it is a fact that A equals two, and also a fact that B equals two,  and also a fact that two plus two equals four, then it must be true that A plus B equals four, and I win my case. (And then I get promoted.) Because "two plus two equals four" would make it impossible for my conclusion to be false, it is sufficient (i.e. enough) to prove my argument. Since it was unstated, it is a sufficient assumption of my argument. If the question had asked "Which one of the following, if true, would allow the conclusion to be properly drawn," or "Which one of the following, if assumed, would allow the conclusion of the argument to be properly inferred," or "Which one of the following would justify the argument's conclusion," then two plus two equals four would be a perfect answer.

My student today didn't want to buy the proposition that "two plus two equals four" was an "assumption" of the argument, because he felt "two plus two equals four" was "implied" by the argument, and that it was "too obvious." My response was: "Yes, exactly." Anything that is "implied" by the argument is a very good candidate for an "assumption" of the argument. Likewise, anything that seems "obvious" based on the argument, but isn't actually stated by the argument (or proven by the other premises of the argument) is probably an assumption.

A couple final notes:

  • Assumptions are sometimes necessary but not sufficient, sometimes sufficient but not necessary, and sometimes both sufficient and necessary, as in this example. I'll return in later posts with examples of assumptions that are just sufficient and just necessary.
  • This "two plus two" example is purposely oversimplified. I doubt a real LSAT question (or a real judge) would ever entertain the proposition that two plus two might actually equal five. But "two plus two equals four" is, by definition, an assumption of the argument I made at the beginning of this post. If you need it, and you didn't explicitly state it, then you've just assumed it. And that's a weakness in your argument--a good lawyer isn't going to leave anything to chance.