Informal Logic: Deductive Reasoning

Informal logic is a big part of the LSAT.

Professor Walker White, who teaches Computer Science at Cornell University, has graciously agreed to share some of his tips on understanding informal logic with everyone reading LSAT Blog.

His discussion includes detailed analysis of a real LSAT Logic Game. I've made a few of the other examples "LSAT Blog"-specific. The first part's below, and the second is Informal Logic: Deduction and Arguments.

Please thank Professor White in the comments for sharing these great articles!

Part 1: Deductive Reasoning

An argument that relies only on deduction is guaranteed to be valid. For example, a deductive argument might consist of two premises of the form:

1. If P is true, then Q is true.
2. P is true.

Deduction allows us to conclude from these two premises that:

3. Q is true.

For example, suppose we use a Google search to demonstrate that LSAT Blog has no articles on ladies footwear. In this case, we are making deduction with two premises:

1. If Google returns no LSAT Blog articles for "LSAT Blog ladies footwear," then LSAT Blog has no articles on ladies footwear.
2. Google returns no LSAT Blog articles for "LSAT Blog ladies footwear."

From these premises, it is valid to conclude that LSAT Blog has no articles on ladies footwear. Again, this does not mean the claim is true. Premise (1) is a complicated premise, and depends on the reliability of Google. But if Google is not reliable, then our debate is about that premise, and not the conclusion.
Students of informal logic sometimes try to split claim (1) into a premise and a conclusion. However, if-then statements are typically a single claim about a relationship between two observations. In this case, premise (1) is a claim about how reliable Google is for finding LSAT Blog articles. One way to think about this is the difference between the following two statements:

• If Google cannot find an article, then it must not exist.
• Because Google cannot find the article, it must not exist.

The first is a single claim about the reliability of Google. The second is an argument where we assert that a Google search has failed, and use this as evidence of the article's absence. In fact, this argument uses the first claim as an unspoken premise.

Deduction works "by definition" (and the principle of identity). When we make a claim like "if P is true, then Q is true," we mean that given argument P is true, this argument also shows Q is true. Given this observation, it does not appear that our deduction is particularly useful. We wanted to prove that LSAT Blog has no articles on ladies footwear, but to do so, we introduced a more complicated premise about Google's reliability. In the case of Google, we may be willing to accept this particular premise on faith. However in general, unless we know how to deduce or evaluate a conditional statement like (1), we are again back where we started.

Fortunately, we can deduce new conditionals as conclusions, provided that we have other conditionals as premises. To deduce a new conditional, we start first with a new premise. This new premise is introduced "for the sake of argument"—we are not making any claims about whether it is true or false. We use the existing conditionals to deduce a new conclusion. If we do this, then the conditional that connects the initial premise with the conclusion is itself a valid conclusion of the existing conditionals.
This explanation confuses even me, so it is best to proceed with an example.

See the rules of the second Logic Game in PrepTest 20 (the October 1996 LSAT), excerpted in Logic Made Easy.

Suppose, in that game, we want to deduce the new conditional statement:

If P is cut, then R is cut.

We start by assuming, "for the sake of argument," that P is cut. Deducing from premise (4), we know that L is not cut. Additionally, premise (5) is actually shorthand for a bunch of conditionals, one of which is "if L is not cut, then M and R are cut." Hence we can deduce that both M and R are cut. We started assuming that P is cut and sequence of deductions provided us with the conclusion that R is cut. That means, from premises (1)-(4), we can deduce the conditional "if P is cut, then R is cut."

From this example, we see that conditionals are a form of hedging our bets. We can have a perfectly valid argument about the consequences of cutting area P without committing to the claim that P is actually going to be cut. It is possible that P is the pet project of the university president and will never be cut, but that does not make our argument invalid. Hence, deductive arguments are another excellent example why we must separate truth from validity.

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Read on for Part 2: Informal Logic: Deduction and Arguments.