A person was asked to analyze the following sentence, but couldn't answer even after some searching. They did not understand that this was a logic puzzle.

If it rains, I'll take an umbrella.

How would one analyze the truth table of the logic of this sentence?

  • Note this Q/A was inspired by another question (closed as of now). This was reinterpreted and given a context that allows it to be answered. – CoolHandLouis Mar 30 '14 at 22:58
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    A corollary of Murphy's Law says, "If I don't take my umbrella, it'll rain." – J.R. Mar 30 '14 at 23:09
  • @StoneyB, Question added. – CoolHandLouis Mar 30 '14 at 23:44
  • @jr But a further corollary is: If you leave your umbrella at home to make it rain, it won't work. – Jay Jan 5 '15 at 14:57

Behold the difference between Logic and Language.

In Logic, as demonstrated by CoolHandLouis, a conditional is a Proposition of a peculiar sort: p ⇒ q. This declares a truth-relationship between two Propositions, p and q, each of which is either True (T) or False (F), and the truth of the conditional Proposition is represented in a Truth Table such as that CoolHandLouis presents.

In Language, however, a conditional is not a Proposition but an Utterance. An Utterance may express a logical Proposition, but most do not; they express not relationships between Propositions but relationships between unactualized Eventualities. Such Eventualities are not current at the time of Utterance, and consequently they can have no truth-value; and in many cases, such as counterfactual conditionals, they can never have truth-value. They are neither True nor False but actualized or unactualized. And even in those cases where the Eventualities are actualized or conclusively not actualized, these outcomes do not necessarily entail a judgment of Truth or Falsity of the Utterance; for non-Propositional Utterances are Promises or Predictions, which are likewise neither True nor False but actualized or unactualized.

In the instant case, if I promise that if it rains I'll bring an umbrella, and in the event it does rain and I don’t bring an umbrella, my soaked wife will not chide me for uttering a falsehood, but for breaking a promise. And if it does not rain and I don’t bring an umbrella, she will not praise me for uttering a truth; she will say “It’s a good thing it didn’t rain.”

For more info, see conditional sentences.

  • This is fantastic! I see you're pointing to some modern philosophy of language that is not typically discussed. Perhaps this would make a better question in the philosophy forum... – CoolHandLouis Mar 31 '14 at 22:30
  • @CoolHandLouis Oh, I dunno nuffin bout birthin no philosophy :) This is straight LitCrit, out of Philip Sidney, moved from poetics into performatives. – StoneyB on hiatus Mar 31 '14 at 22:41
  • @!StoneyB, My answer is more "correct" relative to the question-as-it-is, but it's also rather trite and "findable-anywhereable". I would prefer to reword the question and edit yours into a two-part answer contrasting the simple predicate-logic answer with the utterance/eventuality answer and mark that as "correct". I could reword the question, add my "simple" answer into your answer, and then mark your answer correct. May I have a shot at this? You could simply revert or further edit (both question and answer) as needed. – CoolHandLouis Jun 15 '14 at 5:09
  • @CoolHandLouis Go for it; but take what you like of mine and meld it into yours instead, and I'll delete mine when it's over. ... I think the key thing from an ELL perspective is that the tense rules change: an actualization conditional requires that the protasis be temporally prior to the apodosis, while an inference conditional has no such constraint: you may argue from the truth of an anterior fact to the truth of a posterior fact. – StoneyB on hiatus Jun 15 '14 at 10:42
  • @!StoneyB, Thanks! This is a backburner project for me and there's absolutely no expected timeline on this. It will require me to dig deeper into the theory you presented. I'll notify you if/when done to solicit your review. Thanks. – CoolHandLouis Jun 15 '14 at 11:00

This is a classic example used in logic. See Google Search: "if p then q" rains umbrella

If it rains, (then) I'll take an umbrella.

If p then q.
p = it rains
q = I'll take an umbrella.

Statement is true or false accordingly:

  • True: It rains and I take my umbrella.
  • False: It rains and I don't take my umbrella.
  • True: It doesn't rain and I take my umbrella.
  • True: It doesn't rain and I don't take my umbrella.

Note the abbreviated rule:

  • True: It doesn't rain. (It doesn't matter if I take my umbrella.)

Note the equivalent statement: "I take my umbrella OR it doesn't rain." (Non-exclusive "or")

Also note the alternative logic of Murphey's Law: A corollary of Murphy's Law says, "If I don't take my umbrella, it'll rain." (Credit to @J.R.)

  • I think the equivalent should be: "If I don't take my umbrella, it won't rain." – Damkerng T. Mar 31 '14 at 3:39
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    That logic's wrong. It has all kinds of unpleasant side effects. For example, if you say "It's not true that if it rains, I'll take my umbrella" according to the meaning you've given there, it means "It will rain and I won't take my umbrella" and this is obviously not what that sentence means! – Araucaria - Not here any more. Nov 12 '14 at 1:59
  • My answer is more "correct" relative to the question-as-it-is, and I wrote the question specifically to answer it. However, @StoneyB's answer provides a fantastic alternative answer. – CoolHandLouis Jan 5 '15 at 13:30

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