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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?

Tyler James Young
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CoolHandLouis
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  • 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](http://en.wikipedia.org/wiki/Murphy%27s_law#Other_variations_on_Murphy.27s_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 05 '15 at 14:57

2 Answers2

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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.

CoolHandLouis
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StoneyB on hiatus
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  • 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 05:09
  • @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
  • I'm going to leave things as they are! I just added the link "for more info", if ok with you. – CoolHandLouis Jan 05 '15 at 13:34
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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.)

CoolHandLouis
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  • I think the equivalent should be: *"If I don't take my umbrella, it won't rain."* – Damkerng T. Mar 31 '14 at 03:39
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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 01:59
  • 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 05 '15 at 13:30