## How to analyze this sentence’s logic: “If it rains, I'll take an umbrella.”

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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?

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 – 2014-03-30T22:58:20.947

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A corollary of Murphy's Law says, "If I don't take my umbrella, it'll rain."

– J.R. – 2014-03-30T23:09:15.450

@StoneyB, Question added. – CoolHandLouis – 2014-03-30T23:44:14.940

@jr But a further corollary is: If you leave your umbrella at home to make it rain, it won't work. – Jay – 2015-01-05T14:57:24.410

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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.)

I think the equivalent should be: "If I don't take my umbrella, it won't rain." – Damkerng T. – 2014-03-31T03:39:43.813

1That 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. – 2014-11-12T01:59:06.957

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 – 2015-01-05T13:30:42.330

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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.”