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A Short Proof that Meaning is Not Information

Imagine your phone number is 777-7777, and you need to let somebody know, but your phone company charges texts based upon the amount of logical information they convey. So you send the message “It is either 777-7777 or not 777-7777” which is a tautology, conveys no information and is therefore free. However you have successfully communicated your phone number.

Sure you can go Gricean on me and distinguish between speaker’s meaning and sentence meaning but why believe there is such a thing as sentence meaning?

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8 thoughts on “A Short Proof that Meaning is Not Information

  1. In that example, hiding your phone number in the tautology is really just a code (albeit a very bad one), so you have only successfully communicated your phone number to someone who understands the code. So doesn’t the example only prove that information can be encoded?

    On the other hand, an an alternative version of your argument could be made using the briefer text “7777777.” Whether that text conveys meaning or information is dependent on the message it’s responding to. If it’s sent in response to “What is your phone number?” it has no meaning but conveys information. If it’s sent in response to “Please text me seven 7s,” it conveys neither. If it’s a response to “How many angels can dance on the head of a pin?” it conveys both.

    This is not an effective revenue stream for a phone company.

      • anon says:

        Sure, but this requires ‘or’, ‘not’, and so on to contribute their usual logical constant meanings in ‘It is either 777-7777 or not 777-7777’. But if the only meaning in the utterance of that is the speaker meaning (something along the lines of that your number is 777-7777, plus maybe some other stuff), then it doesn’t seem like they do. In other words, the only tautology here is in what I would want to call the sentence meaning, and if there’s no such thing, then I don’t see where or what the tautology would be. It’s not tautologically true that my phone number is 777-7777.

        Not that this matters too much, though, since I don’t think it’s very plausible to begin with that meaning (sentence or speaker) is whatever ‘logical information’ is conveyed, at least if this implies that all logically equivalent expressions mean the same thing. ‘p v ~p’ doesn’t mean the same thing as ‘~((~p v q) ^ (~q v r)) v (~p v r)’.

  2. But if we claim that “sentence meaning” doesn’t exist and that “speaker meaning” isn’t equivalent to the information contained in a statement, all we’re doing is making a trivial claim about natural language. To wit:

    Person A: “May I help you?”
    Person B: “I’m just looking.”

    And infinitely many other examples.

    Is there a larger point to the original proof that I’m missing?

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