• Harry Hindu
    1.3k
    That was the whole point of the story, ...to illustrate that the standard truth table for such implications can give results that differ from what people ordinarily expect.Michael Ossipoff
    No. The point is that you can know a language, but translating the meaning to another can give results that differ from what people ordinarily expect when you don't translate it correctly.
    A computer program doesn't interpret an "IF...THEN" statement as a logical proposition that a conclusion follows from a premise.

    It takes it as an instruction to do something if a certain proposition t is true.

    Loosely said, it often takes it as an instruction to make a variable take a certain value if a certain equality, inequality, or proposition is true. ... when the action called for is the execution of an assignment-statement.

    ...but it can also just specify an action, such as "IF x = a, THEN PRINT(x)"
    Michael Ossipoff
    Exactly. The sign is written as an IF-THEN statement. IF you give the clerk $5000, THEN you receive the diamond. IF-THEN-(ELSE) is how we make ANY decision.

    You simply need to rewrite the sign so that it actually translates correctly - meaning that you need to remove the IF and the THEN and write it as two indpendent statements.

    You still haven't given us the relationship between giving the clerk $5000 and receiving the diamond. Is it a causal relationship, or what? What does the arrow between p and q actually mean?


    No one is claiming that words always mean the same in logic and in human language.Michael Ossipoff
    Human language is logical.
  • Michael Ossipoff
    1.4k


    Must quit for the evening.

    Replying tomorrow.

    Michael Ossipoff
  • Michael Ossipoff
    1.4k


    I’d said:
    .
    That was the whole point of the story, ...to illustrate that the standard truth table for such implications can give results that differ from what people ordinarily expect.
    .
    You replied:
    .
    No. The point is that you can know a language, but translating the meaning to another can give results that differ from what people ordinarily expect when you don't translate it correctly.
    .
    Incorrect. As the person who posted my post, I’m the one to say what my point was, in posting it.
    .
    Re-quoting you:
    .
    …you can know a language, but translating the meaning to another can give results that differ from what people ordinarily expect when you don't translate it correctly.
    .
    The truth-table that I (and others) quoted wasn’t complicated. It’s unambiguously expressed in English. No, there was no mis-translation of it in my story.
    .
    I’d said:
    .
    A computer program doesn't interpret an "IF...THEN" statement as a logical proposition that a conclusion follows from a premise.

    .
    It takes it as an instruction to do something if a certain proposition t is true.

    .
    Loosely said, it often takes it as an instruction to make a variable take a certain value if a certain equality, inequality, or proposition is true. ... when the action called for is the execution of an assignment-statement.

    .
    ...but it can also just specify an action, such as "IF x = a, THEN PRINT(x)"
    .
    You replied:
    .
    Exactly. The sign is written as an IF-THEN statement. IF you give the clerk $5000, THEN you receive the diamond. IF-THEN-(ELSE) is how we make ANY decision.
    .
    One point that I was making was that a computer language’s IF…THEN statement isn’t the same thing as a logical implication-proposition (…in this case one that’s interpreted in the standard manner of 2-valued truth-functional logic).
    .
    At no time did the clerk tell the customer that the sign was a computer-language statement that was going to be executed after the payment. The clerk merely (correctly) stated the truth-value of the implication-proposition, by the standard 2-valued truth-functional interpretation, at a time before payment was made.
    .
    No mis-translation. No lie.
    .
    You simply need to rewrite the sign so that it actually translates correctly.
    .
    As I said above, there was no mis-translation.
    .
    You still haven't given us the relationship between giving the clerk $5000 and receiving the diamond. Is it a causal relationship, or what? What does the arrow between p and q actually mean?
    .
    It’s called an “implication-proposition”. Depending on what kind of logic one is referring to, there can be various truth-tables for it. In the standard 2-valued truth-functional interpretation, an implication-proposition is true if its premise is false.
    .
    I’d said:
    .
    No one is claiming that words always mean the same in logic and in human language.
    .
    You replied:
    .
    Human language is logical.
    .
    :D
    .
    Well, some languages are more logical than others.
    .
    If you like language to be logical, then I recommend Esperanto. It’s more logical than English, and more logical than at least nearly all natural languages.
    .
    Harry, this conversation has, for some time now, consisted only of repetition. It’s time for us to agree to disagree.
    .
    I’m at these forums to discuss metaphysics.
    .
    Michael Ossipoff
  • Harry Hindu
    1.3k
    This reply is just one giant circular argument.

    In the link that Michael provided on the first page of this thread - and that you agreed with - also explains exactly what it was I've been trying to tell you for several posts now. If you scroll down to the section, "Philosophical problems with material conditional", it explains how the implications aren't completely translatable to a native language.

    Outside of mathematics, it is a matter of some controversy as to whether the truth function for material implication provides an adequate treatment of conditional statements in a natural language such as English, i.e., indicative conditionals and counterfactual conditionals. An indicative conditional is a sentence in the indicative mood with a conditional clause attached. A counterfactual conditional is a false-to-fact sentence in the subjunctive mood. That is to say, critics argue that in some non-mathematical cases, the truth value of a compound statement, "if p then q", is not adequately determined by the truth values of p and q. Examples of non-truth-functional statements include: "q because p", "p before q" and "it is possible that p" — Wikipedia

    It is not surprising that a rigorously defined truth-functional operator does not correspond exactly to all notions of implication or otherwise expressed by 'if ... then ...' sentences in natural languages. For an overview of some of the various analyses, formal and informal, of conditionals, see the "References" section below. Relevance logic attempts to capture these alternate concepts of implication that material implication glosses over. — Wikipedia

    Relevance logic, also called relevant logic, is a kind of non-classical logic requiring the antecedent and consequent of implications to be relevantly related. — Wikipedia

    Your "research" seems to be cherry-picked.
  • Michael Ossipoff
    1.4k


    The difference in meanings and interpretations described in your quote was what my story was intended to illustrate. As I said, that was the whole point of the story.

    Your "research" seems to be cherry-picked.Harry Hindu

    Actually no, the standard 2-valued truth-functional implication truth-table was unanimously identical at every academic website that I checked.

    But we've already been all over this several times.

    Michael Ossipoff
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