Presumably which one the clerk intended when he wrote it? Isn't that part of your theory on meaning; the speaker's intention? In this situation, the customer simply misunderstood. — Michael
You're missing the point. The point is that the customer's interpretation of the sign is just as legitimate as the clerk's. The problem is that they both contradict each other, which means that at least one of the interpretations is wrong.They can't both be right at the same time.Because you're forgetting something important - the interpretation of the customer, which contradicts the clerk's interpretation. — Harry Hindu
Of course. That's why clerk's scam worked.
Yes the customer was intentionally deceived. — Michael Ossipoff
Of course he does. The diamond and the sign would attract attention. No other customers or clerks saw the customer give the clerk the money? There aren't cameras in the jewlery store? All these other behaviors you tell us the clerk engages to cover up the fact that the customer gave them the money in is dishonest. The clerk is a liar simply by his behavior.Obviously the clerk's scam would be illegal. But, as I said, the customer has no proof that he paid for the diamond. — Michael Ossipoff
Again you miss the point. It's not about speaking different languages, it's about using the correct terms in ANY langauge to translate to the correct terms of another language. When your logical system ends up being inconsistent with other logical systems, then something is wrong. They should all be integrated into a consistent whole.My objection to the predicate logic language was only that it seemed an unnecessary complication. If we're having a conversation, and you insist on speaking Latin, that doesn't mean that you're wrong, it just makes it more difficult for me. That was my complaint about predicate logic language. — Harry Hindu
You obviously don't know much about computer programming. ALL computer languages mean the same thing with IF-THEN statements....but that could depend on the company that's using the computer. — Michael Ossipoff
No. It only depends on the truth value of the conclusion. Just look at the table.The truth value of the implication-proposition is function of the truth-values of the premise and the conclusion. — Michael Ossipoff
Exactly. Now you've just contradicted your statement above. See how illogical this is?But of course, by the standard implication truth-table, if the conclusion is true, the implication-proposition is true regardless of whether or not the premise is true. — Michael Ossipoff
You just keep moving the goal posts. This conversation is no longer meaningful.But, as a practical matter, in the story, it doesn't matter. The customer can't prove that he paid, and so the scam worked. The clerk (who is also the store owner and a logician) can assure himself that he didn't lie when he scammed the customer, because his truth-table is the standard one. — Michael Ossipoff
The OP never said the clerk wrote the sign. As a matter of fact, the store owner (which isn't a logician) most likely wrote the sign because he is the one that actually owns the diamond. — Harry Hindu
You're missing the point. The point is that the customer's interpretation of the sign is just as legitimate as the clerk's. The problem is that they both contradict each other, which means that at least one of the interpretations is wrong.They can't both be right at the same time. — Harry Hindu
Obviously the clerk's scam would be illegal. But, as I said, the customer has no proof that he paid for the diamond.
Of course he does. The diamond and the sign would attract attention. No other customers or clerks saw the customer give the clerk the money?
There aren't cameras in the jewelry store?
All these other behaviors you tell us the clerk engages to cover up the fact that the customer gave them the money in is dishonest. The clerk is a liar simply by his behavior.
.My objection to the predicate logic language was only that it seemed an unnecessary complication. If we're having a conversation, and you insist on speaking Latin, that doesn't mean that you're wrong, it just makes it more difficult for me. That was my complaint about predicate logic language.
.Again you miss the point.
.It's not about speaking different languages
., it's about using the correct terms in ANY langauge to translate to the correct terms of another language. When your logical system ends up being inconsistent with other logical systems, then something is wrong. They should all be integrated into a consistent whole.
.You keep claiming that the clerk is a logician. If so, then the clerk would know that there other logical interpretations of the sign and that all logical interpretations should be consistent.
....but that could depend on the company that's using the computer.
.You obviously don't know much about computer programming. ALL computer languages mean the same thing with IF-THEN statements.
.The truth value of the implication-proposition is function of the truth-values of the premise and the conclusion.
.No. It only depends on the truth value of the conclusion. Just look at the table.
.But of course, by the standard implication truth-table, if the conclusion is true, the implication-proposition is true regardless of whether or not the premise is true.
.Exactly. Now you've just contradicted your statement above.
.See how illogical this is?
.But, as a practical matter, in the story, it doesn't matter. The customer can't prove that he paid [a problematic claim], and so the scam worked. The clerk (who is also the store owner and a logician) can assure himself that he didn't lie when he scammed the customer, because his truth-table is the standard one.
Admittedly he'd have to lie to the police about whether the payment was made, and admittedly the implication-proposition in his sign was false (a lie) when he refused to give the diamond.
But he didn't lie to the customer when he said that the sign's implication proposition was true before the payment was made.
.You just keep moving the goal posts.
.This conversation is no longer meaningful.
Whether or not the clerk lied isn't what is being argued against. My argument is that he isn't a logician. What I'm saying is that implication-propositions don't translate to logical "IF-THEN" statements that are used by people and computers via their programming. The customer interpreted the sign correctly as a causal relationship between the act of giving the money and the effect of receiving the diamond. If there is no relationship between the premise and the conclusion, then the sign is wrong to be written the way it is.But the clerk didn't lie to the customer when he said the sign's implication-proposition was true, because that statement was correct,when made, by the standard truth-table for 2-valued truth-functional implication. — Michael Ossipoff
My argument is that [the clerk] isn't a logician — Harry Hindu
What I'm saying is that implication-propositions don't translate to logical "IF-THEN" statements that are used by people and computers via their programming. — Harry Hindu
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.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
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.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
Human language is logical.No one is claiming that words always mean the same in logic and in human language. — Michael Ossipoff
.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.
.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.
.…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)"
.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.
.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.
.Human language is logical.
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. — Harry Hindu
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