The time of payment is decided by the customer. It can only have one value, the one chosen by the customer. For the purposes of the implication, the time-of-payment isn't universally-quantified. It's a constant that has been chosen by the customer. — Michael Ossipoff

That's a bit silly. Yes it's chosen by the customer but he can choose any time.

I'm not sure what the purpose is of this thread. Is it to show that the truth table for material condition isn't an adequate reflection of how we actually speak?

Because you're forgetting something important - the interpretation of the customer, which contradicts the clerk's interpretation. Which interpretation is the correct one? Read below. — Harry Hindu

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.

I think you just need to have a more charitable interpretation of the sign:

If you have given me $5,000 then I will give you the diamond.

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.

Which interpretation is the correct one?

By the definitions that I found in those academic articles, the clerk's interpretation is correct for the 2-valued truth-functional definition and truth-table for implications.

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

The time of payment is decided by the customer. It can only have one value, the one chosen by the customer. For the purposes of the implication, the time-of-payment isn't universally-quantified. It's a constant that has been chosen by the customer. — Michael Ossipoff

That's a bit silly. Yes it's chosen by the customer but he can choose any time. — Benkei

...and when he has done so, by paying, his time of payment becomes a constant. For the purpose of the implication-proposition, the customer's payment-time is a constant.

It isn't a universally-quantified variable, or a variable at all, in the implication-proposition.

I'm not sure what the purpose is of this thread. Is it to show that the truth table for material condition isn't an adequate reflection of how we actually speak? — Benkei

It was intended to illustrate how the, otherwise-useful, 2-valued truth-functional definition and truth-table for implication could have a meaning that most people wouldn't expect.

Michael Ossipoff

...and when he has done so, by paying, his time of payment becomes a constant. For the purpose of the implication-proposition, the customer's payment-time is a constant. — Michael Ossipoff

That makes no difference I'm afraid. If it's random it becomes constant at the time of payment as well.

In any case, as I said, the sign-wording is the important thing, because the sign, and not the predicate logic wording, is in the story. — Michael Ossipoff

Then I was right when I said that you used an improper logical system in translating the logical meaning of the sign.

The sign's implication-proposition can be expressed in the language of propositional or predicate logic.

Neither is wrong.

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.

What I was saying in the passage you quotes was only that the sign itself is the important thing, because that's what my story was about. But if predicate logic language can express the message even more unambiguously, then of course the sign could have been written in that language.

But any of the various ways of saying it are equally proper.

So I certainly didn't and don't mean that predicate logic is improper for translating the sign into logic language.
— Harry Hindu

In "If-THEN" statements, the THEN statement is necessarily dependent upon the truth value of the IF statement.

So far, so good.
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This is the way it works in the English language and computer programming (and I would add that a computer is more logical than a logician because a computer doesn't have greed clouding it's interpretation of the symbols on the sign).

...but that could depend on the company that's using the computer.

If the truth value of the implication-proposition is only dependent upon the truth value of the conclusion, then the truth value of the premise is irrelevant to the truth value of the proposition.

The truth value of the implication-proposition is function of the truth-values of the premise and the conclusion.

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.

If the material conditional only states that q is true when (but not necessarily only when) p is true, and makes no claim that p causes q, then what exactly is the relationship between p and q?

The relationship is only that expressed by implication proposition's truth-table. As you said, nothing is said or meant about causation.

The only observation of p and q truth-values that could establish something about whether p always implies q would be an observation of p true and q false.

The metaphysics that I propose is based on abstract if-then facts for which the conclusion demonstrably follows from the premise. Of course there are lots of such abstract if-then facts. A proved mathematical theorem is such a fact.

The standard 2-valued truth-functional implication truth-table was the basis of my story about the diamond sales scam.

A material conditional is more like simply writing two completely separate statements. Translating to English, it's more like saying,

"Give me $5000."

"I give you the diamond.",

where each part isn't dependent upon each other to be true.

I don't know what you mean by that. The sign's implication proposition said that, at any time, if you've given me the $5000, then at any time more than a minute after you gave it to me, I'll have given you the diamond.

The sign is an IF-THEN statement and that is the logical system that should be used in determining the logical meaning of the sign.

Of course. It was.

The "truth" table produces invalid results precisely because you're using a logical system that doesn't translate to the actual meaning of the sign.

The truth-table's results are ordinarily useful, but their deceptiveness in the story situation is the point of the story. The customer was intentionally deceived. The truth-table made it possible for the clerk to deceive and scam the customer without lying.

But yes, there are some interpretations, some alternative truth-tables, that say that the truth of the implication-proposition is indeterminate when its premise is false. The 2-valued interpretation doesn't allow that.

And the 2-valued truth-functional truth-table is the more standard one.

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.

Personally, speaking for myself, the if-then proposition that seems most relevant to mathematics and metaphysics is one in which the conclusion demonstrably follows from the premise.

Michael Ossipoff

That makes no difference I'm afraid. If it's random it becomes constant at the time of payment as well. — Benkei

Exactly. If the customer flips a coin to decide when to pay, the time of his payment is still a constant with respect to the implication-proposition.

Michael Ossipoff

Exactly. If the customer flips a coin to decide when to pay, the time of his payment is still a constant with respect to the implication-proposition. — Michael Ossipoff

Exactly. That makes andrewk right.

Exactly. If the customer flips a coin to decide when to pay, the time of his payment is still a constant with respect to the implication-proposition. — Michael Ossipoff

Exactly. That makes andrewk right. — Benkei

If he said that, then he's certainly right about it.

But he has represented some times mentioned in the implication-proposition as universally-quantified variables.

That representation is incorrect, because, as I've been saying, the time-of-payment is a constant with respect to the implication-proposition.

Michael Ossipoff

If you have given me $5,000 then I will give you the diamond. — Michael

I don't think that's a reasonable paraphrase of the sign. This version refers only to the present, and whether, at the time the reader is reading the sign, they have already given $5000.

The actual sign emphasises its difference from this paraphrase by use of the words 'at any particular time'. No matter how charitable one is seeking to be, one cannot ignore those words.

What if the words were removed? (goes back to OP to read sign while mentally eliding those words)
Without those words, I think the paraphrase might be considered realistic. However I think almost nobody would pay the money on the basis of such a sign. Those four words are crucial to tricking people into paying the money.

the customer has no proof that he paid for the diamond. — Michael Ossipoff

Didn't he get a receipt upon payment of the money? The OP does not mention whether he does, but only a fool would pay such an amount without immediately obtaining a receipt.

But even if the customer had been so unwise, they could immediately call the police and ask them to retrieve the $5000 cash from the clerk's pocket, dust it for fingerprints and ask the clerk to explain how they came to have $5000 cash in their pocket that had been handled by the customer. They'd be hard pressed to come up with a credible excuse, given the sign about the $5000 is sitting there in plain view, and the customer's testimony.

The customer was too trusting.

Yes, the clerk made a mistake when he just put the money in his pocket, instead of in the cash-register. By that mistake, he could be caught.

I didn't know that finger-prints could be gotten from a currency-bill.

I've been short-changed by being given change for 20 when I'd paid with a 50, or being given change for a 10 when I'd paid with a 20.

In the case of the 10 and the 20, I was later reimbursed by the manager.

In the case of the 20 and the 50, I wasn't reimbursed.

Ideally, when paying with a 20, a 50, or a 100, one should have recorded the serial-numbers of the 20s, 50s and 100s that one is carrying.

Then, the clerk would have a hard time explaining how the customer knows the serial number of that 50, if he only paid with a 20.

It might sound like a lot of trouble, but it wouldn't be so laborious to write down the serial numbers of ones 20s, 50s, and any possible one or more 100s that one might (temporarily, I hope) be carrying.

Ii must admit that I've never recorded serial numbers. That's why I lost $30, when I paid with that 50.

Michael Ossipoff

But the clerk has plenty of opportunity to transfer the $5000 to the cash-register when the customer starts to call the police. When the police arrive, the money will be in the cash-register, untraceable to the customer unless finger-prints can be gotten from a currency-bill.

Michael Ossipoff

Good point.

Cash in cash registers can be reconciled against sales. If he puts $5000 in the register without recording a sale on it, there will be a $5000 discrepancy, which will inculpate him as clearly as having it in his pocket did.

To escape, he would have to hide the cash somewhere that the police will not find it. The customer should not let him out of his sight, so that he can see where he hides it.

Ok, you're right. It looks as if the clerk's scam would be very difficult, if not.impossible, to succeed with.

I should have demanded a register-count when I was shortchanged when paying with the 50..

Michael Ossipoff

The clerk could have an accomplice, who'd take the money off the premises, to somewhere else, before the police arrive.

Michael Ossipoff

You have a knack for story-telling, getting people emotionally invested in your narrative. I'm feeling really cross about that clerk right now.

A jewelry shop would need a security camera, especially if the 20 million dollar diamond is real.

Authorities could ask to look at the security-camera record for the time in question.

Maybe there's a well-concealed security-camera and it's possible to say, "We don't have one yet." (Not necessarily feasible).

Or maybe there's a pre-set-up way that the accomplice could code a signal to an unconcealed security-camera, to delete its record for that day, in a way that successfully mimics a natural failure. That would only work once, before the coincidence became too improbable. And, even once, it might justify a close examination of the camera-system. (So, not necessarily feasible).

So the scam would be problematic.

Michael Ossipoff

Also, it occurs to me that the clerk/logician, who never tells a lie, would have to lie to the police about whether the payment was made. So much for never lying.

Maybe he just prides himself on never lying to a customer.

Michael Ossipoff

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

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.

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

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.

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

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.

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

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. — Michael Ossipoff

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. — Michael Ossipoff

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. — Michael Ossipoff

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, 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

You just keep moving the goal posts. This conversation is no longer meaningful.

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

I said, in the title of the thread, that the store is owned by a logician. I said in my post that the clerk is the owner and logician.

Michael Ossipoff

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

The clerk's interpretation is correct, by the 2-valued truth-functional truth table and definition of implication that several academic sources were unanimous about.

There are other truth-tables for implication. I wouldn't say that some are more "legitimate" than others.

But the clerk's truth-table is the more widely-quoted one, the more standard one.

I'd said:

Obviously the clerk's scam would be illegal. But, as I said, the customer has no proof that he paid for the diamond.

You replied:

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 was only one clerk in the store. But, as i said, he could have had an accomplice, to remove the money from the store before police arrived. There weren't other customers in the store.

There aren't cameras in the jewelry store?

I acknowledged that the security-camera would be a problem, maybe a prohibitive one.

I said, "Don't try this at home."

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.

Of course. He's a liar, because, even though he didn't lie to the customer, he lies to the police about whether the payment was made. So he doesn't really live up to the title of the thread.

And,even though he didn't lie to the customer, of course he defrauded and intentionally deceived the customer. His sign was false (a lie) when the clerk didn't honor it by keeping its promise. So, in that sense, too, the clerk lied (because he'd written and displayed the sign that proved false), even though his earlier assurance was true.

The scam couldn't be repeated. And, after the notoriety of the first time, the store wouldn't get any business. The scam wouldn't be very feasible, if do-able at all. And even if were feasible, it wouldn't be practical.

If he has a 20 million dollar diamond, why does he bother scamming for $5000?

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

I’d said:
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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.

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You replied:
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Again you miss the point.

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I just keep missing that darn point!
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It's not about speaking different languages

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That was what my objection was about.
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, 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.

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There are different truth-tables for implication.

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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.

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He was using the standard truth-table for 2-valued truth-functional implication.
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I’d said:
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...but that could depend on the company that's using the computer.

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You replied:
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You obviously don't know much about computer programming. ALL computer languages mean the same thing with IF-THEN statements.

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I didn’t say that different programming languages mean different things by IF-THEN. You said something about honesty, and that’s what I was replying to. There aren’t dishonest programming languages, but there are dishonest companies. And no doubt phishers and malware-writers use perfectly honest programming languages.
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I’d said:
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The truth value of the implication-proposition is function of the truth-values of the premise and the conclusion.

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You replied:
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No. It only depends on the truth value of the conclusion. Just look at the table.

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Incorrect.
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If the conclusion is false, then the truth of the implication depends on whether or not the premise is true, by the truth-table that I’ve been referring to, the standard 2-valued truth-functional truth-table.
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I’d said:
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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.

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You replied:
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Exactly. Now you've just contradicted your statement above.

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No, I didn’t. If the conclusion is false, then the implication proposition is false if its premise is true, and true if its premise is false.
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You continued:
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See how illogical this is?

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You got that right.
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I’d said:
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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.

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You replied:
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You just keep moving the goal posts.

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Incorrect. That’s what I’ve been saying from the start.
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This conversation is no longer meaningful.

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It never was.
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Michael Ossipoff

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

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.

My argument is that [the clerk] isn't a logician — Harry Hindu

The clerk's interpretation that an implication-proposition is true if its premise is false is unanimously agreed on by the academic sources i found, for 2- valued truth-functional implication.

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

As for people:

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.

And no, i''m not "moving the goalpost". It's something that I've been saying from the start.

As for computer programs:

Of course. So what?

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)"

In general, it's an instruction, like saying, "If he tries to get in, call the police".

Michael Ossipoff.

A familiar difference between definitions in logic and human language, is the meaning of "or".

As you may know, in logic, "A OR B" means "A", "B" or "A and B". If you just want one of them, you must use exclusive OR, abbreviated xOR.

In human language it's the opposite. If the carnival game operator tells you that you've won a stuffed bear or a parasol, and you take both, you're obviously in the wrong.

If you want inclusive OR, you have to say "A or B or both". Or, more briefly, A &/or B".

No one is claiming that words always mean the same in logic and in human language.

Michael Ossipoff