This is completely wrong. In classical logic that "every implication-proposition is true if its premise isn’t true" is based on the fact that there is never any change in the truth value of any proposition — James R Meyer
It was only intended to show that the usual 2-valued truth-functional implication truth-table that I'd read about could lead to an undesirable conclusion. — Michael Ossipoff
The customer asked if the sign was true, not if the implication-proposition was true. The sign includes the premise and the implication-proposition. — Harry Hindu
The clerk said that the sign was true. But only part of it was true and the other part was false. Therefore the clerk lied.
If at any given moment part of the sign is false and part is true, then the clerk can't say that the sign is true.
The sign is both true and false, which just makes the sign illogical.
The sign is an IF-THEN statement. How are IF-THEN statements not true?
They aren't unless we are missing information to put into the logical system. The implication always follows the premise assuming you have all the right information going in. It is only when you don't have all the information can it seem like the conclusion is false when the hypothesis is true. The missing information is what the clerk didn't tell the customer.
If the customer had been given that information then they wouldn't have been tricked.
So this isn't an example of how logic fails. It is an example of how one can use logic to get the wrong answers when they don't have all the information needed to get the right answer. In order for logic to work, you have to put in all the relevant information.
The sign includes the premise and the implication-proposition. — Harry Hindu
That is a contradiction, and therefore can't be logical. That's like saying A x B = 1 if A=0So, "if you have given $5,000 to the sales-clerk then he will give you the diamond" is true if "you have given $5,000 to the sales-clerk" is false. — Michael
That is a contradiction, and therefore can't be logical. That's like saying A x B = 1 if A=0 — Harry Hindu
p q p → q T T T T F F F T T F F T
So then why didn't the clerk give the customer the diamond before the customer gave him the money? The sign would have been true when the customer walked in because the customer had not yet given the clerk the money. Not only that but is the sign true even when no one reads it? If so, then shouldn't everyone who hasn't given the clerk $5000 get the diamond?p → q is logically equivalent to ¬p ∨ q, so "if you have given $5,000 to the sales-clerk then he will give you the diamond" is logically equivalent to "you have not given $5,000 to the sales-clerk or he will give you the diamond". — Michael
The word, "or" seems to separate the two statements - making them independent of each other, which means that the conclusion doesn't necessarily follow the premise. All you are saying is "this condition exists or that condition exists". So when the first condition didn't exist, (the customer hadn't given the clerk any money) then the latter condition exists (the clerk should have given the customer the diamond).If you have not given $5,000 to the sales-clerk then "you have not given $5,000 to the sales-clerk or he will give you the diamond" is true. Therefore, if you have not given $5,000 to the sales-clerk then "if you have given $5,000 to the sales-clerk then he will give you the diamond" is true. — Michael
The latter conditional is saying the same thing as "Give the money to the clerk and he will give you the diamond". The customer gave the money to the clerk, now where is his diamond?Also, p → q is logically equivalent to ¬q → ¬p, so "if you have given $5,000 to the sales-clerk then he will give you the diamond" is logically equivalent to "if he will not give you the diamond then you have not given $5,000 to the sales-clerk". Do you find this latter conditional problematic? — Michael
So then why didn't the clerk give the customer the diamond before the customer gave him the money? The sign would have been true when the customer walked in because the customer had not yet given the clerk the money. Not only that but is the sign true even when no one reads it? If so, then shouldn't everyone who hasn't given the clerk $5000 get the diamond?
...
The word, "or" seems to separate the two statements - making them independent of each other, which means that the conclusion doesn't necessarily follow the premise. All you are saying is "this condition exists or that condition exists". So when the first condition didn't exist, (the customer hadn't given the clerk any money) then the latter condition exists (the clerk should have given the customer the diamond). — Harry Hindu
The latter conditional is saying the same thing as "Give the money to the clerk and he will give you the diamond".
Forget about the "truth" table. Just read the words. They contradict each other, which means that the first statement is never true - ever. In other words, it is a false statement.
It's:
1) You have not given $5,000 to the sales-clerk, or
2) He will give you the diamond
1) is true, so 2) needn't be. — Michael
I said forget about the "truth" table and just read the words. Actually, maybe you should put both conclusions into the truth table and see if that works. Maybe then you'll see the contradiction.They don't contradict each other, as the truth table shows. — Michael
Exactly. If 2 isn't logically dependent upon 1 then he will give you the diamond. It would also be incorrect to use the truth table in this instance because now you are saying that 1 isn't necessarily the premise to the conclusion. The two are only related as they are on the same sign. Again, all you are doing is describing two independent conditions, which can be true or false independent of each other. — Harry Hindu
I said forget about the "truth" table and just read the words.
Therefore, if you have not given $5,000 to the sales-clerk then "if you have given $5,000 to the sales-clerk then he will give you the diamond" is true. — Michael
I'm saying it isn't relevent to the topic. The OP didn't include it. You did later. I'm saying that is you that is off-topic. Just read the sentences. It's more like: if p->q then p is not equal to p.I have read the words. And I won't forget the truth table, because it's relevant to the topic. The store-clerk is a logician who uses the truth-table of the material conditional to help determine the truth of the sign. — Michael
Get involved in philosophical discussions about knowledge, truth, language, consciousness, science, politics, religion, logic and mathematics, art, history, and lots more. No ads, no clutter, and very little agreement — just fascinating conversations.