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. — Harry Hindu
Which is the same as saying that it doesn't matter whether or not p is true or false. q is true regardless of the truth value of p, which means that q is independent of p, which makes p->q false. There is no IF-THEN relationship between p and q.p is "You have given $5,000 to the sales-clerk" and q is "He will give you the diamond".
p → q is equivalent to ¬p ∨ q.
¬p is "You have not given $5,000 to the sales-clerk". — Michael
Then that is the problem with the OP. He's applying a system that is irrelevant to the circumstances, or to what the words actually mean.He says that the store-clerk is a logician who talks about implications being true if the premise (actually "antecedent") is false. He's referring to the material implication truth table. — Michael
Which is the same as saying that it doesn't matter whether or not p is true or false. q is true regardless of the truth value of p, which means that q is independent of p, which makes p->q false. — Harry Hindu
Then that is the problem with the OP. He's applying a system that is irrelevant to the circumstances, or to what the words actually mean.
“If, at any particular time, you have given $5000 to the sales-clerk (under no circumstances will it be returned), then, within 60 seconds after your giving him that money, he will give you this diamond, and it will at that time become yours.” — Michael Ossipoff
I'm saying it isn't relevent to the topic. The OP didn't include it. — Harry Hindu
This offer is a HIRE offer.
It has nothing to do with offering employment.
— charleton
The rest of the scenario is of no consequence and is nothing but sophistry.
"at that time it will be yours" implies a limit.
He's applying a system that is irrelevant to the circumstances, — Harry Hindu
One of those times when time is important in logic.
The sign was true before the man gave the clerk money and then it became false. — TheMadFool
However, the IF-THEN logical form isn't defined in temporal terms.
From the logic books I've read, the IF-THEN logical form is timeless i.e. we can't change its truth value over time or space.
Make "if you have not given $5,000 to the sales-clerk" = p — Harry Hindu
I believe the statement was not true when the person first inquired, because the words 'at any particular time' are not constrained to cover only the past, so they cover the future too. — andrewk
It is a universal quantifier: for all t.
If the person is inquiring at time t1, the quantified part of the statement is true for values of t less than t1, by virtue of the above truth tables Null implication) but it is not true for values of t more than or equal to t1. Hence the statement is not true at time t1 because it is universally quantified and it is not true for all values of t.
So, "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
↪Michael Ossipoff
So, all you've done is create an impossible scenario where someone actually receives the diamond?
Is it really is no different than a sign saying, “If, at any particular time, you have given $5000 to the sales-clerk (under no circumstances will it be returned), then, within 60 seconds after your giving him that money, a unicorn will appear, and it will at that time become your best friend.”?
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
So then why didn't the clerk give the customer the diamond before the customer gave him the money? — Harry Hindu
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?
[in "(not A) or (B)"] 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).
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?
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?
Forget about the "truth" table. Just read the words. They contradict each other, which means that the first statement is never true - ever.
Eh?
I assume you are an American.
In English English people are not hired, cars are hired.
What I meant was The notice implies that the diamond was for RENTAL.
Are we clear? — charleton
The sign said "...the clerk will give the diamond to you, and at that time it will become yours" — Michael Ossipoff
AT THAT TIME. Why is this codicil present?
It's a rental! — charleton
I'm talking about the logical implications of the truth table.Which is the same as saying that it doesn't matter whether or not p is true or false. q is true regardless of the truth value of p, which means that q is independent of p, which makes p->q false. — Harry Hindu
That's just wrong. p → q is true if both p and q are true or if p is false. See the truth table. — Michael
So you're admitting that there is more than one logical way to interpret the sign as the customer did.So as I have twice brought up, this is an example of the paradoxes of material implication, where "if ... then ..." in classical logic doesn't mean what it does in ordinary language, hence the unintuitive conclusions. — Michael
I'm talking about the implications of the truth table and how those p's and q's get translated into English words. Language is logical and they both need to be consistent with each other.No contradiction. It's a universally-agreed part of the truth-table for 2-valued truth-functional implication. — Michael Ossipoff
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