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## Question

puzzle in book:all but 2 of my cars a fords all but 2 of my cars are toyotas and all but 2 of my cars are hondas how many cars do i have

3 cars

couldnt he have 2 cars and none of them be a honda toyota or ford?

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If there were cars they would be Fords. However, there aren't any other cars and therefore there are no fords.

You said ""Remove 2 cars, the rest of them are now fords". Zero cars is empty space! An empty parking lot does not contain Fords. How is "If there were cars they would be Fords" a true statement?

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If the universal quantifier all implies at least one, then the book, and Martini, are correct.

In some forms of logic - I believe the two that differ on this point are Aristotelian and boolean - is does not.

Thus, "All four-legged humans with three brains and two left hands are male" makes sense in - and is true in - boolean logic.

It is equivalent to the statement "No four-legged ... etc. are not male [female or androgenous]," which is more intuitively seen to be true.

In boolean logic, you can discuss all the members of empty sets. But not in Aristotelian logic, where all implies at least one.

So the book probably took the Aristotelian view.

NEWSFLASH: BONANOVA AND I AGREE ON SOMETHING!!

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So ... two plus two equals five.

And please do not talk about rules of arithmetic to comment on whether the statement is correct - I wrote it in English, not in arithmetic.

This example is quite different from the riddle. The person speaking in the riddle stated "all but 2 of my cars a Fords". No arithmetic needed. A certain amount of cars are Fords. Zero amount of cars can't be labeled "Fords".

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You said ""Remove 2 cars, the rest of them are now fords". Zero cars is empty space! An empty parking lot does not contain Fords. How is "If there were cars they would be Fords" a true statement?

Again, this boils down to whether 0 can have units. If you think it can then the answer is "yes" however, if you don't the answer would be "no".

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Again, this boils down to whether 0 can have units. If you think it can then the answer is "yes" however, if you don't the answer would be "no".

I have no problem with the statement "I have zero cars". I do have a problem with "All my cars are Fords, except for two of them, when you don't have any Fords.

The difference is that person speaking in the riddle didn't just mention not having cars or not having Fords, he said that all of his cars are Fords except for two. He went ahead and labeled cars as Fords. You don't label an amount of cars as Fords if the amount of cars is zero. Labeling cars as Fords means the amount of cars is greater than zero.

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You said ""Remove 2 cars, the rest of them are now fords". Zero cars is empty space! An empty parking lot does not contain Fords. How is "If there were cars they would be Fords" a true statement?

Let me ask you: How can it be a false statement?

If A then B is equivalent to {not A} OR B.

If A then B implies either A is false or B is true.

In this case, A is false; so the implication is true.

Not to be demeaning, I mean this simply factually: Have you ever taken a course in logic?

I fear your reply will be that the question is irrelevant - that you're just communicating in English.

But you're not; you asked a question whose answer cannot avoid logic.

How is "If there were cars they would be Fords" a true statement?

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I have no problem with the statement "I have zero cars". I do have a problem with "All my cars are Fords, except for two of them, when you don't have any Fords.

The difference is that person speaking in the riddle didn't just mention not having cars or not having Fords, he said that all of his cars are Fords except for two. He went ahead and labeled cars as Fords. You don't label an amount of cars as Fords if the amount of cars is zero. Labeling cars as Fords means the amount of cars is greater than zero.

Ah, problem found:

I believe that 0 can have units

You believe that 0 cannot have units

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Again, the riddle was not written as a formula; it was written in English. In English, if you say "all of my animals are dogs except for two", you are not telling a true statement if you don't own any dogs.

The following statement is true, both logically, and linguistically:

"Apart from all my cars, all my cars are DeLoreans."

How many cars do I own, and how many are Fords?

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Let me ask you: How can it be a false statement?

See my post above. If you claim all your cars are Fords except for two, you went ahead and put a manufacturers name on a car to distinguish it from two others. This is different than saying "I have zero cars in the garage right now". Once someone goes out of their way to classify a car as being a different make of two others, that car must exist. Zero amount of cars is not a different make from cars that exist.

Not to be demeaning, I mean this simply factually: Have you ever taken a course in logic?

What does "I mean this simply factually" mean? And for what reason could you possibly be asking for if not to use an Appeal to authority? If I say yes, does my argumentation carry more weight?

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Ah, problem found:

I believe that 0 can have units

You believe that 0 cannot have units

That's not what I said. I clearly said that I agree that it's fine to say "I have zero cars". What's not fine is distinguishing a non-existent car from being a different make than two others. Once you define a car as having a different make as others, and you do it by claiming it's part of a group of cars that you own, that car must exist.

Again, this is different than saying "I have zero Fords in the garage".

The person speaking in the riddle specifically said "all but 2 of my cars are Fords". "but 2" means 2 has been subtracted from a greater amount.

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Here is a simple question: If a tree falls in the forest and no one sees it happen, did it in fact happen? This is the same idea as zero having units. Even though you never saw it happen/exist, the tree still fell over. A car can still be a ford even if it doesn't exist.

and, congrats on your crazy arguing skills.

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The following statement is true, both logically, and linguistically:

"Apart from all my cars, all my cars are DeLoreans.

That is not logically or grammatically correct. You can not separate all your cars from all your cars.

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Here is a simple question: If a tree falls in the forest and no one sees it happen, did it in fact happen? This is the same idea as zero having units.

It's not the same idea. If a tree falls in the forest- it exists and it happened. And I already agreed zero is a unit.

A car can still be a ford even if it doesn't exist.

Read my last post in its entirety.

and, congrats on your crazy arguing skills.

Thanks.

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I have no problem with the statement "I have zero cars". I do have a problem with "All my cars are Fords, except for two of them, when you don't have any Fords.

The difference is that person speaking in the riddle didn't just mention not having cars or not having Fords, he said that all of his cars are Fords except for two. He went ahead and labeled cars as Fords. You don't label an amount of cars as Fords if the amount of cars is zero. Labeling cars as Fords means the amount of cars is greater than zero.

How is saying "I have zero cars" valid, and "I have zero Fords" invalid?

Also, with reference to Pw0nzd's comments regarding units: "Ford" is not a unit of "car." You cannot measure cars in Fords. For example, 5 Corvairs = how many Fords?

Your point however, that zero can have units is correct. If I were to announce "I have zero," the first thing you will probably ask me is "Zero what?"

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Here is a simple question: If a tree falls in the forest and no one sees it happen, did it in fact happen?

Did it happen if zero amount of trees fell in the forest?

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Read my last post in its entirety.

OK Scraff, I see where you are coming from. When approached with a grammatical/English standpoint, yes there is only one answer. However, where you separate out the different rules mathematically more options open up. So your answer is correct that there is only one answer when the question is read with grammatical/English in mind (although I reserve the right to continue to disagree from a mathematical standpoint ).

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however, good reasoning was given in this thread so it remains open

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How is saying "I have zero cars" valid, and "I have zero Fords" invalid?

Again, I have no problem with either statement. (I'll even show you below where I said that's fine.) Let's look at the first statement again:

"All but 2 of my cars are Fords."

I'll repeat what I wrote on the last page:

What's not fine is distinguishing a non-existent car from being a different make than two others. Once you define a car as having a different make as others, and you do it by claiming it's part of a group of cars that you own, that car must exist.

Again, this is different than saying "I have zero Fords in the garage".

The person speaking in the riddle specifically said "all but 2 of my cars are Fords". "but 2" means 2 has been subtracted from a greater amount.

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OK Scraff, I see where you are coming from. When approached with a grammatical/English standpoint, yes there is only one answer. However, where you separate out the different rules mathematically more options open up. So your answer is correct that there is only one answer when the question is read with grammatical/English in mind (although I reserve the right to continue to disagree from a mathematical standpoint ).

I have no problem with the using more than one mathematical standpoint. But the riddle is written in English and rules of grammar must apply also. Once you separate an amount of cars from all your cars based on make, that amount separated must be one or greater.

And an even better point:

"All but 2" means you are separating 2 from a number. You can't separate 2 from itself, therefore, the number it is being separated from must be greater than 2.

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Did it happen if zero amount of trees fell in the forest?

Yes, the event where zero trees fell in the forest occurred.

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Yes, the event where zero trees fell in the forest occurred.

Nothing happening is not an event. We're getting on another topic here, but let's look at what was said:

"If a tree falls in the forest... "

Starting with, "If a tree falls in the forest" is asking about what would happen if a tree did in fact fall in the forest. That tree is one tree.

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I can write the following statement in English: two plus two equals five.

Now I claim my statement is true and I prohibit you from introducing the laws of arithmetic

by claiming that this is not an arithmetic statement; it was written in English and it is correct.

Bonanova: Two plus two equals five and you cannot use the laws of arithmetic.

Vig: Yeah, right!

On a broader level, I think the question has to communicate clearly the meaning of the statement. Logic does not begin to play a part until the statements are unambiguous. The duty of resolving vagueness and ambiguity lies with the tool of communication (English) and not the tool of reasoning (Logic). Think about the following situation:

Assume that I am a witness in court and that I own no houses. If I say "All my houses are in Texas", would I be perjuring myself? In any reasonable court, I would assume so. In social circumstances, people would assume that I do own at least one house in Texas. In fact, most people would not even consider the sentence to be ambiguous in terms of illuminating them as to whether I owned a house or not.

The question of school of logic may be relevant in a mathematical/logical analysis of the sentence. But even then, the parsing of the sentence would be done with the information gleaned from the meaning of 'All' in this context which comes back to English rather than set theory. So the OP is correct in saying that it is an English issue and not a Logic issue.

P.S. You are also assuming a meaning for All in Boolean logic to imply inclusion of the null set. One could argue that even in Boolean logic, it includes sets with a cardinality of at least one.

I am also having a hard time accepting the following

Thus, "All four-legged humans with three brains and two left hands are male" makes sense in - and is true in - boolean logic.

It is equivalent to the statement "No four-legged ... etc. are not male [female or androgenous]," which is more intuitively seen to be true.

First off, based on the assumed equivalence of the negation and the assertion, I think we can assume that the following is true.

"All males are not not male"

If "All four-legged humans with three brains and two left hands are male" is true,

"All four-legged humans with three brains and two left hands are NOT male" is equally true.

These three sentences together produce a contradiction

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Here is a simple question: If a tree falls in the forest and no one sees it happen, did it in fact happen? This is the same idea as zero having units. Even though you never saw it happen/exist, the tree still fell over. A car can still be a ford even if it doesn't exist.

and, congrats on your crazy arguing skills.

Cheers!

--

Vig

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This should go a long way in resolving this discussion:

And I would like to reference a favourite response of mine to questions like these:

Cheers!

--

Vig

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On a broader level, I think the question has to communicate clearly the meaning of the statement. Logic does not begin to play a part until the statements are unambiguous. The duty of resolving vagueness and ambiguity lies with the tool of communication (English) and not the tool of reasoning (Logic). Think about the following situation:

I'm afraid I have to disagree with this statement. If the purpose of removing ambiguity "lies with the tool of communication (English)" then we wouldn't be having this discussion. No one is arguing that "all my cars except two are Fords" is not a valid sentence of English (at least I haven't seen anyone arguing against that, ) but people are interpreting the sentence in different ways. That would seem to indicate there is an ambiguity somewhere, but the English language in itself is not the culprit.

English is a means of conveying information, but you need some other mechanism for getting meaning from the statement. In this case, the statement is such that it is fairly easy to convert to logic, and thus to me (and others) it seems appropriate to do the conversion.

If we get this far together, then the obvious place for the ambiguity lies in the domain of logic you are using and therefore the problem has already been identified: Aristotelian logic versus Boolean logic.

I would say that if you think that the only possible answer is 3, then you are probably applying Aristotelian logic, even if you don't realize it.

As such, I believe that 2 is a perfectly valid answer, but that's because:

All my cows are purple! (BTW, I don't own any cows. )

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