Are people aware of this the danger of this kind of ambiguity?

[ryan]

(Please leave out the first "this" in the heading)

For the past 3 years, I have been constantly critiquing and examining my way of thinking in hopes that I will, well, become smarter. Maybe even get my grades next term to 4.0. But it has been SUCH a horrifically grueling process with very little progress (presumably because it is hard for brain processes to find its own faults).

But about a year ago, I thought I found something wrong with my logic - which was great! I had a conflicting answer between me and others about a very simple truth statement about a very simple observation. Sparing you the details about how it happened, I will put it this way instead: If I have 3 oranges in my bag, is it true to say that I have 2 oranges in my bag? My answer was false, but I asked some pretty smart people, and they unanimously said that it's true.

What do you think?

So I was excited for a few months until I recently thought of a reason why maybe my initial thought was correct. To clarify the statement, we are really saying what is in the bag may not be all that is in the bag without actually specifying anything else. In the example given, we are leaving out an orange; apparently that's fine. BUT, does this mean that we can leave out 2 more oranges? In that case, we would be saying that there are no oranges in the bag! If that is still fine, then I guess I am just going to have to get used to this way of looking at what people are saying - especially my professors!

I know in day-to-day life we know that people usually take "what" to mean "what is the total". Like if asked "what classes do you have this semester" this would really mean what are all of the classes you are taking this semester; nobody would just say 1 or 2 of 5 classes. But what is the more rigorous answer if the statements are as ambiguous as they are in my example.

And a danger being how swindled one could get with some kind of a contract where this is relevant.

Please help me.

In addition to any responses, I would also really be interested in what math logic would say about this, if anything at all. Beero?

 

[Lion IRC]

That's interesting.
There is, in theory, half an orange in your bag also.

 

[J842P]

It's called "natural language", and it is ambiguous and the exact meaning can depend on context and cultural/social expectations. If you want precision, use something else.

 

[Lion IRC]

And somewhere in your bag there are no oranges.

 

[PyramidHead]

(Please leave out the first "this" in the heading)

For the past 3 years, I have been constantly critiquing and examining my way of thinking in hopes that I will, well, become smarter. Maybe even get my grades next term to 4.0. But it has been SUCH a horrifically grueling process with very little progress (presumably because it is hard for brain processes to find its own faults).

But about a year ago, I thought I found something wrong with my logic - which was great! I had a conflicting answer between me and others about a very simple truth statement about a very simple observation. Sparing you the details about how it happened, I will put it this way instead: If I have 3 oranges in my bag, is it true to say that I have 2 oranges in my bag? My answer was false, but I asked some pretty smart people, and they unanimously said that it's true.

What do you think?

So I was excited for a few months until I recently thought of a reason why maybe my initial thought was correct. To clarify the statement, we are really saying what is in the bag may not be all that is in the bag without actually specifying anything else. In the example given, we are leaving out an orange; apparently that's fine. BUT, does this mean that we can leave out 2 more oranges? In that case, we would be saying that there are no oranges in the bag! If that is still fine, then I guess I am just going to have to get used to this way of looking at what people are saying - especially my professors!

I know in day-to-day life we know that people usually take "what" to mean "what is the total". Like if asked "what classes do you have this semester" this would really mean what are all of the classes you are taking this semester; nobody would just say 1 or 2 of 5 classes. But what is the more rigorous answer if the statements are as ambiguous as they are in my example.

And a danger being how swindled one could get with some kind of a contract where this is relevant.

Please help me.

In addition to any responses, I would also really be interested in what math logic would say about this, if anything at all. Beero?

You're overthinking it. Numerical quantities other than zero are inclusive of lower quantities, while zero is not inclusive of higher quantities. There is no ambiguity.

 

[Lion IRC]

Yes there is. I think it's simple amphibology.
There's half an orange in ryan's bag - true or false?



I'm glad I'm a man, and so is my wife.

 

[Phil Scott]

Ambiguity is resolved by formalising, and so you could settle your question by insisting on using formal logic. But you could also find a middle ground, stay with plain English, and just spell out your intention.

Rather than saying "I have three oranges in my bag", you might be more precise and say "the number of oranges in my bag is 3." The use of the definite article requires that you've disambiguated between 3 and 2, and the choice of 3 is correct because it's the one that gives the most information about the contents of your bag.

To instead stress the disambiguity, you could say "there are at least three oranges in my bag, and therefore at least two."

Practising mathematicians, by the way, are pretty big on playing with the sort of ambiguities in your OP. For instance, if a mathematician ever begins a sentence with "consider two numbers m and n", they'll very much be allowing that there is, in fact, only one number, and that m = n. If they exclude this, they are required to say something like "consider two numbers m < n."

This wasn't always so, and, historically, some mathematicians have adopted a convention that if you're naming two things, you're naming two different things. I think there are arguments that this shouldn't be the logical convention, but it's not difficult to switch if it is.

 

[Juma]

Are there three oranges in the bag? Yes! (True)

There are three oranges in the bag (true)

Are there two oranges in your bag? Yes! (True)
Are there two oranges in your bag? No! (False)

There are are two oranges in your bag. (True)

There is a set of two oranges in your bag (true)

Are there no oranges in your bag? Yes! (False)
Are there no oranges in your bag? Yes, there are! (True)

There are no oranges in your bag. (False)

There is a set of zero oranges in your bag (true)

 

[ryan]

It's called "natural language", and it is ambiguous and the exact meaning can depend on context and cultural/social expectations. If you want precision, use something else.

Yes, but I am more interested in the logic of it.

 

[ryan]

You're overthinking it. Numerical quantities other than zero are inclusive of lower quantities, while zero is not inclusive of higher quantities. There is no ambiguity.

If you are right, then you have settled my concern over the extreme case of saying that there are no oranges in the bag.

But even the partial answer of 2 oranges is problematic for even, say, the IRS/government. They may ask, "How much money did you make last year". I could legally say $5 even though I made more.

 

[untermensche]

And somewhere in your bag there are no oranges.

Can no oranges be somewhere?

To be somewhere don't you have to be?

 

[beero1000]

(Please leave out the first "this" in the heading)

For the past 3 years, I have been constantly critiquing and examining my way of thinking in hopes that I will, well, become smarter. Maybe even get my grades next term to 4.0. But it has been SUCH a horrifically grueling process with very little progress (presumably because it is hard for brain processes to find its own faults).

But about a year ago, I thought I found something wrong with my logic - which was great! I had a conflicting answer between me and others about a very simple truth statement about a very simple observation. Sparing you the details about how it happened, I will put it this way instead: If I have 3 oranges in my bag, is it true to say that I have 2 oranges in my bag? My answer was false, but I asked some pretty smart people, and they unanimously said that it's true.

What do you think?

So I was excited for a few months until I recently thought of a reason why maybe my initial thought was correct. To clarify the statement, we are really saying what is in the bag may not be all that is in the bag without actually specifying anything else. In the example given, we are leaving out an orange; apparently that's fine. BUT, does this mean that we can leave out 2 more oranges? In that case, we would be saying that there are no oranges in the bag! If that is still fine, then I guess I am just going to have to get used to this way of looking at what people are saying - especially my professors!

I know in day-to-day life we know that people usually take "what" to mean "what is the total". Like if asked "what classes do you have this semester" this would really mean what are all of the classes you are taking this semester; nobody would just say 1 or 2 of 5 classes. But what is the more rigorous answer if the statements are as ambiguous as they are in my example.

And a danger being how swindled one could get with some kind of a contract where this is relevant.

Please help me.

In addition to any responses, I would also really be interested in what math logic would say about this, if anything at all. Beero?

Colloquial language is almost always too ambiguous for really careful thought, which is why technical language exists. As stated, either could be true depending on the intention of the speaker, and either could be inferred depending on the comprehension of the listener. That's a recipe for problems if you really need to know how many oranges are in the bag.

There are many of these ambiguities in English. One I particularly like is "Get at least a 65 on the final or you'll fail the class." Imagine the uproar if both ended up being true... but there's no really nice way to work in XOR into conversational English, and people would look at you funny if you made sure to clarify 'but not both', so we'll just have to go on context. There's also the word 'biweekly' which means completely different things that are basically impossible to tell apart via context. Etc, etc.

Ambiguity is resolved by formalising, and so you could settle your question by insisting on using formal logic. But you could also find a middle ground, stay with plain English, and just spell out your intention.

Rather than saying "I have three oranges in my bag", you might be more precise and say "the number of oranges in my bag is 3." The use of the definite article requires that you've disambiguated between 3 and 2, and the choice of 3 is correct because it's the one that gives the most information about the contents of your bag.

To instead stress the disambiguity, you could say "there are at least three oranges in my bag, and therefore at least two."

Practising mathematicians, by the way, are pretty big on playing with the sort of ambiguities in your OP. For instance, if a mathematician ever begins a sentence with "consider two numbers m and n", they'll very much be allowing that there is, in fact, only one number, and that m = n. If they exclude this, they are required to say something like "consider two numbers m < n."

This wasn't always so, and, historically, some mathematicians have adopted a convention that if you're naming two things, you're naming two different things. I think there are arguments that this shouldn't be the logical convention, but it's not difficult to switch if it is.

Basically this ^^

 

[untermensche]

This is simply a matter of fact.

Do you have two oranges in the bag?

Yes.

Can you prove that? Of course, easily.

End of story. No ambiguity. No dangers.

 

[ryan]

Are there three oranges in the bag? Yes! (True)

There are three oranges in the bag (true)

Are there two oranges in your bag? Yes! (True)
Are there two oranges in your bag? No! (False)

There are are two oranges in your bag. (True)

There is a set of two oranges in your bag (true)

But is there not an empty set in every set? There is a set of no oranges/elements in my bag. Therefore there are no oranges in my bag.

Are there no oranges in your bag? Yes! (False)
Are there no oranges in your bag? Yes, there are! (True)

There are no oranges in your bag. (False)

There is a set of zero oranges in your bag (true)

 

[ryan]

Practising mathematicians, by the way, are pretty big on playing with the sort of ambiguities in your OP. For instance, if a mathematician ever begins a sentence with "consider two numbers m and n", they'll very much be allowing that there is, in fact, only one number, and that m = n. If they exclude this, they are required to say something like "consider two numbers m < n."

This wasn't always so, and, historically, some mathematicians have adopted a convention that if you're naming two things, you're naming two different things. I think there are arguments that this shouldn't be the logical convention, but it's not difficult to switch if it is.

I don't know what this has to do with what I am saying.

 

[ryan]

Colloquial language is almost always too ambiguous for really careful thought, which is why technical language exists. As stated, either could be true depending on the intention of the speaker, and either could be inferred depending on the comprehension of the listener. That's a recipe for problems if you really need to know how many oranges are in the bag.

There are many of these ambiguities in English. One I particularly like is "Get at least a 65 on the final or you'll fail the class." Imagine the uproar if both ended up being true... but there's no really nice way to work in XOR into conversational English, and people would look at you funny if you made sure to clarify 'but not both', so we'll just have to go on context. There's also the word 'biweekly' which means completely different things that are basically impossible to tell apart via context. Etc, etc.

But what about the exact answer to the question: "Is it true that I have no oranges in my bag?". Is this even an answerable question, say, for set theory: "does the set of natural numbers have no elements in it (the empty set)?". If you say no, then I have to ask why because the empty set is in N and nothing is in the empty set. By deduction can't I say that there are no elements in N? Obviously wrong, but put exactly the way I put it, is it true?

 

[beero1000]

Colloquial language is almost always too ambiguous for really careful thought, which is why technical language exists. As stated, either could be true depending on the intention of the speaker, and either could be inferred depending on the comprehension of the listener. That's a recipe for problems if you really need to know how many oranges are in the bag.

There are many of these ambiguities in English. One I particularly like is "Get at least a 65 on the final or you'll fail the class." Imagine the uproar if both ended up being true... but there's no really nice way to work in XOR into conversational English, and people would look at you funny if you made sure to clarify 'but not both', so we'll just have to go on context. There's also the word 'biweekly' which means completely different things that are basically impossible to tell apart via context. Etc, etc.

But what about the exact answer to the question: "Is it true that I have no oranges in my bag?". Is this even an answerable question, say, for set theory: "does the set of natural numbers have no elements in it (the empty set)?". If you say no, then I have to ask why because the empty set is in N and nothing is in the empty set. By deduction can't I say that there are no elements in N? Obviously wrong, but put exactly the way I put it, is it true?

Your question is ambiguous and the different answers correspond to different plausible meanings that haven't been specified. Are you asking:
1. Is it true that there is a collection of zero oranges in my bag?
2. Is it true that the number of oranges in my bag is zero?

 

[ryan]

But what about the exact answer to the question: "Is it true that I have no oranges in my bag?". Is this even an answerable question, say, for set theory: "does the set of natural numbers have no elements in it (the empty set)?". If you say no, then I have to ask why because the empty set is in N and nothing is in the empty set. By deduction can't I say that there are no elements in N? Obviously wrong, but put exactly the way I put it, is it true?

Your question is ambiguous and the different answers correspond to different plausible meanings that haven't been specified. Are you asking:
1. Is it true that there is a collection of zero oranges in my bag?
2. Is it true that the number of oranges in my bag is zero?

Now if the answer to question 1 is yes, does that imply question 2 is also yes?

 

[ryan]

This is simply a matter of fact.

Do you have two oranges in the bag?

Yes.

Can you prove that? Of course, easily.

End of story. No ambiguity. No dangers.

On the surface, this is just frivolous. But imagine if you were trying to create a contract that can't be twisted this way. Then the matter might become more useful. Lawyers could argue that their client is a very logical person, and could only understand the contract with what you are calling a "loophole".

 

[beero1000]

Your question is ambiguous and the different answers correspond to different plausible meanings that haven't been specified. Are you asking:
1. Is it true that there is a collection of zero oranges in my bag?
2. Is it true that the number of oranges in my bag is zero?

Now if the answer to question 1 is yes, does that imply question 2 is also yes?

Not at all. One is saying that there is a collection of zero oranges in my bag and the other is saying that the collection of all oranges in my bag has zero oranges.