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

[ryan]

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.

Okay, but if 0 oranges are in a collection in the bag, then by deduction isn't it true to say that there are 0 oranges in the bag?

 

[beero1000]

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.

Okay, but if 0 oranges are in a collection in the bag, then by deduction isn't it true to say that there are 0 oranges in the bag?

If I reach into the bag and don't take out anything, does that mean that the bag is empty?

 

[ryan]

Okay, but if 0 oranges are in a collection in the bag, then by deduction isn't it true to say that there are 0 oranges in the bag?

If I reach into the bag and don't take out anything, does that mean that the bag is empty?

That's right but this seems to be a problematic root of my thinking process. I always strive for more accurate and precise ways to use logic because the knowledge acquired will be more universal. I assume you know what I am talking about.

So I am more interested in the exact meaning of all of this is and not just what the general population thinks.

 

[Bomb#20]

And the LORD spake, saying, "First shalt thou take out the Holy Pin, then shalt thou count to three, no more, no less. Three shall be the number thou shalt count, and the number of the counting shall be three. Four shalt thou not count, neither count thou two, excepting that thou then proceed to three. Five is right out. Once the number three, being the third number, be reached, then lobbest thou thy Holy Hand Grenade of Antioch towards thy foe, who being naughty in My sight, shall snuff it."

 

[Phil Scott]

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.

Okay, but if 0 oranges are in a collection in the bag, then by deduction isn't it true to say that there are 0 oranges in the bag?

In the language of set theory, there's a pretty important difference between membership (denoted ∈) and inclusion (denoted ⊆), but even mathematicians will write the word "in" and "contains" for both notions, if the intention can be figured out from context.

So I might say that the natural numbers contain the number 1, and that they also contain the even integers, but my two usages of "in" are interpreted differently. I mean to say that 1 is a member of the natural numbers, while the evens are included in the natural numbers.

The only thing that ultimately logically connects membership and inclusion is the following:

given sets A and B, to say that A ⊆ B means precisely that we have x ∈ B whenever x ∈ A.

You can figure out how you can use the logical connection if you figure out your uses of ∈ versus ⊆.

but if 0 oranges are in a collection in the bag, then by deduction isn't it true to say that there are 0 oranges in the bag?

The only way I can interpret this is as: "if A ⊆ B ⊆ C, then A ⊆ C." This is a true statement, being the transitivity rule for inclusion.

Another interpretation would be "if A ∈ B ⊆ C, then A ∈ C". This is also a true statement, but if this is the scheme you meant, you would be saying that your bag contains juicy oranges alongside the less juicy, less corporeal, abstract number 0.

No other interpretations produce a generally valid deduction.

 

[Copernicus]

(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?

What you are really interested in here is not logic, but what linguists refer to as "speech act theory"--the rules that govern cooperative discourse. The seminal work in the field is JL Austin's How to Do Things with Words, but you should also look at HP Grice's Logic and Conversation to understand the issues surrounding your questions. These are seminal works, and they led to a lot of literature on the subject of speech act theory in both linguistics and the philosophy of language. This overview paper might be helpful in a better understanding of what Grice's work is about: Conversational Implicatures.

 

[ryan]

Okay, but if 0 oranges are in a collection in the bag, then by deduction isn't it true to say that there are 0 oranges in the bag?

In the language of set theory, there's a pretty important difference between membership (denoted ∈) and inclusion (denoted ⊆), but even mathematicians will write the word "in" and "contains" for both notions, if the intention can be figured out from context.

So I might say that the natural numbers contain the number 1, and that they also contain the even integers, but my two usages of "in" are interpreted differently. I mean to say that 1 is a member of the natural numbers, while the evens are included in the natural numbers.

The only thing that ultimately logically connects membership and inclusion is the following:

given sets A and B, to say that A ⊆ B means precisely that we have x ∈ B whenever x ∈ A.

You can figure out how you can use the logical connection if you figure out your uses of ∈ versus ⊆.

but if 0 oranges are in a collection in the bag, then by deduction isn't it true to say that there are 0 oranges in the bag?

The only way I can interpret this is as: "if A ⊆ B ⊆ C, then A ⊆ C." This is a true statement, being the transitivity rule for inclusion.

Another interpretation would be "if A ∈ B ⊆ C, then A ∈ C". This is also a true statement, but if this is the scheme you meant, you would be saying that your bag contains juicy oranges alongside the less juicy, less corporeal, abstract number 0.

No other interpretations produce a generally valid deduction.

Yeah, that all makes sense. So in the case of "if A ⊆ B ⊆ C, then A ⊆ C" would you have to say that C contains the set of no apples (no elements), or is it equivalent to say that C contains no apples/elements. If the latter is strictly sufficient, then there seems to be a contradiction.

 

[Phil Scott]

Yeah, that all makes sense. So in the case of "if A ⊆ B ⊆ C, then A ⊆ C" would you have to say that C contains the set of no apples (no elements), or is it equivalent to say that C contains no apples/elements. If the latter is strictly sufficient, then there seems to be a contradiction.

Both are still ambiguous. All sets include (⊆) the empty set of apples. Some sets also have as a member (∊) the empty set. So if you say that C contains A, the ambiguity over the word "contains" can't be resolved by just stipulating that A is a set.

In practice, however, I might read you saying "C contains the set of no apples" and go: "well, in that case, ryan must mean '⊆' when he writes 'contains', since C is supposed to be a physical bag of oranges, but the set of no apples is a non-physical object." In other words, I reject the interpretation in terms of membership because it would catch you in what computer scientists call a type error. The avoidance of type errors is a standard way to disambiguate in formal languages.

 

[bilby]

Yes, most people are aware that language is ambiguous.

Welcome to adulthood.

 

[fast]

If I have 3 oranges in my bag, is it true to say that I have 2 oranges in my bag?

Yes.

What do you think?

I think it's true that you have at least two apples in your bag.

To which you might respond, yes, fast, I think that too, but I didn't ask if I have or if it's true that I have at least two apples in my bag but rather if I have or if it's true that I have two apples in my bag.

To which I respond, yes, I know, and I answered you. Of course you have two apples in your bag. It couldn't be true that you have three apples in your bag if it wasn't true that you have at least two apples in your bag, and it couldn't be true that you have at least two apples in your bag if it was not true that you have two apples in your bag.

The subject matter to review is quantification.

For instance, if I say that dogs have legs, am I really saying, "all dogs have legs." Of course not. Math types and in all their analytical rigor are overwhelmed, as evidenced by their unwavering need to apply mathematical rigor no matter the ambiguity. If the rescue squad asks you how many people are left in the submerged vehicle (and if there are three), do please refrain from merely being minimally accurate.

 

[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.

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".

Give an example.

Because if I am buying something I know what I am buying.

 

[Copernicus]

I suppose that this sounds like its coming out of left field or irrelevant, but there is a reason why logic does not really help to explain meaning in natural language. There is no way to capture presuppositions in formal logical languages. IOW, the meaning of natural language expressions requires some way to capture the context of a speech act, and that is what presuppositions do. They set the conditions under which a natural language expression can be disambiguated and assigned meaning or even carry off as speech acts. So what is going to happen here is that you are going to be trying to imagine conditions under which an utterance could make sense, but you need a theory of discourse in which to approach the question.

 

[ryan]

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".

Give an example.

Because if I am buying something I know what I am buying.

There are many examples outside of day-to-day purchases. Contractors can live well or die by ambiguous contracts. "The devil is in the details" quote exists for a reason. Perhaps the best examples though take place in the courtroom.

 

[ryan]

The subject matter to review is quantification.

What is the subject of quantification? And how would it help?

 

[ryan]

I suppose that this sounds like its coming out of left field or irrelevant, but there is a reason why logic does not really help to explain meaning in natural language. There is no way to capture presuppositions in formal logical languages. IOW, the meaning of natural language expressions requires some way to capture the context of a speech act, and that is what presuppositions do. They set the conditions under which a natural language expression can be disambiguated and assigned meaning or even carry off as speech acts. So what is going to happen here is that you are going to be trying to imagine conditions under which an utterance could make sense, but you need a theory of discourse in which to approach the question.

Welcome to TF!

Are you talking about the metaphysical connection (intentionality) of meaning, or ...?

 

[Copernicus]

I suppose that this sounds like its coming out of left field or irrelevant, but there is a reason why logic does not really help to explain meaning in natural language. There is no way to capture presuppositions in formal logical languages. IOW, the meaning of natural language expressions requires some way to capture the context of a speech act, and that is what presuppositions do. They set the conditions under which a natural language expression can be disambiguated and assigned meaning or even carry off as speech acts. So what is going to happen here is that you are going to be trying to imagine conditions under which an utterance could make sense, but you need a theory of discourse in which to approach the question.

Welcome to TF!

Are you talking about the metaphysical connection (intentionality) of meaning, or ...?

Hi, Ryan. I'm not quite sure how to answer that question. There is a popular misconception about language that linguistic expressions "contain" meaning. That is, they are pipelines or conduits through which meaning gets transmitted from sender to receiver. Formal logical languages are grounded in this metaphorical view of language, but it doesn't really hold up under scrutiny. When we assign meaning to natural language expressions, it is always in the context of a discourse that both speaker and hearer have internal "world models" for. Actual communication depends largely on how well those models harmonize with each other. The "conduit metaphor" is a very powerful one that has helped a lot in developing formal systems of logic, but it doesn't work very well when applied to natural language expressions.

 

[ryan]

Welcome to TF!

Are you talking about the metaphysical connection (intentionality) of meaning, or ...?

Hi, Ryan. I'm not quite sure how to answer that question. There is a popular misconception about language that linguistic expressions "contain" meaning. That is, they are pipelines or conduits through which meaning gets transmitted from sender to receiver. Formal logical languages are grounded in this metaphorical view of language, but it doesn't really hold up under scrutiny. When we assign meaning to natural language expressions, it is always in the context of a discourse that both speaker and hearer have internal "world models" for. Actual communication depends largely on how well those models harmonize with each other. The "conduit metaphor" is a very powerful one that has helped a lot in developing formal systems of logic, but it doesn't work very well when applied to natural language expressions.

Okay, I don't think I am as comfortable with this as you seem to be, so let me just dumb it down a little with an analogy. By "world models", do you mean information processors, like say for instance, 2 robots that may have slightly different information processors but are both programmed to try to talk to each other both having an objective? So let's say one robot will try to get the other to shake "his" hand, and the other robot would be actually trying to do what the other is asking him. But because their processors are a little different, there may not be a successful outcome for either robot.

If I am way off, don't worry about replying. But if it is basically the right idea, then this is very interesting. I never thought of human communication this way, and thus seems more incredible but way more complicated than I ever thought before.

 

[Copernicus]

Hi, Ryan. I'm not quite sure how to answer that question. There is a popular misconception about language that linguistic expressions "contain" meaning. That is, they are pipelines or conduits through which meaning gets transmitted from sender to receiver. Formal logical languages are grounded in this metaphorical view of language, but it doesn't really hold up under scrutiny. When we assign meaning to natural language expressions, it is always in the context of a discourse that both speaker and hearer have internal "world models" for. Actual communication depends largely on how well those models harmonize with each other. The "conduit metaphor" is a very powerful one that has helped a lot in developing formal systems of logic, but it doesn't work very well when applied to natural language expressions.

Okay, I don't think I am as comfortable with this as you seem to be, so let me just dumb it down a little with an analogy. By "world models", do you mean information processors, like say for instance, 2 robots that may have slightly different information processors but are both programmed to try to talk to each other both having an objective? So let's say one robot will try to get the other to shake "his" hand, and the other robot would be actually trying to do what the other is asking him. But because their processors are a little different, there may not be a successful outcome for either robot.

Not a bad analogy. The point is that both robots, being similar constructs, share experiences that allow them to "fill in the blanks". They can "understand" each other, because their "world models" overlap. So it is very much like a handshake in terms of different systems communicating with each other. BTW, have you had training in AI? Are you familiar with Roger Schank's work?

If I am way off, don't worry about replying. But if it is basically the right idea, then this is very interesting. I never thought of human communication this way, and thus seems more incredible but way more complicated than I ever thought before.

Not at all way off. It is very complicated.

 

[Phil Scott]

Welcome to TF!

Are you talking about the metaphysical connection (intentionality) of meaning, or ...?

Hi, Ryan. I'm not quite sure how to answer that question. There is a popular misconception about language that linguistic expressions "contain" meaning. That is, they are pipelines or conduits through which meaning gets transmitted from sender to receiver. Formal logical languages are grounded in this metaphorical view of language, but it doesn't really hold up under scrutiny. When we assign meaning to natural language expressions, it is always in the context of a discourse that both speaker and hearer have internal "world models" for. Actual communication depends largely on how well those models harmonize with each other. The "conduit metaphor" is a very powerful one that has helped a lot in developing formal systems of logic, but it doesn't work very well when applied to natural language expressions.

Just to put my cards on the table: I doubt formal logic is particularly relevant when discussing our day-to-day language use, and I'm not convinced that formal logic has anything to say about psychology. It turns out that modern logic is sufficient to formalise mathematics, and that shouldn't be sniffed at, because it was never a given that maths could be formalised.

I've said for years now is that the real sell of formal logic is that computers can grok it, and when saying this, I like to stress the fact that its history is tied up with the history of computability.

My responses in this thread come from that perspective.

 

[ryan]

Okay, I don't think I am as comfortable with this as you seem to be, so let me just dumb it down a little with an analogy. By "world models", do you mean information processors, like say for instance, 2 robots that may have slightly different information processors but are both programmed to try to talk to each other both having an objective? So let's say one robot will try to get the other to shake "his" hand, and the other robot would be actually trying to do what the other is asking him. But because their processors are a little different, there may not be a successful outcome for either robot.

Not a bad analogy. The point is that both robots, being similar constructs, share experiences that allow them to "fill in the blanks". They can "understand" each other, because their "world models" overlap. So it is very much like a handshake in terms of different systems communicating with each other. BTW, have you had training in AI? Are you familiar with Roger Schank's work?

If I am way off, don't worry about replying. But if it is basically the right idea, then this is very interesting. I never thought of human communication this way, and thus seems more incredible but way more complicated than I ever thought before.

Not at all way off. It is very complicated.

No, I know little about A.I. I am very interested in what you were saying though.

I have been meaning to take a fundamenatals of computer science course. I feel like that will at least help me understand a little of what fields like A.I. are generally about. Damn, there's just not enough time in this life.