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Semantic difficulty

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Brock
1373854.  Sun Feb 07, 2021 6:33 am Reply with quote

This is a post about semantics. If you're not particularly interested in semantics, or language, or philosophy, then I suggest you skip it, because it's likely to seem a bit technical.

Consider the following two sentences:
(1) Cheese is made from milk.
(2) "Cheese" has six letters.

The first is a statement about cheese, the substance: the second is a statement about "cheese", the word. This is known as the use-mention distinction; the first sentence uses the word "cheese" to refer to the substance, the second mentions the word "cheese" without using it to refer to anything else. (I'm going to use double quotes throughout this post to indicate mentions of a word; some people prefer single quotes or italics.)

In everyday life, you're unlikely to confuse cheese with "cheese". You wouldn't pick up a piece of paper with the word "cheese" on it and try to eat it. But in discussions about semantics it can be all too easy to confuse the two.

"Cheese" is a symbol. It normally represents cheese, but it can be used to represent other things. If I say that for the rest of this paragraph, "cheese" will represent the number 5, then I can say things like "cheese + 1 = 6", and it makes sense.

But cheese isn't a symbol; it doesn't represent anything. I can add two slices of bread to a piece of cheese and make a sandwich, but I can't add 1 to cheese and make anything. The concept is incoherent.

This is the difficulty that I was trying to articulate in another thread. We were discussing a puzzle that began with the statement "three birds = 30". I argued that such a statement was incoherent, on the grounds that a bird can't be given a numerical value. The argument made was that in this case, "bird" was being used as algebraic variable (with the value 10).

I don't accept that argument, because of the syntax of the statement. The plural marker "-s" is applied to English nouns, not to algebraic variables. Even if you redefine "bird" to have the value 10, so that "3 x bird" is equal to 30, it doesn't change the meaning of the phrase "three birds". That can only refer to three flying creatures, which don't have numerical values.

It was pointed out that we use similar syntax in statements like "three tens are thirty"; but in that sentence "ten" is an English noun meaning "a group of ten objects", so it can be pluralized. Claiming that "three birds = 30" is an algebraic equation is like claiming that "three x's = 30" is an algebraic equation. You can't just mix mathematical notation and English syntax in that fashion.

So I continue to claim that "three birds = 30" is incoherent, on any reasonable interpretation of the words and symbols therein.

 
ali
1373861.  Sun Feb 07, 2021 7:34 am Reply with quote

I think I see the problem. It is not the case that three birds equals 30, but rather that three birds (or to be more accurate a set of three pictures of birds, as that is how these puzzles usually manifest) is assigned a value of 30. It is not a statement of equality, but an assignation of value.
This distinction is needed in computer languages. For example:

if (x=y) then <do something> contains a test for the equality of the two variables x and y.

x = y (or something like x := y if the language in question makes an overt distinction) assigns to the variable x the current value of the variable y.

 
Brock
1373886.  Sun Feb 07, 2021 2:57 pm Reply with quote

ali wrote:
I think I see the problem. It is not the case that three birds equals 30, but rather that three birds (or to be more accurate a set of three pictures of birds, as that is how these puzzles usually manifest) is assigned a value of 30. It is not a statement of equality, but an assignation of value.


You've hit the nail on the head. That's exactly it. Thank you.

 
CB27
1373909.  Mon Feb 08, 2021 8:25 am Reply with quote

Then what's the issue?

The assignation of value is temporary and is against the algebraic variable.

An algebraic variable is always a "Use", regardless of what it represents, be it the Use or Mention distinction.

Using the Cheese example you gave, it can represent 3 actual pieces of cheese, each of which can be worth 10, or it can represent 3 words of "cheese", each of which can be worth 10.

In either case you count 3 uses, so you pluralise.

 
PDR
1373916.  Mon Feb 08, 2021 9:04 am Reply with quote

Brock wrote:
ali wrote:
I think I see the problem. It is not the case that three birds equals 30, but rather that three birds (or to be more accurate a set of three pictures of birds, as that is how these puzzles usually manifest) is assigned a value of 30. It is not a statement of equality, but an assignation of value.


You've hit the nail on the head. That's exactly it. Thank you.


...which point was made many times in the original thread. So the only remaining mystery is why we needed this second one.

PDR

 
barbados
1373925.  Mon Feb 08, 2021 12:15 pm Reply with quote

I think it could be because cows cant have puppies like elephants would if they were dogs

 
Alfred E Neuman
1373944.  Mon Feb 08, 2021 2:02 pm Reply with quote

barbados wrote:
I think it could be because cows cant have puppies like elephants would if they were dogs

But what about twenty-seven?

 
Brock
1373948.  Mon Feb 08, 2021 2:27 pm Reply with quote

PDR wrote:
Brock wrote:
ali wrote:
I think I see the problem. It is not the case that three birds equals 30, but rather that three birds (or to be more accurate a set of three pictures of birds, as that is how these puzzles usually manifest) is assigned a value of 30. It is not a statement of equality, but an assignation of value.


You've hit the nail on the head. That's exactly it. Thank you.


...which point was made many times in the original thread. So the only remaining mystery is why we needed this second one.

PDR


Nope, that point was not made anywhere at all. No one suggested that the concept of "equality" was being used wrongly, or talked about assignment statements. People just kept on with this red herring about "bird" being the name of a variable, which I don't think it is.

What ali said, if I understand correctly, is that the equality operator was being misused. The statement should have been "three birds are assigned the value thirty", not "three birds are equal to thirty". Those are two entirely different things.

In mathematics (which includes arithmetic and algebra as far as I'm concerned), the equality operator indicates that two entities have the same value, or are in some sense interchangeable. If I write "3 x 10 = 30", that means that the value of the expression "3 x 10" is the same as the value 30. Similarly if I write "3x = 30", that means that there is a value of x (in this case 10) which gives 3x the value of 30.

But if I write "three birds = 30", it doesn't mean that three birds have the value 30; they clearly don't. What it means is, that for the purposes of this problem, we're assigning the value 30 to those three birds. They don't have any inherent numerical value; we're just saying that for the purposes of this problem, each bird will count for 10.

That's not the same as saying "a bird = 10", or even assigning the value 10 to a variable called "bird". It's saying that there are three birds in this problem, and we're temporarily assigning the value 10 to each of them.

So as an assignment statement, it's coherent; as a statement of equality, it isn't.

Unfortunately some computer programming languages (e.g. BASIC) use "=" as the assignment operator, which can lead to confusion in the minds of some people who are more used to computer programming than mathematics. If you use the syntax of a language like Pascal, where ":=" is the assignment operator, the issue is a lot clearer.

So I reckon the problem should have begun with:

Three birds := 30
Three cats := 9
Three dogs := 3

 
barbados
1373949.  Mon Feb 08, 2021 2:31 pm Reply with quote

Alfred E Neuman wrote:
barbados wrote:
I think it could be because cows cant have puppies like elephants would if they were dogs

But what about twenty-seven?


Twenty seven is most definitely cheese.
Or is it a bird? I'm losing track

 
Brock
1373951.  Mon Feb 08, 2021 2:50 pm Reply with quote

barbados wrote:

Twenty seven is most definitely cheese.
Or is it a bird? I'm losing track


Think yourself lucky that you never worked in Cognitive Science as I once did. There were a lot of heavy formal semanticists in my department and their seminars would have made this thread look like child's play...

 
Alfred E Neuman
1373954.  Mon Feb 08, 2021 3:41 pm Reply with quote

barbados wrote:
Alfred E Neuman wrote:
barbados wrote:
I think it could be because cows cant have puppies like elephants would if they were dogs

But what about twenty-seven?


Twenty seven is most definitely cheese.
Or is it a bird? I'm losing track

Toasted. On rye.

 
PDR
1373957.  Mon Feb 08, 2021 3:52 pm Reply with quote

Brock wrote:

Nope, that point was not made anywhere at all. No one suggested that the concept of "equality" was being used wrongly,


...because it isn't, it's just that you won't accept anything other than the one particular usage which supports your (fallacious) argument. As has been pointed out, in other contexts the "=" symbol assigns a value (and the symbol "==" indicates a Boolean comparison. So that's not true.

Quote:
...or talked about assignment statements.


In post 1373751 perhaps:

someone wrote:
In the problem as stated the algebraic symbols bird, cat and dog were assigned values, turning them from symbols into constants. The arithmetic question was only asked AFTER the constants had been defined, so it is perfectly valid.


So that wasn't true either. Want to go for the hat trick?

PDR

 
barbados
1373958.  Mon Feb 08, 2021 4:02 pm Reply with quote

Surely if a hat trick was involved, then one of the animals would have been a rabbit?
Who ever heard of someone pulling a dog or a cat out of a hat!

 
Brock
1373959.  Mon Feb 08, 2021 4:12 pm Reply with quote

PDR wrote:
Brock wrote:

Nope, that point was not made anywhere at all. No one suggested that the concept of "equality" was being used wrongly,


...because it isn't, it's just that you won't accept anything other than the one particular usage which supports your (fallacious) argument. As has been pointed out, in other contexts the "=" symbol assigns a value (and the symbol "==" indicates a Boolean comparison. So that's not true.


Well it does in certain programming languages, yes. (I think C, C++, Java and a few others - I don't know the syntax of every programming language).

But, to be honest, I don't expect simple puzzles like that one to be written in programming language syntax. I expect them to use everyday language and symbols that the majority of the general public would understand.

The only place you'll see "=" used as an assignment symbol is in a computer program. If I write "2 + 2 = 4", I don't mean that 2 + 2 is assigned the value 4. I mean that the value of 2 + 2 is equal to the value 4, and I think that's how pretty much everyone would understand it - including computer programmers.

Quote:
...or talked about assignment statements.


In post 1373751 perhaps:

someone wrote:
In the problem as stated the algebraic symbols bird, cat and dog were assigned values, turning them from symbols into constants. The arithmetic question was only asked AFTER the constants had been defined, so it is perfectly valid.


OK, fair enough. You did say that. I apologize.

Quote:
So that wasn't true either. Want to go for the hat trick?


Don't be silly. I'm not trying to have an argument - I'm trying to understand the issue better.

I don't think that most people, seeing "three birds = 30", would take it to mean "three birds are assigned the value 30". I certainly didn't. I took it to mean "three birds are equal to thirty", which is incoherent. And I've studied both maths and computer programming.

I just don't think the use of the symbol "=" to mean assignment is understood outside the world of computer programming. Was it a puzzle to be solved only by computer programmers?

 
Awitt
1373964.  Mon Feb 08, 2021 4:34 pm Reply with quote

Alfred E Neuman wrote:
barbados wrote:
Alfred E Neuman wrote:
barbados wrote:
I think it could be because cows cant have puppies like elephants would if they were dogs

But what about twenty-seven?


Twenty seven is most definitely cheese.
Or is it a bird? I'm losing track

Toasted. On rye.


With avocado.

 

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