In "10 grams of salt", is the unit "grams"?

Question

The gram is a unit of mass, so "10 grams" has "grams" as the unit. "10 pounds" uses a different unit.

So what is the "salt" in "10 grams of salt", if not a unit? In other words, what is the difference between "10 grams of salt" and "10 grams of sugar", if the units are the same but they refer to different entities?

add 10 grams of salt to your coffee and you'll have your answer. — Rocket Man, Jul 03 '16 at 06:31
I'm voting to close this question as off-topic because it is not mathematics — Zelos Malum, Jul 03 '16 at 06:34
This is philosophy or Type Theory, there is not one unit used here, one unit is used for mass, the other unit is the unit of type. in some context it does not matter what the type is, for example 10 grams of salt and 10 grams of sugar have the same mass, but they have different type qualities. For example 10 grams of ionised salt will not have the same electric field around it as 10 unit of non ionised salt. — jimjim, Jul 03 '16 at 06:35
@ZelosMalum: No, not a joke. I figured this would be appropriate with the "terminology" tag, but if it's closed I will consider posting elsewhere, e.g. Ed_4434's suggestion. — mgiuffrida, Jul 03 '16 at 06:37
I don't see why this is being downvoted. I think this is a good question. Maybe not exactly on topic, but I get what they're asking and I don't think it's too unreasonable to be posted here. — , Jul 03 '16 at 06:40
Suppose we have $10$ grams of sugar and $10$ grams of salt. We could have, say $x$ equals the weight of the sugar, and $y$ equals the weight of the salt. We can then say with confidence that $x=y$. This is not to say that $10$ grams of sugar is the same as $10$ grams of salt, but rather to say that their weights are the same. If we add $10$ grams of sugar to $10$ grams of salt, we will have $20$ grams of salt/sugar mixture, which to be perfectly unambiguous should probably remain described as $10$ grams of sugar plus $10$ grams of salt. — JMoravitz, Jul 03 '16 at 06:41
I don't see why people can't downvote an obvious off-topic post, especially when the question seems to go against common sense. (Mind you, I'm not saying that the OP lacks common sense, but the nature of the question can make a reader feel that.) Some posts are downvoted for less. — Batominovski, Jul 03 '16 at 06:51
@Batominovski I don't quite see how this is off-topic. The question is "is "of salt" considered a "unit"?". I don't think this is off topic or trivial. I have no problem with downvoting, btw. https://data.stackexchange.com/math/query/489156/biggest-downvoters — , Jul 03 '16 at 06:57
"I have no problem with downvoting." "I don't see why this is being downvoted." I don't think you are being consistent. If you had no problem with downvotes, you would never complain about it.
The quoted question does not appear to be a mathematical question like Arjang said. It is more of a philosophical question, and better suite being posted there. — Batominovski, Jul 03 '16 at 07:01
@mgiuffrida : dont worry about downvotws, I too have asked similar questioon and been downvoted, but somebody gave me an answer that was worth it! Whenever you ask a deep question you will most likely be downvoted, but it would be worth it, I think when I was getting started here I got downvoted 100 points! — jimjim, Jul 03 '16 at 07:17

jimjim · Answer 1 · 2016-07-03T07:08:12.440

This is philosophy/math-philosphy or Type Theory, there is not one unit used here, one unit is used for mass, the other unit is the unit of type. in some context it does not matter what the type is, for example 10 grams of salt and 10 grams of sugar have the same mass, but they have different type qualities. For example 10 grams of ionised salt will not have the same electric field around it as 10 unit of non ionised salt.

In math you can have 10 numbers, 10 natural numbers will not have multiplicative in the set, but 10 rational numbers can easyly have their mutiplicative inverses in the same set e.g. $\left \{2,\frac{1}{2} , \cdots \right \}$ etc.

In programming things can be differentiated by their tyeps (class) and their capablities (interfaces).

score 1 · Accepted Answer · edited Apr 13 '17 at 12:19

Simply put, the answer is "No.", but there are different viewpoints that are equally viable:

You can take "grams of salt" as the unit, of which you can have $10$.
1. You can further take "GramsOf" as a function such that "GramsOf(X)" is the unit.
  
  "10 grams of salt" = "$10 \times GramsOf(Salt)$".
You can take "$10$ grams of" like a function, which when applied to "salt" gives 10 grams of it.
1. You can further take "$10$ grams of" to mean "$10$ times of a gram of".
  
  "10 grams of salt" = "$(10 \times GramOf)(Salt)$".

In both cases there is an action of some kind of quantities on some kind of amounts. In the first case we have the action of real numbers (like $10$) on definite physical entities (like "gram of salt"). In the second case we have the action of quantifying functions (like "10 grams of") on indefinite physical entities (like "salt" or "water").

The question of which interpretation is the 'right' one would involve linguistics, but it is certainly an interesting question related to the mathematical notion of action.

I would argue that unless the context indicates otherwise, the second view is the default one. Consider:

not even 10 grams of salt.

Most people would interpret it as "( not even 10 grams of ) salt" rather than "not even 10 ( grams of salt )". Another example:

(ODD) Add 10 grams of fructose syrup or teaspoons of sugar.

People are likely to do a double-take when they reach "teaspoons of", because when reading the first part they would automatically parse it as "( 10 grams of ) fructose syrup", which would leave them wondering whether the sentence means "... or 10 teaspoons of sugar". This would not be an issue if they had parsed it as "10 ( grams of fructose syrup )".

These suggest that the second viewpoint is the default one, and probably because parsing is biased towards binding as early as possible, so "10" binds to "grams of" by default (since they can).

In "10 grams of salt", is the unit "grams"?

2 Answers2