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I recently came across an image posing the question of whether milk would be properly classified as a beverage, broth, or sauce once it's poured on a bowl of cereal. I'm not sure if it's any of those things, though, so I figured that Stack Exchange was the place to get an expert's answer about it.

To show that I have done some research on this: Merriam-Webster Dictionary defines "beverage" as "a drinkable liquid", and I'm not sure if it's a beverage anymore because you don't drink it, at least until you run out of cereal to eat. "Sauce" is defined by them as "a condiment or relish for food; especially: a fluid dressing or topping" which is closer, but most sauces I've used are much thicker than milk is, and I expect that there's probably a technical/jargon definition that's not in a general-use dictionary regarding production processes that excludes milk. It also defines "broth" as "liquid in which meat, fish, cereal grains, or vegetables have been cooked: stock"; I'm not sure that fits, either, because cereal's not cooked once you add milk to it.

Does milk have a formal classification as to its nature or status once you pour it on cereal, and if so, what is it?

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TL:DR It has no such status. People just don't really have the need to categorize it, so it doesn't belong to a special category.

You are somewhat mixing up formal classifications and the process of categorization in everyday language usage. Dictionary definitions apply to everyday language, but they don't have a prescriptive status. Due to the way language and human cognition works, you can never come up with exact criteria that define whether an item belongs to a category or not. So looking up random cooking definitions like "sauce" is pointless in this case, even if an item nominally fits a definition, this does not make it belong to the category if people don't perceive it as belonging to the category.

Formal classifications about food do exist. In them, it is quite likely that you will find prescriptive definitions, intended to be used to determine whether an item falls into the category. These definitions have validity only within the framework itself - for example, a tomato falls in the fruit category when you talk to botanists, but not in the classification of foods used by the Culinary institute of America (it so happens that in this case, common language usage is firmly on the side of one of those, but other cases may be more ambiguous). It is a special feature of formal classifications that they only work well on the items they were intended for - E.g. I have seen several American authors categorize cakes by type of batter, and there is no good way to fit a cake made of quark-oil dough into one of those.

Regarding formal categorizations, I cannot think of a categorization framework that has a category into which "the milk in a bowl of cereal" can fit snugly. I cannot think of either a legal context or a scholarly context where that milk will come into discussion at all. In most cases, the mixture is just not perceived as a separate entity - people buy, prepare and serve bowls of cereal with milk as wholes. Also, there is rarely reason to see the milk in the cereal as a member of a category, as opposed to just "the milk".

The one context which might yield something would be books on food technology, concerned either with grain chemistry or with the industrial preparation of cereal products, like a description of the process for making prepackaged cups of yoghurt and cereal. They could have a need to refer to an abstract category which could include milk, yoghurt, or anything else pourable over cereal, and to discuss its physical properties. I have never read such a highly technical book on this topic, but I suspect it would simply use some quite broad category of everyday language such as "the liquid" and implicitly assume that in the context of the text, it is used for any liquid that is being poured over the cereal. It would be interesting if somebody can come up with an example, but it is quite certain that, if you try to use it in everyday life, it won't be perceived as a specific technical term.

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    Good answer. The only thing I would add is that if I needed to use a word, I'd go with "ingredient": a bowl of cereal is really a dish, and the flakes, milk etc. are the ingredients. In the context of the last paragraph, you could even say the "wet ingredients" or "liquid ingredients" because it could be a combination of milk, yoghurt or other things. – Ratler Jun 10 '18 at 0:11

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