Regarding the first two examples: “brush your teeth” and “animal” are also in another aspect quite different: The first example is a task, a instruction, or a command. “animal” on the other hand is the name of a concept, and it can be used to form the monadic predicate “is an animal”. Which names a property which members of a set (the set of animals) satisfy. Maybe the difference between composition and generalization becomes clearer (or disappears) if we compare composite/generalized predicates only or composite/generalized instructions only.
An additional point regarding the aspect of touchability: Grammatically, the main difference between the terms “tennis” and “tennis ball”, seems to be the fact that the former is not countable, while the latter is. Because of this, you can easily make a predicate out of the later by applying the copula “is a”: “is a tennis ball”. This is not possible for “tennis”: “is a tennis” doesn’t make sense. So you can’t associate tennis with a particular set of things which you could touch. Similar point holds for “fear”. This seems to hold for most “abstract” properties: They are expressed by non-countable nouns.
(An interesting exception is the concept of a number. “Number” is a countable noun, but the concept may be called abstract nonetheless. This could hint at yet a different sense of abstractness.)
Similar to uncountable nouns, adjectives, like “large”, are generally also not countable. They seem intuitively also to be judged abstract, especially when you convert them into properties by naming them via a (uncountable) noun: “Largeness” is not a thing you could touch.
However, the case is not so clear for verbs: “walks” can be converted to a noun by speaking of a “walk”, which seems to be a countable property of a process. As a consequence, it seems not particularly abstract. In conclusion, abstractness in the “philosophical” sense seems to be closely related to uncountable nouns.
Regarding the first two examples: “brush your teeth” and “animal” are also in another aspect quite different: The first example is a task, a instruction, or a command. “animal” on the other hand is the name of a concept, and it can be used to form the monadic predicate “is an animal”. Which names a property which members of a set (the set of animals) satisfy. Maybe the difference between composition and generalization becomes clearer (or disappears) if we compare composite/generalized predicates only or composite/generalized instructions only.
An additional point regarding the aspect of touchability: Grammatically, the main difference between the terms “tennis” and “tennis ball”, seems to be the fact that the former is not countable, while the latter is. Because of this, you can easily make a predicate out of the later by applying the copula “is a”: “is a tennis ball”. This is not possible for “tennis”: “is a tennis” doesn’t make sense. So you can’t associate tennis with a particular set of things which you could touch. Similar point holds for “fear”. This seems to hold for most “abstract” properties: They are expressed by non-countable nouns.
(An interesting exception is the concept of a number. “Number” is a countable noun, but the concept may be called abstract nonetheless. This could hint at yet a different sense of abstractness.)
Similar to uncountable nouns, adjectives, like “large”, are generally also not countable. They seem intuitively also to be judged abstract, especially when you convert them into properties by naming them via a (uncountable) noun: “Largeness” is not a thing you could touch.
However, the case is not so clear for verbs: “walks” can be converted to a noun by speaking of a “walk”, which seems to be a countable property of a process. As a consequence, it seems not particularly abstract. In conclusion, abstractness in the “philosophical” sense seems to be closely related to uncountable nouns.