What precisely do you mean by ‘abstraction’? It’s true that we have a capacity to intuit how others apply words. But Wittgenstein’s point is that we have to use this skill not only when we use words like ‘time’, ‘existence’, ‘algebra’ and other abstract words but also when use more ‘concrete’ words like ‘apple’ and ‘red’. When I point to a red apple and tell a child who doesn’t know the meaning of the terms ‘red’ and ‘apple’ that ‘that is an apple’, how can he know that I mean what those words conventionally mean rather than ‘that is red’? Children actually do misunderstand how we use words sometimes but to the extent that they succeed that is due to what Quine called the ‘pre-established’ harmony between humans: we see the world in similar ways and therefore interpret/intuit linguistic cues in similar ways. So there is really no fundamental difference between ‘observable’/concrete predicates and non-observable/abstract predicates on this score. (It’s true that our interpretations of observational terms generally converge a lot, but so do our interpretations of some non-observational terms—e.g mathematical terms. Proximity to observations is not the only way to ensure convergence of interpretations or exactness even though it’s an important way.)
What precisely do you mean by ‘abstraction’? It’s true that we have a capacity to intuit how others apply words. But Wittgenstein’s point is that we have to use this skill not only when we use words like ‘time’, ‘existence’, ‘algebra’ and other abstract words but also when use more ‘concrete’ words like ‘apple’ and ‘red’. When I point to a red apple and tell a child who doesn’t know the meaning of the terms ‘red’ and ‘apple’ that ‘that is an apple’, how can he know that I mean what those words conventionally mean rather than ‘that is red’? Children actually do misunderstand how we use words sometimes but to the extent that they succeed that is due to what Quine called the ‘pre-established’ harmony between humans: we see the world in similar ways and therefore interpret/intuit linguistic cues in similar ways. So there is really no fundamental difference between ‘observable’/concrete predicates and non-observable/abstract predicates on this score. (It’s true that our interpretations of observational terms generally converge a lot, but so do our interpretations of some non-observational terms—e.g mathematical terms. Proximity to observations is not the only way to ensure convergence of interpretations or exactness even though it’s an important way.)