Epistemic status: exploration of some of the intuitions involved in discussions behind this post at MSFP. Could be considered part of an unstructured sequence titled 'towards fewer type errors in metaphilosophy'
Summary: When moving up or down the ladder of abstraction you're forced to make choices about restriction or relaxation of domain of relevance. Don't just reason about the valid range/scope, reason about your reasoning about the valid range/scope and ask what sort of operations you'd need to be doing to make a different choice seem valid. This resolves many types of confusions and is a crux identifier for 2-place confusions.
Alfred Korzybski directs us to develop the faculty to be conscious of the act of abstracting. This means that that one has meta cognitive awareness when one does things like engage in the substitution effect, analogical reasoning, shifting the coarse-grainedness of an argument, use of the 'to be' verb form, shifting from one Marr Level to another in mid sentence etc. One of the most important skills that winds up developed as a result of such training is much more immediate awareness of what Korzybski calls the multiordinality of words, which one will be familiar with if you have read A Human's Guide to Words (esp. 24 and 36) or are otherwise familiar with the Wittgensteinian shift in analytic philosophy (related: the Indeterminacy of Translation). In short, many words are underdetermined in their referents along more than one dimension, leading to communication problems both between people and internally (for an intuitive example, one can imagine people talking past each other in a discussion of causation when they are discussing different senses of Cause without realizing it).
I want to outline what one might call second order multiordinal words or maybe schematic thinking. With multiordinal words, one is aware of all the values that a word could be referring to. With schematic thinking one is also aware of all the words that could have occupied the space that word occupies. Kind of like seeing everything as an already filled out madlibs and reconstructing the unfilled out version.
This may sound needlessly abstract but you're already familiar with a famous example. One of Charlie Munger's most famous heuristics is inversion. With inversion we can check various ways we might be confused by reversing the meaning of one part of a chain of reasoning and seeing how that affects things. Instead of forward chaining we backwards chain, we prepend 'not' or 'doesn't' to various parts of the plan to construct premortems, we invert whatever just-so story a babbling philosopher said and see if it still makes sense to see if their explanation proves too much.
I claim that this is a specific, actionable instance of schematic thinking. The generalization of this is that one doesn't just restrict oneself to opposites, and doesn't restrict oneself to a single word at a time, though that remains an easy, simple way to break out of mental habit and see more than one possibility for any particular meaning structure.
Let's take first order indeterminacy and apply this and see what happens. To start with you can do a simple inversion of them and see what happens.
First example of first order indeterminacy: universal quantifiers
"all, always, every, never, everyone, no one, no body, none" etc
We already recognize that perverse generalizations of this form cause us problems that can often be repaired by getting specific. The additional question schematic thinking has us ask is: among the choices I can make, what influences me to make this one? Are those good reasons? What if you inverted that choice (all->none, etc), or made a different one?
Second example of first order indeterminacy: modal operators
confusion of possibility and necessity, "should, should not, must, must not, have to, need to, it is necessary" etc
The additional question we ask here as we convert 'shoulds' to 'coulds' and 'musts' to 'mays' is what sorts of mental moves are we making as we do this?
Third example of first order indeterminacy: unspecified verbs
"they are too trusting, that was rude, we will benefit from that, I tried really hard"
The additional question we ask as we get more specific about what happened is 'why are we choosing this level of coarse grainedness?' After all, depending on the context someone could accuse us of being too specific, or not being specific enough. We have intuitions about when those accusations are reasonable. How does that work?
This might seem a bit awkward and unnecessary. The concrete benefit it has brought me is that it gives me a starting point when I am reading or listening to a line of reasoning that strikes me as off in some way, but I can't quite put my finger on how. By seeing many of the distinctions being made to construct the argument as arbitrary and part of a space of possible distinctions I can start rephrasing the argument in a way that makes more sense to me. I then have a much better chance of making substantive critiques/cruxing (or alternatively, becoming convinced) rather than just arguing over misunderstandings the whole time. I've found many philosophical arguments hinge on pulling a switcheroo at some key juncture. I think many people intuitively pick up on this and that this is why people dismiss many philosophical arguments, and I think they are usually correct to do so.