The issue at hand
I just had this thought now; so bear with me if this sounds a bit weird.
What if we theorised about the primitives of certain entities such that we could use very basic propositional calculi upon their analysis; by this, I mean in to the determination of their referent; the proper domain to which we attribute understanding to; and a notation such that we can have a proper (possibly rigorous) construal of such entities to depict them for understanding (analysis in the Kantian sense), and combination such that we may use them to solve, depict, or frustrate new, problems (synthesis in the Kantian sense).
Okay; so what sorts of primitives can we analyse? Lets consider two types of cases.
1. Metaphysics (or, ontological furniture)
2. (Analytical) Philosophical psychology (or, mental furniture)
1. The case of Metaphysics
We may frame the discourse of metaphysics as an analysis into various strata, or sets of things in reality
Categories of being: flexiblity
i. Things that endure, change
ii. Things that stay permanent, do not change
Categories of being: divisibility
iii. Things that are concrete
iv. Things that are indivisible
v. (First order) subvenient abstract objects (mathematical entities)
vii. (second order) supervenient abstract objects (propositions, sets, classes, quantifiers etc.)
viii. Properties that are non-phenomenological
ix. Properties that are phenomenological
x. Amorphous particulars
We may order these as sets; how we may work out the schematisation of them (the above is just a suggestion) is the work of the set theoretic analysis.
1. Are these entities rigorously defined?
2. Can elements be transitively held through sets?
3. Can we instantiate an element whereby its general properties are held as a familial relation to the set; if so, this will be the true work and worth, of any such metaphysical analysis.
4. Can we instantiate an object to which we know little, nothing, or anything about?
2. Philosophical Psychology
I’ve made this suggestion before, and conversed (at ends) with Master Destre on this issue. What if we entertained an endeavour to the effect of endorsing a strictly logical, or even further, set theoretic analysis of our mental furniture; question: what is in our mental furniture?
i. Propositional beliefs
ii. Norms?/the capacity for normative reasoning (to both domains of practical and theoretical reason)
iv. Motivation (which reduces to something of the above)
v. Practical reason for motivational reasoning
We may find issues of what place we have for beliefs, or desires, in a particularly rich and strenuous taxonomy, one which identifies the deep conceptual connections between other aspects of our mental furniture. Just a hand-waving comment for now; but hopefully more can be thought of it (just not now).