So… in my world, transubstantiation isn’t in R2, because I can’t coherently conceive of what a substance is, apart from accidents.
Many mathematicians, scientists, and philosophers believe in things they call ‘sets.’ They believe in sets partly because of the ‘unreasonable effectiveness’ of set theory, partly because they help simplify some of our theories, and partly because of set theory’s sheer intuitiveness. But I have yet to hear anyone explain to me what it means for one non-spatiotemporal object to ‘be an element of’ another. Inasmuch as set theory is not gibberish, we understand it not through causal contact or experiential acquaintance with sets, but by exploring the theoretical role these undefined ‘set’ thingies overall play (assisted, perhaps, by some analogical reasoning).
‘Substance’ and ‘accident’ are antiquated names for a very commonly accepted distinction: Between objects and properties. (Warning: This is an oversimplification. See The Warp and Woof of Metaphysics for the historical account.) Just as the efficacy of mathematics tempts people into reifying the set-member distinction, the efficacy of propositional calculus (or, more generally, of human language!) tempts people into reifying the subject-predicate distinction. The objects (or ‘substances’) are whatever we’re quantifying over, whatever individual(s) are in our domain of discourse, whatever it is that predicates are predicated of; the properties are whatever it is that’s being predicated.
And we don’t need to grant that it’s possible for there to be an object with no properties (∃x(∀P(¬P(x)))), or a completely uninstantiated property (∃P(∀x(¬P(x)))). But once we introduce the distinction, Christians are free to try to exploit it to make sense of their doctrines. If set theory had existed in the Middle Ages, you can be sure that there would have been attempts to explicate the Trinity in set-theoretic terms; but the silliness of such efforts would not necessarily have bled over into delegitimizing set theory itself.
That said, I sympathize with your bafflement. I’m not committed to taking set-membership or property-bearing completely seriously. I just don’t think ‘I can’t imagine what a substance would be like!’ is an adequate argument all on its own. I’m not sure I have a clear grasp on what it means for a set to have an element, or what it means for a number line to be dense and uncountable, or what it means for my left foot to be a complexly-valued amplitude; but in all these cases we can gain at least a little understanding, even from initially undefined terms, based on the theoretical work they do. Since we rely so heavily on such theories, I’m much more hesitant to weigh in on their meaninglessness than on their evidential justification.
I don’t yet have R2-language for talking about a universe being metaphysically made of anything.
You sound like a structural realist. On this view, as I understand it, we don’t have reason to think that our conceptions straightforwardly map reality, but we do have reason to think that a relatively simple and uniform transformation on our map would yield a pattern in the territory.
it seems to me that R3-possibilities falsifying 1, 2, or (a generalization of 3 to other effectively or formally specified physics (e.g. Time-Turners)), and with the proviso that we’re dealing in second-order logic rather than classical first-order logic, all seem to me to pretty much falsify the Great Reductionist Thesis.
So is this a fair characterization of the Great Reductionist Thesis?: “Anything that is the case can in principle be exhaustively expressed in classical second-order predicate logic, relying only on predicates of conventional mathematics (identity, set membership) and of a modestly enriched version of contemporary physics.”
We could then elaborate on what we mean by ‘modest enrichment’ if someone found a good way to add Thoroughly Spooky Doctrines (dualism, idealism, traditional theism, nihilism, trivialism, ineffable whatsits, etc.) into our language. Ideally, we would do this as un-ad-hocily as possible.
I think we both agree that ‘meaning’ won’t ultimately carve at the joints. So it’s OK if R2 and R3 look a bit ugly; we may be eliding some important distinctions when we speak simply of a ‘meaningful vs. meaningless’ binary. It’s certainly my own experience that I can incompletely grasp a term’s meaning, and that this is benign provided that the aspects I haven’t grasped are irrelevant to what I’m reasoning about.
Many mathematicians, scientists, and philosophers believe in things they call ‘sets.’ They believe in sets partly because of the ‘unreasonable effectiveness’ of set theory, partly because they help simplify some of our theories, and partly because of set theory’s sheer intuitiveness. But I have yet to hear anyone explain to me what it means for one non-spatiotemporal object to ‘be an element of’ another. Inasmuch as set theory is not gibberish, we understand it not through causal contact or experiential acquaintance with sets, but by exploring the theoretical role these undefined ‘set’ thingies overall play (assisted, perhaps, by some analogical reasoning).
‘Substance’ and ‘accident’ are antiquated names for a very commonly accepted distinction: Between objects and properties. (Warning: This is an oversimplification. See The Warp and Woof of Metaphysics for the historical account.) Just as the efficacy of mathematics tempts people into reifying the set-member distinction, the efficacy of propositional calculus (or, more generally, of human language!) tempts people into reifying the subject-predicate distinction. The objects (or ‘substances’) are whatever we’re quantifying over, whatever individual(s) are in our domain of discourse, whatever it is that predicates are predicated of; the properties are whatever it is that’s being predicated.
And we don’t need to grant that it’s possible for there to be an object with no properties (∃x(∀P(¬P(x)))), or a completely uninstantiated property (∃P(∀x(¬P(x)))). But once we introduce the distinction, Christians are free to try to exploit it to make sense of their doctrines. If set theory had existed in the Middle Ages, you can be sure that there would have been attempts to explicate the Trinity in set-theoretic terms; but the silliness of such efforts would not necessarily have bled over into delegitimizing set theory itself.
That said, I sympathize with your bafflement. I’m not committed to taking set-membership or property-bearing completely seriously. I just don’t think ‘I can’t imagine what a substance would be like!’ is an adequate argument all on its own. I’m not sure I have a clear grasp on what it means for a set to have an element, or what it means for a number line to be dense and uncountable, or what it means for my left foot to be a complexly-valued amplitude; but in all these cases we can gain at least a little understanding, even from initially undefined terms, based on the theoretical work they do. Since we rely so heavily on such theories, I’m much more hesitant to weigh in on their meaninglessness than on their evidential justification.
You sound like a structural realist. On this view, as I understand it, we don’t have reason to think that our conceptions straightforwardly map reality, but we do have reason to think that a relatively simple and uniform transformation on our map would yield a pattern in the territory.
So is this a fair characterization of the Great Reductionist Thesis?: “Anything that is the case can in principle be exhaustively expressed in classical second-order predicate logic, relying only on predicates of conventional mathematics (identity, set membership) and of a modestly enriched version of contemporary physics.”
We could then elaborate on what we mean by ‘modest enrichment’ if someone found a good way to add Thoroughly Spooky Doctrines (dualism, idealism, traditional theism, nihilism, trivialism, ineffable whatsits, etc.) into our language. Ideally, we would do this as un-ad-hocily as possible.
I think we both agree that ‘meaning’ won’t ultimately carve at the joints. So it’s OK if R2 and R3 look a bit ugly; we may be eliding some important distinctions when we speak simply of a ‘meaningful vs. meaningless’ binary. It’s certainly my own experience that I can incompletely grasp a term’s meaning, and that this is benign provided that the aspects I haven’t grasped are irrelevant to what I’m reasoning about.