Ontology
Physical objects: do they form a fundamental category?
Position: Physical abstractionism
As regards the problem of universals, I subscribe to the abstractionist position (\(\mathbf{\aleph}\mathbf{\prec}\mathbf{3}\)), following which the physical is grounded into the abstract. But that statement needs to be rigorously qualified.
From what precedes, both the abstract and the concrete seem to be on equal footing in our formalism. Granted, the formal language used to describe concrete objects is the same as for abstract objects; but centuries after Galileo, it is no shock to hear that the physical world is couched in the language of logic and mathematics. Abstractionism makes a stronger statement: that’s all there is to it.
The increasing "strangeness" evident in our best theories (and further confirmed by empirical observation) makes it impossible in my opinion to hinge on some paradigmatic characterization of the physical that would rely on non-abstract intuitions like extension in space or perceivability. It’s hard to see what the chair I’m sitting on and a charm quark have in common, save for the fact they can be described within the same mathematical framework, and follow the same fundamental laws.
The abstractionist view then simply posits that physical objects and properties are the "things" that behave in accordance with that framework and those laws. This is a strictly extrinsic criterion: it applies to what an object does, not what it is.
The main issue with this approach is the multiple realizability: if we could develop a perfectly accurate mathematical simulation of our universe, what would be its status? It would not belong to our physical world: a simulated electron does have mass inside the simulation, but that property is demonstrably distinct from mass in our world, since it cannot curve spacetime around me or affect my perceptions in any way. However, it is hard to assess that our universe’s physicality is definitely more fundamental than the simulation’s. The choice made is then purely conventional: the physical world is the one and only where my body exists; distinct, equivalent realizations of the same mathematical structures are all classified as abstract objects.
Of course, this fundamental set of physical laws is only aspirational at the moment; the quest for a "Theory of Everything" lives on. We can only assume that this framework, expressed as a mathematical theory via an axiom schema and initial conditions, exists, and we’ll call the corresponding abstract object \(\mathfrak{ToP}\) (theory of physics).
Mental states: do they form a fundamental category?
Position: Panpsychic monism
Panpsychism is the idea that mental states are ubiquitous, rather than an effluence from animal or human brains only.
It was presented above under the rubric of pan-idealism, which asserts that physical properties are grounded in these ubiquitous mental facts. But no consequent panpsychists would contend that physical objects don’t follow physical laws! I certainly wouldn’t. The only way then for pan-idealism to be true is to find a way in which these laws with all their trappings, in particular the mathematical formulation, emerge Minerva-like from mental facts. Given especially the abstractionist stance we’re taking, whereby logic and mathematics are both more fundamental than the physico-mental world, this doesn’t seem admissible unless mental facts themselves are couched in the language of mathematics. The question of which grounds which between the physical and the mental can then appear trite. Both physicalism and idealism come with major issues, yet this common mathematical background suggests that dualism is a mere facade, nudging us towards our best option: physico-mental monism.
Why would I support this view, which is admittedly far from the scientific doxa? As I see it, not as a brazen act of philosophical provocation, but out of prudence. The largely received view nowadays that mental facts are an emergent phenomenon from certain physical configurations is both intellectually elegant and consistent with our lived experience (every definite manifestation of mentality ever observed has been through animal or human behavior). However the exact mechanism of that emergence remains almost entirely mysterious when one considers phenomenal consciousness or subjectivity. Supporting the received view is then akin to a leap of faith, without a safety net since there is nothing but known physical entities (elementary particles, fields,...) to fall back on.
Is monism definitely better? After all, it suffers from equally glaring puzzles, perhaps even more perplexing: Do we even have a hint of the kind of mathematics to be used to reflect the qualitative and subjective features of the mental? Do mental states interact directly with physical objects at the micro level? How do they aggregate to form our minds? It seems we’ve taken ten steps back! Perhaps physicalism with emergence wasn’t so bad after all...
Well, the difference is that a prudent outline of monism doesn’t close any door. Should emergence be the ultimate truth of our world, then the set of fundamental mental entities can still be deemed to be derivative of physical ones, and our monism to just be physicalism redux. We’re not there yet though — for the time being, talking of phenomenal experience as a brute fact, in the same way as we do mass or electric charge, can’t be helped. We can only hope that our not-so-distant successors will bear witness to enough breakthroughs that this prudent agnosticism can be swapped for a more confident stance, either way the chips fall.
We’ll call the hypothetical, resulting theory \(\mathfrak{ToPM}\) (theory of the physico-mental).
Abstract entities: do they exist?
Position: Metaphysical platonism
Perhaps for the last time before we move down from the strictures of pure ontology, I need to insist about the ambiguities of “existence”.
Formal existence is the broadest, quite simply the wont of anything that a symbol from our formal system may denote.
Logical existence is more restrictive. We’ve seen that Zalta developed that notion (showing it was equivalent to the Quinean “being the value of a variable”) to fend off paradoxes of various kinds.
Ontological existence only makes sense as a distinction if one endorses ontological realism, which I do. In this work, I’ve argued that only individual terms from the formal system are endowed with ontological existence. In what follows, all talk of existence will refer to this notion unless otherwise stated.
Superficially, one could say that I’m a nominalist about universals, since I only believe that individual terms exist. However the comprehension principle acts as an “abstraction pump" that will turn any predicate (properties, relations, properties of properties…) and any formula — in other words, any concept — into an abstract object. The property “being blue” may not exist but the abstract object “blueness” does (or as Plato would have said, the Form “blue”). A distinction without much of a difference, save from a formal standpoint, that allows me to deny the nominalist label and to see myself as a Platonist, on account of the existence and independence of Forms and other abstracta.
But that’s still delving in pure theory and lingering on labels. Getting our hands a bit dirty, we ought to wonder, now that we have a good idea of the structure of the world as outlined by our formal ontology, what exactly is populating it. We’ve got lots of answers from our investigations so far:
The structure of the ontology alone entails the logical existence of predicates like “being a code”, “being a logical symbol”, “being a well-formed formula”, etc. The comprehension principle ensures that the corresponding abstract objects exist.
The formalisation of mathematical theories is a full-on abstracta-making machine. Not only is every theory an abstract object, it can distinguish mathematical objects and predicates (for instance, \(0\) and “being a number” in Peano arithmetic) and recursively generate many more (all natural numbers and related predicates). In the theory, objects exemplify the predicates but in the broader ontology they are identified to codes that encode them. The objects are thus already abstract, and the predicates are “Platonified” into Forms via the comprehension principle.
I’ve conceptualised \(\mathbf{\aleph}\), the concrete world, via a distinguished mathematical theory of the physico-mental, \(\mathfrak{ToPM}\). This theory, which roughly speaking includes (1) the “laws of nature”, (2) initial conditions and (3) “all the maths we need”, generates objects. If that theory is anything like our contemporary models, these objects are quantum wavefunctions, energy-momentum tensors, and so on. With our metaphysical axioms, we’ve associated the concept of concreteness with possible physical or mental existence. The objects of \(\mathfrak{ToPM}\) are then, axiomatically, the concrete objects of the world: as a class they form \(\mathbf{\aleph}\). Predicates within \(\mathfrak{ToPM}\) (e.g. in our current model: “being massless”, “being an electron”…), like any predicates will turn up in the abstract world \(\mathbf{3}\) as Forms, by the grace of the comprehension principle. Predicates such that they are only exemplified by concrete objects can be called “concrete properties” or “concrete relations” colloquially (but let’s not forget that, as Forms, they are most definitely abstract objects). Let’s call this specific part of the abstract realm \(\mathbf{3}_\aleph\).
Taking together these principles which we’ve derived in sections above, we’re getting a clearer picture of the large-scale structure of the world: a distinguished group generated within \(\mathfrak{ToPM}\) gives us our class of concrete objects. And the comprehension principle plays its role, pumping predicates from the formal, mathematical, and physico-mental levels, as well as explicitly abstract objects from the mathematical world, into the abstract realm.