The composition question
For the moment, we’ll consider the question under its most general guise: "Given a class of objects \(\{y\}\), under what conditions is \(x=\sum{y}\) an object too?". We take \(\Sigma\) to represent a mereological sum or fusion, where mereology refers to the study of parts and parthood. Mereological parthood is superficially similar to set-theoretic inclusion (the differences are not integral to our discussion here).
Three broad views about mereology can be outlined:
Mereological conservatism: only ordinary fusions exist.
Mereological universalism: all possible fusions exist.
Mereological nihilism: no fusion exists.
We will examine each one in turn.
Mereological conservatism
has it that some collections of objects form other objects, while others do not. The sole motivation is to create an ontology that’s as close as possible to common sense.
Glancing around me, I’m naturally inclined to say there are a table, a computer, a notebook, a pen. I haven’t really considered whether it would be difficult to separate the tabletop from the legs, or whether the table has a removable extension. I’m typing on the computers’ keys and turning the notebook’s pages, so those might be considered as distinct objects, proper parts of their respective fusions.
In Giza, Egypt, there is a specific pile of limestone blocks known as the Great Pyramid of Giza. Most people would agree that the blocks are objects, and that they compose a larger object: the pyramid. On the site of Chichen Itza in Mexico, there are other limestone blocks that make up an object, the Temple of Kukulcàn, a step-pyramid. Yet, the collection of limestone blocks from Giza and from Chichen Itza does not compose any object — there is no "bi-pyramid of Giza-Kukulcàn".
Cars are objects with many parts: an engine, seats, wheels, windows, a driving stick, etc. However if I affix my bike on the car’s roof for a trip, they don’t compose a new object, nor does the bike become a proper part of the car.
It is clear that mereological conservatives need to present their assessments of objects as brute facts and adopt as their motto: "I know it when I see it".
Needless, to say, there are some major problems with this position:
Arbitrariness: I can only agree with Ned Markosian, who proposed that there is "no true, non-trivial, and finitely long answer to the composition question"— as long as one doesn’t go with mereological universalism or nihilism, there can be no easy formula to define objects.
Some properties are promising candidates, but they usually don’t sustain a closer examination. Take the notion of cohesiveness: it seems fair to say an object is something that’s made of one physically connex piece. But when two men shake hands, they don’t become a single object. If one super-glued their hands, or nailed them together, they wouldn’t become one object either. To take a less grisly example: I can very easily unscrew my living-room table’s legs, yet they’re part of the table; but if the table was nailed to the floor as sometimes happens in public places, and extremely hard to detach, it would not be considered a part of the floor. So, cohesiveness is not a sufficient solution. But it’s not a necessary one either: a bikini or a suit are commonly seen as items rather than collections (if a shopper were to purchase a bikini, a polo and a three-piece suit, they’re bound to say they got three items, not four, five or six).
Conversely, some properties seem preposterous in the general case but work, arbitrarily, for specific classes of objects. Take the incar: it is a hypothetical object that is colocated with my car when it’s in a garage, but the incar ceases to exist as soon as the car comes out. Incars are not even close to the ordinary objects from our daily language. Yet an island is colocated with a portion of the lithosphere when its highest point is above sea level, and ceases to exist when it is below; yet islands’ existence is generally accepted as sound.
All those concerns about arbitrariness can be attributed to a nagging worry that those distinctions come down to either purely linguistic or cultural grounds. Even if we could settle on a finitely long criteria, it’s hard to dispel a sense that it could not survive the evolution of our culture, or a modal shift of perspective ("what would an alien think?"). A typical case is when objecthood is grounded in function: in some cars it might be easier to dismount a seat than to dis-attach a bike from the roof-rack. Yet only the seat is part of the car. This comes down to the seat being delivered with the car, and helping fulfil a basic function of the car (to seat passengers). The function of the bike itself is unrelated to the car. But a human from a few centuries ago wouldn’t know that, and their hunch on objecthood may differ.
Sorites paradox: in addition, conservative accounts in mereology are extremely vulnerable to a class of paradoxes known as sorites.
They typically take the following form.
A chair has a finite number of atoms.
If \(C\) is a chair, has n atoms, and we remove a single atom to create a new object \(C^{-}\) , then \(C^-\) is also a chair.
No object with fewer than 2 atoms can be a chair.
So, there are no chairs.
Sorites paradoxes are a stake through the heart of any attempt at rigorously approaching ordinary objects. With some tweaks they can be applied to properties or processes, so long as they are ground in vagueness ("how many hairs does one need to not be bald?", "what height is tall?", etc.). Naturally, there have been rigorous proposals to circumvent the issue, the point is that they can hardly accommodate a strictly bivalent logic with a unique existence quantifier, which is the standard formulation of ontology: a mereologist cannot have her cake and eat it too.
Problem of coincidence : If I caress a merino sheep, am I touching (1) a pile of wool that happens to be on an animal’s back, (2) an animal or (3) both? On a drive, I am sitting (1) on a car seat, (2) in a car, or (3) both?
(1) seems hard to argue for: ordinary objects are grounded in common sense and nobody would look at a sheep and say there are two objects there (an animal and some wool). (2) is typical of a maximalist account that precludes proper parts: there’s only a sheep, only a car there. This seems quite neat for a snapshot, but places the bar very low in terms of unfastening: simple actions like detaching a wiper, shearing a sheep, can conjure new objects out of existence. A bit of wool that sheds naturally comes into objecthood only at that very moment. (3) can seem more flexible: it accepts the existence of proper parts — the car, its seats, wipers, wheels, etc. all exist simultaneously. This wreaks havoc with traditional accounts of coincidence ("there cannot be two objects at the same time and the same place"), countability ("if there’s a car in the garage, is there one object or fifty?"), and causality ("did the car cause the damage, or was it the front bumper?").
This is not a crippling issue; we can do without these concepts, argue they are ill-defined and not suitable to our ontology. In doing so, we are firmly moving towards mereological universalism. This may not lead to any logical inconsistency, but it somewhat contradicts the mission that conservatism set for itself, to stick with common-sense accounts of objects.
All in all, mereological conservatism suffers from such serious issues, the reader may understandably wonder: have I taken us on a useless detour, leading up to a predictable cul-de-sac? Shouldn’t the topic of ordinary objects be left to psychologists and anthropologists? That may well be. But as we shall see, alternative accounts have their own issues. Better to highlight conservatism’s problems now to make the alternatives more palatable when we come to them.
Mereological universalism
is one of the main revisionist positions, in the sense that it rejects common-sense accounts of objecthood. Instead it advocates for a principle of unrestricted composition. All fusions, complements, intersections of objects are valid objects themselves. We could say that this mereology is a representation of discrete topology: any part of the physical universe, however defined, constitutes an object that we can talk about or quantify over.
This view has one important merit: clarity. However it can be challenged from several angles as well.
Counter-intuitiveness is sometimes mentioned as a drawback. Universalism accepts a variety of exotic objects, like the aforementioned "incars", or the proverbial "trouturkeys" (creatures made from the front half of a trout and the rear half of a turkey). There’s no limit to the kind of silly spatio-temporal combination that can be conjured into existence ("the fusion of Joe Biden between the years 1975 and 1978 and all Helium nuclei in Proxima Centauri 1,000 years ago").
The brand of critics this attracts is frequently flying the banner of common sense. But it seems that the only way to introduce common sense as a factor in ontological discussions about objecthood is to adhere to conservatism.
Yet from my perspective, the weaknesses of conservatism are quite insurmountable. If it is the only solution to the perceived counter-intuitiveness of universalism, then the remedy is probably worse than the disease. This is not to say we can’t define or talk about ordinary objects — restricted quantification or relative identity (more on this one later) allow just that — but their special status of "common-sense acceptability" doesn’t make them ontologically different from the most outlandish compositions.
Profuseness is another oft-mentioned drawback. Universalist mereology is tremendously profligate: consider a toy universe with one ordinary object, a bottle of water, at a single point in time, and whose basic bricks are \(\text{H\_2}O\) molecules (for 1 liter, around \(3\cdot10^{25}\) of them). The number of possible molecule combinations (legitimate objects according to the universalist) is on the order of \(10^{10^{25}}\), an unthinkably high number (there are around \(10^{81}\) elementary particles in the physical universe). And that’s just from one instantaneous snapshot of some small amount of water...
Most arguments against the gratuitousness of universalism seem to stem from some aesthetic preference for ontological parsimony. That is not very convincing to me. There are sets in mathematics that are several "orders of infinity" larger than the natural numbers, and yet humans have been doing arithmetics just fine without worrying too much about them.
Ockham’s razor arguments carry more weight: do we really need all these objects? Unless there’s some revolutionary position in the works, it appears that we do, save one case: it is possible to wield the razor and sheath the unseemly googolplexes of objects crowding our ontology, but the shave will be extremely close, so much so that only nihilism remains. We’ll discuss this position in the next section.
The problem of identity is not specific to universalism. It is an impediment to any view that accept composite objects, including conservatism (I didn’t mention it then — that view had enough issues of its own). We’ll need to come back to the topics of identity and constitution later as it warrants a whole section in itself.
Mereological nihilism
is the polar opposite of universalism: it posits a principle of impossible composition. In that view, there are no composite objects, only simples — object with no proper parts. Two main flavors of nihilism can be distinguished:
Atomism: this covers a family of views whereby there are many simples. Of course this is the intuitively "correct" position to us moderns given the spectacular success of atomic models and particle physics in the past century and a half (although physical atomism and mereological atomism should not be confused).
In an atomist picture, a mereological nihilist would say that there are no dogs nor tables, only "heaps of simples arranged dog-wise or table-wise".
Stuff: we’ve been spontaneously speaking of objects in our foray into the physical world. But to proponents of stuff ontologies (as opposed to thing ontologies, there is simply no such thing as a thing. Instead there is really only stuff, whilst objects are illusions emerging from the properties of stuff.
The world can be made of one stuff (mereological monism), in which case there is but one simple, or of several (mereological pluralism). Think of the pre-Socratics and of arguments whether the world was made of water, of air, or of four elements. According to Anaximenes, "air can apparently take on various properties of color, temperature, humidity, motion, taste, and smell". Moreover, "it is the condensation and rarefaction of air that naturally determine the particular characters of the things produced from the originating stuff. Rarified, air becomes fire; more and more condensed, it becomes progressively wind, cloud, water, earth, and finally stones..
This is strictly illustrative; I do know that Anaximenes’s ideas are not the best account of matter that we have today. But think of one our best accounts: quantum field theory. A direct consequence thereof is that many-particles systems need to be represented as single wavefunctions. Ultimately, physics can be said to describe the evolution of a single "wavefunction of the universe". The resulting system might be deemed a two-simples ontology: the universal wavefunction, and spacetime.
As I’ve mentioned above, mereology and physics are orthogonal, but if physical intuition must at least serve as a guide, one can see that contrary to atomist doxa, stuff ontologies have assets too.
In any of its guises, mereological nihilism has some powerful arguments in it favour. First it is, by definition, parsimonious, and thus completely bulletproof to the kind of criticism levied against universalism’s profligacy. Second, it simply dissolves all paradoxes of identity. These all start by asking whether certain composite objects are identical, and then evidence some contradiction. Nihilism simply states there are no composite objects, and therefore no paradox.
Be that as it may, there are also issues — big ones — with this account:
Atomless gunk: objects with proper parts have been christened with the poetic-sounding name of "gunk" by David Lewis. The concern here is that we’ve posited the existence of simples, but have conveniently ignored the possibility they might not exist. Nihilism, at least as presented here, would simply crumble then. I feel pretty confident in dismissing this. It is generally assumed that spacetime is ultimately quantized in some way, and can be represented as a lattice with Planck length/time periods. In addition, the nature of quantum theory precludes the possibility of atomless gunk — even if it was discovered that quarks have sub-components, which themselves are made of more fundamental particles, and so on ad infinitum, all possible many-particle systems could be represented by a common wavefunction which could act as the ultimate simple. One may dislike the wavefunction-as-stuff conceit, but it seems to show that bottomless gunk is not a logical wrench in nihilism’s gears.
Emergence: it’s all well and good to talk of "simples arranged woman-wise" when talking about a friend, but (1) it sounds quite rude, and (2) it makes one wonder about all the properties that I would normally associate with my friend, such as being tall, or being 30 years old.
Clearly, none of the electrons and quarks making her up are tall nor 30 years old. If she, as a composite object, does not exist, she can’t instantiate these properties either. There are three responses to this.
The first is to deny these properties exist. It’s an entirely consistent position, however most would say — I certainly would — that no composite object nor complex properties makes for a very poor ontology, that’s basically thankless to talk about and honestly quite useless.
The second response is to drop the atomist posit and to adopt monism. In this instance, when I say my friend is tall, I’m actually saying that the universe instantiates the property: "has a restriction to this specific region of spacetime that has the characteristics of a tall person". This can be made consistent too but ultimately takes ontology far away from notions borne out of our experience and into a purely mathematical viewpoint.
Finally the last attempt at a response is to accept both atomic simples and properties, but to try and develop a model of "collective instantiation" of those properties. The difficulty is to show how that’s actually different from having composite objects, and not just a verbal conceit...
Mereological nihilism has strong assets in principle, but it’s really hard to shake the challenge of emergent properties. Even more concerning is the diffuse feeling that the whole position amounts to a verbal game rather than a robust ontological position.
I can declare that my table doesn’t exist, nothing will fall on the floor — it’s all firmly supported by a group of simples arranged table-wise. Conservatism is a far cry from universalism in that it considers ordinary objects as a class of ontological import. Nihilism feels more like the mirror image, and ultimately exact equivalent, of universalism, a switch of perspective to artfully swerve from the problems of identity, in a way which I suspect could just be spurious. Agreeing as much could be seen as a form of mereological deflationism.
Towards a typology of mental states
Consciousness
Another word is ubiquitous in discourse about the mind — consciousness. Alas, the polysemy of this umbrella term is formidable and in dire need of being defused before we can go any further.
Let’s consider some of the common meanings of conscious:
Sentience/mindedness: "being conscious of" is often used as a synonym to "being mindful of", so that any mental state would be a state of consciousness. I could be conscious of an experience I’m having, but also conscious of some fact, in the sense that I know that fact. Consciousness and mind thus become essentially synonyms. This is not just down to common parlance: many scientific writings on consciousness are actually about generic mentation activity.
Wakefulness: it is sometimes required that to be conscious, an organism must be awake and normally alert. Experiences in dreams would thus not be considered as conscious.
Phenomenality: "consciousness" is oftenwise used as a complete synonym for "phenomenality", which we’ve outlined above. In a laudable effort to avoid doubts, some authors use "phenomenal consciousness" as their term of choice which, when they entertain no other form of consciousness, can seem strangely pleonastic.
Self-consciousness: the most demanding sense of all might define conscious creatures as those that are not only aware, but also aware that they are aware. A less ambiguous way to describe this ability is as self-consciousness or self-awareness. This meaning has been coming a long way: Descartes already suggested that "to be conscious is both to think and to reflect on one’s thought". This use of "consciousness" as tied to a reflective knowledge about one’s own mental occurences spread rapidly amongst his contemporaries. Locke writes that "consciousness is the perception of what passes in a man’s own mind". In modern terminology, mental states that are about oneself or one’s mental states are called introspective.
Access consciousness: recent authors have embraced this polysemy. Ned Block acknowledges it by calling consciousness a "mongrel concept". Beyond phenomenal consciousness he introduces access-consciouness. Those are states endowed with some representation that can be accessed and broadcast for free use in reasoning, speech or action.
It can’t seem to the reader I’ve accomplished much here. If you were not entirely sure what consciousness was before reading this, you’re surely worse for wear now. Let’s try to be more constructive then, and to make explicit our own understanding of the term. I’ll start from two principles:
All options listed above have some merit. Since the definition of "consciousness" varies so much between authors and eras, since even its use in daily conversations is highly polysemic, it’s for us to take our pick as a convention. There is no logical argument that could lead to an unequivocal choice.
I’ll make the most useful pick. For me, that means a definition that does not make "consciousness" a synonym for one of the other, more unambiguous terms at our disposal: mind, self-awareness, phenomenality, wakefulness,...
So, I don’t want conscious states to be limited to phenomenal states, to introspective (self-conscious) states, nor to wakeful states. That seems to lead to a very inclusive concept, extending to representational states. But I also want to preclude consciousness to be equated with the broader concept of mind. What within the mental world can I contrast conscious states with? The answer is: unconscious states. This is not a humorous answer: the existence of unconscious mental states is actually subject to much polemic in philosophy or psychology.
For our purposes here we will conservatively assume they exist and refine their definition. Unconscious obviously cannot just mean non-conscious, lest we include nearly everything in the universe. A rock, or the Sun are certainly in non-conscious states, but not unconscious. I will call unconscious mental states those that cannot be brought to introspective self-consciousness.
A two-dimensional model
Bringing it all together, and in particular having sharply distinguished between the concepts of conscious and of phenomenal experience, we end up with a two-axes model:
The first dimension is a phenomenal-intentional axis: every mental state exhibits phenomenal and/or intentional properties and can be placed on a spectrum from phenomenal-only (qualia) to intentional-only. In the second part of this section on the mental world, we will focus on the phenomenal-intentional axis and on the relationship between these concepts.
The second dimension would distinguish between self-conscious states (introspection), conscious states (which includes introspection, plus all states that can be accessed for introspection), and unconscious states (hypothetically, mental states that are not available for introspection).
A rough typology could be as follows:
self-conscious phenomenal states (by which I mean "mostly phenomenal", a convention I will keep to): for instance, visual perceptions from an object I am intently looking at, or a throbbing pain in my toe won’t go away.
self-conscious intentional states: that’s any intentional state whose object is my mental state , for example an inner monologue about my own thoughts or feelings.
conscious phenomenal states also include phenomenal experiences that I’m not introspective about, but could be. For instance, a sound that my ears are hearing but has gone "to the background" as I was focusing, or the beating of my heart.
conscious intentional states: any thought, belief, fear, desire, hope, love that is not at the forefront of my stream of thought but could be called up to that level.
unconscious phenomenal states: their existence is controversial. One example that’s often mentioned in the literature is that of blindsight: some patients who have lost sight can still respond to visual stimuli with an accuracy much higher than chance. They deny having any conscious visual experience: whatever visual data the brain is processing cannot be brought to introspection; but the reactivity to the same stimuli suggests we can still call the resulting states phenomenal.
unconscious intentional states: things that "we don’t know we know". Those are closely associated with Freudian theories, where they help fill certain theoretical gaps in the explanation of conscious mental activity and behavior, but also with advances in cognitive science, where Chomsky has proposed the existence of a "universal grammar" that humans are born with and underlies language acquisition, even as it cannot be accessed or put into words.
Disjunctivism and intentionalism
Disjunctivism
Our characterization of mental states has yielded results. I can accept that something is a mental state if and only if it is phenomenal, intentional, or both. Our next question is no less daunting: is there unity in the mental realm? From Descartes and Locke to Brentano and Husserl, the question might have seen specious: mentation was always considered as a single package. But more recent developments have often seemed to study the two marks of the mental on parallel tracks that hardly met. This kind of attitude is sometimes called separatist.
If phenomenality and intentionality have no conceptual connection, there seems to be no good reason to abbreviate "phenomenal or intentional" into "mental". This drains the term of its significance and makes the grouping arbitrary: why not create an adjective to denote "physical and/or phenomenal" states instead?
There are compelling reasons to think there is a conceptual connection: in practice, phenomenal and intentional properties seem to work in lockstep and to be mutually implicating in multiple ways. Setting aside positions on animal cognition, panpsychism or artificial intelligence of a more speculative nature, it appears that one doesn’t go without the other.
That’s not a logical indictment of a disjunctive approach to the phenomenal and the intentional: it has its proponents and is not contradictory per se. But the interface between the two has received increasing attention.
Weak or strong intentionalism
Intentionalism is a general term for theories that propound a specific relationship between phenomenal and intentional (or representational) properties. For this discussion it’s important to remember the three-fold nature of intentional states: they have object, content and mode. In what follows I’m heavily indebted to Chalmers as I’m reproducing the steps of his enlightening discussion of intentionalism.
The simplest possible relation these properties could entertain is that of entailment:
Do phenomenal properties entail intentional properties? This would mean that every phenomenal experience is necessarily accompanied by a certain representation of the world: every pain would be directed at its source, every mood at someone, the world, the self. This position, the simplest step to break with full separatism, is often called weak intentionalism. Following Brentano’s lead, its direct corollary is that all mental states have intentional properties, making the intentional a necessary condition for the mental. A consequence is that pure qualia cannot exist as independent states, yet this version of intentionalism does not seek to explain them; as other phenomenal properties, they are still ontologically autonomous and irreducible. This approach is more characteristic of the "continental" phenomenologist brethren of Brentano, from Husserl to Sartre.
Do intentional properties entail phenomenal properties? That seems hard to argue — as we’ve seen, most intentional states are not self-consciously held. I know that Hugues Capet became the king of France in 987, but before I brought this fact to self-consciousness this instant, that representation did not seem to have phenomenal properties. I can’t say it "feels like something" to know facts about Hugues Capet as compared to not knowing them, the same way it feels like something to have a toothache.
Perhaps we can be more specific then; there is a case to be made that the intentional properties associated with phenomenal experience are characterized by their mode. For instance, knowing I am hurt, seeing my injury, and feeling pain from it would be states with the same object, similar content, and very distinct modes. If we accept that we can circumvent a set of phenomenal modes such as feeling, sensing, seeing, hearing, etc., then we can say by definition that: phenomenal-mode intentional properties entail phenomenal properties.
The combination of "weak intentionalism" with this last assertion is often called strong intentionalism. Since two reverse entailments is an equivalence, this leads to the following corollary: phenomenal properties are equivalent to phenomenal-mode intentional properties.
Reducive or nonreducive intentionalism
Now, that statement may still seem somewhat circular. Once we establish that phenomenal properties are equivalent to some intentional properties, do we need to refer to phenomenality still?
Nonreducive intentionalists do think so. This position can either be a neutral one, for lack of a convincing way to explain phenomenality, or a positive statement that phenomenality is an irreducible feature of the mental, even though it may not be as fundamental as intentionality. Should we stick to this position, the reader may be excused for thinking this is just a big sleigh of hand, replacing "phenomenal properties" with "phenomenal-mode intentional properties". It is not the case: "phenomenal-mode intentional properties" may need to appeal to the phenomenal for their mode, but unlike raw phenomenal properties, have an object and content. Phenomenal properties also supervene on them, in such a way that two beings in the same physical and intentional states would necessarily have the same phenomenal experience.
Reducive intentionalists, on the other hand, believe that the intentional properties that are equivalent to phenomenal properties can be fully understood and described without phenomenal notions. Amongst the numerous ways this has been attempted we can mention functional, causal, teleological approaches, as well as higher-level representation theories. We will not do more than dip our toe here.
Broad or narrow intentionalism
An arduous problem for all forms of intentionalism lies in the question of broad (or wide) and narrow content.
Narrow mental content is entirely determined by a subject’s intrinsic properties.
Broad mental content is not just determined by a subject’s intrinsic properties.
On first encounter it may seem incongruous that we’re even talking of broad content at all. If all things mental are private and subjective, how could mental content depend on anything that’s not solely internal? Sure, we do perceive and feel things from outside our own body, but, following Descartes, the only thing I can be sure of is that these perceptions and feelings are in my mind. In his radically skeptic account, Descartes imagines an "evil deceiver" who could create a perfectly lifelike hallucination or dream state. A more modern example is the proverbial "brain-in-the-vat": if we were able to provide that human brain with the exact physical stimuli that a duplicate "brain-in-a-head" is receiving, many would agree the former would have the same mental states as the latter. It appears to be a clear-cut case that mental content supervenes on intrinsic properties.
But it is important to understand that broad content is not meant to be externally located but externally individuated, which has to do with meaning. This idea shares roots with anti-individualist notions in Sartre, Heidegger or Vygotsky, but it’s been formalized in analytical philosophy by Putnam, whose best-remembered example is that of the Twin-Earths. Let’s imagine there is a twin planet of ours where nearly everything is identical. Every human has a doppelgänger who has lived the same life, gone through the same experiences and has had the same thoughts and beliefs. I’ve said twin-Earth was "nearly identical" to Earth — here is the difference: all the gold on Earth (Au) is replaced on twin-Earth by another element with atomic symbol Xy. It takes the form of a golden-colored, shiny, heavy metal, and its socio-cultural role is exactly the same as gold’s on Earth. Let’s further contend that in twin-England, the word to designate that metal is also "gold". Now let’s consider an English subject from the year 1000, Jon, and his doppelgänger twin-Jon.
Both live in the medieval era, so they have no idea about atomic weights, crystalline structure or fine physical properties. Nothing in their mental make-up would allow them to differentiate between Au and Xy. So, since Jon and twin-Jon have lived the exact same life with the same experiences, on twin planets, with the only actual difference being completely inaccessible to their senses, cognition, and those of any human around them, it seems clear that they areexact duplicates of each other. Therefore they should share all intrinsic properties. And yet, when Jon thinks "gold is shiny" and twin-Jon thinks "gold is shiny", the intentional objects of these thoughts differ: they may not know it, but Jon thinks of Au, and twin-Jon of Xy. Per some definitions of intentional content, the difference in object entails a difference in content. Hence it seems we are indeed facing broad content. Most externalists (believers in broad content) don’t argue that the object itself, Au or Xy, is part of the mental content. Again, it is still internally located. However, the basic idea is that if you fixate the intrinsic properties and variate the external environment, you end up with different mental content.
Externalism v Internalism about mental content is as far from a settled case as it gets in modern philosophy. Both positions have heavyweight proponents and countless arguments and counter-arguments in their favor. One thing to keep in mind is that radical versions of this positions (that there is only broad or only narrow content) stem from different basic intuitions about the mind, based on posits that are arguably impossible to debunk from the other side. Many theories fall towards the middle, accepting that broad and narrow content coexist, or deriving narrow concepts from the content proper.
Let’s bring this discussion back to intentionalism. The gist of this approach is to consider that phenomenal properties are equivalent to certain intentional properties. It seems extremely plausible to say that phenomenal properties are narrow: it’s a very difficult argument to make that the phenomenal experience of pain depends on anything besides one’s nervous system, or that two duplicate individuals with the same eyes, retinas, optical nerves and brains could have different visual experiences. But if phenomenal properties are indeed narrow, then the equivalent intentional properties need to have narrow content as well. This is in contradiction with radical externalism but consistent with radical internalism, and with moderate forms that don’t deny broad content but accept the existence of narrow content.
Mereology
Physical composition: when do objects compose other objects?
Position: Mereological universalism
The composition question for physical objects has been discussed at length in a previous section ("the physical world"). I’ve highlighted the problems inherent to mereological conservatism (chiefly the difficulty to define mind-independent criteria for objecthood). Mereological nihilism is blessed with simplicity, but both its main flavours carry major issues. Pluralist nihilism only recognizes atomic elements of the world, but still needs to allow discourse about ordinary objects and their properties, ultimately looking like covert universalism — a case of having one’s ontological cake and eating it too. Monist nihilism is seductive but a one-object view of the world is a major imposition upon \(\mathfrak{ToP}\). Our modern physics has a more monistic feel than its Newtonian predecessor (think of quantum field theory, or purely geometrical versions of general relativity), but (1) the aggregate of our "best theories" is most definitely not monistic, and (2) we have no idea whether those are even close to some "ultimate truth": for all we know, the next batch of theories might be atomist and Cartesian all over again.
Mereological universalism, the idea that every union of physical entities is an object too, thus seems to be the safest option ontologically. Should monism turn out to be true, or should one of the canonical physical entities be a "big object" (for instance, the whole universe under general relativity), we can still turn universalism inwards and with the right continuity features, slice and dice in every way imaginable, creating proper parts objects in the process (e.g. a segment of spacetime, or the restriction of a wavefunction along some of its variables).
Mental structure: how does macroscopic mentality emerge?
Position: Phenomenal intentionality
The question of physical composition is mirrored in that of mental structure. In exploring such matters however, we’re getting deep into speculative territory. Our discourse about “the concrete” or a hypothetical theory of the “physico-mental” has preserved the illusion of equality between the concrete world \(\aleph\)’s component realms, but the facts tell a different story: even though we may not know the final word about physical laws, our best models tell us something which certainly guides our reflection on physical mereology. About the mental we know very little…
Let us still remind ourselves of some facts, garnered through a previous section (“the mental world”).
The panpsychist credo which we’ve just endorsed has it that mental states are ubiquitous (and not limited to animal and human minds).
The mental realm has its own sub-components in the phenomenal (“what it’s like”) and the intentional (content directed at an object).
Although there is near-universal agreement that the phenomenal and the intentional are conceptually different, their metaphysical relationship is up for grabs. Some would say they are disjunct (realized in strictly distinct mental states), others that they can coexist but nothing more, and finally there are larger groups that prefer to posit that the intentional grounds the phenomenal (intentionalists) or vice versa (phenomenalists). What are the consequences of panpsychist monism in that regard? By adopting it, I’ve already rejected the idea that the mental could just be reduced to the physical. However the difficulties encountered in achieving such reduction are often due to phenomenal attributes like subjectivity or privacy, whilst the intentional is more amenable to functional explanation. The super-computers, “brains-in-a-vat” or “galaxy brains” from classic thought experiments are also more easily conceived in terms of purely intentional states. So the idea of the intentional being at least partly grounded in the physical shouldn’t be dismissed.
On the other hand, the ubiquity of mental states in panpsychism can be more easily envisaged as a ubiquity of qualia (atoms of pure phenomenality). We don’t expect a rock to get started on a memoir anytime soon (“what it’s like to be me”), but seeing its basic qualia as a form of proto-consciousness (being to the consciousness of a sponge what that is to a human’s) can at least be entertained. It is more difficult to picture a rock with intentional states: what would they be directed at and with what content? If qualia are ubiquitous and intentionality seems to be at least partly reducible to the physical (more precisely, it appears to emerge from some complex structures), we could then see the intentional as emerging from the combination of physical and phenomenal states.
I will go one step further and sketch a speculative model as follows:
\(\mathfrak{ToPM}\) will represent the phenomenal via a single ubiquitous “stuff”, which I would call the qualium field \(\mathfrak{Q}\).
\(\mathfrak{Q}\) interacts with physical objects by breaking up into several terms (in a similar way, to paint a picture, that quantum fields do at low energy). Reminding ourselves that \(\aleph\) represents the whole concrete realm and \(\mathbf{1}\) and \(\mathbf{2}\) the physical and mental respectively, we would have it, roughly, that: \[\begin{aligned} [\textrm{Human}\otimes \mathfrak{Q}]_{\aleph} &\approx \textrm{Human}_\mathbf{1} \oplus \mathfrak{Q}^{\textrm{Human}}_{\mathbf{2}} \oplus \mathfrak{I}^{\textrm{Human}}_{\mathbf{2}} \oplus \cdots \\ [\textrm{Computer} \otimes \mathfrak{Q}]_{\aleph} &\approx \textrm{Computer}_\mathbf{1} \oplus \mathfrak{I}^{\textrm{Computer}}_{\mathbf{2}} \oplus \cdots\\ [e^{-} \otimes \mathfrak{Q}]_{\aleph} &\approx e_\mathbf{1} \oplus \cdots \end{aligned}\] So the interaction of a human being’s physical structure with the qualium in \(\aleph\) gives rise as an approximation to mental states that are distinct from that physicality and, again as an approximation, can be decomposed over the phenomenal/intentional divide (with \(\mathfrak{Q}\) for qualia and \(\mathfrak{I}\) for intentions).
A computer’s physical structure allows to convey information in a form that could be considered as intentionally comparable to a mind’s states, although the phenomenal term would be close to that of brute matter and then "near-zero" by any metric.
Simple, unstructured matter, like an electron, also combines with the qualium field but that interaction is fruitless: although qualia are ubiquitous, their "intensity" is near-zero here too, and the lack of complexity also precludes any significant intentionality.
The mental states hereby generated form a class of objects within the theory that can be incorporated into the same mereology as physical objects, thus allowing for the union of mental states together, or of mental and physical entities. Let’s remind ourselves that such unions have ontological existence (hence they can have properties or relations, as we’ll see), but in the general case this doesn’t mean they’re canonical entities of any relevance.
Abstract algebra: how do abstract entities combine?
Position: Abstract combinatorialism
Having just discussed the mereology of physico-mental entities, one could also mull over the existence of such a structure for the abstract world \(\mathbf{3}\). The notion of an algebra of concepts, like so many things, is an old idea that’s been first properly formalized by Leibniz.
The basics are pretty simple: where there are two properties, there should exist an addition and a multiplication of those, defined as \(\forall x ( (B+R)x \leftrightarrow Bx \vee Rx )\) and \(\forall x ( (B \times R)x \leftrightarrow Bx \wedge Rx )\). If \(B\) is "blue" and \(R\) "red", then quite clearly \(B+R\) and \(B \times R\) would be respectively "blue or red" and "blue and red".
In a similar vein we can define inclusion as: \(I < B \leftrightarrow \forall x ( Ix \implies Bx)\) ("indigo" is included in "blue" because anything that’s indigo is also blue). With limited mathematical labor, together with a few other definitions, we can demonstrate that we are really building a Boolean algebra, which, once we remove the zero point, is in fact equivalent to a mereology.
It is not difficult to extend the Leibnizian conceptual algrebra to our abstract realm, give or take a switch to the encoding point of view. This ensures that we have all the predicates and abstracta we need to discuss anything at the macro-level. Remember, physical mereology helps us build macro-objects through a union of simples, e.g. a man. However, it doesn’t help defining any of that union’s properties, since the only concrete predicates we’ve accepted so far are the ones native to \(\mathfrak{ToPM}\), such as "being a photon" or "having mass \(m_e\)". The conceptual algebra allows us to combine those ad infinitum, generating properties of the mereological complexes. Even something as simple (to humans) a "being round" will require a long build-up from wavefunctions to elementary particles, composite like atoms, expected positions, and finally to the shape of polyatomic objects.
With our complete abstract mereology in place, the bare universe borne out of our basic formalism, of mathematical theories, and of \(\mathfrak{ToPM}\), has become considerably richer. We can now harness the original formalism to deal with complex physico-mental entities and abstracta, as well as their properties and relations. Notation-wise, we’ll use \(\odot\) as an all-purpose mereological operator, for brevity (ignoring the profound differences between the physical, mental and abstract mereologies, over which we won’t delve in the present work). The class of mereologically constructed physical or mental objects (via fusion, division, the hypothetical physical-qualium combination...) — the mereological span of \(\aleph\) — can then be denoted as \(\aleph^{\bigodot}\). \[\aleph^{\bigodot} \hat{=} \{ \bigodot x_i, \forall i(x_i \in \aleph) \}\] As to the abstract realm, it can actually be shown that the logical-formal machinery, together with the comprehension principle, ensures that it is, as a whole, mereologically stable, i.e. \[\mathbf{3}^{\bigodot} \cong \mathbf{3}\] However this wouldn’t be the case for sub-spaces of the abstract realm. \(\mathbf{3}_\aleph\) is the raw class of predicates appearing in \(\mathfrak{ToPM}\), but \((\mathbf{3}_\aleph)^{\bigodot}\) is the minimal algebra spanned by those predicates. It contains the class of predicates exemplified by macro-objects, hence \[(\mathbf{3}^{\bigodot})_\aleph \subset (\mathbf{3}_\aleph)^{\bigodot}\]