I've been thinking and writing a lot recently about  a conception of 
reality which avoids the debates about what is fundamental in reality. It 
seems to me that with regards to materialism, we find it very difficult to 
escape the evolutionarily evolved, inbuilt notion of "things" and "stuff" 
that our brains need in order to manipulate the world. Yet QM and 
importantly the expected dissolution of time and space as fundamental 
entities in physics have made any such simple mechanistic notion of matter 
obsolete - what is left of matter except mathematics and some strange thing 
we can only call "instantiation" - the fact that things have specific 
values rather than (seeming to be) pure abstractions? What does a 
sophisticated materialist today place his or her faith in exactly? 
Something along the lines of the idea that the world is fundamentally 
describable by mathematics, impersonal and reducible to the operation of 
its simplest components. With regards to the last part - reductionism - 
that also seems to be hitting a limit in the sense that, while we have some 
supposed candidates for fundamental entities (whether quantum fields, 
branes or whatever), there is always a problem with anything considered 
"fundamental" - namely the old turtle stack problem. If the world is really 
made of any fundamental entity, then *fundamentally* it is made of magic - 
since the properties of that fundamental thing must simply be given rather 
than depending on some other set of relations. While physicists on the one 
hand continually search for such an entity, on the other they immediately 
reject any candidate as soon as it is found, since the question naturally 
arises, why this way and not that? What do these properties depend on? 
Furthermore, the fine tuning problem, unless it can be solved by proof that 
the world *has* to be the way it is – a forlorn hope it seems to me – 
suggests that the idea that we can explain all of reality in terms of the 
analysis of parts (emergent relationships) is likely to collapse – we will 
need to invoke a cosmological context in order to explain the behaviour of 
the parts. It's no wonder so many physicists hate that idea, since it runs 
against the deep reductionist grain. And after all, analysis of emergent 
relationships (the parts of a thing) is always so much easier than analysis 
of contextual relationships (what a thing is part of). 

To get to the point then, I am considering the idea of a purely relational 
ontology, one in which all that exists are relationships. There are no 
entities with intrinsic properties, but only a web of relational 
properties. Entities with intrinsic properties are necessary components of 
any finite, bounded theory, and in fact such entities form the boundaries 
of the theory, the "approximations" it necessarily invokes in order to draw 
a line somewhere in the potentially unbounded phenomenological field. In 
economic theory for instance, we have “rational, self-interested” agents 
invoked as fundamental entities with rationality and self-interest deemed 
intrinsic, even though clearly such properties are, in reality, relational 
properties that depend on evolutionary and psychological factors, that, 
when analysed, reveal the inaccuracies and approximations of that theory. I 
am claiming that all properties imagined as intrinsic are approximations of 
this sort - ultimately to be revealed as derived from relations either 
external or internal to that entity.

Of course, a purely relational ontology necessarily involves an infinite 
regress of relationships, but it seems to me that we must choose our poison 
here - the magic of intrinsic properties, or the infinite regress of only 
relational ones. I prefer the latter. (Note that I am using a definition of 
relational properties that includes emergent properties as relational, 
though the traditional philosophical use of those terms probably would not. 
The reason is that I am interested in what is *ontologically* intrinsic, 
not *semantically* intrinsic.) 

What would such a conception imply in the philosophy of mind? 
Traditionally, the “qualiophiles” have defined qualia as intrinsic 
properties, yet (while I am no fan of eliminativism) I think Dennett has 
made a strong case against this idea. Qualia appear to me to be properties 
of relationships between organisms and their environments. They are not 
fundamental, but then neither is the “stuff” of which organisms and 
environments are made. We simply cannot ask about fundamental properties, 
but must confine ourselves to the networks of relationships we find 
ourselves embedded in, and from which we, as observer-participants, cannot 
be extricated. “Third person” accounts, including physics, are abstractions 
from aggregations of first person accounts, and none can rise so high above 
the field of observation as to entirely transcend their origins in the 
first person. Thus there are certainly objective truths, but not Objective 
Truths, that is truths that are entirely unbound to any observer and which 
nominate the absolute properties of real objective things.

Note that the “relationalism” I am proposing does not in any way imply 
*relativism*, which flattens out truth claims at the level of culture. Nor 
does it make consciousness “primary”, or mathematics. I cannot personally 
reconcile the interior views (qualia, if you like, though I think that 
terms places an unwarranted emphasis on “what experiences are like” rather 
than the mere fact of experience) with a purely mathematical ontology.

One obvious objection to this whole idea is the counter-intuitiveness of 
the idea of relationships without “things” being related. Yet I think the 
fault lies with intuition here. Western thinking is deeply intellectually 
addicted to the notion of “things”. David Mermin has interpreted QM in 
terms of “correlations only” – correlations without correlata as he puts it 
– an application of similar ideas to quantum theory. Part of the objection 
I think lies in the semantics of the word “relationship”, which 
automatically causes us to imagine two things on either side of the 
relation. It would be better to think in terms of a web, then, than 
individual, related entities. Or simply say that the related entities are 
themselves sets of relationships. Mathematics provides a good example of 
such a purely relational domain – a number exists solely by virtue of its 
relationships with other numbers. It has no intrinsic properties.

Yet what then of the problem of specific values – the instantiation aspect 
of materialism? To quote Hedda Mørch:  “… physical structure must be 
realized or implemented by some stuff or substance that is itself not 
purely structural. Otherwise, there would be no clear difference between 
physical and mere mathematical structure, or between the concrete universe 
and a mere abstraction.”

We can overcome such an objection by invoking the first person perspective. 
Mørch credits the specific values of entities in our environment (some 
specific electron having this position, that momentum and so on) to some 
property of “being instantiated in something intrinsic”, harking back to 
Kant’s *Ding an Sich*. Yet there is an alternative way of viewing the 
situation.  Let us imagine that each integer was conscious and able to 
survey its context in the field of all numbers. Take some number, let us 
say 7965. When number 7965 looks around, it sees the number 7964 right 
behind it, and the number 7966 right ahead. Trying to understand itself and 
the nature of its world, it starts doing arithmetic and finds that 
everything  around it can be understood purely in terms of relational 
properties. Yet it says to itself, how can this be? Why do the numbers 
around me have the specific values they do? What “breathes fire” into those 
arithmetical relations to instantiate the specific world I see? Yet 7965 is 
wrong. It is ignoring the significance of the first-person relation that 
places it within a specific context that defines both it and the world it 
sees.

Note that I am not, like Bruno, actually suggesting that numbers are 
conscious. The point of the thought experiment is merely to show how 
specific values can exist within a first person account, without us needing 
to invoke some unknowable thing-in-itself or substrate of intrinsic 
properties. 

Grateful for any comments/critiques.

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