The Potential of Self-Reference

A second-order language - more precisely, any language rich enough to encode the Peano arithmetic - has the potential for self-reference. We have known since Gödel that this leads to the eventuality of true statements in the language that cannot be derived. But there has been little consideration of the practical upshot. If we view such languages as production systems: the expressivity of the language allows us to specify a set of rules for building and revising sets of production rules which constitute theories of the world. Self-reference allows for the possibility that this very set of production rules would be self-applicable, hence, self-revising. Thus, a finite set of axioms could be authored with an interpretation that nonetheless allowed for infinite adaptability, so to speak, over the long term. In second-order languages, the control afforded by rule sets need not be a fundamentally limitative feature.

The human intuition is that this infinite potential is in some way characteristic of living systems. Certainly ecologies evolving stochastically under conditions of natural selection evince it. And complex agents that learn and adapt within such ecologies may evince it, too.

Consciousness as Natural Selection

Experience - conscious experience, if you will - is as much a matter of ruling things out as it is of ruling things in. To experience everything as infinite, in William Blake’s memorable turn-of-phrase, is to experience nothing, strictly speaking. Consciousness is sharpened precisely to the degree that it is focused, and it is focused by exclusion, by selecting among potential factors.

Consciousness is selection. Indeed, I am tempted to say, ‘natural selection’. Is there, after all, any other kind?

Huxley on Perception-as-Filtration

Not long ago, I was dipping into Huxley's The Doors of Perception, and thinking about Huxley’s thesis, as reflected in his title, drawn from the William Blake quote: ‘If the doors of perception were cleansed, we should see everything as it truly is - infinite.’ Huxley’s idea was that our sensory organs are essentially filters, with their selectivity determined by the requirements of survival. Huxley came to believe that LSD and Mescalin were capable of widening the bandwidth of our sensors so that they would accept sense data that would ordinarily be rejected, and that the experience of this weakened selectivity approximated the allegedly heightened sensitivity of artistic personalities. Huxley is, I think, not altogether wrong about this, but his analysis may be weakened by failing to distinguish between selectivity that derives from the natural history and evolution of the species and selectivity that is due to internal organization and selection within the multicellular organism.

Given a particular location in space-time, there are certainly any number of facts which are may be truly predicated of it; indeed, it becomes clear upon consideration that the cardinality of such facts is not only infinite, but uncountably infinite. Consider the fragment of the plenum that constitutes my coffee cup from, say, 8:00 a.m. to 10:00 a.m. this morning. throughout this time, it has a certain determinate diameter, a certain determinate height, a certain determinate volume. It remains at a certain average distance from the center of the earth, at a certain average distance from the center of the sun, at a certain average distance from the center of Alpha Centauri. It contains a certain number of carbon atoms. It reflects light within a certain range of amplitudes and wavelenghts. It is capable of containing hot water. Arguably, any feature that may be instantiated anywhere in the cosmos is reflected in some fact that may be predicated about my coffee cup during this delimited period of time.

It seems equally clear that any one of these facts could be ‘directly detected’ by the right sensorium - in the strict sense that it should be possible to build any number of devices of which it may be truly said that the device will produce a signal if and only if the fact in question obtains. And, it may be added, if intelligent design can produce such a device, we can safely assume that evolution by natural selection can do it.

Having said this, it should also be noted that for any given piece of space-time there is also an infinitude of facts which do not obtain. It is not true that my coffee cup from 8 a.m. to 10 a.m. this morning, contains any uranium, not true that it has a diameter of a mile, not true that it is 5 feet from the center of the earth, or 𝍦 feet from the center of the earth...A given detection of a fact may be equally said to be a filtration, or a negative detection, or a ruling-out. Detecting that a proposition p may equally well be said to be a detection of the negations of all propositions that are inconsistent with p.

It is also surely the case that, given the sensoria we actually have, what we directly detect regarding any given region of the plenum is the tiniest fraction of what could have been detected with the right physical sensory apparatus. If our organism responds consistently to the instantiation of some feature at a given place and time by instantiating some other feature at a spacetime location bearing a determinate relation to the first, this is because it was, on the balance, advantageous to some ancestor of ours to do this, and certainly not because what we detect as ‘given’ is in any way simple in its own right.

Finally, it is worth reminding ourselves that, as multicellular organisms, we have hierarchically organized sensory apparatus that is optimized for information fusion. As symbiosis and then colonialization occurred, single-celled organisms that exhibited responses to certain stimuli were organized into cohorts with collated responses, able to detect features that were compositions of those original stimuli. Also, we may be reasonably sure that evolution in multicellular organisms hit upon the trick of playing sensors and cohorts of sensors off against one another in a kind of internalized selection that could converge on those complex feature detections of maximal advantage to the organism as a whole. In vertebrates, the organization likely goes several levels deep, with selective competition occurring at all levels, and with commensurate elaboration on the efferent side mediating complex and plastic autonomic responses. The key thing to realize about the sensory hierarchy is that information is probably thrown away at every level, in the strict sense that some detections that are made by agents at one level go unused at the next level of organization, or are used only for the purpose of culling the detectors.

I can well believe that LSD and related drugs interfere with this process, to the extent of allowing information that would ordinarily be thrown away in the sense described to be used instead as data for information fusion, and it may even be that they disrupt the organization of sensor-cohorts to the point that certain complex features may be detected via data fusion that would not ordinarily be detected. But I cannot believe that any drug could allow direct detection of features that an organism lacks sensoria to respond to, or features with components to which no ‘atomic’ sensory agent that the organism possesses will respond: that is a logical impossibility.