Thinking the Unthinkable?
Yet what could it mean for 0, zero properties, to be the case - whether in mathematics, natural science, or as in what is the case simpliciter? On an unavowed and psychologistic level, it's easy to confuse 0 with just an indefinite extension of the inky introspective void that results from closing one's eyes. Such a (mis)conception of 0 already presupposes existence with a generous measure of properties. This is borne out by the neurological syndrome that occurs when a subject's primary and associative visual cortex are bilaterally lost through brain damage. In such cases, the victim isn't even aware of an inky void which the rest of us misconstrue as analogous to 'nothing'."Existence appears to me like a conquest over nought...If I ask myself why bodies or minds exist rather than nothing, I find no answer; but that a logical principle, such as A = A, should have the power of creating itself, triumphing over the nought throughout eternity, seems to be natural...Suppose then the principle on which all things rest, and which all things manifest, possesses an existence of the same nature as that of definition of a circle, or of that as the axiom A = A: the mystery of existence vanishes..."
Intuitively, it is possible conceptually to subtract all the objects or events from a given system, leaving no objects or events at all - the default condition where there isn't anything to be explained. But it is problematic to assume one can conceptually do the same with properties - i.e. notionally to subtract all the properties from a given system, leaving no properties at all, as distinct from merely exchanging one property for another. Properties don't cease to be properties simply in virtue of being described in terms of the absence of other properties.
Nonetheless, one's pre-theoretic intuition that a complete absence of properties is intelligible, and indeed ought to be the "natural" logical default condition, isn't totally misconceived. In fact the Zero Ontology is committed to the proposal that something analogous what we conceive as zero properties is the case. So the antithesis is misconceived. But a condition of zero properties rigorously defined embodies a far richer, deeper, more fertile state of affairs than an inky void [or for that matter a dimensionless point or quantum vacuum], which one's untutored intuition of 'propertylessness' entails. For counterintuitively, the manifestation of zero properties is a world that includes objects and events, sticks and stones, and people - whose local occurence is inseparable from the global conservation of 0. Likewise, cancelling out to 0 can't be akin to a simple-minded binary co-existence of ying and yang, a balance of polar opposites. If quantum cosmology is correct, it's a multi-dimensional, perhaps an infinite-dimensional, cancellation process: a superposition of alternative histories whose relative frequency is quantified by the universal wave function or state vector. The formalism is exact; the cancellation is precise; alas its significance remains tantalisingly obscure.
Deep problems still remain of course in trying to conceptualise the opposite to the existence of anything at all, i,e. not even a quantum vacuum or dimensionless point. Is the linguistically expressible but unimaginable absence of space-time (or of any other dimension), and the absence of energy, matter or any other entity or property meant to be (or meant to be the possibility of) a peculiar non-spatio-temporal condition or state of affairs? If not, and if the proposition couldn't have any truth-conditions because on such a scenario their prima facie satisfaction would mean that there wasn't any meaning or reference in the first instance, then nonsense looms. This should scarcely be surprising. By the lights of standard physicalism, the status of folk-traditional semantic categories is problematic enough as it is.
Is 0 supposed to be some abstract principle or platonic existent; or, alternatively, is it, as it were, something somehow concrete? Or neither? The nominalist project in mathematics stems from a suspicion of the putative causally inert (and hence naturalistically inaccessible?) abstract entities that platonists presuppose. Yet what could it mean to nominalise 0? If there weren't even anything analogous to truth, then there couldn't be any truth-conditions, so one popular(!) way of analysing semantic meaning is blocked. But what does it mean for something to "cancel out"? Is cancelling out some sort of dynamic subsistent process? [quantum mechanical interference, the physical expression of a logical principle(?), rather than interaction, a force mediated by carrier particles??] If so, how and why does the ubiquitous cancellation process, expressed in the principle of superposition, occur with such phenomenal manifestations? Why does a Zero ontology need a phenomenology at all?