Broadly speaking, one can speak of two types of systems in nature: analog and digital. Analog systems are defined by continuous variables, like the distance between points or changes in velocity; rulers, thermometers, or accelerator pedals are all examples of analog systems. Digital systems, by contrast, are defined by discontinuous or discrete variables: as with the ten 'digits' of the fingers, digital systems, unlike analog systems, involve discontinutous 'jumps' between measurement values. Thus the transistor based computer, with it's on/off electrical gates, is an example of a digital system.

Now, one particular feature of analog systems that they admit of no negation. Because analog systems employ continuous variables, there cannot be any 'gaps' in the variables of the system: all the quantities involved are always positive; there are no minus quantities (consider the movement of mercury in a thermometer - it is a smooth, continuous variation). Anthony Wilden, speaking in terms of the difference between analog and digital computation, puts it like this:

"It is impossible to represent the truth functions of symbolic logic in an analog computer, because the analog computer cannot say 'not-A'. Negation in any language or simulated language depends upon syntax, which is a special form of combination, and the analog computer has no syntax beyond the level of pure sequence (and that only in a positive direction). There is no 'either/or' for the analog computer because everything in it is only 'more or less', that is to say: everything in it is 'both-and' ... Because the analog does not have the syntax necessary to say 'No' or to say anything involving 'not', one can refuse or reject in the analog, but one cannot deny or negate.' (Wilden, System and Structure).

How then, do we turn an analog system into a digital one? By doing nothing other than introducing negation into the analog continuum: that is, by placing a 'cut' into the continuum which would prase the continuum into A and not-A. Doing this creates a boundary in the continuum. Here is Wilden again: "Boundaries are the condition of distinguishing the 'elements' of a continuum from the continuum itself. 'Not' is such a boundary. ... the differential boundary of the figure and ground is a primitive digitalization generating a distinction, and the distinction may then become an opposition. [Thus], figure and ground form a binary relation, one and two form a binary distinction, [and] A and non-A in analytical logic form a binary opposition (an identity). 'Not' is a rule about how to make either/or distinctions themselves."

A few quite important things follow from this, but I want to focus on one: it is clear that if the above is the case, the very notion of identity is a digital notion which is parasitic on the introduction of negation into an analog continuum. To the degree that analog systems do not admit negation, it follows that nothing in an analog system has an identity as such. Although analog systems are composed of differences, these differences are not yet differences between identities; they are simply differences of the 'more or less', or relative degrees, rather than 'either/or' differences. The same follows for the principle of the excluded middle, which, to the degree that it is defined by the disjunction between an identity and it's negation ("either p or not-p" [⊢pv¬p]), is rendered inoperative at the level of the analog.

A way to summarise all of the above is this: to the degree that nature is a continuum, there are no brute identities in nature. Or less provocatively, to the degree that there are identities in nature, they are constructed and derivative of analogic differences. Nothing is 'equal to' or 'identical to itself', 'in-itself'. These notions are heuristics that are imposed upon nature for the sake of communicative ease. As Wilden acknowledges, 'boundaries in fact are the conditions of all communication'; but it will not do to confuse those conditions which those of nature. The all-too-quick takeaway I want to draw from this - the thread is getting too long now - is that any kind of ontology or metaphysics which would rely on the machinery of formal logic to do it's heavy lifting would be severely crippled one (here's to looking at you, analytic metaphysics!).