[Mike Todd]

Hi Don,<div>
</div><div>I hope you’ll accept a brief overview for now; I’ll return in a few days to address specific observations you’ve made.</div><div>
</div><div>Let me preface all this by saying that the following definitions and views are, as ever, my own, although, as far as establishing context, they align with more broadly-accepted views within mainstream science and philosophy.</div><div>
</div><div>Phenomenal reality is the world of phenomena, of observable events. Don’t let the word “events” fool you, however: observable events are nothing if not mundane – for the greatest part. Examples of observable events are: a black cat crossing ahead, the sound of a bell carried on the wind, the fragrance of a rose garden, the taste of tiramisu, the touch of a plush throw. These examples make clear that observable events, phenomena, are what we would informally refer to as perceptions, or, formally and collectively, the perceptual content of individuated consciousness or awareness.</div><div>
</div><div>Phenomena appear to us as possessing qualities, and I don’t believe this appearance is false – quality inheres at all levels of reality, on my view. However, the perceptual qualities apparent in individuated consciousness or awareness are undoubtedly categorically distinct from the qualities that exist apart from it: the qualities we perceive, sometimes referred to as qualia, do not exist outside of perception at any level of reality other than the phenomenal. These qualities are aspects of our perceptual system, viz., a (categorical) reframing of qualities that exist apart from it.</div><div>
</div><div>Yet as much as they are an aspect of individuation, these qualities are far from individual or arbitrary. Rather, there is an overwhelming degree of regularity in their manifestation. Consequently, they are amenable to analysis in the form of quantification – measurement – the assignment of numerical value: the colour(s) of a cat may be assigned value(s); so, too, the sound(s) of a bell; the regularities of rose fragrance and tiramisu taste may also be subjected to analysis and assigned values, albeit of a subtly different tang than those of colour and sound; and at the level of fabric or lower, the regularities of plushness may also yield to the strictures of number.</div><div>
</div><div>So it is that phenomenal reality may be said to possess both quality and quantity. Nearly all laypersons and most so-called experts would agree on this much. Disagreement arises, most pointedly, on the question of the extent to which quality and quantity may be considered real, or as I would prefer to say, at which levels of reality they inhere – bearing in mind that any levels one might postulate are themselves an arbitrary imposition. My view is that quality, of categorically distinct types, inheres at all levels of reality; quantity, on the other hand, inheres only at levels within which regularities manifest. On my view, then, quantity inheres only at the levels of noumenal and phenomenal reality, and it may therefore be considered, in a sense, less real than quality. (This begs the rather thorny question of whether numbers, and mathematics in general, may be said to exist at deeper levels of reality. I confess to having no answer, much as I admire Lakoff’s theory of embodied mathematics.)</div><div>
</div><div>So what can be done with quantity? Quite a lot, I would say. Our capacity to recognise regularities and to derive quantities thereof is the fulcrum by which mathematics and physics, and all other disciplines reliant upon quantification, achieve leverage. The proviso here is that what these disciplines describe may be no more (or less) than the reality manifest within our (possibly species-specific) perceptual and conceptual frameworks. Great swathes of philosophers and scientists will throw their arms up in horror at this suggestion, but, as much as I have enormous respect for, and great confidence in the findings of, science as a whole, as well as being grounded in it academically, it’s how I see things. Nevertheless, for all that my take entails a rather limited purview for science – in the words of Robert Frost, a “diminished thing” – I still consider it one of our farthest-reaching roads into reality, a path piercing the deep heart of the woods, although, admittedly, stopping just short of the other side.</div>