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Beware of the Blob: Cautions for Would-be Metaphysicians Mark Wilson, University of Pittsburgh And as for the mixed mathematics I may only make this prediction, that there cannot fail to be more kinds of them, as Nature grows further disclosed --Francis Bacon (i) In this essay, I will voice a discomfort that some of us have entertained with respect to the waves of philosophical speculation about the constitution of matter that have become abundant within the past fifteen years or so (for want of a better term, Ill dub this literature the new metaphysics 1). In rough measure, such investigations revolve around sweeping questions of the sort, How might an extended object be comprised of smaller parts? In many ways, musings of this general character appear familiar enough, for they display many affinities with discussions found in noted savants of the past such as Leibniz, Kant, Bolzano and Whitehead. Nonetheless, that was then and this is now, a consideration that leaves the discomfited puzzled by the fact that the modern discussions forge ahead relying upon the strongly classical terminology of older days. Consider the following passage from J. R. G. Williams, typical of this literature: People once took atoms to be physically indivisible units sitting at the most fundamental level of reality. Advances in science showed that atoms could be decomposed into further micro-particles; and, on the standard model, quarks, bosons and leptons are held to be indivisible units. But just as the atoms role was supplanted by quarks, future discoveries may reveal that the quarks decompose into yet more fundamental entities: sub-quarks. And below the sub-quarks there could lie further layers of reality. Imagine this process of discovery proceeding ad infinitum; in such a scenario, every kind of micro-particles would be underlain by smaller entities. This would be a world of infinite descent: in such a scenario, there is no most fundamental layer of particles. 2 This characterization serves as a prelude to a strange (in my estimation) debate whether a certain thesis of metaphysical nihilism is wholly necessary, viz., that the only physical entities that truly exist are nature's most fundamental and smallest physical parts. I dont propose that we follow Williams into these mists; let us linger with the conception of smallest part that propels him onward. From modern physics point of view, the most striking feature of this

-2passage is that it employs strongly classical terminology quite freely--specifically, in its unshaded appeal to part--in application to inherently quantum phenomena such as the behavior of quarks et al. Yet one of quantum mechanics many foibles lies in the fact that its basic phenomena do not appear to be neatly localizable: critical events occur only within some loose and relatively ample effective volume that can be spatially sharpened only at the cost of gaining ruinous uncertainty with respect to momentum. True: to the best of our knowledge, electrons and quarks act as dimensionless scattering centers, but this phrase encapsulates a technical concept that does not align neatly with trackable, localized positions. A better analogy for thinking of the compositional parts of a quantum system is to consider the overtone components found within a vibrating string. To unravel its complicated patterns, physicists (under the heading of Fourier analysis) allocate different packets of energy to sundry vibrational modes hidden in the string: firstly, to its simple back and forth sine wave movements that transpire at, for example, 440 cycles per second; secondly to the doubled octave movements that leave the half-way point of the string fixed;-- and so on, running through a spectrum of increasingly rapid patterns of movement, in an infinite ascent that runs through its possible overtones. Scientists often describe this energy decomposition in particle terms: they declare that the string is composed of phonons, here regarded as the quanta of an acoustic disturbance. However, in the case at hand, it should be recognized that such phonons are not unique (other manners of decomposition can prove salient) nor are they spatially smaller than the original string; they coexist over exactly the same region as its entire cord. Their part of a string nature is explicated in terms of the smaller quantities of energy that each phonon mode stores, not because these specialized patterns display any further measure of spatial localization. Within a true quantum setting, the entire particle notion becomes considerably stranger, for many of these only exist in a virtual manner that manifest a large array of utterly queer features. But if we wish to debate the ontology of the real universe, we should be wary of leaning upon part in Williams' manner. In truth, few scientists (except impetuous dogmatists) pretend that we understand the ontology of quantum mechanics well at the present time. A few splinter groups (e.g., the school of David Bohm) assign quantum behaviors more sharply localized trajectories than meet the eye, but such views are scarcely accepted as orthodoxy today. Surely, as long as such substantive interpretational difficulties persist, our new metaphysicians should be wary of hastily importing classical assumptions about fundamental particles, their spatial parts and trajectories into the quantum realm. Yet, to all appearances, Williams has done

-3precisely that in the passage quoted above. It would also seem, from my limited sampling of the literature, that many allied philosophers freely imitate Williams in his classically-biased rashness, evoking classical spatial part in contexts where basic quantum experience would advise greater caution. Such morose reflections suggest that prudent metaphysicians might set some of their favorite projects on hold until the happy day that we unravel quantum behavior in a more satisfactory manner. Yet no such restraint seems evident. Why? A popular manner of reply appeals to the fact that we still evoke the classical notion of spatial part quite profitably at the macroscopic level in both everyday life and engineering; indeed, spatial part proves exactly the stuff of which the substantial branch of modern engineering known as continuum mechanics is made. The continuum approach captures a possible way the world might be, a reply to our doubts elaborates, so we metaphysicians, in our wide ranging toleration of possible circumstance, should wish to understand how part of behaves in classical possible worlds like these. Indeed, the story of how modern continuum mechanics addresses the classic worries about continuous matter found in the great philosopher/scientists of the past is both fascinating and informative (this essay will outline its basic contours). In this regard, however, such philosophers fail to appreciate that the modern technical work suggests surprising conclusions that often do not conform happily to their possible world expectations. In particular, applied mathematicians usually rationalize their conceptual innovations as the mathematical tools that naturally emerge when one anti-averages, on a macroscopic level, over an underlying base of quantum fact. The expectation is never to produce the complete worlds anticipated in metaphysical speculation, but merely to extract useful descriptive fragments that can successfully clock a complex macroscopic system over a certain range of behaviors (outside of that range, it is expected that direct attention to phenomena at a lower size scale will be required). Nonetheless, insofar as any hope remains for providing precise mathematical accounts of the classical possible worlds filled with continuously distributed matter prized by our metaphysicians, these constructions must utilize technical innovations akin to the delicate procedures fashioned by modern experts in continuum mechanics for their own purposes (for brevity's sake, let us dub the desired constructions blob worlds in the sequel). In other words, a self-consistent blob universe suitable for metaphysical speculation will need to be fitted out with shock fronts, Young's measures and the allied innovations to be surveyed in this essay. But such supplements frequently render Williams-like appeals to smallest spatial parts

-4murky or problematic. My primary aim in this essay is to provide a gentle introduction to some of these unfamiliar constructions for a philosophical audience. Let me reframe these motivating observations in more general terms. When we probe our ordinary conceptions of what physical object X might possibly do carefully, our answers actually open out into a hierarchy of claims structured in a scale-sensitive manner that I elsewhere call the lousy encyclopedia phenomenon.3 That is, we normally provide partial answers S 1, S 2, S 3,... whose validity obtains only locally and up to a certain scale of resolution. When we require possibility answers with a larger range of validity, we find that we must often override our old answers with a substantially altered set S* 1, S* 2, S* 3,... In many natural situations (including classical blob talk), this series of replacements never reaches a stable bottom. But new metaphysicians rarely anticipate that everyday possibility talk will prove structured in this localized/lousy encyclopedia manner, but instead adopt tacit globalized assumptions of the sort outlined in section (ii). The chief moral of this essay is to warn against philosophical tropisms of this ilk. However, there is an interesting wrinkle that complicates this simple dichotomy about possibility talk in the case of classical blobs. Twentieth century mathematicians have discovered a wide range of sophisticated ways in which the utility of basic S1, S2, S3 talk can be maintained far beyond the oldfashioned limits where we would be otherwise forced to adopt S* 1, S* 2, S* 3 replacements. But as these stay on the S 1, S 2, S3 level e