#gary l. herstein

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By “eternal objects,” Whitehead means possibilities. We will use the terms “possibility” and “eternal object” interchangeably (as indeed we have been doing up to this point), but we favor the term “possibility.” There are those among Whitehead’s interpreters who are misled by the name Whitehead chose for this category of entities. Some seem to think that Whitehead must be “naturalized,” and that eternal objects are somehow non-natural or even unnatural. The term “possibility” is much less confusing on this point. Anyone who wants to rid Whitehead’s philosophy of eternal objects is actually attempting to cut out the category of possibility. It is neither necessary nor possible to do that while preserving any semblance of the philosophy of organism. Taking possibility seriously is a requirement of all process philosophy.

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… we feel all actual occasions in our actual world, but only a selection of the possibilities is felt… It does not follow that the unfelt possibilities do not exist, or exist only in a Platonic realm of forms, as the caricature of Whitehead maintains. Such views trade in the obligation to account for the reality of determinate modes of order in our cosmic epoch for a crypto-determinism in which possibility has no role in limiting real potentiality. To dump the eternal objects is the same as reductionism, and many of the so-called naturalists are committed to the materialism Whitehead criticized in Science and the Modern World. That was not their intent, but eternal objects are indispensable to Whitehead’s cosmology, and they are not “Platonic forms” or “universals,” if by that one means that they are non-natural.

Randall E. Auxier and Gary L. Herstein, The Quantum of Explanation: Whitehead’s Radical Empiricism

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… according to Einstein the very geometry of space is contingent and variable, its nature at any given point being dependent upon the varying influences of matter and energy throughout the universe upon that point. And here we have the crux of the measurement problem of cosmology. If the structure of space is a contingent aspect of physical influences, then we must first know the nature and distribution of those physical factors before we can know the geometry of any spatial region. But in order to know this distribution of physical factors, we must be able to make accurate and reliable spatial measurements properly to place and relate those contingent, physical influences upon any given point of space. But in order to make accurate and reliable spatial measurements, we must have a robust understanding of the geometry of the spaces in and through which we are measuring. Only with this latter can we understand the effects on our standard unit of measurement of the non-uniform and contingent projective relations of those spaces, and thereby establish a logically meaningful system of conjugacy with the things to be measured. Yet such a robust understanding of the geometry of space is precisely what we do not have, and cannot establish, for it is exactly what GR refuses to grant us. We must know the complete distribution of matter and energy in the universe prior to knowing its geometry. But we must have a comprehensive grasp of this geometry in order to discover this distribution. As Whitehead pointed out, with GR as our theory of space and gravity, we are saddled with a situation where we must first know everything before we can know anything.

… if the very geometry of space is something we cannot know until after we can confidently engage in measurement, then cosmology as a science teeters on the brink of nonsense. For while we must first measure before we can know, GR requires that we know before we can measure.

… And yet, GR appears to be successfully employed in formulating and evaluating cosmological measurements all the time. Indeed, general relativity and quantum mechanics are often held up as the premier examples of the most successful physical theories ever conceived. How are we to reconcile such practical successes with the supposed philosophical issues raised above?

The question almost undoes itself in the asking, for it is a well-known fact that these two theories are mathematically irreconcilable. But it is not just at the small scales of micro-physics that GR runs into problems. At the very large scales of physical cosmology, GR has also proven to be inadequate. In an effort to account for observed phenomena—phenomena of which physicists assume they have meaningful measurements—it has been necessary to reintroduce the idea of the “cosmological constant,” as well as to invent such extravagant new ideas as “dark matter” and “dark energy” in an attempt to account for the evident behavior of the cosmos.

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… It was [Whitehead’s] observation that if we do not maintain the separation between geometry and physics, then we lose the logical basis of the rules for conjugacy and projection that make spatial measurement possible. …

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So instead of Einstein’s “mono-metrical” approach, as we have termed it, Whitehead proposed what has now come to be known as a “bimetric” solution. Instead of shoe-horning all of the metrical relations into a single tensor (the “gμν”), collapsing geometry and physics, Whitehead’s theory utilized two metrical tensors: His “J” tensor representing the contingent physical relations of gravity and other forces, and his “G” tensor or the necessary spatial relations of geometry. …

… There are now many other members of this class than just Whitehead’s, and many of these theories are known to be viable alternatives to GR. Each of these bimetric theories separates the geometrical relations from the contingent facts of physics, and thus they have the required level of uniformity available to them to permit of the projective relations needed for meaningful measurements.

It is a matter of no great philosophical relevance whether Whitehead’s specific scientific proposal still offers a viable alternative to GR. Whitehead himself never viewed this as anything more than an application of his general philosophical principles. What we have instead is much more interesting: a developed system of philosophical ideas that are well vindicated by an entire family of scientific exemplars that are known to be formally and empirically valid. Moreover, these alternative theories are also much more linear in their formulations. This means that testable predictions can be calculated directly from these theories, and that they are far more easily reconciled with quantum mechanics.

Randall E. Auxier and Gary L. Herstein, The Quantum of Explanation: Whitehead’s Radical Empiricism

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It seems at least a little ironic that it should be a mathematician reminding us that comprehensive explanation depends not only upon empirical adequacy and logical coherence, but also upon the “narrative intelligibility” of an account as well. That is to say, no small part of the explanatory force of an idea comes from the kind of appreciation that only emerges from a pan-synoptic grasp of the whole that is both cognitive and felt, this latter term being chosen quite deliberately.

Randall E. Auxier and Gary L. Herstein, The Quantum of Explanation: Whitehead’s Radical Empiricism

[perkwunos]

As Whitehead says, “the region is, after all, divisible, although in the genetic growth it is undivided.” You can dissect the frog and you can actually divide organic spaces, but not while maintaining the organicity. It is often overlooked that perception and judgment have the same sort of organicity at a different level of generality. In short, meaning genuinely exists, but its type of presentational space doesn’t survive actual division into subjective and objective sides. Value accrues organically as well …

Randall E. Auxier and Gary L. Herstein, The Quantum of Explanation: Whitehead’s Radical Empiricism

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One notable group of computer scientists is working on the formal and practical characteristics of the artificial intelligence of visual processing. A less technical phrase for that would be “the folks trying to teach robots to see.” It is a widely acknowledged fact in this sub-discipline that Alfred North Whitehead’s work on extension is foundational for their enterprise. Our experience has been that Whitehead scholars are simply astounded to learn of this fact. Yet we should have expected and even predicted such a connection. After all, Whitehead was digging into the fundamental structures of perception as these connect directly to nature and natural philosophy. Meanwhile, the only way a computer scientist will ever teach a robot genuinely to see is by becoming a radical empiricist about visual and spatial relationships.

Randall E. Auxier and Gary L. Herstein, The Quantum of Explanation: Whitehead’s Radical Empiricism

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At first blush it might seem odd, even unreasonable, to speak of a mathematician as a radical empiricist. After all, a mathematician trades in high abstractions, while radical empiricism is about the concrete fullness of experience. However, this way of phrasing matters rushes past essential aspects of that very experience which we are supposed to be attending to. Specifically, experience in its concrete fullness includes multiple layers and dimensions of robust relational connections as an ineliminable component of that concreteness. James spoke of the immediate experience of such relations as “and,” “or,” and “but.” However, these terms represent only the thinnest and most tepid of the relational possibilities to be found in experience. Other relations include such things as rotational and translational forms of symmetry, congruence (an example that Whitehead frequently uses), continuity, and discontinuity, whole and part. When we look at such relations in their purest forms—and this is true of “and,” “or,” and “but” as well—our inquiry has centered itself solidly within the field of mathematics. Absent a thorough grasp of mathematical reasoning, the true wealth of relational connections that infuses our experiences might easily be overlooked for its subtlety.

Randall E. Auxier and Gary L. Herstein, The Quantum of Explanation: Whitehead’s Radical Empiricism

[perkwunos]

The search for a proper theory of extension or spatiality was the guiding thread in all of Whitehead’s philosophizing, culminating in the infamously impenetrable Part IV of Process and Reality, wherein Whitehead invents what has since come to be called mereotopology (current applications include programming the visual systems of robots). But his magnum opus is titled Process and Reality, not Extension and Reality. Why?

In a second edition of Principles of Natural Knowledge (202), Whitehead writes:

“this book is dominated by the idea that the relation of extension has a unique preeminence and that everything can be got out of it. During the development of this theme, it gradually became evident that this is not the case…[T]he true doctrine, that ‘process’ is the fundamental idea, was not in my mind with sufficient emphasis. Extension is derivative from process, and is required by it.”

… Auxier and Herstein argue for the continuity of Whitehead’s thought by pointing out that already in A Treatise on Universal Algebra (1897) Whitehead was hard at work on the problem of spatiality (QE 63). I agree with them that Whitehead’s theory of extension is the golden thread linking his work in mathematics, physics, philosophy of science, cosmology, and metaphysics. There are no sharp breaks or revolutions in the story of his philosophical genesis, but there is evidence of a gradual shift in Whitehead’s thought toward an emphasis on the creative originality of process and its accretion of value over the pure possibility of extension. Yes: process requires extension to express itself. But extension, and the process of extensive abstraction by which we come to know anything about it, are functions of process. The primality of process or tension as such over extension is part of what follows, I would think, from Auxier and Herstein’s stated radical empiricism, “that concrete existence explains the abstract aspects of experience and not vice-versa.”

Matthew T. Segall, Whitehead’s Quantum of Explanation: Thinking with Auxier and Herstein

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While [An Enquiry into the Principles of Natural Knowledge] is much more formally technical than [The Concept of Nature], both books share a common and radical view of nature and science that rejects the identification of nature with the mathematical tools used to characterize its relational structures. Nature for Whitehead is that which is experienced through the senses. For this reason, Whitehead argues that there are no such things as “points” of either time or space. An infinitesimal point is a high abstraction with no experiential reality, while time and space are irreducibly extensional in character.

To account for the effectiveness of mathematical abstractions in their application to natural knowledge, Whitehead introduced his theory of “extensive abstraction.” By using the logical and topological structures of concentric part-whole relations, Whitehead argued that abstract entities such as geometric points could be derived from the concrete, extensive relations of space and time. These abstract entities, in their turn, could be shown to be significant of the nature they had been abstractively derived from. Moreover, since these abstract entities were formally easier to use, their significance of nature could be retained through their various deductive relations, thereby giving evidence for further natural significances by this detour through purely abstract relations.

Whitehead also rejected “objects” as abstractions, and argued that the fundamental realities of both experience and nature are events. Events are themselves irreducibly extended entities, where the temporal / durational extension is primary. “Objects” are the idealized significances that retain a stable meaning through an event or family of events.

It is important to note here that Whitehead is arguing for a kind of empiricism. But, as Victor Lowe has noted, this empiricism is more akin to the ideas of William James than it is to the logical positivism of Whitehead’s day. In other words, Whitehead is arguing for a kind of Jamesian “radical empiricism,” in which sense-data are abstractions, and the basic deliverances of raw experience include such things as relations and complex events.

Gary L. Herstein, IEP article for Alfred North Whitehead