Whitehead’s Early Harvard Period, Hartshorne and the Transcendental Project

Whitehead at Harvard, 1924-1925

Brian G. Henning (ed.), Joseph Petek (ed.)

 

CHAPTER 12

Whitehead’s Early Harvard Period, Hartshorne and the Transcendental Project 

 

George W. Shields

https://doi.org/10.3366/edinburgh/9781474461351.003.0013 Pages 226-268

Published: February 2020

Abstract

In this chapter, George Shields compares Whitehead’s Harvard lectures to the philosophy of Charles Hartshorne, arguing that the two are united in defending the possibility of a ‘transcendental project’ and an ‘ontological approach’. The chapter argues that for both philosophers, ‘something exists’ is a necessary postulate, ontology precedes epistemology, that their critiques of Kant’s noumena are sound and their return to pre-Kantian modes of thought is justified, and that formal logic and mathematical analysis are wholly necessary in philosophy.

Keywords: Alfred North Whitehead, Charles Hartshorne, Kant, philosophy, ontology, epistemology

Subject: Metaphysics

Introductory Remarks

When Whitehead arrived at Harvard in Fall 1924 and delivered his first Lowell lecture, ‘Philosophical Presuppositions of Science’, most of the assembled audience of philosophy majors, graduate students and faculty were not receptive to his apparent interest in the grand questions of cosmology and metaphysics. In fact, most were quite perplexed, as they had expected a display of the technical scientific mind behind the Enquiry Concerning the Principles of Natural Knowledge and his (at the time) much-read The Concept of Nature. The mood of the majority was well described by R. W. Miller’s remembrance:

The opening lecture plunged us into a morass of absolutely unintelligible metaphysics … [Whitehead’s] longest and most difficult sentences all ended … with the gleaming words, “. .. you know.” We, of course, didn’t know anything, so far as that lecture was concerned. When the hour ended we were completely baffled and in despair about the course, but we were also all in love with Whitehead as a person, for somehow the overwhelming magic of his being had shown through.¹

Miller was typical of the students assembled: concern with questions of epistemology and a focus on the perspectives of Hume and Russell accompanied by little interest in grand-scale metaphysics was the prevailing orientation of the day. In Victor Lowe’s pithy expression, ‘profundity was out, cool analysis was in’.² However, a minority of the audience members were quite sympathetic to the direction of Whitehead’s thought, including the unflappable metaphysician William Ernest Hocking and Department of Philosophy p. 227 Chair James Haughton Woods, the specialist in Sanskrit and Indian philosophy. k Had Charles Hartshorne, often regarded as Whitehead’s greatest ‘intellectual descendant’, been present, he surely would have sided with his former professor, Hocking, and former chief advisor, Woods. For, one year and some months earlier, Hartshorne had produced an ambitious 306-page PhD dissertation in the tradition of grand systematic metaphysical philosophy entitled ‘An Outline and Defense of the Argument for the Unity of Being in the Absolute or Divine Good’. Hartshorne returned to Harvard in Fall 1925, after completion of his Traveling Sheldon Fellowship in Europe. He was then made Instructor in Philosophy and Research Assistant, assigned to Whitehead. This assignment initiated a personal relationship with Whitehead in the early Harvard period (lasting from 1925 to 1928) that would affect Hartshorne’s entire subsequent career and consequently would profoundly shape the direction of Whitehead studies throughout the twentieth century and beyond.

The exact nature of this relationship, however, has been the subject of considerable scholarly discussion. Hartshorne himself has declared that, contrary to the frequent descriptions of him as a ‘disciple of Whitehead’, and the common practice of mentioning ‘Whitehead and Hartshorne’ together in the same breath, in fact he has been an original philosopher in his own right, and his encounter with Whitehead (as well as Peirce) could be characterised, not as one of discipleship, but rather as one of ‘pre-established harmony’. He says that, in his doctoral thesis, he had already ‘reached the main outlines of the philosophy to which I still adhere … [but his encounter with Whitehead showed him] a coherent system containing most of the significant ideas which I had detected as scattered fragments in various twentieth century philosophers’ (WP, 112).

In a now deservedly famous essay on ‘Hartshorne ’ s Early Philosophy’, William Ladd Sessions expounds upon this theme at some length and shows that a close study of Hartshorne’s thesis on ‘The Unity of Being’ asserts major philosophical tenets that Hartshorne would hold in his mature philosophy: for example, the basic doctrines that experience is socially structured, that experience and value are coeval, that temporal process is objectively real, that the future is open to determination, that not even God can absolutely determine other entities who have some autonomy of decision, etc.³ Consequently, Whitehead provided primarily the means for clarification and deeper elucidation of such tenets but was not the source of such tenets. However, Sessions does not touch upon a number of issues that lie underneath the concerns with specific material doctrines that preoccupy his discussion. In particular, and what will be the focus of this essay, is the deep and mutual commitment to the very possibility of metaphysics, or to use the p. 228 contemporary parlance favoured by Karl Otto-Apel and Franklin Gamwell,⁴ the possibility of the l, ‘Transcendental Project’ – that is to say, the limning of the presuppositions or preconditions of all coherent discursive thought. In this essay, I shall argue that what Sessions and David Griffin have intimated – namely, that there is a sharp divergence between Whitehead and Hartshorne on the topic of the Ontological Argument – requires important, perhaps even severe, qualification. My contention is rather that, while Whitehead was certainly not a proponent of any detailed historical version of the Argument as found in Anselm or Descartes or Leibniz, etc., he nonetheless was a proponent – from the Principia through the Harvard Lectures, Process and Reality and Modes of Thought – of what Hartshorne calls the ‘essential argumentative kernel’ of the Ontological Argument, that is to say, Hartshorne’s ground-level Principle Zero (or ‘P-Zero’), the proposition that ‘something exists is a necessary truth’ (PCH, 571). Indeed, in Process and Reality, Whitehead will quite explicitly connect the necessity of this proposition with ‘the primordial power’ of the universe or with an eternal ‘aboriginal actuality’ – in effect, God – via the Ontological Principle and the Principle of Process that God aboriginally exemplifies (PR, 21-4, cross-indexed with 345 for God’s

consequent nature as ‘everlasting’ and primordial nature as ‘infinite’). Importantly, the probity of the Ontological Argument’s essential kernel and the possibility of the Transcendental Project are intimately connected, since justification of this kernel is ipso facto justification of the Transcendental Project; as the Scholastic logicians would famously have it, ab esse ad posse valet consequentia (idiomatically translated: ‘from what is assertorically the case, we may validly infer what is possibly the case’). In effect, the Transcendental Project is possible precisely because there are actual examples of Transcendental Argument which appear to be sound and which appear to stand up against critical scrutiny.

As this volume intends to reflect upon and celebrate Whitehead’s Harvard lectures, I shall put a special focus upon various passages in the lectures which are relevant to the two connected themes of the possibility of the Transcendental Project and the precise nature of the special relationship between Whitehead and Hartshorne. With these basic themes in mind, in the following essay, I wish to argue that Whitehead’s Harvard lectures display a philosopher who is convinced of the following positions – each shared by Charles Hartshorne – that could be unified under the banner of the ‘Ontological Approach’ to fundamental questions of philosophy:

• ‘Something exists’ is a necessary, or, as Whitehead puts it, ‘eternal’ truth. This is Hartshorne’s ‘Principle Zero’ (P-Zero). This truth is a precondition for all coherent thinking, a position corroborated by the doctrine of Principia Mathematica that the universe of discourse cannot be empty.

1. 229 2) l, Because P-Zero is a precondition of all coherent thinking, it follows that ontology precedes

epistemology, not vice versa as in the apparently prevailing opinion at Harvard in 1924-25. Philosophy begins, for Whitehead, with the ontological, with the encounter with something given.

• However, any adequate ontology must coherently ‘make room’ for a plausible epistemology. In the Harvard lectures, Whitehead develops this motif by suggesting the main theme of his work on Symbolism, namely, the important distinction between prehension in the mode of causal efficacy and in the mode of presentational immediacy. Here the doctrines of Hume and Kant are taken as foils for Whitehead’s epistemological outlook. In effect, Whitehead presents a reversal of Kant’s ‘Copernican Revolution’. Parallel to this, Charles Hartshorne’s later synthesis of ‘realism and idealism’, while in some respects anticipated in his Harvard dissertation, requires the crucial addition of Whitehead’s event (as contrasted with substance) ontology. Consequently, if the Principle of Universal Objectivity (in particular) is to be preserved, an event ontology is logically required for the systemic coherence of his (Harts-horne’s) synthesis. Thus, the interpretation of Hartshorne as standing in ‘pre-established harmony’ with Whitehead is here profoundly qualified, since, in at least the case of Universal Objectivity, Whitehead is its ultimate source.
• Correlated with the above, Whitehead’s Harvard lectures present a critique of Kant’s crucial distinction between the noumena or things-in-themselves altogether outside the Categories of the Understanding and the a priori forms of intuition and the phenomena which are subject to the Categories and the a priori It will be argued that this critique is sound, and thus a principal objection to P-Zero, an objection advocated by Richard Rorty, is undermined. Contra Rorty, there are no noumena to be taken as pure existential surds, and thus P-Zero remains unscathed by Kant’s doctrine of noumena.
• Whitehead’s Harvard lectures present us with a philosopher who possesses a ‘global’ approach to philosophical problems, an approach characterised by ‘balanced definiteness’ in Hartshorne’s felicitous expression. In effect, in doing metaphysics or speculative philosophy in any adequate way, philosophers must avail themselves of the resources of formal logic and mathematical analysis, balanced by appeals to phenomenological and intuitive considerations, as well as the aesthetic
  sensibilities of poets and novelists. The appeals to all of these components are thus never merely adventitious to the endeavour of philosophy.

In course I shall offer various defences of these theses against some important potential objections, but will p. 230 also offer some corroborating arguments u from philosophers outside the ambit of process philosophy (wittingly from James F. Ross and unwittingly from W. V. Quine) – thus illustrating the indispensability of P-Zero as a precondition of rational thought. In effect, I not only wish to offer an interpretation of Whitehead in the early Harvard period (HL1, SMW, RM and PR included) which emphasises his agreement with Hartshorne on a broad Ontological Approach to philosophy, but also to argue that both Whitehead and Hartshorne are in fact correct in this approach, and that consequently the detractors of metaphysics or ‘ a priori ontology’ or the Transcendental Project are patently wrong. Thus, the focus here is not only on historical interpretation, but on considerations of much contemporary relevance. The latter focus represents an important philosophical contention in an era still dominated by anti-metaphysical tendencies among large swaths of philosophers and humanities scholars generally.

The Primacy of Metaphysical/Ontological Inquiry Over Epistemological Inquiry

Given the evidence provided by Victor Lowe and by reports of many of Whitehead’s graduate students attending his early Lowell lectures and seminars in metaphysics and philosophy of science,⁵ the intellectual atmosphere at Harvard was strongly influenced by C. I. Lewis’s focus upon epistemology and Kant’s critical philosophy, and by the so-called New Realism of Ralph Barton Perry, which was fundamentally oriented towards epistemological questions. Epistemology was primary and metaphysics (if engaged at all) was secondary. Whitehead’s fundamental inclination was, as it were, to swim against the Harvard tide. This is, of course, not to say that, for Whitehead, epistemological inquiries were unimportant or unnecessary, since, for instance, his earlier Principles of Natural Knowledge was preoccupied with questions concerning the foundations of empirical scientific knowledge. In fact, in his first year Harvard course he asserts at HL1, Lecture 76, Bell’s Notes, 5 May 1925, 363 that ‘[The] test of self-consistency of any ontology is in its possibility of giving a place to epistemology.’ However, epistemology defined as inquiry into how knowledge is possible is not ‘the first step in Philosophy’ (HL1, 363). Ontological inquiry is first: ‘You can’t express yourself until you have a minimum of ontological doctrine – i.e. a certain general description of what is known. … That’s ultimately based on your apprehension of the immediate occasion’ (HL1, 363). Here the encounter with reality, with the actual occasion, is the starting point. This affirmation of the primacy of encounter with the actual occasion is logically connected to Whitehead’s aversion to Kant’s phenomenalism and doctrine of noumena (see discussion below).

1. 231 This also clearly seems to be Hartshorne’s orientation from the dissertation through the mature works, and surely counts as an important part of the ‘pre-established harmony’ with Whitehead. For, in the PhD thesis, being and knowledge are coincident, and every experience is by virtue of its very constitution an encounter with being; this is also to say that every experience is somehow, however obliquely or subliminally, an experience of God (cf. the chain of arguments regarding the interconnectedness between being, value, knowledge and God (OD, 210-81)). The latter doctrine becomes a mainstay of Hartshorne’s metaphysics throughout his career, although it later receives a technical Whiteheadian refinement as the ‘total prehension’ of the divine consequent nature with its cues, impulses or desiderata for the temporal and contextual situation (cf. DR, 142). Moreover, a phenomenological insight that Hartshorne embraces from the ‘Unity of Being’ thesis to his essays on Husserl and most complete statement on phenomenology in his ‘My Eclectic Approach to Phenomenology’ (CRE, Ch. 5) is another way of stating Whitehead’s ‘ontological minimum’: every experience is ‘experience of’ something that is not itself identical to the experience, and so all experience has an immediately social structure. This is clearly in line with Whitehead’s declaration of
   an ‘ontological minimum’ that involves immediate apprehension of the objective occasion. This ‘first step’ in philosophy, I suggest, evades all the modern epistemological anxieties about external realism, subjective idealism, solipsism and the Husserlian need for an epoche. As Hartshorne would more fully articulate this perspective when responding to the transcendental idealism of Husserl’s Ideen and Cartesian Meditations: Every experience is already contact with reality extra mente, since every experience is analysable as involving bodily occasions, indeed neuronal occasions, as data of the experience. In effect, a full account of ‘experience of’ requires the positing of a content of the experience which is really independent of the experience. For consider: ‘No experience is merely “of” that very experience, nor even merely of an earlier moment in the same stream of experiences [it would then simply be indistinguishable from that earlier moment], nor can merely “intending” an object that may not exist constitute the “of” in “experience of” [because the projection of possibilities is grounded somehow in actual objects of experience]’ (IO, 275).

It is also to be noticed that Whitehead’s insistence upon the primacy of the ontological, yet within the context of an ontology that has ‘room for’ or logically accommodates an epistemology, is well illustrated by Hartshorne’s brilliant and now classic essay on synthesising epistemic realism and ontological or ‘objective’ idealism (‘A Synthesis of Realism and Idealism’ reprinted as chapter 8 of ZF). Here Hartshorne p. 232 argues that ontological and epistemic l, theses of certain types are not only logically compatible, but are mutually complementary; respectively, the Principle of Objective Independence (objects exist outside the knowing subject), the Principle of Subjective Dependence (every subject derives some of its character from entities of which the subject is aware), the Principle of Universal Objectivity (any entity must be or be destined to become an object for some subject or subjects), and the Principle of Universal Subjectivity (any concrete entity is a subject or set of subjects such that any other concrete entity or entities of which it or they are aware is also a subject). Importantly, Whitehead is explicitly listed as the one philosopher who upholds all of these doctrines (see ZF, 138-9). I would suggest that through his emphasis on the ‘coming together’ of entities and ideal forms in process and the development of the concept of prehension in the first year of Harvard lectures (examine, e.g., HL1, 162-5, 243, 473, 487 and also SMW, 69, 148), Whitehead enfolds all of these general ‘core’ doctrines of process philosophy. For prehension as the mechanism of causal influence involves internal relatedness to or dependence on data being prehended by the subject of prehension, but involves external relatedness to or independence of the subject of prehension on the part of the data prehended. This logically enfolds all four principles, by definition. Thus, Hartshorne’s synthesis here is a thoroughly Whiteheadian one. But I point out that it is not at all clear how at least the Principle of Universal Objectivity could be embraced by the monistic substance philosophy of the dissertation, since Universal Objectivity requires a notion of unit events or occasions and a clear notion of prehension as the fundamental concept of causal influence (substances are what they are over time and only accrue accidental properties externally), but both of these notions (unit-events and prehensions) are absent from the dissertation. With the loss of Universal Objectivity, as with any other of the four principles, the systematic character of Hartshorne’s ontological-epistemic synthesis would be suborned. Thus, the exposure to Whitehead in achieving this synthesis is critical and transformative. This is a profound qualification of the ‘pre-established harmony’ thesis.

The Starting Point of Metaphysics: ‘Something Exists’⁶

The Argument from Logical Foundations⁷

Let us consider Hartshorne’s central tenet of neoclassical metaphysics, held at least as early as the thesis on ‘The Unity of Being’, namely, the proposition that ‘something exists’. For Hartshorne, this proposition is p. 233 necessarily true; consequently, Kant and Hume were wrong in their widely held doctrine that l, ‘“something exists” and “nothing exists” are both contingent propositions’, implying the possibility of an absolutely empty universe. Hartshorne holds that this often uncritically examined ‘dogma’ of modern philosophy is in fact incoherent and self-defeating upon careful reflection. For ‘something exists’ passes the two critical tests for genuine metaphysical status: 1) by deflnition, the proposition is verified by every conceivable state of affairs or state-description, and 2) it cannot be falsified by any conceivable state of affairs or state­description. For consider: ‘nothing exists’ – the logical contradictory of ‘something exists’ – cannot be verifled in principle since any attempt at veriflcation would posit a veriflcation-event which would in turn falsify ‘nothing exists’.⁸ This result in turn entails that the contradictory of ‘nothing exists’ cannot be falsified. Yet, further, this ‘something’ cannot be fundamentally abstract, since the abstract is always in the concrete not vice versa, that is to say, all abstraction is intelligible only as abstraction from the concrete. For instance, where virtually any illustration will do, the abstraction ‘redness’ refers to a class of red hues instantiated in red perceptual objects. (Hartshorne is prepared to defend this Aristotelian principle against numerous objections.) Thus, ‘necessarily, something exists’ becomes quickly ramified into what Hartshorne calls ‘the essential argumentative kernel of the ontological argument’, namely, the proposition that ‘necessarily, something actual exists’ or that God (or more minimally the Universe) is always somehow actualised, reflecting the very title of Hartshorne’s Anselm’s Discovery, Part I.

Whitehead likewise holds that ‘something exists’ is an ‘eternal’ truth. In fact, this was a position prepared for even as early as Principia Mathematica (PM). For Whitehead and Russell confront the question of whether the PM universe of discourse can be empty, can make no assumption of objects or entities with certain properties. Their decision was that any such supposition of emptiness would be incoherent, as it would make certain logical principles of the quantiflcational calculus potentially falsified, as in the case of Universal Instantiation: (vx) (Px) ^ (ax) (Px), where ^ is so-called Russellian or material implication. Thus, they adopt the following provision as axiomatic for the PM universe of discourse: (ax) (Fx V ~ Fx) where F is a one-place predicate. In effect, there must be at least one object that either has or does not have some arbitrary predicate F. The incoherence would occur in this way: with an empty semantical domain, (ax) (Fx)would be falsified, as there simply would be no x, but the provisional assumption of (vx) (Px) would then yield a truth-value scenario where the antecedent is presumed T and the consequent F, which in turn falsifies the theorem of Universal Instantiation. (In fact, this result would occur whether we are employing p. 234 Russellian implication or Lewisian strict implication: it can never be logically consistent to draw a l> false consequent from a true antecedent.) Not incidentally, Hartshorne echoes this argument in the following passage in Anselm’s Discovery (283) where he is commenting on the work of German logician Heinrich Scholz:

logic can admit the notion of existential necessity in the form, (x) fx ■* (Ex) fx; properties universally instantiated cannot be uninstantiated, or in other words, logic cannot deal with a simply empty universe. The widest class cannot be empty. The case for this contention, which Scholz himself accepts, seems to me conclusively made by two recent authors, Jonathan Cohen and William [and wife Martha] Kneale.⁹

It is important to notice also that PM logic is a system designed to have cognitive import as a method for formalisation of propositions across scientific domains and ordinary language arguments concerning ‘how
the world is’. Since I would concur with Whitehead’s basic realist epistemological stance, and I would argue, with Kripke, that de re modality with quantification is perfectly intelligible, I see no credible hindrance to the inference from what is required of logic to what is required of ‘the scaffolding of the world’.¹⁰ Logical systems which seek freedom from the constraints of systems with existential import, as in the case of free logics, encounter difficulties in explaining exactly what cognitive import (if any) they have, and exactly how to make their semantical domains clear (see the discussion of free logics below).

I want to consider the ‘argument from the foundations of logic’ in much further detail. For I submit that one of the most powerful counter-arguments against the contemporary Neo-Pragmatist refusal of the Transcendental Project is to show just how, from a number of angles as shown in the following three corroborating arguments (thus providing a strong unifying cumulative case), P-Zero displays pragmatic credentials as it is arguably doing real intellectual work. It does real intellectual work because, as each of the following arguments explicate, its assumption is a presupposition of rational discourse, while its denial seems to be a case of ‘language idling’ in Wittgenstein’s famous expression.¹¹ As it were, the Transcendental Project is pragmatically efficacious, because at least one proposition – Whitehead and Hartshorne’s Principle Zero – provides a transcendental condition for having theses, and is thus not itself a mere thesis among other happenstance theses. As Umberto Eco once insightfully put it, we must eventually face not only the question terminus a quem, ‘What are we talking about?’ but also the deeper pre-linguistic question terminus a quo, ‘Why do we make signs? Why do we even talk at all?’ We make signs, we talk, says p. 235 Eco, precisely because there is something.12 Leibniz’s U question, ‘why is there something rather than nothing?’ – if not shorthand for the question, ‘Why does a universe of finite entities in space-time exist even if God would exist?’ – is to be immediately dissolved, for the only answer there could be is, ‘there is something rather nothing, because there is something’. As the only answer to such a question, and since being is the ‘amniotic fluid’ in which all thought takes place, this answer is neither circular nor trivial.¹³

Three Corroborating Arguments: Ross’s Quantificational Deduction of Existential Necessity, Quine’s Curious Affirmation of Non-Emptiness, and Bergson’s Thought-Experiment with General Non-Being

Ross’s Deduction. It is interesting to notice James F. Ross’s reduction to absurdity proof of precisely Whitehead and Russell’s ‘axiomatic’ existential quantification in his treatise on Philosophical Theology. If correct, Ross’s argument brings out the ‘logical necessity’ of the existentially quantified formula with particular clarity and force (within standard quantificational logic which assumes Universal Instantiation). In the context of showing the demonstrable falsehood of both David Hume’s and Alvin Plantinga’s often repeated principle that ‘no existential statement has a logically contradictory denial’, Ross presents the following argument.¹⁴ I re-state it here with some alterations of format and with a fuller explication of the proof-step justifications:

Since step (12) is a direct contradiction, it follows that the denial of the assumed assertion at step (1) is absurd; thus, step (1) is as logically necessary as the reductio ad absurdum theorem of the propositional p. 236 calculus. Under k Ross’s interpretation of the predicate F as the ‘disjunction of all possible properties and combinations thereof’ (104), it is clear that the assumed denial of the Indirect Proof at step (2) is ‘equivalent to the assertion that nothing exists at all’. Thus, by Indirect Proof, there is at least one existential assertion that is necessarily, not contingently, true. This, of course, means that the proof is directly relevant to Whitehead’s non-emptiness assumption in PM, Whitehead’s later submission of the Ontological Principle (see below), and Hartshorne’s similar arguments for the essential argumentative kernel of the Ontological Argument.

Quine. It is indeed difficult for philosophers to escape commitment to the ‘non-emptiness’ requirement of the Principia, even philosophers who appear to attack the very distinction between necessary and contingent propositions such as, in particular, W. V. Quine, who recall went to Harvard specifically to study the Principia with Whitehead. For instance, Franklin Gamwell, in his important essay ‘On Transcendental Argument’ (see endnote 4), provides a compelling critical discussion of Quine’s arguments on the untenability of the necessity-contingency distinction. As Gamwell perceptively notes, Quine’s underlying idea that purported necessary propositions (upon analysis of the act of defining their constituent terms) cannot succeed in making non-circular appeals to ‘analyticity’ is simply insufficient for showing that such circularity renders a constituent term or proposition ‘senseless’. To the contrary,

The circumstance that a term cannot be defined except by using other terms that presuppose it does not, so far as I can see, make the term senseless. Indeed, the Transcendental Project not only concedes but also insists that any transcendental condition of human thought has this character, since transcendental conditions are presupposed by all thought.¹⁵

Quine is thus merely asserting, rather than properly arguing for, the impossibility of a transcendental argument for ‘something exists’. What I think could have been further argued at this precise juncture is that, not only does Quine fail to give a proper argument for the impossibility of the Transcendental Project, but he also in fact explicitly commits himself to the very proposal that Gamwell has submitted as an exemplar of necessary propositions (thus my

earlier reference to the difficulty of escaping ‘the “non-emptiness” requirement of the Principia ’). It is interesting and important that, in his classic essay ‘On What There Is’, Quine declares that there is one decision about what there is which cannot be a merely ‘ontic’ one, namely, that we must admit some object or another into our universe of discourse. In effect, for Quine, l, what objects exist is relative to and contingent upon the natural or theoretical language we happen to speak, but that we must speak of objects in speaking a natural or theoretical language is inescapable.¹⁶ Even for Quine, then, logic and language commit us to that much ontology, since we cannot speak sensibly of nothing at all. As Ilham Dillman notes in his tightly reasoned (but for my tastes too polemical) treatise on Quine on Ontology, Necessity and Experience, Quine commits himself in this instance to an ontological or non-ontic claim, but then drops it from his philosophical purview altogether and fails to comment upon its significance for the question of existential modalities.¹⁷ Thus, Dillman is indeed correct in claiming that Quine’s overall position in modal theory is self-contradictory: he affirms at least one necessary proposition, namely, the non-emptiness assumption of the Principia, yet also holds that all propositions are contingent or they are nothing at all. This bears witness to the presuppositional necessity of ‘something exists’, and ipso facto issues a forceful objection to the view that all propositions are contingent.

Bergson on ‘General Non-Being’. Another important corroborating argument is suggested by Henri Bergson in his classic Creative Evolution,18 an argument explicitly endorsed by Hartshorne (cf. CS, 245) and implicitly congenial to Whitehead’s references to ‘not-being’ in SMW. Bergson contends that the concept of general non-being is a ‘false problem’ generated by an unwarranted abstract opposition to all being; in fact, meaningful specific ‘negations’ are always upon analysis expressions of a ‘need of substituting for an affirmative judgment another affirmative judgment’.¹⁹ If I say, for instance, that ‘we did not win the game’, I do not assert some absolute privation, but rather imply that other or alternative affirmative states of affairs (for example, that ‘the other team won the game’, or ‘we forfeited the game’, or ‘the game was cancelled’, or perhaps even ‘the result was a tie’, etc.) are to be asserted in place of the affirmative judgement that ‘we won the game’. Negations make coherent sense as functions presupposing and logically attached to affirmative states of affairs. While Whitehead does not explicitly discuss this matter in HL1, he implicitly agrees with Bergson in the 1925 Lowell lectures, for at SMW, 162-3, he speaks of ‘not-being’ as attaching to actual occasions: While no occasion can include an eternal object A in all its determinate relationships, some being contraries, an actual occasion will include some relationships in A and exclude others; thus, an occasion is to be described as a synthesis of being and not-being (‘not-being’ is Whitehead’s actual expression). But, for Whitehead, there is only contextualised or relative not-being – not-being as related to a particular occasion – while there is no reference to absolute not-being or privation. Whitehead is here groping towards the doctrine of negative prehensions developed in PR.

1. 238 However, asks Bergson, what are we thinking when we posit absolute or general non-being? We could only be thinking of being as an abstract collection that then has a complete or total opposition in general non­being, but this presupposes being in its very conception. In effect, general non-being requires a background context of being (taken as noun), and thus it cannot be asserted without contradicting that very background. This is not coherent, and as such is a ‘false problem’ as famously declared by Gilles Deleuze in his arresting lectures on Bergsonism .²⁰

We could gloss Bergson’s contentions about general non-being as the negation of being in the following more logically precise way: The conceptual intention involved in invoking a concept of absolute non-being or emptiness is tantamount to presenting an indefinitely long list of negated states of affairs. Symbolically, we could render this as statement N1, where ‘ nth ’ represents the continual repetition of distinctive negated states through an absolutely unlimited range, indeed, throughout the entire universe of discourse:

N1: { ~A & ~B & ~C … nth}

The conjunctivity of the negated states of affairs is required, since even a single affirmation would be logically sufficient for establishing the counter-thesis that ‘something exists’. Thus, an unlimited range of affirmative statements must each be denied if we are to express the notion that truly ‘nothing exists’. Moreover, it is extremely interesting to notice what occurs when we apply De Morgan’s Theorem to N1. We see that the formula is rendered:

N2: ~ {A VB V C^ nth}

Since N2 expresses a series of disjunctions without any limits whatsoever throughout the entire universe of discourse, and by the standard law of association includes any and all combinations of disjunctions, it is clear that this is tantamount to denying alternativeness itself. But this result is absurd, as it would deny all contingent and all necessary states of affairs (necessity being defined in the modern modal logical sense of ‘what is in common with all alternatives or possibilities’).

It is to be granted that not all philosophers agree that Bergson’s argument establishes the conceptual absurdity of ‘nothing exists’, although such distinguished figures as Hartshorne and Gilles Deleuze (at least as I interpret him) hold that it does. For instance, Donald Viney has called attention to the criticism that Bergson’s argument commits the fallacy of composition:²¹ since each state or attribute is denied, it is a p. 239 fallacy of composition to say that the U composed whole of states or attributes is to be denied. However, this is a misapplication of the fallacy of composition. While it is true that, in the normal case, each class member’s possession of an attribute does not allow imputing that attribute of the composed whole or class, there are notable exceptions where causal relationships are involved – as in, for instance, ‘each particle of this piece of chalk has mass, therefore, the whole piece of chalk has mass’. Likewise, the negation of all members of a class does entail the negation of the class as a whole. If no tigers existed in any particular locale whatsoever, there would be no compositional class of actual tigers. The fallacy of composition does not apply where sheer denials of membership in classes are involved, as in the case of Bergson’s argument.

Perhaps a more challenging objection is posed by Richard Gale. Gale analyses Bergson’s argument in the light of the ‘at least one object’ commitment of Principia Mathematica, and argues that it involves a subtle begging of the question. Consider the proposition that ‘Every object has some property incompatible with unicornness’ (labelled E5 by Gale).²² A proposition such as E5 could be asserted, says Gale, but it would not require that there be at least one object in the universe of discourse, and this shows that Bergson’s reasoning is circular. Writes Gale:

if there were Nothing, no objects, E5 would be true – vacuously true (to use a pun). Bergson might counter that a system of quantificational logic must presuppose that there exists at least one object in the domain over which its bound variables range: without this assumption the rule of universal instantiation faces counter-examples. But why must Bergson’s opponent grant that this is a necessary presupposition?²³

I want to object to this that ‘nothing exists’ as the semantical presupposition for E5 would in fact render E5 as neither true nor false. Rather E5, under such a semantical presupposition, is simply unassertable. For consider: if the semantical domain of the language in terms of which E5 is expressed were completely empty, we should in fact understand E5 as the mere schema: ‘Every is incompatible with

.’ For ‘object’ and ‘unicornness’ are already ‘somethings’; more charitably, at the very least, they involve oblique references to ‘somethings’, and in the case of ‘unicornness’, oblique references to actual objects and attributes such as ‘horns’ and ‘white equines’. Such oblique references are quite impossible if the semantical domain is sheerly empty. Pace the claims for various so-called free logics (see below), a language system does require, as Richard Martin once put it, a ‘non-logical ontology’ in the modern formal p. 240 semantical sense of an ontology as a domain of entities taken as the values for variables and attributes l, or predicables of variables.²⁴ Indeed, how is it possible to explicate the grammatical function of general terms,
individual constants, or predicates in a logical language without reference to non-logical values for the semiotic units we take to represent general terms, individual constants, or predicates? A general term is a different sort of linguistic entity from an individual constant, and rules of quantiffcational logic involved with, for example, restrictions on proper existential and universal generalisations break down if we fail to note the difference. Indeed, how can term difference matter in the case of a truly empty semantical domain? There is an essential matter of content to be discerned in making the distinction between general term and constant.

Gale might well respond that his notion of ‘Nothing’ in the citation above refers to the notion that the semantical domain contains ‘no actual objects’ as the value for the variables present in the existential quantifications that may be included within the scope of N1. If you remove actual objects from the semantical domain of the language expressing E5, E5 would be vacuously true, since, to state the logically equivalent obverse of E5, there would simply be no actual objects that possess some property compatible with ‘unicornness’. However, while this is perfectly legitimate so far as it goes with such a restricted domain, I do not see that it represents a principled refutation of Bergson’s doctrine that the concept of general or absolute non-being collapses into incoherence. This is because it is a logically contingent matter as to whether E5 is true or false if we allow actual objects into the semantical domain; it is true when the semantical domain is restricted to actual objects, but not true in other possible worlds whose semantical domains include, for example, creatures whose DNA instructions include horn sites on the noses of white equine bodies (there is nothing logically impossible about this combination, indeed, some such mutations might have existed in this actual world – I certainly would include a ‘unicorn’ as a possibility ‘accessible’ from the actual world, which can thus be modelled in terms of Kripke semantics for quantiffcational S4). What I find to be unintelligible, what Bergson finds to be unintelligible, is a truly empty semantical domain that simply does not have any objects or attributes – whether actual or ‘potential’; in effect, a semantical ‘domain’ that really is not a domain containing some kind of content, a domain which represents the sheer absence of a ‘non-logical ontology’. But such a situation is what we are presented with on the supposition that ‘nothing exists’ in the absolute sense considered by Bergson; to say otherwise is, it seems to me, not to take into account the metaphysically strong conceptual intention embodied in the supposition that literally ‘nothing exists’. This is why I contend that a truly empty semantical domain at best allows for empty schemas with mere rhemes for object and attribute positions. (And even this would be questionable, e.g., p. 241 how does one explain ‘compatible l, with’ in E5 without objects or attributes as presuppositions for making conceptual connections of ‘compatibility’ or ‘incompatibility’? Note that any example that might be employed to explicate ‘compatibility’ or ‘incompatibility’ would require at least a dyad of objects that would stand in a relation of compatibility or lack of it.) Again, mere rhemes are simply not assertable.

Free logics, of course, are designed to operate with so-called ‘empty domains’, and consequently such logics are constructed in ways that alter the usual quantification rules. (Thus, for example, universal generalisation [UG] in free logic will include a two-step process, where a provisional assumption for free UG is made followed by application of a free UG rule containing three conditions that include the appropriate discharging of provisional assumptions.) However, as I see it, the existence of free logics does nothing to address the properly philosophical issues involved here. This is, again, because their semantics do not represent truly empty domains in the strong metaphysical sense attacked by Bergson, even in cases where we have a so-called ‘null Leblanc-Thomason (LT) structure’, where both the inner and outer semantical domains are assumed to be empty. While the null LT case assumes that the inner domain D is empty, as well as the outer domain D’ (D’ is normally taken to be empty in the non-null LT structures), the way in which D and D’ are described – their ‘nullness’ – comes from the fact that they ‘contain nonexistent [i.e., non­actual] objects ’. They still reference content as in free logic quantiffcational representations of such sentences as ‘Batman is a super-hero’. The concepts involved in such sentences are rich with oblique references to actual entities or attributes, in the case of this example – ‘bats’, ‘men’, ‘courage’, ‘crime fighters’, etc. In fact, we might present a dilemma to anyone wishing to employ free logic as a counter­
example to true non-emptiness of the semantical domain. If a free logic FLhas any cognitive import, i.e., can be used to formalise fictional scenarios, then FLought to assume fictional objects that obliquely reference actual states of affairs. In that case FLis not truly empty. If FLhas no cognitive import, then FLis meaningless (comparable to allowing ‘I ate nothingness’ or ‘nothingness is wigwam’) precisely because it has no semantical domain. In that case, free logics have no point. So, either free logics make oblique references to actual states of affairs and are not truly empty, or they are entirely pointless from a cognitive point of view.²⁵

The Argument from the Ontological Principle

Whitehead shows his commitment to the non-emptiness thesis, at minimum inchoately but discernibly, in among his very first public expressions of metaphysical doctrine in the Harvard lectures. At page 60 of HL1 p. 242 (Lecture 17, l. Bell’s Notes, 1 November 1924), in the context of discussing the ‘prime puzzle’ of the relation between the dipolar concepts of the Eternal and the Contingent, we find Whitehead stating: ‘You’re always pushing the Contingent back and back, but never get quite rid of it. If there’s no Eternal in this sense there’s nothing to be said, no Metaphysics, no Science, etc., etc. It’s because there’s something Eternal that we keep going at all.’ Later in HL1 (Heath’s Notes, 4 November 1924, 446), Whitehead broaches the notion that is central to process metaphysics, i.e., the creative advance as an Eternal process of enrichment. The Eternal is a ‘general envisagement’ that is always ‘relevant to a particular occasion’ and integral to each occasion that demands a ‘solution’ (in the later vocabulary of PR a ‘satisfaction’), and with this ‘solution’ an ‘extrusion of irrelevant detail’ (PR’s ‘negative prehension’ contrasted with ‘proximate prehension’). Once realised, the occasion stands as an ‘eternal enrichment of [the] eternal ground of becoming’ (HL1, 446). The very notion of an eternal ground of becoming relevant to occasions clearly posits P-Zero as ‘necessarily, something actual exists’.

In the language of PR, this assumption of ontological non-emptines s will be codified in the eighteenth Category of Explanation, the so-called ‘Ontological Principle’ (PR, 24). Perhaps we should say more cautiously, ‘necessarily, something actual exists’ is an obvious corollary of the Ontological Principle, since, as Whitehead says when defining the principle, to search for any reason is to search for an actuality or some character of an actuality, and, of course, an actuality counts as ‘something’. Put obversely, ‘utter absence of actuality’ could never serve as a referent for any rational inquiry or discourse because all reference requires reference to something.²⁶

A more refined expression of a Whiteheadian modal or ontological type argument for an Eternal something as ground of contingency is articulated by Hartshorne when drawing upon Whitehead’s later utterance at PR, 72 (Hartshorne is using the original pagination): ‘The general possibility of the universe must be somewhere ’ (my emphasis). Drawing out this passage’s several logical implications, Hartshorne writes:

If possibility is meaningless without existence, then it cannot be that all existents are contingent; for this is to say that the being of possibility is also contingent, that it might have been that nothing was possible … The conclusion of this argument is that there is a primordial power whose nonexistence is not a possibility, since possibility presupposes its existence.

(WP, 80; first italics my emphasis, second italics Hartshorne’s)

Put another way, given, by definition, the eternity of the domain of eternal objects – a view held by p. 243 Whitehead from the very first introduction of this l, vocabulary at HL1, Bell’s Notes, 8 January 1925, 161, where Whitehead also says they are ‘Existences’ but are ‘not real’, which I take to mean not instantiated in an event or actual occasion – any proposed absolutely otiose condition of such domain would be entirely counter-intuitive, like proposing a ‘possibility’ that could never be actualised, yet haunts reality (does ‘it’
then deserve the name ‘possibility’?), and thus there must be a primordial actuality that serves as ground of such potential.

It should be noticed that, if this interpretation of Whitehead is correct, then it follows that, in addition to the other kinds of theistic argument that might be located in Whitehead (surveying the Lowell lectures through Modes of Thought, Hartshorne locates five strains of argument, see WP, 78-83), an ‘ontological type argument’ – that is to say, an argument that turns on logical requirements relating to concepts of modality – must be included. At least at face value, this seems contrary to such treatments of Whitehead’s natural theology as David Griffin’s, which explicitly reject ontological arguments and claim that Whitehead concurs.²⁷ But that the above ought to be classified as an ontological type argument would appear to be borne out by comparison of the line of thought encoded in PR, 72 with Paul Tillich’s argument for an ‘Ontological Approach’²⁸ to philosophy of religion: like Whitehead’s contentions regarding an aboriginal actual ground of potentiality, the power of being²⁹ cannot itself be non-existent because this would entail that potentiality itself could emerge from nothing, from no potentiality at all. (Thus, in effect, as Tillich says repeatedly, God defined as the power of Being-itself is the presupposition of the question of God.) The latter consequent of the above entailment seems conceptually absurd or incoherent, and thus by reductio ad absurdum, the power of being is a presupposition of, a prius of, coherent thinking. The structure of Tillich’s reasoning as given here, where P = ‘the power of being exists’ and x = ‘something exists’, might be symbolised in modal propositional logic as follows:

◊ ~ P ■* (~ ◊ x -» ◊x), but the consequent is a contradiction (where ■* is strict implication as seems required by the de re context of ontological transition from non-being to being), and so by the rule of reductio ad absurdum it follows that ~ (~ ◊ x -» ◊x), which in turn by modus tollens ensures that ~ ◊ ~ P, which by modal definition is equivalent to □ P. Note, again, that the consequent of the original proposition is contradictory in any Lewisian modal system employing strict implication. By modal definition, the use of strict implication in the consequent shows it to be logically equivalent to □ ~ (~ ◊ x A ~ ◊x) – as such this is equivalent to denying the tautologous law of Repetition in every 30 possible world, which is absurd.

p.244 Whitehead, Hartshorne and the Return to Pre-Kantian Modes of Thought³¹

Whitehead’s famous declaration in Process and Reality that the philosophy of organism represents a return to pre-Kantian modes of thought was expressed as early as the first year of the Harvard lectures. At HL1, Bell’s Notes, Lecture 27, 24 November 1924, 113, it is noteworthy that Whitehead begins with the suggestion of a counter-revolution to Kant’s Copernican one: ‘Whitehead trying to turn Kant on his head – without Kant’s “Copernican Revolution”’. This utterance makes complete sense in the light of notions Whitehead is expounding in this and the several subsequent lectures on the role of objects in ‘the coming together’ constitutive of processive events and the concomitant denial of the modern assumption of ‘simple location’ that undergirds the problematic ‘bifurcation of nature’. For Kant’s sharp distinction between the noumena and phenomena is the very embodiment of such bifurcation; as Kant himself realised, if left unqualified, the critical philosophy exposes itself to the charge of unwitting commitment to subjective idealism, or even worse, solipsism.

Kant’s mature doctrine of noumena as developed in the B edition of the first Critique does not in fact provide a coherent example of ‘existential possibilities which are yet strictly inconceivable’, such putative existential possibilities standing as a clear objection to the necessity of the ontological non-emptiness thesis. The argument against the possibility of Transcendental Argument inspired by Kant – as endorsed by Stephan Korner and Richard Rorty³² – is such that, even if ‘nothing exists’ turns out to be inconceivable, it would not establish that ‘nothing exists’ is logically impossible. This allegedly follows from the general principle that what is in fact conceivable does not exhaust the possible, as exemplified by Kant’s notion of
noumena. However, upon careful analysis, I argue that Kant’s noumena do not provide coherent examples of the general principle that certain putative existential possibilities outstrip our capacity of conception. Thus, if Korner and Rorty wish to defend the general notion of existential possibilities which are yet inconceivable, they cannot find support for it in Kant’s doctrine of noumena. I also find that, as early as the Harvard lectures, Whitehead had already anticipated or was committed to the particular objections regarding the intelligibility of Kant’s ‘revolution’ to be explicated below (see my documentation of Whitehead regarding items 1-3 below).

As mentioned earlier, after the original A edition of the Critique had been published for some years, Kant came to realise that the critical philosophy was vulnerable to the charge that it collapses into ‘subjective p. 245 idealism’ – l, the doctrine that no real things exist outside the knowing subject, and that consequently only subjects and their phenomena or ‘ideas’ exist. In answer to this charge, he added to the revised B edition a section entitled ‘The Refutation of Idealism’. Kant’s all-important distinction – the core idea of his ‘Copernican Revolution’ in philosophy – was the distinction between, on the one hand, the noumena or things-in-themselves beyond sensibility, intuition and the categories of the understanding, and, on the other hand, the phenomena or the objects that we can know through the faculty of sensibility and applications of the categories and the forms of intuition. However, if this distinction is left unqualified and the noumena are strictly ‘unknowable’, why postulate their existence at all? What justification is there for even invoking the existence of noumena? To answer this, Kant argues in the ‘Refutation’ that we can know that the noumena exist, because if they did not, there would be nothing to appear. The manifold of sense has an ‘objective’ side which is the very ground for the existence of appearances. In effect, without noumena, our percepts would be empty. As such, Kant wants the following metaphysical scenario: The noumena exist, but only their mere existence as ground of phenomena is knowable. At the same time, the noumena are entirely outside the application of both the categories of the understanding and the a priori forms of intuition – the noumena are thus outside ‘conceptualisation’, yet they exist and are possible.

This metaphysical scenario is hiding subtle incoherence. In fact, it is not possible to be a consistent Kantian, that is to say, one cannot maintain the sharp divide between noumena and phenomena (where no categories or forms of intuition have application to the noumena), and at the same time resist subjective idealism or solipsism. For by providing a reason for the existence of noumena, Kant opens the door to categorical and intuitive conceptualisations of the noumena. In fact, I would argue that the noumena are not ‘mere Xs’, but must be positively conceived in four distinctive ways. The Whitehead of HL1 concurs:

• What Kant does not adequately account for in his system is that, by holding that the noumena are grounds for the appearances, he is in fact committed to the idea that noumena are causes. As such the category of causality cannot be strictly confined to the domain of phenomena. Noumena are thus describable as causal agents. To be sure, if we grant Kant the notion that our cognitive apparatus constructs phenomena, noumena are necessary causal conditions for appearances, rather than sufficient conditions, but they are causal conditions nonetheless. This difficulty was observed as early as F. H. Jacobi’s 1787 essay ‘On

1. 246 Transcendental Idealism’. l, As Korner has expressed Jacobi’s insight: ‘Kant assumes without qualification that perception is in part caused by the action of things-in-themselves on the perceiving self … The assumption that things-in-themselves act upon the senses is thus contradictory.’³³ In the Harvard lectures, Whitehead also pinpoints this issue with things – in-themselves or objects extra mente as problematic for Kant. As he says at HL1, Hocking’s Notes, 23 October 1924, 432, where he is commenting on Edward Caird’s interpretation of Kant: ‘Whenever therefore we can make any universal assertions as to objects presented through sense … our assertions must be based on [the] nature of our own sensibility*, and not on [the] nature of the object affected * [Whitehead] does disagree on negative statement after.’ So, then, for Whitehead, the nature of our sensibility or cognitive apparatus does affect our resultant perceptual experience, but the nature of the object outside that apparatus also has an essential role to play – here in
   germ is Whitehead’s important distinction between perceptual modes, i.e., initial causal efficacy of the object, and physiological-cognitive processing towards the end of presentational immediacy.³⁴

• In an important sense, there cannot be the ontological distinction between the noumena as grounds of phenomena and the phenomena themselves if the noumena are not co-existents with the phenomena. While perhaps the self is noumenal (as Kant suggests in the discussion of the Third Antinomy of reason), there must be at least some noumena extrinsic to the noumenal self on pain of collapsing into solipsism. As such, the noumena must be ‘outer’ in relation to any self. The very difference between noumena as ground of phenomena and the phenomena themselves thus posits space as real separation between subjects constructing appearances and noumena as grounds of appearances. For consider that space, as Leibniz famously pointed out, is the order of discriminable co-existents, whatever else it may be. Thus, the noumena must be describable as ‘spatially other’ than the subjects that entertain appearances. Again, Whitehead, who famously defended a relational theory of space as part and parcel of his defence of a revised theory of relativity, acknowledges Leibniz’s contribution. At HL1, Bell’s Notes, 17 March 1925, 269, Whitehead asserts: ‘Leibniz says [that] space is relation between bodies in space. Then the point is a logical … construct from two or more [presumably bodies].’ But space, on the Leibnizian criterion, exists as a relation between co-existents not as a pre-existent fixed matrix, and any Kantian escape from compression into solipsism must also posit a spatial distinction between knowing subject and object known. Space as relational in this manner thus transcends its characterisation as an a priori form of intuition imposed upon 247 the objects of perception. Related to this, Whitehead U also sees Kant as infected with a Newtonian

Absolute conception of the ‘point-moment’ as a least unit of extensive quantity, which carries with it the paradox of an occupied point whose ‘pointiness’ is incompatible with occupation of content (cf. HL1, 305). Whitehead adds that, ‘Now, no respectable person’ – that is, any person acquainted with relativity theory – can abide by an Absolute Theory of space-time (HL1, 305f). Kant’s thinking about space is illicit, as its framework is Absolute rather than Relational; indeed, Kant’s spurious commitment to the necessity of Euclidean geometry is precisely countermanded by the very non-Euclidean geometry that opens the door to relativistic considerations.

• Noticed as early as Schopenhauer’s Criticism of the Kantian Philosophy, the category of quantity is applicable to the noumena on pain of violating the law of non-contradiction. For the noumena cannot be ‘neither one nor many’. What would it mean to say otherwise? Kant cannot say that they ‘correspond to zero’ or ‘there are zero noumena’, for this is not distinguishable from saying ‘there are no noumena’, a proposition which Kant is anxious to deny in the ‘Refutation’. On the other hand, how can the cardinality of the noumena be, say, one-and-two or one-and-ten simultaneously? As S. F. Barker says similarly when critically examining intuitionism in his operculum on The Philosophy of Mathematics, the claim that something is beyond the very domain of quantity – is neither one nor many – ‘is too close to contradiction to be plausible’.³⁵ Thus, in order to maintain intelligibility, the noumena must again cross the chasm into the realm of categories to become describable as at least ‘either one or many’. I argue that Whitehead concurs in principle with Barker, as he (Whitehead) is in no way committed to L. E. J. Brouwer’s classical intuitionism that would ultimately reject the law of excluded middle in the analytic sense of propositional bivalence. While, granted, Whitehead rejects excluded middle insofar as it is wrongfully applied by Aristotle in a rigid way to the notion of transition where some S as not qualified by P transitions to S as qualified by P – a transition of ‘jumping’ from one state to another as in the flicker of a cinematic tape (HL1, Bell’s Notes, 48-9) – Whitehead never dismisses excluded middle in the analytic sense of A V ~ A that can be applied to the description of actual states, to realised or satisfied occasions, in effect, to states of being. Whitehead’s philosophy of mathematics is indeed a complicated affair that, again granted, does involve an element of constructivism and finitism, but not without retaining a strong element of realism that would countermand any defence of Kant here based on Brouwer’s principles. The definitive case for this interpretation of Whitehead has been made, in my view, by my late friend James A. Bradley.³⁶

1. 248 4) Most obviously, in asserting that the noumena exist, Kant is committed to the notion that they share two modal features with phenomena, namely, possibility and actuality (phenomena are actual when we are actually having experiences). The noumena are not mere possibilities, for otherwise the phenomena would be merely possible and not actual.

All told, then, if Kant is to preserve the law of non-contradiction while fending off subjective idealism (or, stronger still, solipsism), then the noumena are not sheerly inconceivable, but are co-existent and actual, spatially other, causal agents, subject to quantification. Thus, Kantian noumena do not represent entities which are possible and yet are strictly inconceivable. Even on Kant’s own epistemic criteria and admissions, there is a good deal we can say descriptively and a good deal we can know about noumena beyond and precisely because of the very positing of their existence. Summarily, we might say that Kant’s own ‘Refutation’ deconstructs the doctrine of noumena taken as pure existential surds. For the reasons provided above and their textual correlations in the Harvard lectures, Whitehead concurs that Kant’s standpoint and its entanglement with subjective idealism and solipsism is to be strongly rejected (also cf. HL1, 57, 83, 311, 313, 337, 339, 425, 441).

In addition to the critique of Kant’s view, Whitehead provides a coherent and intelligible alternative. The quest for contact with reality outside the human knower and its organising faculties that gets us beyond Kant’s epistemic ‘prison’ is found in what Victor Lowe and Hartshorne have deemed the ‘truly revolutionary’ aspect of Whitehead’s philosophy, namely, the notion of initial physical prehension, or in the technical language which we first encounter in Symbolism, ‘perception in the mode of causal efficacy’. In the light of this construct, the problem which Kant faces concerning the necessity of affirming the causal role of noumenal objects in order to give rise to phenomena in the first place is not a problem which can occur within the Whiteheadian framework. The problem of ‘external realism’ which so occupied ‘modern’ philosophy from Descartes to Hume and Kant is simply outside the ambit of the Whiteheadian conceptuality from the 1924-25 Harvard lectures onward – this alone justifies the now common characterisation of Whitehead (and Hartshorne) as a constructive post-modernist. Here Whitehead joins C. S. Peirce’s doctrine of the primary icon and related critique of Cartesian methodical doubt; Heidegger’s analysis of Dasein as always and inescapably Mitwelt or being-in-the-world; and Merleau-Ponty’s roughly equivalent notion of human existents as l’etre au monde. None of these thinkers have any preoccupation with the problem of external realism in the important sense that, within their respective philosophical frameworks, the question of epistemic grounding of access to external reality does not arise.

Coda: The Use of Formal Logic and Mathematical Analysis as a Necessary Component of Philosophical Reasoning/The Necessity of Their Limitations/The Aesthetic Dimension

Whitehead’s international fame first came from his collaboration with Bertrand Russell on the multi­volume Principia Mathematica. The publication of this work became one of the hallmark, indeed founding, events in the history of Cambridge analytic philosophy, as the power of first order quantificational logic to elucidate language and the logical structure of argumentative reasoning became quickly evident. But it is often assumed that, after Whitehead dropped his focus on philosophy of physics, as well as his still influential developments of topological mereology, his approach to philosophical problems that employs rigorous appeals to formal logic and mathematics was essentially over; consequently, the gap between PM and PR is wide and yawning. Even a Whitehead scholar as knowledgeable as Victor Lowe casually makes the claim that Whitehead dropped the use of mathematics and logical formulae in his later published work since the beginning of his Harvard period. While this is evident in a large number of Whitehead’s later publications, there are very important exceptions. The difficult chapter on ‘Abstraction’ in SMW, while not employing the notation of PM logic, does include considerable use of variables (such as A for eternal object, a for actual occasion, and R for relation); here we see ideas explicated in a quasi-formal manner reminiscent of the light formalism found in, say, F. H. Bradley’s Principles of Logic, Vol. II. Part IV of PR in the chapters on extensive connection, loci and strains is also rigorously formalistic and diagrammatic as would be required in any sophisticated discussion of the theory of extension. The later Essays in Science and Philosophy contains technical mathematical discussions such as the important chapter on ‘Indication, Classes, Numbers, Validation’. One of the most important revelations of the newly discovered Harvard lectures is the fact that Whitehead the logician and mathematician is very much alive in the development of his ontological and epistemological ideas, as even the most cursory review of HL1 will show. Consider, for example, just the short stretch of lectures from 15-17 February 1925, where Whitehead employs twenty-six formulae of propositional and quantificational logic (HL1, Heath’s Notes, 474-7); or note the employment of twenty- nine diagrams in the stretch of lectures from 17-30 March 1925 when discussing relativity theory (HL1, 494-503); or the casual provision of six Larmor invariance equations compared with the ‘regular Newtonian system’ (HL1, Hocking’s Notes, 408). This is a mere sampling used to illustrate; an inventory of the entire volume would yield an enormous number of formulae, equations and formal diagrams. In the light of this, the l> community of process scholars owes the editors, Paul Bogaard and Jason Bell, a great ^p. ²⁵⁰ debt of gratitude for the painstaking way in which the various notes were transcribed and reproduced, including this wealth of technical logicomathematical and diagrammatic material. This material clearly indicates that, while Whitehead the profound metaphysician of the opening Lowell lectures was mystifying to many, HL1 reveals that he was also every bit the logician and technical scientific mind that the audience had expected from the author of The Concept of Nature and the Principia.

Perhaps a deeper consideration is that it is arguable that the Categoreal Scheme of PR is throughout undergirded by the quantificational principles, axioms and deductions of the Principia. This is the overall thesis of John Lango’s neglected Whitehead’s Ontology, which accordingly challenges the standard view that there are disconnected or bifurcated periods in Whitehead’s career that are alienated from the ‘Mediterranean clarity’ of PM (to use Russell’s characterisation). As Lango asserts concisely in his Preface: ‘although Whitehead’s career is often divided into periods, there is no hiatus between his later metaphysical speculation and his earlier writings in mathematics, logic, physics, and the philosophy of science. In short, this indicates that the Whitehead of Principia Mathematica is at work in Process and Reality.’³⁷

Despite the complexity (and granted some considerable obscurity³⁸) in the literary exposition of PR, the Categoreal Scheme is arguably logically coherent, like a system of axiomatic mathematical notions, as Lango attempts to demonstrate with a set of eighteen formal quantificational Definitions and four deducible

Theorems (important alternative formalisations have been developed by R. M. Martin and Lucio Chiaraviglio).³⁹

Let me briefly illustrate this last comment concretely by providing an exposition of some selected items in Lango’s PM-based account of Whitehead’s Categories of Existence: actual entities, eternal objects, subjective forms, prehensions, contrasts and nexus (plural). Each of these Categories, argues Lango, is definable in terms of the formal properties of a basic and all-pervasive relation in PR (also pervasive in the Harvard lectures, cf. the repetitive references to ‘togetherness’ of entities in processes of realisation) that Lango deems ‘synonty’. Synonty is the fundamental relation such that ‘ x is synontic to y when x has being for y’ (WO, 76). It is immediately suggested by Whitehead’s central metaphysical intuition, expressive of the very essence of creative process, that ‘the many become one and are increased by one’ (PR, 32), that is, since the many actual occasions have ‘being for’ the new occasion in its process of becoming. Put another way, synonty expresses the relation of ontological ‘togetherness’ which is found across the Categoreal Scheme;

1. 251 for example, to take only two of numerous instances, the many U entities in the actual world are said to be ‘together with’ (prehended by) the actual entity in its process of becoming, and eternal objects are said to be ‘together with’ (ingress into) the actual entity in its process of becoming. (Formally, ‘synontic to’ can be rendered ‘^’ as distinguished from the Principia material conditional.) Given this, such basic notions as, for instance, eternal object, subjective form, prehension and created mental entity can be quantificationally formalised as follows:

Since any eternal object (Whitehead’s ‘forms of definiteness’) is synontic to every other entity and all other entities are synontic to it, in contrast to God who is synontic to every entity (including self) and every entity to God, an eternal object can be precisely defined as follows, where EO abbreviates ‘eternal object’ (D14):

(Vx) (EOx iff . Ex . ~ x -» x)

Given CM for ‘created mental entity’, SFfor ‘subjective form’, PR for ‘prehension’ and A for ‘compresent with’, we can formulate quantificational deflnitions for subjective forms and prehensions respectively as follows (D15 and D16):

(Vx) [SFx iff . CMx . (Vy) (x # y . x A y . 3 . x ■* y . y ^ x)]

(Vx) {[PRx iff . CMx . (ay)[x# y . x A y . (~ x -» y V ~ y -» x)]}

In effect, something is a subjective form ‘if and only if it is a created mental entity such that it is synontic to every other entity with which it is compresent and every other entity with which it is compresent is synontic to it’. On the other hand, something is a prehension ‘if and only if it is a created mental entity such that it is not synontic to any other entity with which it is compresent or some other entity with which it is compresent is not synontic to it’.⁴⁰ From these two deflnitions the theorem logically follows that, if something is a created mental entity, then it is a subjective form if and only if it is not a prehension:

(Vx) (CMx 3 . SFx iff ~ PRx)

While this illustration is necessarily quite terse, the point is to show that an important subset of items in the Categoreal Scheme, namely, the Categories of Existence, has, much akin to a mathematical system, a discernible structure that admits of precise PM-based quantificational deflnition. Moreover, these Categories arguably exhibit a relational unity as found in their universal involvement with formal properties of synonty. While even this subset of Categories is quite complex (far more so than this brief summary can convey), its undeniable features of precision and uniflcation under a common relational motif strongly p. 252 argue against any quick dismissal of the Categories as simply l, ‘muddleheaded’. On this reading of

Whitehead, Russell’s earlier assessment of Whitehead’s Harvard metaphysical work as ‘mystical’ and ‘muddleheaded’ is simply off the mark.

Charles Hartshorne is also a philosopher who employed and explicitly insisted upon both the use of formal logic and mathematical analysis in the work of speculative philosophy (in particular, see the section on ‘Formal Logic’ in ‘Some Principles of Method’, CS, Ch. V). Again, this counts as a significant element in Hartshorne’s perception of his ‘pre-established harmony’ with Whitehead. While Whitehead certainly reinforced this belief, especially given the use of logic and mathematics in the Harvard lectures which Hartshorne attended and transcribed as his assistant (as of Fall 1925), there is no direct evidence that Hartshorne derived his specific uses of formal logic from Whitehead. Rather, his primary influences on this score were his Harvard teachers of advanced symbolic logic, namely, C. I. Lewis and H. M. Sheffer. Also, C. S. Peirce’s Exact Logic, which Hartshorne co-edited with Paul Weiss, was further reinforcement of Hartshorne’s position on the uses of formal logic.⁴¹ I demonstrate immediately below with brief accounts of some of Hartshorne’s highly original uses of formal approaches to philosophical issues: i) use of Peirce’s position matrices, ii) use of and reflection upon modal logic and modal theorems for insight into the logical structure of metaphysical concepts, iii) reflection upon the defining power of asymmetrical Sheffer functions and its implications for metaphysics, and iv) a formal triadic solution to the traditional problem of future contingents:

Importantly, through exposure to Peirce’s matrices, Hartshorne’s so-called ‘mathematical analysis of theism’ published in Philosophers Speak of God as his ‘Epilogue: The Logic of Panentheism’ (a revision of his earlier 1943 article ‘A Mathematics of Theism’) details a six-fold table of logically possible positions on modes of being relating to reflexive and nonreflexive notions of the relations ‘superior to’ or ‘inferior to’ (PSG, 507-8). This was a first published warm-up for his later development and employment of Peirce’s doctrinal position matrices.⁴² Hartshorne’s approach here – using the logically exhaustive quantifiers (all, no, and some) on the modal contrasts of necessity and contingency in application to God and world, thus arriving at sixteen possibilities – represents a genuine advance in metaphysical or philosophical theology, since it provides a matrix that may well suggest missed possibilities in traditional or conventional ways of thinking. Indeed, the position matrix is arguably necessary, since, until all possibilities are exhaustively exhibited, the complete rational adjudication of a metaphysical issue simply cannot occur. Furthermore, Hartshorne’s method can be extended: similar sixteen-fold matrices can be made for other polar p. 253 metaphysical contrasts such as infinite/finite, eternal/temporal, and so on. If l, any two matrices are combined (16 X 16) the number of formal alternatives leaps to 256. More generally, if m equals the number of contrasts one wishes to include in talking about God and the world, then 16^m is the number of formal alternatives available. There is no apparent antecedent in the history of metaphysics for Hartshorne’s specific and revised doctrinal matrices.

A later influence on Hartshorne was the work of Rudolf Carnap, especially his Meaning and Necessity: A Study in Semantics and Modal Logic. As Hartshorne makes clear in his autobiography, Carnap was helpful in assisting his (Harts-horne’s) formal reduction to absurdity proof of the incoherence of the ensemble of classical theistic attributes regarding omniscience, foreknowledge and world contingency as found at DR, 12-14 (really a formalisation of Spinoza’s famous argument for such incoherence in the Ethics, Part I, prop. 33, scholium). Moreover, the technically competent discussion of ‘Relativity and Logical Entailment’ owes much to Carnap as any examination of its text and footnotes will reveal (see DR, esp. 100-1, n 2). The direct influence of Lewis and Sheffer is also significant. Hartshorne’s famous and much discussed modal formalisation of the Ontological Argument – again the first in the history of philosophy – as found in The Logic of Perfection, employs C. I. Lewis’s S5 and includes use of Becker’s Postulate or the Strong Reduction Principle (i.e., the Principle that the modal status of a proposition is always itself necessary – a postulate I find with A. N. Prior to be intuitively convincing, but which if judged problematic can be avoided altogether in a simpler formation of the argument such as we find in Hartshorne’s ‘Foreword’ to Goodwin and

elsewhere).⁴³ Similarly, Harts-horne reflects on the significance of various theorems of modal logic as a key to understanding, for example, how contingency includes necessity rather than vice versa, as reflected in the theorem that [(□p & ◊q) -» ◊ (p & q)]: The conjunction of necessary and contingent propositions logically entails the contingency of the conjunction of the same propositions taken assertorically. On the other hand, one of Hartshorne’s most important arguments for the basicality of Peirce’s asymmetrical notion of logical implication is his (Hartshorne’s) meta-logical reflection on the defining power of the asymmetrical Sheffer functions as contrasted with symmetrical equivalence (cf. ‘The Prejudice in Favor of Symmetry’, CS, 205­26). Here, after explicating in detail the sixteen propositional-function possibilities encompassed by Sheffer’s asymmetrical monary stroke and daggar operators, he announces that, although Peirce’s asymmetrical logic of relatives has been ‘with us for nearly a century’, nonetheless ‘philosophers for the most part have yet to realize the importance of this logic for metaphysics or speculative philosophy’ (CS, 205). In effect, the important general point is that, for Hartshorne, there has been insufficient recognition p. 254 of the fact that ‘some rather simple, though neglected, truths of formal logic as it now stands l, seem to me quite relevant to traditional philosophical problems’ (CS, 82). Somewhat similarly, Whitehead envisions an expanded Symbolic Logic that will be of important use to aesthetics, ethics and theology (see ESP, 99).

A perfect illustration of Hartshorne’s adage at CS, 82 is the simple but neglected application of the traditional quantifiers of classical syllogistic (all, some, and no) to causal conditions of future events. By such application Hartshorne shows the fallacy in the Stoic Master Argument for fatalism (also apparently held by Russell during his University of Chicago sojourn where he discussed the issue briefly with Hartshorne) that our choices reduce to ‘All causal conditions at t are such that x will occur’ and ‘No causal conditions at t are such that x will occur’. This excludes by omission the available commonsense notion that at t it is indefinite whether x will occur as embodied by the sub-alternative assertions that ‘some causal conditions at t are such that x will occur and some at t are such that x will not occur’. The Stoic dichotomy of propositions is guaranteed to yield fatalism, and this begs the question. What is needed to exhaust the possibilities is a triad of propositional schemes: x will occur, x will not occur, or x may-or-may-not occur.⁴⁴ This triadic formulation can be displayed as a perfectly consistent modal-tense version of the square of opposition that will preserve both the law of excluded middle and the law of non-contradiction.⁴⁵

Thus, while Whitehead encouraged Hartshorne’s employment of formal logic in a general way especially through the exposure at Harvard, Hartshorne developed his own distinctive formal devices owing more to the four-fold influences of Peirce, Lewis, Sheffer and Carnap. At the same time, it is to be noted with some emphasis that Hartshorne, like Whitehead, was quite cognisant of the limitations of formal approaches to philosophical problems. Intuition is an indispensable aspect of philosophy no matter how thorough and systematic the use of formal logical analysis (WP, 112). Adequate philosophising involves far more than achieving clarity and precision in the formulation and analysis of concepts. Recall here Whitehead’s famous qualification that, while ‘Logic is a superb instrument’, when taken as an adequate analysis of the advance of human thought, it is a ‘fake’, indeed ‘exactness is a fake’ (ESP, 74). The question terminus a quem, ‘what are we talking about?’, when probed to its depths, compels an encounter with qualitative dimensions of experience that are uniquely accessible to artists, novelists, poets and musicians. The imaginative exploration of aesthetic possibilities, phenomenological description and the voices of poets and litterateurs are mandatory to philosophical adequacy. In Hartshorne’s pithy expression, ideally ‘philosophers ought to be poets and logicians’ (CS, xvii). As Whitehead says similarly and again famously, literature is ‘the laboratory of philosophical ideas’ as it explores the heights and depths of human experience.

1. 255 For this reason concerning adequacy and the need for aesthetic depth, Hartshorne suggests (WP, 6) that Whitehead did not explicitly employ, in the main, formal logic or mathematics in his later philosophical masterpieces, although (assuming Lango’s thesis) I do not see that Hartshorne was sufficiently aware of just how extensively the logic of the Principia was at work, albeit tacitly, in the formulation of the Categoreal Scheme. Above all, however, for both philosophers, philosophy requires a balanced approach where logic,
   mathematics, reflections on the best results of empirical science, fine arts, poetry, music (and even, in Hartshorne’s case, given his scientific work on birdsong, bio -musicology), literature and religious studies all work together towards a coherent, comprehensive world-view narrative – the goal being what might be called ‘global thinking’ or ‘thinking with the whole brain’. Whitehead was Hartshorne’s archetypical model for such global thinking and integrated ‘balance with definiteness’ (CS, 92-8 and WP, 112). I emphasise here that the Harvard lectures clearly exhibit this ideal of enormously wide and balanced erudition, and such erudition is in fact one of their most impressive overall features. Standing alongside the many explorations of the history of philosophy from Plato and Aristotle to medieval Scholastics to Spinoza to Hume and Kant to Hegel to Russell and Dewey, experimental psychology, geometry both Euclidean and non-Euclidean, relativity and quantum theory, Newtonian mechanics, and epochs in the history of science, are the manifold references to poets and novelists – for instance, Dante, Milton, Shelley, Tolstoy, Virgil and Wordsworth (see HL1, 41, 47, 108-9, 136, 530, 533). This depth of erudition and concomitant appeal to aesthetic dimensions of experience will, of course, become a hallmark of Whitehead’s later published work.

In summation, Whitehead and Hartshorne call philosophers to the highest and most daunting aspirations of philosophy as the ‘appetite for every kind of learning’ (Plato); as such philosophy is nothing less than the audacious aspiration to the grand narrative of the University.

Concluding Remarks

What all the above analysis and argument shows, I think, is that Whitehead and Hartshorne were united in the Transcendental Project and its defence through meta-logical reflection on the universe of discourse assumed in first-order quantificational logic, and through what could be called the ‘Ontological Approach’ to the most basic fundaments of metaphysical theory (necessity of existence, the ultimacy of creativity and its embodiment in an ‘aboriginal actuality’, the eternity of the domain of potentials, God). This emphasis on p. 256 l, the Ontological Approach provides an important qualification of Sessions’ account in ‘Hartshorne’s Early Philosophy’, which, while quite correct in envisioning many specific elements of the ‘pre-established harmony’, altogether lacks the logico-ontological dimension I have presented here. This unity of approach is also clearly reflected in Whitehead’s Harvard lectures, as I have attempted to document throughout. I have also attempted to argue that the commitment to the necessity of ontological non-emptiness in both philosophers stands unscathed against a number of important potential objections, including Rorty’s argument from an appeal to Kant’s doctrine of noumena as existential surds. If this is correct, the Ontological Approach is strongly plausible and demands to be taken seriously. Embracing this Approach, Whitehead and Hartshorne stand as exemplary twentieth-century defenders of a philosophia perennis tradition that extends back to Parmenides.⁴⁶ Further, I have shown that Whitehead and Hartshorne are united in understanding the importance of the use of formal logic and mathematics in assisting the philosopher, while at the same time they envision the limits of this use and observe the requirement that there must be other kinds of consideration both aesthetic and phenomenological in order to achieve adequacy. Wisdom demands nothing less.

Notes

1. Lowe, Alfred North Whitehead, Volume II,
2. Lowe, Alfred North Whitehead, Volume II, 142.
3. Sessions, ‘Hartshorne’s Early Philosophy’, 34.
4. See Gamwell’s important treatise, originating from his University of Chicago seminar on ‘Foundations of Ethics’ with Paul

Ricoeur, The Divine Good: Modern Moral Theory and the Necessity of God, esp. chapter 4, ‘On Transcendental Argument’, 85­126. Also see his analysis of Apel’s ‘transcendental pragmatic’ approach to moral norms and its lack of success without a metaphysical framework in ‘Metaphysics and the Moral Law: A Conversation with Karl-Otto Apel’.

5. Lowe, Alfred North Whitehead, Volume II.
6. For obvious reasons of space, I will be unable to treat here all relevant objections to the necessity of P-Zero. I have instead

focused attention on issues and objections more directly relevant to Hartshorne and Whitehead’s Harvard lectures. However, for supplementation of my perspective, consult William L. Reese’s thorough and competent examination of conceptions of non-being ranging from Plato’s Sophist to Sartre’s neantising in his classic ‘Non-Being and Negative Reference’. Also see my ‘Appendix: Hartshorne’s Ontological Argument and Continental Doctrines of “Nothingness”’ in the p. 257 forthcoming The Mind of Charles Hartshorne, co-authored with Don Viney (manuscript, chapter VI, 54-68). Here l, we consider conceptions of non-being in Barth, Berdyaev, Heidegger, Moltmann, Sartre, Tillich and the Japanese Buddhist philosopher Nishida. We argue that the intelligible conceptions of non-being are equivalent to Berdyaev’s non-being as meontic potency, which correlates with process conceptions of ‘creativity’ (Heidegger, Moltmann, Nishida and Tillich, we argue, all advocate meontic conceptions). The other conceptions are either contradictory or unintelligible (Barth’s ‘impossible possibility’ of das Nichtige) or present us with thought-experiments that result in the description of possible worlds with mere differences of content (Sartre’s neantising and mental acts in ‘the imaginary’), thus reducing to Platonic ‘othering’. Nowhere in these Continental and Buddhist thinkers is there an intelligible conception of or successful analogue for ‘absolute nothingness’. It should also be noted in this context that Deleuze stands with Bergson on this issue (see note 19 below).

7. Although I have here used the vocabulary of ‘foundations’, I do not hold that this entails any commitment to classical epistemic foundationalism. (Nor do I hold that either Whitehead or Hartshorne are foundationalists.) While I am making the claim that Whitehead and Hartshorne are correct in contending that P-Zero is necessary and presuppositional, this does not in and by itself entail that such principle is an absolutely, epistemically incorrigible foundation. If it were so, there would be no point in engaging the potential ‘defeaters’ of P-Zero, ranging from considerations of the implications of non- classical free logics to considerations of the ontological status of a primordial quantum vacuum to considerations of the status of sunyatta in Buddhist metaphysics, etc.
8. Some philosophers who are sympathetic to Hartshorne and process philosophy generally, such as Eugene Peters, have expressed doubts about the necessity of bringing in the notion of observers into the primordial situation (see Peters, ‘Methodology in the Metaphysics of Charles Hartshorne’, 9-10. However, his objection can be circumvented by arguments for existential necessity that are confined to strictly logical ‘class membership’ considerations as in Gamwell’s quasi- formal presentation of a Transcendental Argument in the previously referenced Ch. 4 of The Divine Good. Gamwell’s argument is parallel to Hartshorne’s observation that ‘nothing exists’ cannot be true of any state of affairs.
9. Cohen, The Diversity of Meanings, 255-64; W. and M. Kneale, The Development of Logic, 706.
10. See Goodwin, The Ontological Argument of Charles Hartshorne, chapter IV; Kripke, ‘Semantical Considerations on Quantified Modal Logic’; see my discussion of Goodwin’s interpretation of Kripke and Quine’s objections to de re modality in Process and Analysis, 21-3.
11. In a neglected but important commentary on the early Wittgenstein by John Moran entitled Toward the World and Wisdom of Wittgenstein’s Tractatus, it is argued that there is an implicit Ontological Argument in the Tractatus. For Wittgenstein is contending that an absolutely empty domain for the universe-class is impossible for logic. The argument can be found by 258 ruminating on passages U 2.021 through 2.0212. ‘Objects make up the substance of the world (2.021) … If the world had no substance [and thus no objects by virtue of 2.021], then whether a proposition had sense would depend on whether another proposition was true … In that case we could not sketch any picture of the world (true or false).’ The assumption of objects (of some sort) – in effect, the non-emptiness of the universe of discourse – is thus a precondition for logical coherence in picturing the world.
12. Eco, Kant, 49.
13. Eco, Kant, 18.
14. Ross, Philosophical Theology, 104; this refers to the earlier Plantinga of God and Other Minds, not the Plantinga of the later The Nature of Necessity. In the latter work Plantinga develops what he calls a ‘victorious’ version of the Ontological

Argument. For a discussion see my biographical essay ‘Alvin Plantinga’ in American Philosophers, 1950-2000, 215-25, esp. 220-1.

15. Gamwell, The Divine Good, 96, n4.
16. Quine, ‘On What There Is’, 12.
17. Dillman, Quine on Ontology, 81-3.
18. Bergson, Creative Evolution, 296-324, see esp. 304-5.
19. Bergson, Creative Evolution, 314.
20. Deleuze, Bergsonism, 17-23, 44-7, 101-3.
21. Viney, Charles Hartshorne, 63.
22. Gale, Negation and Non-Being, 113, more generally see esp. 105-16.
23. Gale, Negation and Non-Being, 112.
24. Martin, ‘Ontology, Category Words, and Modal Logic’, 27.
25. An excellent primer on free logics is to be found in Priest, An Introduction to Non-Classical Logic, chapter 13, ‘Free Logics’, 290-307. On the surface, and on the basis of non-classical free logic, Priest would seem to disagree with my argument from the existence assumption of the Principia, which is a form of classical logic. As he puts it plainly, ‘[in free logic] particular generalization fails, since a constant can denote a non-existent object; and the logic is not committed to the logical truth that something exists, for there are interpretations where E [the inner semantical domain] is the empty set’ (293). But what I am after in defending Bergson’s argument concerns the meta-linguistic (or perhaps pre-linguistic) consideration about the conceptual origination of and ultimate referent for the objects of the inner domain E. Note that the examples Priest provides for members of E are ‘Sherlock Holmes’ and ‘Pegasus’. While I understand their description as ‘non-existent objects’, I ultimately object to the use of the vocabulary of ‘non-existence’ for the purposes of the appropriate metaphysical context of Bergson’s argument. There is a sense in which such objects exist as potentialities or as a combination of potentials, otherwise we could not countenance the truth of such sentences as ‘In the novels by Arthur Conan Doyle, Sherlock Holmes lived in Baker St’ (to use a sentence which Priest agrees is true and constitutes one of his 259 ‘philosophical objections’ to the Negativity Constraint Rule of certain free logics, see 275). In effect, again, free logics with empty inner domains are not truly relevant to the properly ontological issues at stake. For one could well agree with the employment of free logics for the quantificational formalisation of sentences involving Sherlock Holmes, and yet agree with Hartshorne’s assertion that the domain of ‘possibility’ is not to be contrasted with the domain of ‘existence’ (or the real), but rather with the domain of ‘actuality’ (RSP, 52). In effect, I hold with Whitehead and Hartshorne that potentialities of actual states are not ‘unreal’ or ‘in every sense absent’; if they were we could not meaningfully refer to them. A linguistic entity with a truly metaphysically empty inner domain such as ‘lives in Baker St’ is not a proposition that can be asserted. Such examples as Sherlock Holmes make my point that free logics involve oblique references to actual states of affairs since Holmes is some sort of composite of actual properties in non-realised combinations.
26. It is uncanny how close this is to Parmenides’ reasoning about the utter futility of ‘the way of non-being’; see reference below on Milton Munitz’s interpretation of Parmenides.
27. See Griffin, Reenchantment without Supernatualism, 171. Griffin cites RM, 68 as the textual basis for holding that

Whitehead rejects ontological type arguments. However, my own examination of this text and the ensuing discussion through RM, 69-70 shows that Whitehead describes the ‘Ontological proof’ of Anselm and Descartes as the ‘only possible’ proof because arguments from the actual world cannot get beyond the metaphysical principles inherent in the actual world to infer a transcendent God. Rather, he says, and we are left presumably to infer his agreement, Christianity has taken neither Anselm’s nor Descartes’ approach, nor presumably the so-called a posteriori approaches of Aquinas and Neo-Thomists. Contrary to these alternatives, he says that the ‘genius’ of Christianity is found in the subordination of religious metaphysics to its traditional ‘religious facts’, which he then identifies as the spiritual internalisation of the ‘Kingdom of Heaven’ and the invocation of St John that ‘God is love’. But none of this precludes Whitehead from appealing in the same course of lectures to an argument much in line with Hartshorne’s and Tillich’s very similar modal reasoning. At

RM, 146 (my emphasis), he holds that ‘the whole process itself … requires a definite entity, already actual among the formative elements, an antecedent ground for the entry of the ideal forms [potentialities] into the definite process of the temporal world’. Thus, that Whitehead might affirm a more general modal argument to God as ‘the primordial power’ – the ‘complete aboriginal actuality’ in Whitehead’s vocabulary (RM, 146) – is by no means prohibited. Perhaps this is partly a semantical issue as to how we differentiate and classify types of theistic argumentation. But there certainly is a plausible tradition of interpretation which sees such reasoning as Hartshorne outlines above as of the properly ontological sort that trades in a priori or conceptual rather than restrictively empirical concepts.

28. 260 28. l, I challenge those who wish to dismiss this approach in a facile way with fashionable slogans like ‘ontologism’. Philosophers enamoured with Heidegger should be cautious here. For there is a strong case to be made for the position that Heidegger’s ‘The Nothing’ is to be equated with Being as No-thingness, as infinite meontic potency, as that which is ‘most void’ (because it is ontically empty, it is not a ‘thing’ or aggregate of ‘things’ which exists or ‘stands out’ in space­time) and yet as potency is ‘most abundant’ and is ‘being-er (seinender) than the beings’. The point of Heidegger’s Postscript to the 4th edition of Was ist Metaphysik ? was in fact to correct the ‘nihilistic’ interpretations of his talk about ‘the Nothing’ (das Nicht) which he explicitly disassociates from das Wesenlose, the ‘merely nugatory’, or that which lacks essence or potency (Brock trans., Existence and Being, 46). Moreover, if we follow up on Heidegger’s own famous footnote suggestion for philosophical theology – his suggestion of God as infinitely temporal rather than as the timeless nunc sans of the tradition – we see direct implications for an affirmation of ontological non-emptiness. See Sein undZeit, 427, n. 1. On the other hand, for a staunch critique of Heidegger’s claim that his way of thinking radically transcends the metaphysical tradition which allegedly fails to grasp the ‘ontological difference’, see Puntel, Being and God, 99-112. Puntel directly approaches the issue of ontological emptiness and argues, in agreement with Whitehead and Hartshorne, that the concept of the possibility of absolute nothingness is a ‘pseudo-concept’, see esp. 227-30. He reformulates and then rigorously defends a version of Aquinas’s ‘Third Way’ to the conclusion that there must be what Puntel calls an ‘absolute dimension of Being’. He presents the argument as a simple modus tollens syllogism (a reformulation which avoids the quantifier-shift fallacy of Aquinas’s original): ‘If everything – that is, Being as such and as a whole – were contingent, then absolute nothingness would be possible, but absolute nothingness is impossible; therefore, not everything is contingent.’ This affirms Whitehead’s notion in his Harvard lectures that ‘it is because something is Eternal’ that coherent thinking in science and metaphysics is even possible. In general, Heidegger is roundly taken to task by Puntel for confused, deficient and logically spurious modes of thinking. See Being and God, chapter 2, ‘Heidegger’s Thinking of Being: A Flawed Development of a Significant Approach’.
29. See Tillich’s discussion of the ‘Ontological Approach’ in his celebrated essay ‘Two Types of Philosophy of Religion’ in Theology of Culture, esp. 27, where he asserts that the power of being is ‘the power in everything that has power’ and where being-itself is taken as a prius of all thought, is ‘first in the intellect’, citing St Bonaventure. He also regards as ‘more consciously ontological’ Whitehead’s conception of the primordial nature of God and Hartshorne’s efforts at resurrecting the Ontological Argument while combining elements of the contingent in God (21-2). Also see Tillich, Systematic Theology, Vol. 1, Part II, Section II, B ‘The Actuality of God’, 235-41. I would suggest that Tillich’s concept of the ‘power of being’ is to 261 be correlated with Whitehead’s concept of Creativity, but l> is not identical to it. Perhaps it is arguable that it would be more accurate to say that ‘power of being’ correlates with all three of the primordial Formative Elements of RM taken together (Creativity, the Eternal Objects and God). Yet, the issue is complicated. For although Whitehead’s God arguably includes the ‘power of being’, nonetheless, for Whitehead, God is literally and univocally a ‘personal’ entity, and consequently is more than the ‘power of being’. Tillich’s doctrine that the power of being ‘includes’ the personal or is ‘the ground of everything personal’, and thus God is personal in some metaphorical sense, is essentially unclear. Whitehead’s doctrine straightforwardly conforms with Richard Swinburne’s criterion for attributing personality to an entity by virtue of possessing at least one high-order P-predicate (or higher-order mental property, following P. F. Strawson’s vocabulary of classes and sub-classes of P-predicates and M-predicates); a fortiori God as consciously envisioning eternal objects, evaluating their relevance and value for particular historical contexts, and then providing ideal subjective aims for the guidance of finite entities, is to possess numerous high-order P-predicates (cf. Swinburne, The Coherence of Theism, 101). However, Tillich is right, I think, to hold that both Whitehead and Hartshorne are mixing or synthesising ontological and cosmological approaches by offering a theistic model in which there are properly a priori ontological and personal monotheistic elements (Theology of Culture, 26-7), an ideal that Tillich himself wants, although I think dipolar panentheism more clearly achieves. Of course, these statements require much more clarification and qualification than I can provide here.
30. An important potential objection to ontological non-emptiness comes from ‘empirical’ cosmological inquiry based on interpretations of quantum mechanics. Some recent cosmologists have advocated notions of creatio exnihilo purportedly without any pre-existent agent or agency. Such cosmological scenarios are sometimes described by professional

physicists and by some popular science authors as events in which ‘something comes from nothing’ – the idea being that rules of quantum mechanics ranging over a primordial quantum vacuum would allow some probability of an event which ‘tunnels’ out of the vacuum analogous to the behaviour of virtual particles popping out of quantum foam. Self-proclaimed ‘new atheist’ physicist Lawrence Krauss has offered such a proposal under the revealing title A Universe from Nothing: Why There is Something Rather Than Nothing. Cosmologists A. Vilkenkin, Stephen Hawking, James Hartle and Y. B. Yel’dovich have also boldly suggested that, based on principles of quantum physics, there is some probability that the universe could have ‘appear[ed] from nothing’ (Hartle and Hawking, ‘Wave Function of the Universe’; for references to Linde, Vilenkin, Yel’dovich and related literature, see my bibliography in Shields, ‘The Wider Design Argument and the New Physics’, 192­6). An adequate reply to this potential objection could well occupy an entire monograph, and for obvious reasons of space I cannot provide this here and now. However, I can quickly suggest a couple of lines of argument which support my (and p. 262 no doubt Whitehead’s) strong L, objection to any such proposal. 1) The ‘vacuum’ which is postulated is clearly a ‘something’ with a quite substantial physical description as a ‘diffuse energy field’. As John Gribbin puts it rather explicitly in an entry on ‘vacuum’ in his encyclopedia of particle physics: ‘In quantum physics, the vacuum is not nothing at all, but seethes with activity … the vacuum is a superposition of states for many different kinds of field’ (Gribbin, Encyclopedia, 418). 2) Consider the following ‘fundamental equation of quantum mechanics’: p q | q p = h (divided by 2n) /i (where p is the matrix variable for the momentum parameter, q is the matrix variable for the position parameter, h is Planck’s Constant and i is the square root of –1). To what are these terms referring in application to nothing whatsoever? What constitutes or plays the role of, say, the momentum parameter or position parameter or Planck’s Constant (inherently involving energy measurements in terms of joules per second), when the formula must purportedly function on the posited primordial absolute emptiness? I simply do not know what any such exnihilo theory could mean when there is no referent of any sort for the mathematical terms of the quantum formalism. For some suggestions regarding ‘origins of cosmic epochs’ that are purportedly congenial to both Whitehead’s thought and recent cosmological physics, see Griffin, Panentheism, chapters 2-3. See also my chapter (with Don Viney) on ‘Dipolar Theism and Cosmology’ in our The Mind of Charles Hartshorne (manuscript, chapter 8, forthcoming).

31. This section invites comparison with the chapter by Bell and Iyengar, ‘Whitehead and Kant at Copenhagen’, included in this volume. At first glance our approaches to the relationship between Whitehead and Kant would seem to stand in stark contrast. But I would suggest that I am simply articulating in a concrete way Whitehead’s specific rejection of Kant’s view of noumena as existential surds, leaving open the possibility of a special sense in which Whitehead offers a kind of ‘Kantian’ way forward toward a ‘future metaphysics’ that coalesces with quantum mechanical philosophy, as developed by Bell and Iyengar. They themselves acknowledge, of course, that Whitehead offers a critique of Kant’s perspective in the Harvard lectures; I am articulating important elements of that critique. But so far as I can see, this does not preclude Whitehead’s recognition of Kant’s genius nor does it preclude other qualified senses in which there can be ‘Kantian’ elements in Whitehead’s perspective.
32. Korner, Understanding Philosophy, 215-16; Rorty, ‘Transcendental Argument’, 82-3.
33. Korner, Kant, 41, my emphasis.
34. Compare Hartshorne’s quite similar rejection of the noumena/phenomena distinction in his commentary on Kant at PSG, 147.
35. Barker, Philosophy of Mathematics, 77.
36. Bradley, ‘Whitehead and the Analysis of the Propositional Function’, 139-51. Also see the section on ‘Anti-Realism and Excluded Middle’ in my paper ‘ A Logical Analysis of Relational Realism’ in Physics and Speculative Philosophy, 127-40.
37. Lango, Whitehead’s Ontology, ix.
38. 263 38. l, Leemon McHenry and I agree that there is some validity to the complaint of some analytic philosophers that the literary exposition of PR lends itself to obscurantism, but there is little merit in the perception that Whitehead did not give good reasons for his views. Indeed, a number of analytic philosophers have made their way full circle to embracing some central tenets of the philosophy of organism, including its panexperientialist-physicalist standpoint. See our ‘Analytical Critiques of Whitehead’s Metaphysics’; also available online at <http://journals.cambridge.org> (August 2016 issue). For what it is worth, Galen Strawson, whose perspective in his contemporary classic on ‘Realistic Monism’ is discussed in this paper, has expressed enthusiasm for our project.
39. See Martin, Whitehead’s Categoreal Scheme, esp. 1-26, for an extensionalist event-logical formalisation; Chiaraviglio,

‘Extension and Abstraction’, 205-16 for a set theoretic formalisation.

40. Lango, Whitehead’s Ontology, 95.
41. While Hartshorne often downplayed his expertise in this field, it is not often enough noticed that, because of his Harvard training in advanced logic as well as his editorial experience with Peirce’s logical papers, Hartshorne was tasked with teaching Symbolic Logic at the University of Chicago until Rudolf Carnap’s arrival. I venture the comment here that, for many professional philosophers, being assigned to teach logic at such a prestigious institution would be an imprimatur of one’s competence in the discipline.
42. Don Viney and I have articulated Hartshorne’s mature doctrine of matrices, tracking the history of its revisions, in our forthcoming volume The Mind of Charles Hartshorne (manuscript, chapter III, 14-17); see also our article ‘Hartshorne: Neoclassical Metaphysics’, in The Internet Encyclopedia of Philosophy <utm.edu>* the section on ‘Position Matrices’.
43. Hartshorne, ‘Foreword’ in Goodwin, The Ontological Argument, xv. See also the simple modal syllogistic presentation at CRE, 107. This version likewise dispenses with Becker’s Postulate. For A. N. Prior’s defence of Lewis’s S5, which includes Strong Reduction, see his Formal Logic, 2nd edition, esp. 198-206, section on ‘Iterated Modalities’. Because it concerns the abstract notion of necessary existence or ‘universal existential tolerance’, not concrete actualities, I submit that Hartshorne was correct to employ S5 as the appropriate modal system for the Argument’s presentation.
44. See CRE, 81-92 for a full explication.
45. For a defence of Hartshorne’s doctrine of future contingents against the objections of Steven Cahn, see my article on ‘Fate

and Logic’, 369-78; for an elaboration of the modal square of opposition for future tense propositions see my essay with Don Viney on ‘The Logic of Future Contingents’, in Process and Analysis, 216-21.

46. For a profound defence of Parmenides’ rejection of the possibility of sheer ontological emptiness, and one that shows that it is naive and implausible to assume that Parmenides rejected deep common-sense notions of a world of plural entities which move and change, see Munitz, ‘Making Sense of Parmenides’ in his Existence and Logic, 19-41. Also, see my paper ‘The Esti/To Eon Distinction in Parmenides’ Proem: A Defense of the Munitz Interpretation’ presented at the March 2016 annual meeting of the Metaphysical Society of America, Annapolis, MD. (This paper has not yet been submitted for publication but is available by request via email at emeritus. shieldsg@kysu.edu.)

 

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Abbreviations of Works Cited by Charles Hartshorne

AD

rj

Anselm’s Discovery: A Re-examination of the Ontological Proof for God’s Existence (La Salle, IL: Open Court, 1965)/

BH

Beyond Humanism: Essays in the Philosophy of Nature (Chicago: Willett, Clark & Company, 1937). Republished in 1975 by Peter Smith/¹

CAP

Creativity in American Philosophy (Albany: State University of New York Press, 1984)/

CRE

Creative Experiencing: A Philosophy of Freedom, ed. Donald Wayne Viney and Jincheol O (Albany: State University of New York Press, 2011)/¹

CS

Creative Synthesis and Philosophic Method (La Salle, IL: Open Court, 1970)/¹

DL

The Darkness and the Light: A Philosopher Reflects Upon His Fortunate Career and Those Who Made it Possible (Albany: State University of New York Press, 1990).

DR

The Divine Relativity: A Social Conception of God (New Haven: Yale University Press, 1948)/

EA

John B. Cobb, Jr. and Franklin L Gamwell (eds), Existence and Actuality: Conversations with Charles Hartshorne (Chicago: r—|

University of Chicago Press, 1984)/

IO

Insights and Oversights of Great Thinkers: An Evaluation of Western Philosophy (Albany: State University of New York Press, 1983).-’'”‘

LP

rj

The Logic of Perfection and Other Essays in Neoclassical Metaphysics (La Salle, IL: Open Court, 1962)/

OD

r-j

An Outline and Defense of the Unity of Being in the Absolute or Divine Good (PhD Dissertation, Harvard University, 1923)/

PCH

Lewis Edwin Hahn (ed.), The Philosophy of Charles Hartshorne, The Library of Living Philosophers, Volume XX (La Salle, IL: Open Court, 1991).

PSG

Philosophers Speak of God, with William L. Reese (Chicago: University of Chicago Press, 1953). Republished in 2000 by Humanity Books/

RSP

Reality as Social Process: Studies in Metaphysics and Religion (Boston: Beacon Press, 1953). Republished in 1971 by Hafner Publishing/”¹

WP

Whitehead’s Philosophy: Selected Essays, 1935-1970 (Lincoln: University of Nebraska Press, 1972)/”¹

ZF

r-j

The Zero Fallacy and Other Essays in Neoclassical Philosophy, ed. Mohammad Valady (Peru, IL: Open Court, 1997)/

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