In this paper, I inspect the grounds for the mature Spinozist argument for substance monism. The argument is succinctly stated at Ethics Part 1, Proposition 14. The argument appeals to two explicit premises: (1) that there must be a substance with all attributes; (2) that substances cannot share their attributes. In conjunction with a third implicit premise, that a substance cannot not have any attribute whatsoever, Spinoza infers that there can be no more than one (...) class='Hi'>substance. I begin the inspection with the analysis of the first premise, which is provided in the form of the four proofs of God’s existence in Ethics Part 1, Proposition 11. While demonstrating how Spinoza adopts a progressive approach, where the fourth proof of God’s existence is more successful and persuasive than the third, which is more successful than the second, etc., I also unpack concepts central to Spinoza’s thinking here, including the concepts of reason (ratio) and power (potesta or potentia). I then analyze the second premise of the Spinozist argument for substance monism, as established by Ethics Part 1, Proposition 4 in conjunction with Ethics Part 1, Proposition 5. I take up and respond to the objection attributed to Leibniz that a substance p can have the attributes x and y and a substance q can have the attributes y and z, and thus that substances can share some attributes while remaining distinct. Throughout the study, my attention is focused on the argumentative procedures Spinoza adopts. This yields a close, internalist reading of the text where Spinoza effectively embraces substance monism. In conclusion to this study, I underscore to the originality of Spinoza’s argument for seventeenth century theories of substance. (shrink)

Neuere Interpretationen von Leibniz' Notizen zur Metaphysik aus den Jahren 1675-1676 tendieren dazu, diese Texte im Licht eines spinozistischen Substanz-Monismus zu lesen. Obwohl es für eine solche Interpretation überzeugende Anhaltspunkte gibt, vertritt Leibniz jedoch in denselben Texten auch einen Substanzen-Pluralismus in Bezug auf geistige Substanzen. Substanz-Monismus und Substanzen-Pluralismus scheinen miteinander vereinbar zu sein, weil für Leibniz, ähnlich wie für Descartes in den Principia philosophiae, der Terminus ‚Substanz‛ nicht in univoker Weise von Gott und von Gegenständen in der Welt ausgesagt werden (...) kann. (shrink)

In this paper I try to combine the objectology of Meinong with a neutral substance monism of the kind originally proposed by Spinoza (deus sive natura). Yet Spinoza was still stuck in the Cartesian paradigm and therefore rather gave a dual monism (extensio et intellectus) than a proper neutral monism. I propose that there are only two attributes of the one substance: existence and non-existence. Everything else is/are mere modes of them.

Between 1653 and 1655 Margaret Cavendish makes a radical transition in her theory of matter, rejecting her earlier atomism in favour of an infinitely-extended and infinitely-divisible material plenum, with matter being ubiquitously self-moving, sensing, and rational. It is unclear, however, if Cavendish can actually dispense of atomism. One of her arguments against atomism, for example, depends upon the created world being harmonious and orderly, a premise Cavendish herself repeatedly undermines by noting nature’s many disorders. I argue that her supposed difficulties (...) with atomism expose a deeper tension in her work between two fundamental metaphysical commitments each of which has substantial philosophical support: her monist theory of the material world (which maintains that there exists just one natural substance which is the single principal cause) and her occasional theory of causation (which requires multiple finite principal causes in nature -- causes that might be considered individual substances). Her monism undermines atomism while her theory of occasional cause seems to rest on a conception of nature that would be especially friendly to atomism. I argue further that we can solve this tension within a Cavendishian framework in such a way as to preserve her theory of causation and her monism, but that this solution depends upon our taking her monism in a particular (and weak) form. I finally note that we can best make sense of her unique and interesting form of monism by acknowledging her social-political motivations in addition to her motivations in natural philosophy. (shrink)

An old question in Spinoza scholarship is how finite, non-eternal things transitively caused by other finite, non-eternal things (i. e., the entities described in propositions like E1p28) are caused by the infinite, eternal substance, given that what follows either directly or indirectly from the divine nature is infinite and eternal (E1p21–23). In “Spinoza’s Monism I,” “Spinoza’s Monism I,” in the previous issue of this journal. I pointed out that most commentators answer this question by invoking entities that (...) are indefinite and sempiternal, but argued that perhaps we should not be so quick to assume that in Spinoza’s system, an infinite and eternal substance could cause such indefinite, sempiternal entities. But if such eternal-durational causation is denied, then it seems harder to see how Spinoza’s system could be coherent: if Spinoza holds that the infinite, eternal substance cannot cause anything that is not infinite and not eternal, then how can he also hold that all things are modes immanently caused by substance (E1p15, E1p18, E1p25)? In this essay, I explain how Spinoza’s system could be understood in light of a denial of eternal-durational causation. On the interpretation I offer, God is the cause of all things and all things are modes because the essences of all things follow from the divine nature and all essences enjoy infinite, eternal reality as modes immanently caused by the infinite, eternal substance. The same non-substantial essences can also be conceived as enjoying non-infinite, non-eternal reality, but so conceived, they are enduring, finite (or sempiternal, indefinite) entities that cannot be conceived as modes caused by and inhering in the one infinite, eternal substance. I conclude by pointing out that if we take this interpretive route, we do have to understand Spinoza as committed to acosmism, or a denial of the reality of the world – at least the world of enduring, finite things. (shrink)

‘Substance’ (substantia, zelfstandigheid) is a key term of Spinoza’s philosophy. Like almost all of Spinoza’s philosophical vocabulary, Spinoza did not invent this term, which has a long history that can be traced back at least to Aristotle. Yet, Spinoza radicalized the traditional notion of substance and made a very powerful use of it by demonstrating – or at least attempting to demonstrate -- that there is only one, unique substance -- God (or Nature) -- and that all (...) other things are merely modes or states of God. Some of Spinoza’s readers understood these claims as committing him to the view that only God truly exists, and while this interpretation is not groundless, we will later see that this enticing and bold reading of Spinoza as an ‘acosmist’ comes at the expense of another audacious claim Spinoza advances, i.e., that God/Nature is absolutely and actually infinite. But before we reach this last conclusion, we have a long way to go. So, let me first provide an overview of our plan. In the first section of this paper we will examine Spinoza’s definitions of ‘substance’ and ‘God’ at the opening of his magnum opus, the Ethics. Following a preliminary clarification of these two terms and their relations to the other key terms defined at the beginning of the Ethics, we will briefly address the Aristotelian and Cartesian background of Spinoza’s discussion of substance. In the second section, we will study the properties of the fundamental binary relations pertaining to Spinoza’s substance: inherence, conception, and causation. The third section will be dedicated to a clarification of Spinoza’s claim that God, the unique substance, is absolutely infinite. This essential feature of Spinoza’s substance has been largely neglected in recent Anglo-American scholarship, a neglect which has brought about an unfortunate tendency to domesticate Spinoza’s metaphysics to more contemporary views. The fourth section will study the nature of Spinoza’s monism. It will discuss and criticize the interesting yet controversial views of the eminent Spinoza scholar, Martial Gueroult, about the plurality of substances in the beginning of the Ethics; address Spinoza’s claim in Letter 50 that, strictly speaking, it is improper to describe God as “one”; and, finally, evaluate Spinoza’s kind of monism against the distinction between existence and priority monism recently introduced into the contemporary philosophical literature. The fifth and final section will explain the nature, reality, and manner of existence of modes. We therefore have an ambitious plan; let’s get down to business. (shrink)

‘Substance’ (substantia, zelfstandigheid) is a key term of Spinoza’s philosophy. Like almost all of Spinoza’s philosophical vocabulary, Spinoza did not invent this term, which has a long history that can be traced back at least to Aristotle. Yet, Spinoza radicalized the traditional notion of substance and made a very powerful use of it by demonstrating – or at least attempting to demonstrate -- that there is only one, unique substance -- God (or Nature) -- and that all (...) other things are merely modes or states of God. Some of Spinoza’s readers understood these claims as committing him to the view that only God truly exists, and while this interpretation is not groundless, we will later see that this enticing and bold reading of Spinoza as an ‘acosmist’ comes at the expense of another audacious claim Spinoza advances, i.e., that God/Nature is absolutely and actually infinite. But before we reach this last conclusion, we have a long way to go. So, let me first provide an overview of our plan. In the first section of this paper we will examine Spinoza’s definitions of ‘substance’ and ‘God’ at the opening of his magnum opus, the Ethics. Following a preliminary clarification of these two terms and their relations to the other key terms defined at the beginning of the Ethics, we will briefly address the Aristotelian and Cartesian background of Spinoza’s discussion of substance. In the second section, we will study the properties of the fundamental binary relations pertaining to Spinoza’s substance: inherence, conception, and causation. The third section will be dedicated to a clarification of Spinoza’s claim that God, the unique substance, is absolutely infinite. This essential feature of Spinoza’s substance has been largely neglected in recent Anglo-American scholarship, a neglect which has brought about an unfortunate tendency to domesticate Spinoza’s metaphysics to more contemporary views. The fourth section will study the nature of Spinoza’s monism. It will discuss and criticize the interesting yet controversial views of the eminent Spinoza scholar, Martial Gueroult, about the plurality of substances in the beginning of the Ethics; address Spinoza’s claim in Letter 50 that, strictly speaking, it is improper to describe God as “one”; and, finally, evaluate Spinoza’s kind of monism against the distinction between existence and priority monism recently introduced into the contemporary philosophical literature. The fifth and final section will explain the nature, reality, and manner of existence of modes. We therefore have an ambitious plan; let’s get down to business. (shrink)

According to “existence monism,” there is only one concrete particular, the cosmos as a whole (Horgan and Potrč 2000, 2008). According to “priority monism,” there are many concrete particulars, but all are ontologically dependent upon the cosmos as a whole, which accordingly is the only fundamental concrete particular (Schaffer 2010a, 2010b). In essence, the difference between them is that existence monism does not recognize any parts of the cosmos, whereas priority monism does – it just insists (...) that the parts are ontologically dependent upon the whole in this case. Brentano never maintained either of these views. But in the last two years of his life, he seems to have held the following approximation: there is only one physical substance, namely, the material universe as a whole. This is twice removed from existence or priority monism: first, it allows for a plurality of mental substances (souls); secondly, it allows for a plurality of physical accidents, which in Brentano’s reistic ontology are also concrete particulars. Still, the view that the only physical substance is the universe as a whole is quite radical and finds little precedent in the history of philosophy. (shrink)

In this essay, I suggest that Spinoza acknowledges a distinction between formal reality that is infinite and timelessly eternal and formal reality that is non-infinite (i. e., finite or indefinite) and non-eternal (i. e., enduring). I also argue that if, in Spinoza’s system, only intelligible causation is genuine causation, then infinite, timelessly eternal formal reality cannot cause non-infinite, non-eternal formal reality. A denial of eternal-durational causation generates a puzzle, however: if no enduring thing – not even the sempiternal, indefinite individual (...) composed of all finite, enduring things – is caused by the infinite, eternal substance, then how can Spinoza consistently hold that the one infinite, eternal substance is the cause of all things and that all things are modes of that substance? At the end of this essay, I sketch how Spinoza could deny eternal-durational causation while still holding that an infinite, eternal God is the cause of all things and that all things are modes. I develop the interpretation more in the companion essay.1 1 In “Spinoza’s Monism II,” in the next issue of this journal. (shrink)

According to the Monist Interpretation of Descartes, there is really only one corporeal substance—the entire extended plenum. Evidence for this interpretation seems to be provided by Descartes in the Synopsis of the Meditations, where he claims that all substances are incorruptible. Finite bodies, being corruptible, would then fail to be substances. On the other hand, ‘body, taken in the general sense,’ being incorruptible, would be a corporeal substance. In this paper, I defend a Pluralist Interpretation of Descartes, according (...) to which there are many corporeal substances. In particular, I show that none of the claims in the Synopsis about incorruptibility and substance entail either that finite bodies are not substances, or that the only corporeal substance is the entire plenum. (shrink)

Yitzhak Melamed here offers a new and systematic interpretation of the core of Spinoza's metaphysics. In the first part of the book, he proposes a new reading of the metaphysics of substance in Spinoza: he argues that for Spinoza modes both inhere in and are predicated of God. Using extensive textual evidence, he shows that Spinoza considered modes to be God's propria. He goes on to clarify Spinoza's understanding of infinity, mereological relations, infinite modes, and the flow of finite (...) things from God's essence. In the second part of the book, Melamed relies on this interpretation of the substance-mode relation and the nature of infinite modes and puts forward two interrelated theses about the structure of the attribute of Thought and its overarching role in Spinoza's metaphysics. First, he shows that Spinoza had not one, but two independent doctrines of parallelism. Then, in his final main thesis, Melamed argues that, for Spinoza, ideas have a multifaceted structure that allows one and the same idea to represent the infinitely many modes which are parallel to it in the infinitely many attributes. Thought turns out to be coextensive with the whole of nature. Spinoza cannot embrace an idealist reduction of Extension to Thought because of his commitment to the conceptual separation of the attributes. Yet, within Spinoza's metaphysics, Thought clearly has primacy over the other attributes insofar as it is the only attribute which is as elaborate, as complex, and, in some senses, as powerful as God. (shrink)

In their book on Descartes’s Changing Mind, Peter Machamer and J. E. McGuire argue that Descartes discarded dualism to embrace a kind of monism. Descartes famously proposed that there are two separate substances, mind and body, with distinct attributes of thought and extension. According to Machamer and McGuire, because of the limitations of our intellect, we cannot have insight into the nature of either substance. After reviewing their argument in some detail, I will argue that Descartes did not (...) relinquish his favorite doctrine but may have actually fooled himself about the nature of his dualism. It is my contention that the problem with Cartesian dualism stems from the definition of mind and body as substances and the role of their respective attributes—thought and extension—in the definition of substances. (shrink)

Experiences of enlightened unity with Nature or with Deity are reported not only in the mystical literature of the past but also in contemporary accounts of the psychedelic adventurer. In Chapter 13, Peter Sjöstedt-Hughes seeks to fathom such reported states within the framework of the metaphysics of Benedict de Spinoza – a metaphysics encompassing monism, pantheism, panpsychism, and the eternal substance: the timelessness of pure Nature, God itself. God is Nature for Spinoza. To achieve this framework, the tenets (...) of Spinozism are explicated with a culmination in the Intellectual Love of God, amor Dei intellectualis, where the finite mind and infinite intellect of Nature unite. Sjöstedt-Hughes then provides a phenomenological account of the unitive states occasioned by certain psychedelic substances, notably the ever-so potent 5-MeO-DMT, comparing these phenomenological elements to the ontological aspects of Spinozism. This comparative analysis will proffer a Spinozan-Psychedelic symbiosis: that certain psychedelic states can be understood through the Spinozan system, and that the Spinozan system can be intuited through certain psychedelic states – a blinding flash of Spinozism that can change one’s relation to oneself and to Nature itself. (shrink)

What is the role of the principle of sufficient reason in Baruch Spinoza’s ontological proof for God’s existence? Is this role identical within Spinoza’s early work on method, the Treatise on the Emendation of the Intellect, and his magnum opus, the Ethics? This paper argues affirmatively that the methodology employed within the Ethics is consonant with that method found within the Treatise, and this claim is substantiated through an engagement with the influential works of Don Garrett and Aaron Garrett. It (...) is also demonstrated through an original reconstruction of the Treatise itself. In this reconstruction, basic premises are identified which can validly prove Spinoza’s intended conclusion of substance monism. It is finally determined that what the Treatise and the Ethics share, specifically, is a methodology which begins with non-nominal definitions that denote the real, sufficient causes of their respective objects. However, at certain junctures, this methodology is expressed with greater consistency within the Treatise as opposed to within the Ethics. Evidence for this will be provided from the primary texts themselves and from the subsequent analyses of Don Garrett and Aaron Garret as well. (shrink)

This paper addresses the issue of how to best account for the diversity of our (synchronic) mental activities. The discussion starts with Mark Textor’s mental monism. According to mental monism, our mental life is constituted by just one simple mental act, in which different sub-acts can be conceptually distinguished. Textor grounds this view in the work of the early Brentano and contrasts it with the theory of the later Brentano, who introduces a mental substance into his philosophy. (...) According to Textor, Brentano needs a substance because he is unable to explain how mental monism can account for the separability of our mental activities, e.g. the fact that I can stop hearing F while still seeing blue. Textor argues, however, that mental monism can solve this problem. I address two issues regarding Textor’s view. First, I challenge his interpretation of Brentano by arguing that the early Brentano imports ontological complexity into our mental life; I defend Brentano’s view against possible criticisms, and I address some objections to mental monism. Second, I oppose Textor’s narrative about the mental substance. I argue that Brentano needs a substance not to explain separability, but rather to individuate our mental acts. I still argue, however, that Brentano’s earlier view (understood in my sense) is better than the substance account for dividing the mind. (shrink)

This essay offers an interpretation of Descartes’ treatment of the concepts of place and space in the Principles of Philosophy. On the basis of that interpretation, I argue that his understanding and application of the concept of space supports a pluralist interpretation of Descartes on extended substance. I survey the Scholastic evolution of issues in the Aristotelian theory of place and clarify elements of Descartes’ appropriation and transformation thereof: the relationship between internal and external place, the precise content of (...) the claim that space and body are really identical, and the way we conceptually distinguish space from body. Descartes applies his concept of space in ways that illuminate the metaphysical structure of extension. In particular, he uses the concept to specify the degree to which finite parts of matter are independent of each other. I argue that for Descartes, conceiving extension as indivisible is an artifact of conceiving it as a space. That is, pace the monistic reading of Cartesian extended substance, regarding extension as indivisible is an artifact of conceiving it in a way more removed from its real nature. (shrink)

This paper will set out in plain language the basic ontology of “Deleuze’s Spinoza”; it will then critically examine whether such a Spinoza has, or indeed could have, ever truly existed. In this, it will be shown that Deleuze’s reading of Spinoza involves the imposition of three interlocking, formal principles. These are (1) Necessitarianism, (2) Immanence, and (3) Univocity. The uncovering of Deleuze’s use of these three principles, how they relate to one another, and what they jointly imply in terms (...) of ontology, will occupy Part 1 of this paper. The critique of these principles from a Spinozist perspective, i.e. that their use by Deleuze is incompatible with Spinoza’s own metaphysics, will occupy Part 2 of this paper. (shrink)

ABSTRACTMost of Spinoza’s arguments for God’s existence do not rely on any special feature of God, but instead on merely general features of substance. This raises the following worry: those arguments prove the existence of non-divine substances just as much as they prove God’s existence, and yet there is not enough room in Spinoza’s system for all these substances. I argue that Spinoza attempts to solve this problem by using a principle of plenitude to rule out the existence of (...) other substances and that the principle cannot be derived from the PSR, as many claim.Abbreviation: PSR: Principle of Sufficient Reason. (shrink)

“Why did God create the World?” is one of the traditional questions of theology. In the twentieth century this question was rephrased in a secularized manner as “Why is there something rather than nothing?” While creation - at least in its traditional, temporal, sense - has little place in Spinoza’s system, a variant of the same questions puts Spinoza’s system under significant pressure. According to Spinoza, God, or the substance, has infinitely many modes. This infinity of modes follow from (...) the essence of God. If we ask: “Why must God have modes?,” we seem to be trapped in a real catch. On the one hand, Spinoza’s commitment to thoroughgoing rationalism demands that there must be a reason for the existence of the radical plurality of modes. On the other hand, the asymmetric dependence of modes on the substance seems to imply that the substance does not need the modes, and that it can exist without the modes. But if the substance does not need the modes, then why are there modes at all? Furthermore, Spinoza cannot explain the existence of modes as an arbitrary act of grace on God’s side since Spinoza’s God does not act arbitrarily. Surprisingly, this problem has hardly been addressed in the existing literature on Spinoza’s metaphysics, and it is my primary aim here to draw attention to this problem. In the first part of the paper I will present and explain the problem of justifying the existence of infinite plurality modes in Spinoza’s system. In the second part of the paper I consider the radical solution to the problem according to which modes do not really exist, and show that this solution must be rejected upon consideration. In the third and final part of the paper I will suggest my own solution according to which the essence of God is active and it is this feature of God’s essence which requires the flow of modes from God’s essence. I also suggest that Spinoza considered radical infinity and radical unity to be roughly the same, and that the absolute infinity of what follow from God’s essence is grounded in the absolute infinity of God’s essence itself. (shrink)

In Ethics 1p5, Spinoza asserts that “In Nature there cannot be two or more substances of the same nature or attribute”. This claim serves as a crucial premise in Spinoza’s argument for substance monism, yet Spinoza’s demonstration of the 1p5 claim is surprisingly brief and appears to have obvious difficulties. This paper answers the principle difficulties that have been raised in response to Spinoza’s argument for 1p5. The key to understanding the 1p5 argument lies in a proper understanding (...) of the substance-attribute relationship and the principles of metaphysical individuation that Spinoza accepts. (shrink)

This article has two goals: a historical and a speculative one. The historical goal is to offer a coherent account of Spinoza’s view on mereological composition. The speculative goal is to show that Spinoza’s substance monism is distinct from versions of monism that are currently defended in metaphysics and that it deserves the attention of contemporary metaphysicians. Regarding the second goal, two versions of monism are currently defended and discussed in contemporary metaphysics: existence monism according (...) to which there actually exists exactly one concrete entity; and priority monism that is famously defended by Jonathan Schaffer and according to which there exists exactly one fundamental concrete being, the cosmos, and several derivative concrete beings that are the parts of the cosmos. In this article, I argue that substance monism is neither an existence nor a priority monism because, while Spinoza’s monist is committed to the existence of a unique fundamental individual—the substance—and to the existence of several derivative individuals—the bodies or modes of extension—, Spinoza denies that the substance is mereologically complex. Regarding the first goal, the paper solves several interpretative puzzles by arguing that Spinoza distinguishes between three kinds of composition and that his talk of composition between the substance and its modes is by his own light not to be interpreted as literally true. (shrink)

François Lamy, a Benedictine monk and Cartesian philosopher whose extensive relations with Arnauld, Bossuet, Fénélon, and Malebranche put him into contact with the intellectual elite of late-seventeenth-century France, authored the very first detailed and explicit refutation of Spinoza’s Ethics in French, Le nouvel athéisme renversé. Regrettably overlooked in the secondary literature on Spinoza, Lamy is an interesting figure in his own right, and his anti-Spinozist work sheds important light on Cartesian assumptions that inform the earliest phase of Spinoza’s critical reception (...) in the seventeenth-century. I begin by presenting Lamy’s life and the contentious state of Spinoza’s French reception in the 1680 and 1690s. I then discuss a central argument in Lamy’s refutation, namely the Cartesian objection that Spinoza’s account of the conceptual independence of attributes is incompatible with the theory of substance monism. Contrasting Lamy’s objection with questions put to Spinoza by de Vries and Tschirnhaus, I maintain that by exhibiting the direction Spinoza’s views on substance and attribute took in maturing we may accurately assess the strength of Spinoza’s position vis-à-vis his Cartesian objector, and I argue that, in fact, Spinoza’s mature account of God as an expressive ens realissimum is not vulnerable to Lamy’s criticism. In conclusion, I turn to Lamy’s objection that Spinoza’s philosophy is question-begging in view of Spinoza’s account of God, and I exhibit what this point of criticism tells us about the intentions of the first French Cartesian rebuttal of the Ethics. (shrink)

It is well known that Kant seeks to discredit rational psychology on the grounds that we cannot access the nature of the soul by reflecting upon the ‘I think’ of self-consciousness. What is far less understood, however, is why Kant still believes the theorems of rational psychology are analytically true insofar as they represent the ‘I’ through the categories of substance, reality, unity, and existence. Early post-Kantian thinkers like Fichte would abandon this restriction and approach the concept of the (...) ‘I’ instead through the category of community or reciprocal interaction. The result was nothing less than a radical shift in thinking about persons after Kant, yet in a way that would bear a striking affinity to the substance monism of Spinoza. The aim of this chapter is to trace the origin of this shift and its aftermath in Fichte’s effort to defend a new conception of the ‘I’. (shrink)

This paper argues that Nietzsche is a panpsychist. Panpsychism holds that mental features are ubiquitous and fundamental in reality. I first argue that Nietzsche’s rejection of Cartesian dualism leads him to substance monism. To better understand his monism, I examine Nietzsche’s rejection of Newtonian atomism. Nietzsche holds that bundles of forces, or will to power, are more fundamental than hard, extended atoms. So, will to power is fundamental. I then investigate Nietzsche’s remarks on organic and inorganic nature (...) to show that he believes both are will to power. So, will to power is ubiquitous. The final step to panpsychism is to show that Nietzsche believes will to power exhibits mental qualities. If all goes well, it should emerge that Nietzsche thinks mental features are fundamental and ubiquitous in reality. (shrink)

Andrew Chignell and Omri Boehm have recently argued that Kant’s pre-Critical proof for the existence of God entails a Spinozistic conception of God and hence substance monism. The basis for this reading is the assumption common in the literature that God grounds possibilities by exemplifying them. In this article I take issue with this assumption and argue for an alternative Leibnizian reading, according to which possibilities are grounded in essences united in God’s mind (later also described as Platonic (...) ideas intuited by God). I show that this view about the distinction between God’s cognition of essences as the ground of possibility and the actual world is not only explicitly stated by Kant, but is also consistent with his metaphysical picture of teleology in nature and causality during the pre-Critical period. Finally, I suggest that the distinction between the conceptual order of essences embodied in the idea of God and the order of the objects of experience plays a role in the transition into the Critical system, where it is transformed into the distinction between the intelligible and the sensible worlds. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Newton's Metaphysics: Essays by Eric SchliesserMarius StanEric Schliesser. Newton's Metaphysics: Essays. Oxford: Oxford University Press, 2021. Pp. 328. Hardback, $99.90.Newton owes his high regard to the quantitative science he left us, but his overall picture of the world had some robustly metaphysical threads woven in as well. Posthumous judgment about the value of these threads has varied wildly. Christian Wolff thought him a metaphysical rustic, as did Hans (...) Reichenbach some two centuries later ("Die Bewegungslehre bei Newton, Leibniz und Huygens," Kant-Studien 29 [1924]: 416–38). In the 1960s, the tide would turn, as Howard Stein and James Edward McGuire separately began to show that Newton's metaphysics was not just sophisticated, but often more compelling than its early modern alternatives (see respectively "Newtonian Spacetime," Texas Quarterly 10 [1967]: 174–200; and Tradition and Innovation: Newton's Metaphysics of Nature [Dordrecht: Kluwer Academic Publishers, 1995]). Eric Schliesser's book unfolds in that same register of appreciative, high scholarship, and it attests to the enduring attraction of its subject.The book grew out of previous discrete papers, to which he added a few more for this occasion. Accordingly, it does not come with a master argument. Rather, it is an in-depth exploration of some key metaphysical themes in Newton. As such, it befits its subject figure, who reflected on themes and concepts while stopping short of working out systems.The first major theme is Newton and Spinozism. The latter does not denote Spinoza's metaphysics. In fact, Schliesser explains, Newton shared with Spinoza some weighty commitments, for example, to space being actually infinite, and to substance monism: "for Newton, there is strictly speaking only one genuine substance," namely, God (33). Rather, "Spinozism" is an interpreter's category for a bundle of three theses: identifying God and nature; denying final causation in the physical world; and the assumption of "blind" metaphysical necessity. Some counted Hobbes and John Toland as Spinozist in this sense, and even Epicurus, avant la lettre. Newton and his followers argued vehemently against this package, as Schliesser shows in chapters 4, 5, and 8. Their chief complaint was that Spinozism is unable to account for the "origin of motion," for a certain type of order, and for the stability of cosmological structure—and to do so in a way that "meets the standards of Newtonian mechanics" (122). This interpretive lens allows Schliesser to draw Kant in, by reading his youthful Theory of Heaven as a possible Spinozist reply to their objections (chapter 3). [End Page 157]A second theme is the metaphysics of mechanics, where Schliesser weaves together several strands. One is the ontology of gravity, for which he offers a novel construal: for Newton, gravity counts as real, but in a qualified sense. Namely, it is not essential and not intrinsic: "even after creation, a lonely partless particle of matter in the universe would not be said to gravitate." And gravity is relational: a "shared quality" of two or more bits of matter, which obtains in virtue of their sharing a nature (19). Another strand is Newton's ontology of time—really, a subtle, difficult topic long neglected. Famously, Newton in Principia defends absolute, true, and mathematical time. The question is what these three qualifiers denote, and whether Newton thought they were synonymous. Schliesser in chapter 7 argues for the provocative view that "absolute" and "true" time are not identical concepts; rather, they pick out different entities. These entities share a common structure, namely, metric and topological. That makes them species of "mathematical" time (179). But, Schliesser contends, Newton has unequal warrant for his two concepts of time.Yet another theme is formal causation. It comes to the fore in chapter 5, which grapples with Newton's opaque idea that space is an "emanative effect." Schliesser explains that here, "emanation picks out a species of formal causation" (147), but in a novel, early modern sense that comes from Bacon, not Aristotle. If space has a formal cause, then so has its twin brother, time, the topic of chapter 7. God is their common formal cause. Then in chapter 6 (coauthored with Zvi Biener) Schliesser adds that, for Newton, laws... (shrink)

Can the neo-Aristotelian uphold a pluralist substance ontology while taking seriously the recent arguments in favour of monism based on quantum holism and other arguments from quantum mechanics? In this article, Jonathan Schaffer’s priority monism will be the main target. It will be argued that the case from quantum mechanics in favour of priority monism does face some challenges. Moreover, if the neo-Aristotelian is willing to consider alternative ways to understand ‘substance’, there may yet be (...) hope for a pluralist substance ontology. A speculative case for such an ontology will be constructed based on primitive incompatibility. (shrink)

This paper offers a new interpretation of Spinoza's doctrine of parallelism. It argues Spinoza reinterprets the ancient doctrine of metaphysical sympathy among ostensibly disconnected and distant beings in terms of fully intelligible relations of 1) identity between formal and objective reality, and in terms of 2) "real identity," grounded in Spinoza's substance-monism. Finally, the paper argues against the standard reading of mind-body pairs as "numerically identical".

Spinoza’s account of memory has not received enough attention, even though it is relevant for his theory of consciousness. Recent literature has studied the “pancreas problem.” This paper argues that there is an analogous problem for memories: if memories are in the mind, why is the mind not conscious of them? I argue that Spinoza’s account of memory can be better reconstructed in the context of Descartes’s account to show that Spinoza responded to these views. Descartes accounted for the preservation (...) of memories by holding that they are brain states without corresponding mental states, and that the mind is able to interpret perception either as new experience or as memory. Spinoza has none of these conceptual resources because of his substance monism. Spinoza accounts for memories as the mind’s ability to generate ideas according to the order of images. This ability consists in the connection of ideas, which is not an actual property, but only a dispositional one and thus not conscious. It is, however, grounded in the actual property of parts of the body, of which ideas are conscious. (shrink)

The tenth proposition of Spinoza’s Ethics reads: ‘Each attribute of substance must be conceived through itself.’ Developing and defending the argument for this single proposition, it turns out, is vital to Spinoza’s philosophical project. Indeed, it’s virtually impossible to overstate its importance. Spinoza and his interpreters have used EIp10 to prove central claims in his metaphysics and philosophy of mind (i.e., substance monism, mind-body parallelism, mind-body identity, and finite subject individuation). It’s crucial for making sense of his (...) epistemology (i.e., Spinoza’s account of knowledge and response to skepticism) and in resolving puzzles within the Ethics (i.e., explaining human ignorance of all but two attributes). Even those who do not attribute some of the above claims to Spinoza need EIp10 to defend much of what they believe about Spinoza’s system. This paper locates a previously unnoticed argument for this proposition in Spinoza’s Short Treatise on God, Man, and His Well Being. There, Spinoza shows himself concerned with a powerful and underappreciated form of philosophical skepticism, one with surprising echoes in the work of his contemporary Leibniz as well as in the later Wittgenstein. Spinoza’s introduction of E1p10 in the Ethics circumvents this form of skepticism, solving the problem the Short Treatise envisions while also explaining that text’s argument’s absence from the explicit justificatory structure of the Ethics. (shrink)

"This 'paper' is meant to be an introduction to three other papers of mine, namely: 'The "Emergence" of Existence' (cf. http://www.academia.edu/4310644/The_Emergence_of_Existence_-_from_Pregeometry_to_Prephysics), 'Names and Objects' (cf. http://www.academia.edu/4310705/Names_and_Objects_-_Outlines_of_an_Essentialist_Nominalism), and 'Information Monism' (cf. http://www.academia.edu/4310969/Information_Monism_-_and_its_Concepts_of_Substance_Attributes_and_Em ergent_Modes). In this introduction also some light shall be shed on the mutual dependence and interrelatedness of these mentioned papers. It also includes a hefty attack on Russell's 'On Denotation' with respect to his alleged refutation of Meinong's Gegenstandstheorie (objectology aka theory of objects).".

This paper introduces an innovative analogy between two conceptual trios: 'form, matter, substance' from Aristotelian hylomorphism, and the original 'metaphor, consciousness, emergence' trio, which, while inspired by contemporary philosophy of language, is a novel contribution not previously articulated in the literature. This exploration delves into the intricate interplay of these concepts, seeking to illuminate their profound interconnectedness and its implications for our understanding of reality. By redefining key terms and incorporating the overarching concept of 'thing', this study aims to (...) unravel the complex interplay within these trios and its consequences, thereby challenging conventional interpretations and inviting a reevaluation of fundamental philosophical principles. The analogy seeks not only to provide new perspectives for understanding the intricacies of these concepts but also to expand upon the definitions of the terms themselves. It endeavors to bridge the gap between metaphysical insights and linguistic theories, thereby offering a unique synthesis that contributes to both fields and enhances our conceptual vocabulary. Furthermore, the paper extends the discussion to monistic views of the universe, proposing a synthesis of diverse theories under a single, unifying reality. This approach offers fresh insights, especially in understanding the dynamic nature of consciousness and matter, as well as our perception of reality and creation. Just as Plato's allegory of the cave revealed truths about perception and reality, this paper attempts to uncover deeper metaphysical and linguistic connections. It posits that these connections offer a more comprehensive understanding of the complexities of human cognition and the nature of existence. This analogy represents a metaphorical journey itself, reflecting the continuous quest for deeper understanding in the vast and intricate landscape of philosophical thought. It invites readers to consider the multifaceted nature of reality and its profound impact in shaping our perceptions and understanding of the world. (shrink)

In this essay, I present the basics of Spinoza’s ontology and attempt to go some distance toward clarifying its most pertinent problems. I start by considering the relationship between the concepts of substance and mode; my aim is to show that despite his somewhat peculiar vocabulary there is much here that we should find rather familiar and intelligible, as Spinoza’s understanding of these matters harks back to the traditional distinction of substance and accident, or thing and property. After (...) this I move on to fitting the concept of attribute into Spinoza’s conceptual architecture, and then examine the implications concerning real existents and causation that Spinoza sees these fundamental conceptual commitments as having. The most startling of these implications is of course his monism, according to which there is only one substance. Through this examination it becomes clear that it is only when Spinoza makes the transition from considerations concerning concepts to existential claims that the collision with what was previously commonly accepted becomes inevitable. (shrink)

Advocating a sociological explanation of scientific knowledge, David Bloor protests against the adherents of the autonomy of knowledge; i.e., those who asymmetrically explain the credibility of theories in the history of science. These philosophers and historians regard the credibility of true and rational theories due to their proper reasons, while accounting for the acceptance of false or irrational beliefs by citing social causes. Bloor assumes that the credibility of all beliefs is socially influenced, and therefore considers all in need of (...) sociological explanation. To substantiate this claim, he argues that all epistemic factors that are appealed to in explaining true or rational beliefs are really social. However, this argument aligns rational entities with social factors, and thus, undermines the ground of this division. Therefore, his prior complaint of the autonomy of knowledge would be invalidated. Hence, there is a conflict between Bloor’s objection to the asymmetrical explanation of scientific theories and his account of the social construction of epistemic reasons. In this paper, we reveal this concealed conflict and attempt to suggest ways to resolve it. (shrink)

Does Anne Conway (1631–79) hold that the created world consists of a single underlying substance? Some have argued that she does; others have argued that she is a priority monist and so holds that there are many created substances, but the whole created world is ontologically prior to each particular creature. Against both of these proposals, this article makes the case for a substance pluralist interpretation of Conway: individual creatures are distinct substances, and the whole created world is (...) not ontologically prior to the individual creatures that compose it. The basic argument for such a view draws on Conway's claims about the freedom and moral responsibility of individual creatures. The pluralist reading is straightforwardly compatible with these claims, while the monistic readings are not. (shrink)

I argue that Schaffer’s recent defence of Spinozan Monism—the thesis that the cosmos is the only substance, or the only fundamental and integrated thing— fails to establish that the universe is uniquely fundamental. In addition, Schaffer’s own defence of his thesis offers the pluralist about fundamentality a model for responding to Schaffer’s criticism of pluralism.

I will introduce and motivate eliminativist super-relationism. This is the conjunction of relationism about spacetime and eliminativism about material objects. According to the view, the universe is a big collection of spatio-temporal relations and natural properties, and no substance (material or spatio-temporal) exists in it. The view is original since eliminativism about material objects, when understood as including not only ordinary objects like tables or chairs but also physical particles, is generally taken to imply substantivalism about spacetime: if properties (...) are directly instantiated by spacetime without the mediation of material objects, then, surely, spacetime has to be a substance. After introducing briefly the two debates about spacetime (§1) and material objects (§2), I will present Schaffer's super-substantivalism (§3), the conjunction of substantivalism about spacetime and eliminativism about material objects at the fundamental level. I shall then expose and discuss the assumption from which the implication from eliminativism to substantivalism is drawn, and discuss the compatibility of eliminativism with relationism: if spacetime is not a substance, and if material objects are not real, how are we to understand the instantiation of properties (§4)? And what are the relata of spatio-temporal relations (§5)? I then show that each argument in favor of super-substantivalism offered by Schaffer also holds for super-relationism (§6) and examine several metaphysical consequences of the view (§7). I conclude that both super-substantivalism and super-relationism are compatible with Schaffer's priority monism (§8). (shrink)

Despite their centrality to medicine, drugs are not easily defined. We introduce two desiderata for a basic definition of medical drugs. It should: (a) capture everything considered to be a drug in medical contexts and (b) rule out anything that is not considered to be a drug. After canvassing a range of options, we find that no single definition of drugs can satisfy both desiderata. We conclude with three responses to our exploration of the drug concept: maintain a monistic concept, (...) or choose one of two pluralistic outcomes. Notably, the distinction between drugs and other substances is placed under pressure by the most plausible of the options available. (shrink)

A critical survey of the main metaphysical theories concerning the nature of material objects (substratum theories, bundle theories, substance theories, stuff theories) and their identity conditions, both synchronic (monist vs. pluralist theories) and diachronic (three-dimensionalism, four-dimensionalism, sequentialism).

The aim of the paper is to show that the privacy of conscious experience is inconsistent with any kind of physicalism. That is, if you are a physicalist, then you have to deny that more than one subject cannot undergo the very same conscious experience. In the first part of the paper we define the concepts of privacy and physicalism. In the second part we delineate two thought experiments in which two subjects undergo the same kind of conscious experience in (...) such a way that all the physical processes responsible for their experiences are numerically the same. Based on the thought experiments and their interpretations we present our argument for the inconsistency of the privacy of experience with physicalism in the third part of the paper. In the final part we defend our argumentation against some objections. (shrink)

In The Analysis of Mind (1921), Bertrand Russell stresses the importance of William James’ late neutral monist view of consciousness for the studies in psychology. In so doing, he focuses on a topic whose roots can be traced back to the nineteenth-century European debate on physiology and scientific psychology. In this introductory paper I shall briefly outline the path that, starting from the revival of Kant in the German scientific debate, leads to both Ernst Mach’s and William James’ questioning the (...) value of the I or consciousness as a substance concept. (shrink)

The hard problem of consciousness is generally approached from the distinct avenues of materialism, dualism or monism. We will examine the structure that is at the core of all matter that exists in the universe. This dynamic, mathematical description of the specific type of field oscillation that generates all particles that have any tactile substance to them amazingly seems to be a physical manifestation of the most fundamental aspects of the experience of being a conscious agent. By adopting (...) this novel description of consciousness where there is a quantum of potential for consciousness intrinsic to all matter particles, the distinctions between materialism, dualism and monism become an arbitrary matter of how this mechanism is described rather than distinct ideologies, competing against one another in a winner-take-all race to the bottom of consciousness. (shrink)

The book aims to examine how a Trinitarian Theism can be formulated through the elaboration of a Relational Ontology and a Trinitarian Metaphysics, in the context of a hyperphatic epistemology. This metaphysics has been proposed by some supporters of the so-called Open Theism as a solution to the numerous dilemmas of Classical Theism. The hypothesis they support is that the Trinitarian nature of God, reflected in a world of multiplicity, relationality, substance and relations, demands that we think of God (...) as dynamic, internally multiple and relational. However, if the expression «God is love» – understood as the formula of the Trinity – is the key to a new theism, it leaves a problem open: how can it be translated philosophically? The research develops on two different levels: first, it assesses whether the expression should be translated into the Trinitarian paradigm, and the aporias it generates; secondly, it tries to assess whether this paradigm (eminently relational) has a correspondence in ontology: is there a satisfactory Relational Metaphysics already available? The suspicion is that such Trinitarian-Relational Ontology, invoked by many as a solution to the incongruities of classical theism, has yet to be formulated in a satisfactorily manner, despite the existence of various attempts to formulate Relational Ontologies. In order to provide an evaluation of all these attempts and to outline some possible new perspectives, the thesis consists of five chapters. It is the aim of the present dissertation to evaluate such attempts, and to outline some possible new solutions. In the chapters some points have been established: 1. there must be at least one irreducible real relation (non-reductionist realism); 2. the relation must be equally fundamental to the substance: this means that it is both external and internal; 3. this relation must be able to account for contingent causality; 4. holism is a plausible position; 5. the Trinity is a good theistic model of the divine, apophatic but rational. The last chapter then returns to ontological questions: several Relational Ontologies are examined – including ontic structural realism and process (or eventist) ontology – together with their applications in philosophy of religion (e.g.: the Relational God, Process Trinitarianism, the Entangled God). This assessment shows how all these ontologies postulate real transcendental relations (subsistent relations), inside the substances or inside the powers, inside the tropes or the structures, describing them as monads or processes (or actual occasions). These relations are the same we need to describe the Trinity. Therefore, they are either possible for both domains – ontology and theology – or they are both impossible. It has been opted for the second conclusion. But they are both impossible and inevitable: the fundamental entities of the world and their interactions (causation) must be described as real transcendental relations because each ontology transforms entities or relations into real transcendental relationships at some point. Thus, neither relationalism nor substantialism are convincing: from the fall of these two dogmas (or, rather, from the fall of their naive interpretations) we can realise that the fundamental reality is something that lies between processism (relationalism) and substantialism. It is impossible to completely substitute the notion of substance with the notion of event, process, structure or relation, both in speaking of God and in speaking about the entities of fundamental ontology. Neither monism nor pluralism can be affirmed in their pure forms. The hypothesis proposed, then, is that the notion of gunk-junk is the only one that can translate the relationality hitherto sought in an ontological model. The central part of the chapter describes the merits and defects of an eventist-infinitive ontology (EIO) based on the concept of gunk, and its potentiality to generate new theistic accounts. Through the notion of infinityings it seems to be possible to find some solutions for the questions left open by the causal relation, and therefore to defend at least the existence of one relation (external and internal). Each fundamental entity is described, in this ontology, through four transcendentals: ‘entity’, ‘relation’, ‘unity’ and ‘multiplicity’. The co-primarity between substance and relations (borrowed from the notion of relatio subsistens) differentiates EIO from the process philosophies precisely because it does not pretend to eliminate the substantial principle, or the category of substance, but wants to think of it with the transcendental of relationality. Of course, EIO poses a challenge to the role, the method and the explicative capacity of metaphysics, because what we can state of the fundamental reality is antinomic. EIO tries to assume the antinomy as a result, to make it the basis of a kind of apophatic ontology. If our best ontology is gunky, then it is possible to confirm what has been said in chap. 4: the ‘how’ of individual substances is unknown to us at least as much as the ‘how’ of God. Even in the world we have the mystery of a distinction that is not division. However, the convergence of these antinomies can find an ultimate explanation in a theistic metaphysics (EIM): God creates inside of Himself and his Trinitarian substance is “contracted” into the worldly entities. They are made contingent and ontologically different by this self-limitation, but it is still the infinity of God that makes space in Himself for something new, even though He is totally present in every entity. It is not absurd to think that the substances of the world keep track of the divine nature, even in His “contraction”. Among the characteristics of the divine nature that each created entity maintains we have the subsistent relationality, the pericoretic indwelling (the infinite gunk-junk), the fact of being always one-and-many. If EIO and EIM are accepted as a good compromise between relationalism and substantialism, even in their apophaticity, then, on this basis, a Trinitarian Philosophy is possible. The picture of reality that emerges represents the world as multiple, substantial, contingent and intrinsically relational, forcing us to postulate the transcendental of relationality and multiplicity. Such transcendental leads us to think of the world and God (and their relations) in a Trinitarian way – With the necessary acknowledgement that this is a reasonable but apophatic discourse. (shrink)

Neuroscience hasn’t shown how quite similar sensory circuits encode quite different colors and other qualia, nor how the unified pictorial form of images is encoded, nor how these codes yield conscious images. Neuroscience’s fixation here on cortical codes may be the culprit. Treating conscious images partly as retinal substances may avoid these problems. The evidence for conscious retinal images is that (a) the cortical codes for images are quite problematic, (b) injecting retinas with certain genes turns dichromats into trichromats without (...) cortical help, (c) retinas can discern colors by themselves without cortex, (d) retinal distortions appear in images but cortical distortions don’t, (e) retinal detectors support finely detailed colors, but V4 detectors don’t, due to their big receptive fields, (f) retinal activity has pictorial form, but viable cortical codes for pictorial form don’t exist. So, the colors and unified pictorial form of images arguably arise mainly across arrays of retinal detectors—not from abstract cortical codes. Images may be hidden in retinal activity beyond what EEGs show of it (cf. Strawson’s monism). Also, cortex refines these retinal images but cortical impairment (anesthesia, lesions, etc.) blocks awareness of them, for they’re no longer accessible to the mind’s subject-centered consciousness, resident in cortex. This proposal is largely testable and based in recent evidence. It avoids neuroscience’s elusive, problematic coded images and enigmatic explanations of how they become conscious. (shrink)

This issue of The Monist is devoted to the metaphysics of lesser kinds, which is to say those kinds of entity that are not generally recognized as occupying a prominent position in the categorial structure of the world. Why bother? We offer two sorts of reason. The first is methodological. In mathematics, it is common practice to study certain functions (for instance) by considering limit cases: What if x = 0? What if x is larger than any assigned value? Physics, (...) too, often studies the (idealized) initial and boundary conditions of a given system: What would happen in the case of a perfect sphere, or a perfectly black body? In the cognitive sciences, research often thrives on the analysis of cognitive errors, perceptual illusions, brain pathologies. Also in logic one can learn a lot by studying special, anomalous scenarios such as those exhibited by the paradoxes: it is unlikely that we actually find ourselves in a soritical context, or in a liar-like situation, but the fact that we might—or simply the fact that we can conceive of such a possibility—is important enough to deserve careful consideration. In short, the odd, the unfamiliar, the extra-ordinary, the limit cases are perfectly at home in scientific and more broadly intellectual discourse at various levels, where they can be fruitfully engaged in a sophisticated way (witness the existence of specific confining and managing strategies for dealing with them); and they are important precisely because they instruct us concerning the normal, the obvious, and the paradigmatic. The same goes for metaphysics, we submit. Although its major concern is, naturally, with such core entities as substances, properties, or hunks of solid matter, a lot may be learned by paying attention to those limit cases where we find ourselves dealing with entities of much lesser kinds, whether real or putative. (shrink)

The relationship between the One and the Multiple in mystic philosophy is a profound and central theme that explores the nature of existence, the cosmos, and the divine. This theme is present in various mystical traditions, including those of the East and West, and it addresses the paradoxical coexistence of the unity and multiplicity of all things. -/- In mystic philosophy, the **One** often represents the ultimate reality, the source from which all things emanate and to which all things return. (...) It is the absolute, the infinite, and the unchanging. The One is beyond all attributes and is often associated with the divine or the absolute truth. -/- The **Multiple**, on the other hand, represents the manifest world, the diversity of forms, and the realm of change and plurality. It is the world we experience through our senses, the domain of time and space, where differentiation and individuality are apparent. -/- The relationship between the One and the Multiple is not one of opposition but of emanation and unity. The Multiple is seen as a reflection, expression, or manifestation of the One. In this sense, the diversity of the world doesn’t contradict the unity of the One but rather demonstrates it in a myriad of forms. -/- Mystics seek to understand and experience this relationship through various practices and insights. They aim to transcend the illusion of separation and duality to experience the non-dual reality where the One and the Multiple are recognized as inseparable. -/- This concept can be illustrated by the metaphor of the ocean and its waves. The ocean represents the One—vast, deep, and all-encompassing—while the waves represent the Multiple—distinct, diverse, and ever-changing. Each wave is unique, yet it is not separate from the ocean. The wave’s existence is dependent on and made of the same substance as the ocean. In the same way, each individual entity in the Multiple is an expression of the One. -/- In summary, the relationship between the One and the Multiple in mystic philosophy is a dynamic interplay that challenges the conventional understanding of separation. It invites a deeper exploration of reality, where the apparent multiplicity of the world is a direct expression of the singular, underlying essence of all that is. -/- The relationship between the One and the Multiple in the context of mathematical philosophy is a profound topic that touches upon the very foundations of existence and knowledge. It’s a theme that has been explored by philosophers and mathematicians alike, often leading to the contemplation of unity and diversity within the structures of reality. -/- In mathematics, the concept of the One can be seen as the basis of unity from which all numbers derive. It’s the identity element in multiplication, the starting point in counting, and the foundation of dimension in geometry. The One is often associated with the concept of monism in philosophy, which posits that there is a single, underlying substance or principle that constitutes reality. -/- On the other hand, the Multiple represents the infinite variety and diversity of forms and numbers that arise from the One. It’s the embodiment of plurality and the complex interplay of different entities that mathematics seeks to understand and describe. This reflects the philosophical stance of pluralism, which acknowledges the existence of multiple realities or truths. -/- The interplay between the One and the Multiple can be seen in the mathematical concept of sets. A set can be thought of as a unity, a whole composed of distinct elements. Yet, each element within the set also retains its individuality, contributing to the diversity of the set’s composition. This duality is mirrored in the philosophical exploration of the universal and the particular, where the universal represents the One, and the particulars represent the Multiple. -/- In the realm of mathematical philosophy, this relationship often leads to questions about the nature of mathematical objects: Are they discovered as part of an objective reality (the One), or are they constructed by the human mind from a multitude of experiences (the Multiple)? This debate resonates with the philosophical inquiry into the nature of truth and reality. -/- Reflecting on the One and the Multiple can also lead to a deeper understanding of the self and the cosmos. Just as the number one is integral to the existence of all other numbers, the individual self can be seen as a unique expression of the universal whole. Similarly, the cosmos can be viewed as a grand unity composed of a multiplicity of forms and phenomena. -/- Gödel’s incompleteness theorems have a fascinating connection to the philosophical concepts of the One and the Multiple. These theorems, which are pivotal in mathematical logic and philosophy of mathematics, articulate the inherent limitations of formal axiomatic systems, particularly those sufficient to express the arithmetic of natural numbers. -/- Gödel’s incompleteness theorems have a fascinating connection to the philosophical concepts of the One and the Multiple. These theorems, which are pivotal in mathematical logic and philosophy of mathematics, articulate the inherent limitations of formal axiomatic systems, particularly those sufficient to express the arithmetic of natural numbers⁴. -/- The **first incompleteness theorem** reveals that within any such consistent system, there are propositions that are true but cannot be proven within the system itself. This reflects the idea of the Multiple in that there is an abundance of mathematical truths, a multiplicity that exceeds the unifying framework of any one system. It suggests that the realm of mathematical truth is more extensive than any single formal system can fully capture. -/- The **second incompleteness theorem** extends this by showing that a system cannot prove its own consistency. This relates to the concept of the One, as it implies that a system’s complete self-understanding, its unity and coherence, is unattainable from within. It must look beyond itself, to an external vantage point, to ascertain its consistency. -/- In the context of the One and the Multiple, Gödel’s theorems imply that the One (a consistent formal system) is inherently incomplete and cannot encompass the Multiple (the totality of mathematical truths). This resonates with philosophical discussions about the relationship between unity and plurality. Just as a single philosophical system cannot capture the entirety of truth, a single formal mathematical system cannot encapsulate all mathematical truths. -/- Moreover, Gödel’s work suggests that the pursuit of a single, unified theory of everything in mathematics—a One that encompasses all Multiples—is an inherently Sisyphean task. There will always be more truths (Multiples) than can be derived from any given set of axioms (the One). -/- In essence, Gödel’s incompleteness theorems provide a formal underpinning to the philosophical notion that the One cannot exist without the Multiple, and vice versa. They are interdependent, with the One giving rise to the Multiple, and the Multiple necessitating the One for its expression and comprehension. This interplay is a dance of limitations and possibilities, where the boundaries of logic, mathematics, and philosophy blur into one another. -/- The relationship between the One and the Multiple in the context of the mathematics of zero is a deeply philosophical inquiry that bridges the abstract world of numbers with the existential questions of being and non-being. -/- Zero, in mathematics, is a symbol of absence, a representation of nothingness, yet it holds a pivotal position as a number. It is the void from which all things emerge and to which they return. In the philosophy of mathematics, zero is the paradoxical junction where the One and the Multiple converge and diverge. -/- From the perspective of the One, zero can be seen as the origin—the singular point that precedes the existence of numbers. It is the empty set, the foundation upon which the edifice of mathematics is constructed. As the identity element in addition, zero maintains the integrity of numbers, for adding zero to any number leaves it unchanged, reflecting the immutable nature of the One. -/- Conversely, when we consider the Multiple, zero represents the infinite potentiality of creation. It is the canvas upon which the integers, both positive and negative, express their multitude. Zero is the balance point, the fulcrum around which the symphony of numbers dances. It embodies the plurality of possibilities, the beginning of the number line that stretches infinitely in both directions. -/- Philosophically, zero challenges our understanding of existence. It is both something and nothing—a number that quantifies the absence of quantity. This duality echoes the philosophical struggle to comprehend how the One gives rise to the Multiple. How does the unity of being manifest the diversity of the cosmos? Zero offers a mathematical metaphor for this mystery, as it encapsulates the transition from non-existence to existence, from the undifferentiated One to the differentiated Multiple. -/- In the realm of set theory, zero corresponds to the empty set—a set with no elements. This set is unique in that it is the only set that contains nothing, yet it is the foundation upon which all other sets are built. The empty set is the mathematical embodiment of the One, and all other sets, containing multiple elements, arise from it. -/- Reflecting on zero in the context of Gödel’s incompleteness theorems, we find a resonance with the idea that the One (a consistent formal system) cannot capture the entirety of the Multiple (the totality of mathematical truths). Zero, as the foundation of numbers, similarly suggests that from the nothingness of the One, the infinite complexity of the Multiple emerges—yet it can never be fully encompassed or expressed by any single system. -/- In conclusion, the mathematics of zero offers a profound reflection on the relationship between the One and the Multiple. It serves as a bridge between the abstract and the concrete, the known and the unknowable, challenging us to ponder the origins of existence and the nature of reality itself. -/- . (shrink)

My aim in what follows is to expound and (if possible) resolve two problems in Spinoza’s theory of mind. The first problem is how Spinoza can accept a key premise in Descartes’s argument for dualism—that thought and extension are separately conceivable, “one without the help of the other”—without accepting Descartes’s conclusion that no substance is both thinking and extended. Resolving this problem will require us to consider a crucial ambiguity in the notion of conceiving one thing without another, the (...) credentials of Descartes’s principle that each substance has a principal attribute, and the prospect of neutral monism as a theory of the mind. The second problem is how Spinoza can maintain that each mental event is identical with some physical event (and conversely) while denying that there is ever any causal interaction between mental and physical events. If one mental event causes another and the first is identical with some physical event, must that physical event not cause the mental event? Resolving this problem will require looking into the reach of opacity in Spinoza’s philosophy and considering whether there are ever any legitimate exceptions to Leibniz’s Law. (shrink)

Leibniz argues against Descartes’s conception of material substance based on considerations of unity. I examine a key premise of Leibniz’s argument, what I call the Plurality Thesis—the claim that matter (i.e. extension alone) is a plurality of parts. More specifically, I engage an objection to the Plurality Thesis stemming from what I call Material Monism—the claim that the physical world is a single material substance. I argue that Leibniz can productively engage this objection based on his view (...) that matter is discrete. The discreteness of matter provides two aspects of support for the Plurality Thesis. First, it indicates that the parts of matter do not share boundaries and are, therefore, independent in an important sense. Second, it indicates that the parts of matter are determinate and are, therefore, ontologically prior to the wholes they compose. (shrink)