Posts Tagged ‘leibniz’

Leibnizian Supercomprehension

In a recent paper, Juan Garcia has argued that Leibniz is, in an important sense, “a friend of Molinism.”1 For those who are familiar with contemporary versions of Molinism (e.g., Flint), this suggestion is rather surprising, since Leibniz is clearly a theological determinist: he holds that God chooses every detail of the actual world. Further, a key feature of Molinism (particularly as it is understood in recent analytic philosophy) is the idea that God’s options for creation are limited by contingent but prevolitional counterfactuals of creaturely freedom. The contrary assumption, that God could have actualized any possible world, was dubbed by Plantinga, ‘Leibniz’s Lapse’. Now, Plantinga is clearly unfair in calling this a ‘lapse’: it’s a theoretical commitment Leibniz embraces clear-sightedly, with awareness that there are alternatives to it and that it has some implausible-looking consequences. Nevertheless, Leibniz does embrace this view. As a result, Leibniz surrenders the two main advantages typically assigned to Molinism in recent analytic philosophy: the ability to combine theological libertarianism with strong providence, and any Plantinga-style free will defence.

Still, Leibniz’s view does have significant similarities with Molinism and seem to employ some Molinist strategies. The main burden of Garcia’s article is to argue that Leibniz holds that counterfactuals of creaturely freedom are contingent and that God knows them prevolitionally. This seems right in a certain sense or to a certain extent, but the key issue (which Garcia does not discuss) is how Leibniz can maintain this, and here Leibniz’s notoriously weak notion of contingency is doing real work.

According to traditional Molinism, an agent’s essence or character does not include all the facts about what the agent would do in hypothetical situations, because this would render the agent’s actions in those situations necessary. Nevertheless, God ‘supercomprehends’ this essence or character in order to know facts that go beyond what is included in it. It is in this way that God knows what the agent would do.2

This doctrine is rather obscure. It leaves unexplained how or why these facts could be true of this essence. (This is, of course, a version of the ‘grounding objection’.) It also seems to have God seeing in the essence something that isn’t there.

Leibniz, however, is able to give an account of how this works. In the Arnauld correspondence, Leibniz says that, in deciding to create Adam, God employs a ‘complete individual concept’ (CIC) of Adam which includes, essentially, an entire possible world. This is because the CIC must include everything that can be truly predicated of Adam, and there are true propositions such as Adam lived before I wrote this blog post. Hence, my writing this post is included in Adam’s CIC.

How, then, can any of Adam’s actions be contingent? In a certain sense they can’t, and Leibniz makes important use of this in his discussions of the problem of evil. (See the discussion of Judas in the Discourse on Metaphysics and the discussion of Sextus at the end of Theodicy.) Arnauld, therefore, objects that Leibniz’s view falsely implies that he (Arnauld) is necessarily a celibate theologian. In fact (Arnauld says) he could instead have been a married physician. Leibniz responds by diagnosing a kind of ambiguity: this Arnauld (the one in the actual world) is necessarily a celibate theologian, but there are other Arnaulds, in other possible worlds, who are married physicians. (I’ve written about this before.) This, according to Leibniz, gives us enough contingency for moral responsibility and so forth.

This ambiguity, it seems to me, is what allows Leibniz to combine these Molinist principles with theological determinism. God knows precisely what will happen if God creates this Arnauld. At the same time, it is contingent that Arnauld, in these circumstances, becomes a celibate theologian.

On the other hand, Leibniz’s strategy does not make what is perhaps the most characteristic move of both historical and contemporary Molinism: he does not open up any middle ground between natural knowledge and free knowledge. That Arnauld, placed in these circumstances, would freely decide to become a celibate theologian is true (on the interpretation on which it is contingent) because God decided to create this Arnauld, rather than one of those other Arnaulds. Hence this is part of God’s free knowledge. That this Arnauld freely so decides is necessary, since it follows from his CIC. (Leibniz often seems like he wants to wriggle out of the conclusion that this is necessary, even when we specify this Arnauld, but the comments about Judas and Sextus and so forth seem to push the other direction.) Thus it is Leibniz’s view that counterfactuals of creaturely freedom are systematically ambiguous, and on one interpretation they are part of God’s natural knowledge while on another they are part of God’s free knowledge.

(Cross-posted at blog.kennypearce.net.)


  1. A while back, Brandon Watson also suggested, in a blog comment, that Leibniz can be understood as endorsing a kind of ‘modified Molinism’.
  2. I rely on Adams for this characterization of ‘supercomprehension’.

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This is Part 3 in an exploration of Leibniz’s complaint about “Locke and his followers” in his letter to Caroline (part of the “Leibniz-Clarke” correspondence). What is the problem that Leibniz sees with British philosophy circa 1714? In addition to the problems raised against Newton and his followers, what goes mostly unexplored in the Leibniz-Clarke-Caroline correspondence is the problem with the materiality and natural mortality of the soul because Clarke, too, is opposed to both the materiality and natural mortality of the soul.

Part 1: Henry Dodwell and Anthony Collins

Part 2: Catherine Trotter Cockburn

In 1696, John Toland published Christianity Not Mysterious, raising both his international profile and his notoriety. This was followed by multiple tracts—including, importantly, defenses of republicanism, of the Hanoverian succession, and of the importance of securing Protestant rule in England—before his 1704 Letters to Serena. His pamphlets in support of the Hanoverian succession secured him a spot in the envoy to welcome Frederick, Sophie, Sophie Charlotte, and Caroline. This greatly developed his international network and resulted in a series of debates with Leibniz, which may have served as a basis for Letters to Serena (where Sophie Charlotte is a plausible candidate for the pseudonymous “Serena”).

This is important for our purposes in that it gave Leibniz an opportunity to meet a British philosopher in whom he saw the destructive elements left open by Locke’s failure to condemn thinking matter. Leibniz held a very low opinion of Toland’s philosophical and historical abilities. (He told Sophie that Toland “likes to make grand discourses; in a word, he wants to be an author. … Instead of dabbling in philosophy, which is not his forte, he would do better to restrict himself to the search for facts.” [Strickland, Leibniz and the Two Sophies, 291]) Leibniz, though, took Toland’s views to be important enough that he wrote down multiple lengthy letters for Sophie Charlotte refuting Toland’s views even after he had debated the points in her presence previously. His “Letter on what is independent of sense and matter” went through multiple drafts and culminated in an argument that there are immaterial substances that are outside of matter. (See Strickland’s Leibniz and the Two Sophies, 220ff, esp. 233-236 and 245-247.) Sophie Charlotte passed Leibniz’s letter to Toland, who responded, partly by side-stepping the issue of immortality of the soul by saying he only ever meant to discuss the “present state.” Leibniz again goes through multiple drafts in composing a response. Leibniz and Toland also corresponded directly, including Leibniz’s essay known as “Reflections on the doctrine of a single universal spirit,” which emphasizes the importance of individual souls.

Toland should certainly be included among “Locke and his followers,” despite Locke’s desire to be disassociated from Toland’s notorious religious and political views. Leibniz certainly was distressed by Toland’s views and perhaps also Sophie Charlotte’s openness to his views.

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Yesterday I wrote about Henry Dodwell and Anthony Collins as potential candidates for Locke’s “followers.” These posts are an exploration of the problem that Leibniz sees with British philosophy circa 1714 but that goes mostly unexplored in the Leibniz-Clarke-Caroline correspondence because Clarke, too, is opposed to both the materiality and natural mortality of the soul.

Let’s review Leibniz’s charge, originally written to Caroline as part of a longer letter, as it gets excerpted in editions of the Leibniz-Clarke correspondence.

1. Natural religion itself seems to decay very much. Many will have human souls to be material; others make God himself a corporeal being.

2. Mr. Locke and his followers are uncertain at least whether the soul is not material and naturally perishable.

The next candidate for “Locke and his followers” is Catherine Trotter (later Catherine Trotter Cockburn). Notice Leibniz’s language: these folks “are uncertain at least whether…” For Leibniz, it matters not just that the soul is not material and naturally perishable but that we know this to be the case with certainty.

In a 1706 letter to his primary British correspondent/gossipmonger, Leibniz thanks Thomas Burnett for sending him a “defence of Mr Locke written by a very spirited young lady…” (Side note: Thank you to Lloyd Strickland for not only his excellent book that makes available Leibniz’s correspondence with Sophie and Sophie Charlotte, but also the website where he provides important translations like this one.) The timing of this letter, its topic, and its use of “defence” make it overwhelmingly likely that Leibniz is discussing Cockburn’s A Defence of the Essay of Human Understanding (1702).

Her defense of Locke is focused on arguing that Locke relies on a distinction between what is available by the “light of nature” (unaided or amplified but not supplemented human reason) and what is available through special revelation. She finds it obvious that the soul is immortal and all agree on this.

That the immortality of the soul is only highly probable by the light of nature, none can deny, who believe that Apostle, by whom we are told, that life and immortality is brought to light by Jesus Christ through the gospel. Why then is it objected against Mr. Locke’s principles, that they give us no certainty of the immortality of the soul without revelation? By what other way can we be certain of anything, that is only highly probably by the light of nature? (From p53 in Patricia Sheridan’s very useful edition for Broadview).

3D16DF2F-7515-42C4-9ACE-B87F27BE7920We do not have demonstrative knowledge, without revelation, that the soul is immortal, according to Cockburn’s reading of Locke. She is critical of attempts in natural theology to arrive at the immortality of the soul through routes such as arguing for the soul’s immateriality. It “may be dangerous” to require the soul’s immortality to depend on its immateriality because some people will fail to follow a good proof; arguments (even very good ones) affect people differently. Putting the argument for the soul’s immortality on “false or uncertain grounds” is an aid to those who oppose the soul’s immortality (Sheridan 63-64). Those who want to defend “the future state” (which many worried was necessary to keep people doing good in this life) ought not require demonstrations of immortality of the soul that require immateriality.

This is just one of her lines of argument, nestled in other questions about whether a thinking substance must be always thinking and other abstruse questions. One of her key points, though, is that by reason alone we can establish with high probability that the soul is immortal and special revelation gives us certainty. Leibniz, remember, is concerned about those who are “uncertain at least whether the soul is not material and naturally perishable.” By denying that immateriality and natural imperishability are required to establish immortality and by furthermore arguing that, by the light of nature alone, it is “highly probable” (rather than certain) that the soul is immortal, Leibniz would have seen her “spirited” defense as not going far enough in establishing what can be known through natural theology (without special revelation).

It seems likely, then, that Trotter (Cockburn) is included in “Locke and his followers,” who fall short of guaranteeing demonstrative certainty of the soul’s immateriality without the aid of revelation.

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When Leibniz writes to Caroline to express his concern over the dangerous thinking in England he specifically names “Locke and his followers” and “Newton and his followers.” But who exactly were Locke’s “followers,” and why don’t we talk about them more in the context of the Leibniz-Clarke correspondence?

First, some context. Sophie Charlotte and her husband, King Frederick I of Prussia, were (for a while) guardians to Princess Caroline of Ansbach. Sophie Charlotte frequently hosted Leibniz in Berlin and elsewhere (while Leibniz was supposed to be working on his history of the Brunswick family), and it is in her court that he met Caroline and eventually became her tutor. Caroline would become the central (but hidden) figure in the Leibniz-Clarke correspondence, passing the letters between them with her own observations stated in accompanying letters. In addition to the broader public and the official correspondent, Caroline is the unstated audience for both Leibniz and Clarke. (See Meli 1999 for more on Caroline’s role in the Leibniz-Clarke correspondence.)

Leibniz’s initial letter to Caroline (printed as the first letter in the Leibniz-Clarke correspondence) is an attempt to keep Caroline from straying from his views and toward the (to Leibniz) dangerous views in England. He specifically mentions “Locke and his followers” and “Newton and his followers” in his opening salvo.

Because Clarke, who takes up the cause of English “natural religion,” is clearly a member of “Newton and his followers” and defends (half-heartedly) Newton’s use of sensorium and defends (very well) Newton’s “very odd opinion concerning God’s workmanship,” scholarship has focused on the letters as a debate between Leibniz on the one side and Newton-Clarke (with various weightings assigned to Newton and Clarke as author) on the other. Partly this is because Clarke is clearly opposed to the position ascribed to “Locke and his followers” that they “aren’t sure whether the soul is material and naturally perishable.” In asking who “Locke and his followers” are, we can look to those who think the soul is “material and naturally perishable.”

The debate about a “naturally perishable” soul focused in early eighteenth century Britain on Henry Dodwell, who had argued that the soul only became immortal at baptism. Clarke opposes this view in a typically public letter. Anthony Collins responds, and the two men’s subsequent correspondence (1707-1708) on the immateriality and natural immortality of the soul is a fascinating example of a substance dualist (who unlike Cartesian dualists is open to the soul being extended) and someone working towards an emergentist view long before such views became popular. Collins holds the sort of view that Leibniz sees as following from Locke’s openness to thinking matter in the later editions of the Essay Concerning Human Understanding, while Clarke defends a thinking, immaterial soul. Leibniz is aware of Dodwell as early as 1706, due perhaps to his primary British correspondent Thomas Burnett. Dodwell, then, is the first candidate for “Locke and his followers,” with Collins worth consideration, as well.

The debate between Clarke and Leibniz quickly focuses on Leibniz’s objections to Newton and Clarke rather than on the thinking matter views entertained by Locke and Collins because Clarke is the clear opponent of both Dodwell and Collins. This is part of why, I think, we think today of the Leibniz-Clarke correspondence as about Leibniz’s problems with Newtonian natural philosophy and Clarkean natural theology rather than with post-Lockean concerns about whether all souls are immortal. Because it was Clarke who, at Caroline’s request, answered Leibniz’s charge, the Leibniz-Clarke correspondence focuses on the immortality question only insofar as it is connected to questions like the nature of the sensorium and God’s relationship to space (e.g., as a world-soul).

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Interested in self-consciousness and personal identity? This week the Descartes Research Group at Western University, lead by Benjamin Hill, is holding a virtual masters seminar on Udo Thiel’s The Early Modern Subject (2011). Event details:

Friday April 29
9:00-11:00 am EDT
Western University
Arts & Humanities Building, Room 2R07

For virtual attendance, join here. The portal will open 30 minutes before the session begins.

Benjamin Hill writes:

“The session will involve Prof. Thiel answering questions and responding to critical reflections that the research group as well as a number of external experts have formulated. Philosophers interested in personal identity, consciousness, and their relationship will be especially interested in Prof Thiel’s thoughts.”

A great opportunity to dive into early modern identity questions (if you weren’t sucked into those already).

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Anonymous Modern Philosophy
Panel of the Society for Modern Philosophy
APA Pacific Division Meeting 2016
Thursday Evening, March 31: 8:00-10:00 P.M.


  • Juli Joráti (Ohio State): Early Modern vs. Medieval Anonymity
  • Alexander X. Douglas (Heythrop College/St Andrews): The Spinozist Model of Anonymity and the Tractatus-Theologico Politicus
  • Sandra Lapointe (McMaster): Rooting for the Underdogs

Authorship is central to our grasp of philosophical contributions. People tend to associate an idea with its originator—think of: ‘Platonist’, ‘Humean’—and especially for the modern period, scholarship on seven big names dominates the field. However, not all philosophical moves have been made by identified figures. Sometimes authors made deliberate efforts to remain hidden from view, be it to allow for a more neutral assessment of their work, or to distance themselves from controversial opinions. As yet, only fragmented attention has been paid to the anonymous and pseudonymous face of modern philosophy.

This panel will begin to address this gap. Its findings will have implications not only for efforts to reshape the philosophical canon, but also for thinking about named authorship in research practices more generally.

Event hashtag: #AnonModPhil
Web: http://anonphil.github.io


Early Modern vs. Medieval Anonymity

It was not at all rare for early modern philosophers to publish or circulate their work anonymously. In fact, nearly all commonly studied early modern figures did so at least once: Descartes, Spinoza, Conway, Locke, Masham, du Chatelet, and Hume, to name just a few. Nevertheless, the early modern period is also a period in which named authorship becomes more and more important. It is in this period that ideas come to be viewed increasingly as the property of those who first expressed them, and in which authors come to expect to be given credit when others make use of their ideas. This is evident, for instance, in the heated dispute between Leibniz and Newton over the invention of the calculus. Some early modern philosophers even argue for intellectual property rights explicitly. My paper aims to show that as a result of this new attitude toward named authorship, anonymity also takes on a different meaning for both authors and readers.

More specifically, the paper explores the shift in attitudes toward named authorship—and, relatedly, toward anonymity—that appears to coincide roughly with the transition from the medieval to the early modern period. A widely accepted narrative has it that it was quite common in the medieval period to circulate one’s work anonymously but that this changed radically shortly after the advent of the printed book. While medieval authors were not all that interested in putting their name on their work, renaissance and early modern authors were usually eager to do so, except in special cases. The shift is often attributed partly to print conventionsand partly to changing views about the centrality of the identity of the author. To put it starkly, the common narrative claims that early modern authors generally have bigger egos than their medieval counterparts, and hence stronger desires that their ideas be associated with their names.

This narrative, like most broad narratives that draw a sharp contrast between medieval and early modern attitudes, is of course over-simplified. Yet, there is some truth in it as well: the notions of intellectual property, copyright, and plagiarism seem to have developed after the invention of the printing press. The identity of the author becomes increasingly important in early modern Europe and certain authors even attain the status of celebrities. As a result, publishing under one’s name starts to become the default, which in turn means that when an author withholds her name, it is quite likely that she thinks there are special reasons in favor of anonymity. While it is entirely possible for a medieval author to write anonymously without giving much thought to the matter, it is quite unlikely in the case of early modern authors. This in turn, my paper contends, also changes the ways in which readers perceive anonymity.

The Spinozist Model of Anonymity and the Tractatus-Theologico Politicus

Why did Spinoza choose to publish his philosophy anonymously? He might have done so in order to protect himself from persecution. But there are reasons to doubt that this was his main motive.

Perhaps Spinoza aimed to show himself to be above ambition, which was in those days recognised as a vice. Descartes and his followers in the Dutch Republic were accused of harbouring this vice: while claiming to pursue truth, it was alleged, what they actually sought was to be admired for their cleverness.

Spinoza, in the Tractatus, turned the accusation against the accusers: those who condemn the writings of others do in order to win “the applause of the crowd”; they are the ones corrupted by ambition. But he then risked having the accusation turned back upon himself. Anonymous publication made any such counter accusation appear much less plausible.

It was, however, very important for Spinoza not simply to appear unmotivated by ambition in writing his philosophy, but also to be so unmotivated. His psychological theory rules it impossible to convey one’s philosophical thoughts to somebody without also transferring to her the motivations that prompted those thoughts. If ambition is among those motivations, the philosophy will have a corrupting effect. And the contagion of ambition is, for Spinoza, among the most dangerous of all the social pathologies.

Rooting for the Underdogs

There are many things wrong about our conception of what counts as canonical in philosophy in the nineteenth century, and with the idea of a canon in general. Considering the case of Bernard Bolzano is quite enlightening. It shows that the value of philosophical ideas has little to do with authorship and popularity. Our focus on “founding giants” and “great minds” is tainted by perspective, prejudice and all sorts of complicated assumptions, most of which are fed by bias. At the same time, part of the interest of doing the history of philosophy—as opposed to rational reconstruction—is to tell a story, explain how theories arise and develop in context, and anonymity is not a very good engine for narratives. This raises a number of questions about historical methodology and surprisingly little has been written on the topic. In this talk I will make a few suggestions.

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Thanks again to Chloe Armstrong and Jeff McDonough for their discussion last week. Here are links to all the relevant posts.

The paper being discussed: “Leibniz, Spinoza and an Alleged Dilemma for Rationalists”

Chloe’s first post, A Leibnizian Way Out of the Rationalist’s Dilemma (Part 1): https://philosophymodsquad.wordpress.com/2016/02/22/a-leibnizian-way-out-of-the-rationalists-dilemma-part-1/

Jeff’s first reply: https://philosophymodsquad.wordpress.com/2016/02/23/a-leibnizian-way-out-of-the-rationalists-dilemma-mcdonough-reply-part-1/

Chloe’s second post: A Leibnizian Way Out of the Rationalist’s Dilemma (Part 2): https://philosophymodsquad.wordpress.com/2016/02/24/a-leibnizian-way-out-of-the-rationalists-dilemma-part-2/

Jeff’s second reply: https://philosophymodsquad.wordpress.com/2016/02/25/mcdonough-reply-part-2/

Comments on all these posts will remain open for another couple of weeks, if anyone else wants to contribute to the discussion.


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Image from: Giovanni Aldini, Essai théorique et expérimental sur le galvanisme (Paris, 1804)

The conference program for Life and Death in Early Modern Philosophy, to be held in London on April 14–16 this year, has been announced. And it’s looking good.


Thursday 14th April 2016

The Great Hall, King’s College London, Strand, London WC2R 2LS

2.30–4.00 Tea and Registration in the Foyer of the Great Hall
4.00–4.30 Susan James, Welcome and Introduction
4.30–6.00 Michael Moriarty, The thought of death changes all our ideas and condemns our plans


Friday 15th April 2016

Birkbeck College, Clore Management Centre, Torrington Square, London WC1E 7JL

9.30–11.00 Ursula Renz, Our Consciousness of Being Alive as a Source of Knowledge
 11.15–12.45 Session 1 Session 2 Session 3
Meghan Robison

But a Movement of Limbs: On the Movement of life in Hobbes’ Leviathan

Steph Marston

Affects and Effects: Spinoza on Life

John Callanan

The Historical Context of Kant’s Opposition to Suicide

Barnaby Hutchins

Descartes’s ‘Vitalism’

Julie Klein

Life and Death in Spinoza: Power and Reconfiguration

Jonas Jervell Indregard

Kant on Beauty and the Promotion of Life

12.45–2.00 Lunch, coinciding with meeting of agreed and likely contributors to research network
2.00–3.30 Martine Pécharman, The Moral Import of Afterlife Arguments in Pascal and Locke
3.45–5.15 Session 1 Session 2 Session 3
Hannah Laurens

An Eternal Part of the Body? Spinoza on Human Existence Beyond Life and Death

Andreas Scheib

Johannes Clauberg and the Development of Anthropology after Descartes

Sarah Tropper

When the Manner of Death Disagrees with the Status of Life. The Intricate Question of Suicide in Early Modern Philosophy

Filip Buyse

Spinoza on conatus, inertia and the impossibility of self-destruction

Andrea Strazzoni

Particles, Medicaments and Method. The Medical Cartesianism of Henricius Regius

Teresa Tato Lima

Suicide and Hume’s Perspective about Human Life

5.30–7.00 Mariafranca Spallanzani, ‘Tota philosophorum vita commentatio mortis est’. Death of philosophers


Saturday 16th April 2016

Birkbeck College, Clore Management Centre, Torrington Square, London WC1E 7JL

9.30–11.00 Session 1 Session 2 Session 3
Kate Abramson

Living well, well-being and ethical normativity in Hume’s ethics

Dolores Iorizzo

Francis Bacon’s Natural and Experimental History of Life and Death (1623): A Lacuna in Accounts of the Scientific Revolution

Oliver Istvan Toth

Do we really need to die? Spinoza on the Necessity of Death in the Ethics

Giuliana di Biase

Human’s life as a “state of mediocrity” in John Locke’s Essay and in his other works

Gianni Paganini

Life, Mind and Body. Campanella and Descartes’ Connections

Piet Steenbakkers

Living Well, Dying Well: Life and Death in Spinoza’s Philosophy and Biography

11.15–12.45 Charles Wolfe, How I learned to love Vitalism
12.45–2.00 Lunch
2.00–3.30 Session 1 Session 2 Session 3
Sean Winkler

The Persistence of Identity in Spinoza’s Account of Individuals

Piero Schiavo

Controlling Death. Democritus and the myth of a death en philosophe

Matteo Favaretti

Camposampiero, The Ban of Death: Leibniz’s Scandalous Immortalism

  Mogens Laerke

The Living God. On Spinoza’s Hebrew Grammar and Cogitata Metaphysica II,6

Michael Jaworzyn

Clauberg, Geulincx, and philosophy as meditatio mortis after Descartes

Audrey Borowski,

Leibniz’s natural Mechanism. Life and Death Revisited

3.45–4.15 Meetings of learned societies
4.15–5.45 Lisa Shapiro, Learning to Live a Fully Human Life
5.45–6.00 Conclusion and Farewell

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At the end of her last post, Armstrong raised the question of why we should be tempted to follow Leibniz’s way out of Della Rocca’s Dilemma if we reject key aspects of Leibniz’s way into the problem. The short answer, I think, is that the aspects of Leibniz’s way into the problem that are most problematic are not essential to his way out of Della Rocca’s Dilemma. Leibniz’s suspect commitment to relations being at least partially ontologically grounded in the divine intellect makes Della Rocca’s Dilemma more challenging, not less. Watching Leibniz juggle five balls makes it easier to see how we can juggle three.


I introduced the distinction between ontological and semantic grounding largely to explain the sense in which relations are and are not ideal for Leibniz. If we turn specifically to Della Rocca’s argument against the possibility of relata jointly grounding relations I don’t think that distinction is particularly important. What is important is the thought that at least some relational facts might be wholly grounded in their relata, that, for example, the fact that a and b co-exist might be wholly grounded in the existence of a and the existence of b. Borrowing notation that I learned from my colleague Selim Berker, we might express (what I’ll call) Leibniz’s Key Thought by saying that [p • q] <- [p], [q] where “[p]” is shorthand for “the fact that p,” and “[p] <- [q]” is shorthand for “[p] is fully grounded in [q].”


Although I think most contemporary philosophers accept Leibniz’s Key Thought, Della Rocca and Bradley would, I believe, demur. They think that [p], [q] cannot fully ground [p • q] on their own. Something more, in their view, is needed, namely, [p] and [q]’s standing in a certain relation, call it “R.” So, to fully ground [p • q], we’d need at least [p], [q] and R. But wait, they’ll say, [p], [q] and R also can’t fully ground [p • q] on their own. For the same reason as before, something more is needed, namely, their standing in some relation, call it “R’”. And so on. If one allows the first regress, obviously we’ll be off to the races. Either we will be committed to doubling back at some point, falling into a vicious circle, or we’ll be launched on an infinite regress. I think contemporary rationalists should follow Leibniz’s lead and nip the regress in the bud by accepting his Key Thought.


If I’ve understood her correctly, Armstrong sees Della Rocca’s argument against the possibility of relata jointly grounding relations slightly differently. Her suggestion is that, according to Della Rocca, “the coexistence of a and b requires the relation of partial grounding, which is itself grounded in the coexistence of a and b.” This suggestion, she thinks, generates an “additional fact in need of explanation … namely, why does the fact that a’s existence partially grounds a and b’s coexistence require appeal to both a and b?” But, as I think Armstrong would agree, if there is such a fact as a’s existence partially grounds a and b’s coexistence, it looks like it too can be grounded in a’s existence and b’s existence. Using Berker’s shorthand, and letting “[p] <- – – [q]” stand for “[p] is partially grounded in [q],” we can say [[p • q] <- – -[p]] <- [p], [q]. If Leibniz’s Key Thought is accepted, it will take care not only of Della Rocca’s Dilemma as I’ve interpreted it, but also as Armstrong has interpreted it. Either way, contemporary rationalists could do a whole lot worse than to follow Leibniz’s way out of Della Rocca’s Dilemma.


Thanks again to Armstrong for her careful reading and thoughtful comments. And thanks to Stewart Duncan for setting up our exchange.


[Posted on behalf of Jeff McDonough]

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In Part 1, I raised some questions about how to understand semantic grounding as a response to the Rationalist’s Dilemma within Leibniz’s system. In this post, I will explore the notion of semantic grounding as a response to the dilemma as it arises for adherents to the PSR more generally.


According to McDonough’s solution, relations are semantically grounded in their relata jointly and still satisfy the PSR. In particular, McDonough thinks that the relation of coexistence is unproblematically grounded in the existence of its relata:


If one has an explanation for the fact that my dog exists, and one has an explanation for the fact that my cat exists, then ipsis factis one has an explanation for the fact that both my dog and cat exist…what is harder to imagine is [Leibniz] agreeing with the intuition that, say, having explained the fact that one substance exists and the fact that another substance exists, there should remain an additional fact still standing in need of explanation, namely, the fact that both substances exist (McDonough 379).


However, Della Rocca offers an argument against the possibility of relata jointly grounding relations. This argument is part of what makes Della Rocca’s dilemma worrisome for those that accept the PSR but reject Leibniz’s views on the ideality of relations (or substance-accident ontology for that matter). Della Rocca argues that the coexistence of objects cannot be grounded in the existence of those objects as follows:


…in order for a relation between a and b to hold, the relation must be partially grounded in a (and also partially grounded in b). Call this relation of partial grounding (between a and R) R’. So R holds in part because R’ holds. Why does R’, the relation of partial grounding between a and R, hold? There’s a relation, R’, of partial grounding between a and R only because a coexists with b. Call the relation of coexistence R”…Now in virtue of what do a and b co-exist, i.e. in virtue of what does the relation, R”, of coexistence hold? Just as R’ obtains in part because a and b coexist, so too R” obtains because a and b coexist…so R” holds in part because R” holds…And here we reach a circular explanation of a relation (Della Rocca 149).


The key move in the above argument is that grounding the coexistence of a and b requires the relation of partial grounding, which is itself grounded in the coexistence of a and b. McDonough, as we saw above, thinks that coexistence can be semantically grounded in existence, because it’s unlikely that “there should remain an additional fact still standing in need of explanation, namely, the fact that both substances exist.” It is, however, worth revisiting this issue precisely because Della Rocca does not think that coexistence directly appeals to the coexistence of both a and b. Instead, the relation of partial grounding generates appeals to the coexistence of a and b. My point is that the additional fact in need of explanation is a fact about grounding—namely, why does the fact that a’s existence partially grounds a and b’s coexistence require appeal to both a and b?


Perhaps Della Rocca is emphasizing the partial aspect of this relation. In order for it to be true that a partially grounds the coexistence of a and b, b must also partially ground coexistence. So the conditions under which a partially grounds a and b’s coexistence depends upon both a and b existing, or their coexistence.


On the one hand, I’m not sure I’m doing Della Rocca’s objection justice for, when reframed this way, it is still difficult to see why the partial grounding relation requires appeal to coexistence. The partial grounding relation itself is not so specific as to involve the other objects involved in partial grounding. Thus, to my mind, a’s existing partially grounds the coexistence of a and b in the same way that a’s existing partially grounds the coexistence of a and c, in the same way it would partially ground the coexistence of a, b, and c.


On the other hand, it is also true that a’s existence does not partially ground a and b’s coexistence without b’s existence. This, at least for me, gives Della Rocca’s worry some bite. But what this suggests is that a’s partial grounding depends on b’s existence, and thus only derivatively on the coexistence of a and b. So we have reason to think that a’s partial grounding relation too depends on a’s existence and b’s existence. This is consistent with what McDonough says about semantic grounding: not only is coexistence grounded in existence, but also the partial grounding of coexistence is grounded in existence. What is surprising, perhaps, is that a’s partial grounding depends upon b’s existence, but as long as it does not depend on their coexistence it is not circular.


Della Rocca’s argument above focuses on circularity, but he also raises an infinite regress worry—a Bradley-style regress—whereby the relation between x and y is grounded in a further relation which is grounded in other relations which are themselves grounded in other relations and so on (151). The relation of partial grounding is itself partially grounded thus there is the possibility for an infinite regress of grounding relations. While Leibniz seems opposed to an ontological regress of relations (see Mugnai 2010) it is less clear whether he would object to a semantic regress. Because the issue here is rooted in the ontological aspect of relations I have focused more on the circularity worry. However, if partial grounding can be grounded in existence, then even if there are an infinite number of semantic grounding relations as long as the ground for each is not itself a relation there is not a vicious semantic regress.


I’ll leave it to the reader to determine the gravity of Della Rocca’s objection, and the viability of my recommendations using McDonough’s resources. But, as I’ve rendered it, I think that Della Rocca’s objections raise the following important questions for developing a notion of semantic grounding:


  1. Do semantically grounded relations generate further truths about grounding?
  2. If grounding is a relation, are its instances semantically grounded?
  3. Is coexistence the (partial?) ground of the grounding relation for coexistence?


Works Cited

Della Rocca, Michael (2012). “Violations of the Principle of Sufficient Reason in Leibniz and Spinoza.” In Fabrice Correia and Benjamin Schnieder (Eds.), Metaphysical Grounding, Understanding the Structure of Reality (139-164). Cambridge University Press.


McDonough, Jeffrey (2015). “An Alleged Dilemma for Rationalists.Ergo, 2, 367-392.


Mugnai, Massimo (2010). “Leibniz and ‘Bradley’s Regress.’” The Leibniz Review, 20, 1-12.

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