Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-18T10:21:14.191Z Has data issue: false hasContentIssue false

Why the Good is supremely good: a defence of the Monologion proof

Published online by Cambridge University Press:  11 August 2021

Christophe de Ray*
Affiliation:
Department of Philosophy, King's College London, Strand, London WC2R 2LS, UK
*
Corresponding author: Christophe de Ray, email: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

The opening chapters of Anselm's Monologion contain a ‘proof’ of a perfect being, which has received far less attention than the more famous Proslogion proof, and the ontological arguments derived from it. I wish to rectify this by developing an argument in defence of a crucial premise of the Monologion proof. This premise states that ‘the Good’, i.e. that in virtue of which numerically distinct things may all be good, must itself be a supremely good thing (if it exists). I motivate the argument before considering objections to both premises, as well as putative ‘parodies’ of my argument. Part of the motivation of my argument will involve the claim that the Good, if it is good at all, must be a paradigm good thing. I conclude that theists have a second kind of ontological argument at their disposal.

Type
Original Article
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
Copyright © The Author(s), 2021. Published by Cambridge University Press

Introduction

The Monologion Proof

While Anselm's famous argument for theism in the Proslogion has spawned a huge literature and countless iterations, the arguments in the Monologion have received far less attention. In particular, the ‘proof’ of God's existence developed in the opening chapters of the latter work is not much discussed in contemporary analytic philosophy of religion. Such unpopularity is undeserved, in my view. What follows is an attempt to rectify this, by defending one of its premises.

The Monologion proof may be presented as follows:Footnote 1

  1. (I) The Good exists.

  2. (II) The Good, if it exists, is itself a supremely good thing.

  3. (III) If a supremely good thing exists, God exists.

  4. (IV) Therefore, God exists.

The Good

‘The Good’ here refers to some individual entity, such that to be a good thing is to stand in some relation R to it – as Anselm puts it, ‘some one thing through which all good things whatsoever are good’.Footnote 2 ‘Good’ here must be taken in a very broad sense, including but not exhausted by moral goodness and beauty. A thing is ‘good’ in this sense to the degree that it has what Alexander Pruss and Joshua Rasmussen (Reference Pruss and Rasmussen2018) call ‘positive properties’, that is, properties that confer value on their bearers. I will follow Anselm in treating ‘goodness’ and ‘greatness’ as interchangeable.Footnote 3 As such, things may have varying degrees of goodness, or on the present account, stand in R to the Good to greater or lesser extents. The precise nature of R will depend on the sort of thing that the Good turns out to be, a subject on which I shall have much more to say later on. Suffice it to say for now that, whatever R is, good things logically must stand in R to the Good, in order to be good (indeed, this just is what it means for a thing to be good).

In light of this, it is clear that (I) is a controversial premise. However, assessing its plausibility would effectively require settling the age-old metaphysical dispute between realists and nominalists, the latter of which would almost all deny that the proposition ‘Bob is good’ is made true by Bob's standing in some relation to the Good.Footnote 4 They may instead propose that it is made true by Bob's standing in resemblance relations to other good things, or by his belonging to the set of all good things (Rodriguez-Pereyra (Reference Rodriguez-Pereyra2002)). Realists, in contrast, may identify the Good with an abstract form or a concrete universal, and R with the instantiation relation. Not all realists need accept the existence of the Good, however, since they may hold that all propositions predicating ‘goodness’ of any object are false, or less radically, that they are reducible to more fundamental propositions, and that only the predicates of irreducible propositions correspond to real universals.Footnote 5

In the face of such variety, I will need to assume that there exists such a thing as the Good, and hope that this position is common enough to form the basis of an interesting argument for theism.

For want of a better term, I will refer to as ‘Platonists’ all who believe that the Good (as I have characterized it) exists, and thus that (I) is true.

Supreme goodness

I will take a supremely good thing to be a thing which could not possibly be better, that is, more ‘good’ than it is, where ‘good’ is once again taken in a very broad sense. This, it has long been thought, is precisely what it means for something to be God, in which case (III) is true. The premise is nevertheless not immune to criticism, not least because the traditional divine attributes (such as omnipotence and omnibenevolence) are sometimes argued to be jointly inconsistent (cf. Mackie (Reference Mackie1955)Footnote 6). If this is true, and if these attributes are essential to God, then it follows that God cannot possibly exist, and thus that something which could not possibly be better than it is would not be God.

Here again, however, I must treat the plausibility of (III) as a given for the purposes of this article.

Premise (II)

Much can and has been argued in favour of the claims contained in premises (I) and (III), even if not in view of defending the Monologion argument itself – arguments for Realism about the Good abound, as do defences of perfect being theology. The claim contained in (II), by contrast, receives little (if any) support in the contemporary literature. I wish to fill this gap by offering an argument for (II), which is structurally similar to the one advanced by Anselm.

Having established the existence of the Good, Anselm goes on to argue that the Good is itself supremely good:

But who could doubt that that through which all [good] things are good is [itself] a great good? Therefore, it is good through itself, since every [good] thing is good through it. So it follows that all other [good] things are good through something other than what they are and that this other alone [is good] through itself. But no good which is [good] through something other [than itself] is equal to or greater than that good which is good through itself. Hence, only that which alone is good through itself is supremely good; for that is supreme which so excels others that it has neither an equal nor a superior.

One may distinguish two stages in this brief argument. The first stage involves the claim that the Good is itself a good thing (and a ‘great’ one, at that). The second stage infers from this that the Good is supremely good. This allows us to lay out the argument as follows:

  1. (1) The Good is itself good.

  2. (2) If the Good is itself good, it must be supremely good.

  3. (3) Therefore, the Good is itself supremely good.

While I wish to remain faithful to this structure, the motivations of (1) and (2) that I will put forward will sometimes differ to (and hopefully improve upon) those advanced by Anselm. It is to these premises that I now turn.

Motivating (1)

‘But who could doubt that that through which all [good] things are good is [itself] a great good?’

This is about all that Anselm has to say in support of (1). The absence of an explicit motivation has led Visser and Williams (Reference Visser and Williams2008) to suggest that (1) could be supported through an appeal to something along the lines of the scholastic ‘principle of proportionate causality’, whereby a thing cannot give (through causation) a property that it does not already have (Feser (Reference Feser2014), 171). Hence, Anselm may be thinking that the Good could not ‘give’ goodness to anything, unless it is itself good.

The principle is not uncontroversial, and the authors argue that it admits of many counter-examples (e.g. the hot stove caused me pain when I touched it, even though the stove is not itself in pain).

Fortunately, Anselm does not in fact need to appeal to this principle. He may instead draw on the following, simpler principle:

Universality of Goodness (UG): everything that exists is good to some degree.

UG should be distinguished from the far more controversial Thomistic claim to the effect that ‘Goodness and being are really the same’ (Summa Theologiae, IA 5.1). The principle does not commit one to believing that an object's degree of goodness is a function of its ‘degree of being’, but rather that goodness and existence are always co-instantiated (if existence is something that can be instantiated), or that all existing things also instantiate goodness, in addition to existing.

Nor does UG entail the view that evils are mere privations of good. The proposition that all existing things are good to some degree is consistent with the proposition that some of these things are (say) cruel, even if cruelty is not identical to the absence of kindness (or any positive property).

UG has a great deal of intuitive plausibility – it is indeed difficult to imagine anything such that there would be nothing good about this thing, if it existed. We may offer the following simple argument in its defence (where to instantiate a property is to exist in some way):

  1. (i) Every existing thing instantiates properties.

  2. (ii) It is good to instantiate properties.

  3. (iii) Therefore, every existing thing is good.

(i) is intuitively obvious, since the thought of something that existed without existing in some way is intuitively absurd.Footnote 7 (ii) enjoys support from the strong intuition that a world in which (per impossibile?) no properties were instantiated (in effect, an empty world) would be worse than one in which some properties were instantiated, all other things being equal.Footnote 8

If this does not suffice, there is another motivation in support of (1), which may be closer to what Anselm had in mind. The Good, we are told, is something which is such that any object is ‘good’ just in virtue of bearing some relation R to it. This entails that the Good can enable other things to be good. And surely, being the sort of thing that can enable countless other things to have goodness is itself a great good. Hence, there is at least one thing that is good about the Good. The Good, therefore, is good to some degree.

While one may perhaps doubt that merely instantiating a property is, in and of itself, a good (even a very slight one), it seems exceedingly difficult to deny that instantiating the property of being that from which good things (if they exist) may derive their goodness – their kindness, wisdom, beauty, power (etc.) – makes the thing that has it better than it otherwise would be. Note that the property in question is not simply a relation that holds between the Good and good things, and which wouldn't exist if nothing other than the Good existed. Even if the Good were the only existing thing, it would still be true that the Good has the intrinsic property (or properties) P (Q, etc.) required to enable other things to have goodness.

I conclude that (1) is well motivated, and that there are strong grounds for believing that the Good is itself good.

Motivating (2)

Granted that the Good is itself a good thing, why think that it is supremely good? I will first consider Anselm's case for (2), before presenting an alternative.

Anselm's motivation for (2)

But no good which is [good] through something other [than itself] is equal to or greater than that good which is good through itself. Hence, only that which alone is good through itself is supremely good; for that is supreme which so excels others that it has neither an equal nor a superior.

Ordinary good things derive their goodness from the Good. The Good, in contrast, does not depend on anything else for its goodness. This difference, Anselm tells us, entails that the Good is ‘supremely good’, being greater than all other good things, actual or possible.

Let us say, following Anselm, that the Good has goodness-through-itself (GTI), while ordinary good things have goodness-through-another (GTA). Clearly, having GTI is greater than having GTA, such that all other things being equal, something with GTI will be greater than something with GTA.

But it does not follow from this that anything with GTI is necessarily greater than anything with GTA. Compare: to be courageous is better than to be cowardly, implying that all other things being equal, a courageous person is more excellent than a cowardly person. But it is surely mistaken to infer from this that, necessarily, a courageous person is more excellent than a cowardly person. For all other things need not be equal: a cruel but courageous man is not obviously more excellent than a kind but cowardly man.

Similarly, and for all we know, something with GTI might lack some positive property P had by something with GTA, such that the former thing (all things considered) is not greater than the latter thing.

It may be, however, that something with GTI will necessarily also have all other positive properties, and will have them to the highest possible degree. Some have argued that an ontologically independent being, which does not depend on any other being for its existence, would also have omnipotence, omniscience, perfect freedom, and so on (Rasmussen (Reference Rasmussen2009), Byerly (Reference Byerly2019)). Perhaps something similar applies to a being that does not depend on any other being for its goodness.

Anselm's case for (2), then, is at best incomplete: we need reasons to believe that something which has GTI would also have all the other properties that jointly constitute supreme goodness. I will now present such a reason.

The arbitrariness problem

I will argue that attributing goodness to the Good generates a serious problem, which cannot be solved unless supreme goodness is attributed to the Good.

The Good, we are told, is ‘good through itself’, while ordinary good things are ‘good through another’. Hence, there is at least one good thing whose goodness does not consist in its standing in a relation R to some other thing. It is natural to ask at this point, ‘if the goodness of the Good does consist in something other than standing in a relation R to some other thing, why should the goodness of any good consist in this? In other words, why shouldn't all good things be ‘good through themselves’?

It may be tempting to respond that no explanation is needed here – perhaps it is just a brute fact that the Good, unlike other good things, does not logically derive its goodness from other things. After all, some facts will need to be brute (unless we are willing to countenance an infinite regress of explanation), and couldn't this be one of them?

This response will not do. To see why, let us recall why Anselm and other Platonists have found it necessary to postulate the Good – namely, to provide a metaphysical explanation of the fact that two or more numerically distinct things can all be good. To explain this fact, Platonists tell us, it is not enough to posit the good things themselves, one must also recognize a further thing, the Good, in which all good things share. But the goodness of the Good cannot consist in the Good ‘sharing’ some further thing with other good things. Hence, the goodness of the Good seems to eliminate the original grounds for positing the Good in the first place, that is, the supposed need for good things to all share in the same further thing, in order to be good.

A closely related problem finds its roots in Plato's Parmenides, which famously contains an argument to the effect that the theory of forms is vulnerable to a vicious regress. It is commonly believed that what gives rise to the regress is the middle platonic ‘Self-Predication’ (SP) principle (Vlastos (Reference Vlastos1954), Wedberg (Reference Wedberg and Wedberg1995)), such that:

(SP): if particulars have some property P by virtue of participating in some form F, F also has P.

In particular, a vicious regress looms if it is held that the Good is itself good. For on the assumption that all good things must relate to some further thing by virtue of which they are good, the Good and all ordinary good things must all relate to some other thing, which we may call Good′. But if the arguments for the Goodness of the good given earlier were successful, Good′ must also itself be good (since it exists, and since it enables other good things to exist). And so on ad infinitum.

Both threats could be averted, if there were good reasons to believe that the goodness of the Good is a bona fide ‘special case’, rather than an arbitrary exception. In effect, if there is a good explanation why the Good can be good ‘through itself’ while other good things cannot, the independence of the Good with respect to its goodness would offer no support to the suggestion that ordinary good things might likewise be independent. Moreover, the (putatively) vicious ‘third man’ regress would be nipped in the bud, since we would have strong reasons for denying that the goodness of the Good requires the existence of some further good thing (and so on). I will argue that such reasons exist, if the Good is taken to be a paradigm good.

A solution: the paradigm good

Consider all extant copies of some famous painting, such as Van Gogh's The Starry Night. While numerically distinct, the paintings all bear the same relation to the original. In effect, to be what they are, that is, The Starry Night paintings, just is to bear that relation to the original. For any given copy, it would be accurate to say, ‘this is The Starry Night’ and such a statement would be made true by the fact that said copy bears some relation to a further painting. But note that while it would also be accurate to say this of the original, the statement would not in this case be made true by the fact that the painting bears some relation to some other painting. One might say that while the copy is The Starry Night ‘through another’, the original is The Starry Night ‘through itself’.

Of course, some copies will be better than others. Their goodness as copies of The Starry Night will be a function of the extent to which they resemble the original. We may say that the copies have varying degrees of starry-night-ness. Accordingly, it would be absurd to suggest that one of the copies might be a better The Starry Night than the original (though one of the copies might perhaps be a better painting than the original). There is no such thing as a painting that has more starry-night-ness than Van Gogh's original painting, because nothing could possibly resemble the original more than the original itself.Footnote 9 We may thus say that the original is supremely The Starry Night.

Plato's middle period dialogues frequently describe particular good things as imperfect ‘copies’ or ‘images’ of the Good, which is the perfect ‘model’ or ‘original’ (Silverman (Reference Silverman and Zalta2014)). This has led some to interpret the Good as a good thing par excellence, rather than a universal (Geach (Reference Geach1956), Malcolm (Reference Malcolm1991)). Whatever Plato himself may have thought, many of those he inspired certainly have taken that view.Footnote 10 As such, the identification of the Good with a paradigmatic good thing is not new.

What is interesting for our purposes is that this account of the Good offers a neat solution to the problem just raised. For if what we call ‘the Good’ is really the perfect model of goodness, it is certainly not arbitrary that it should be good ‘through itself’. The key is that, in our example, saying of a painting that it is The Starry Night apparently means that it resembles Van Gogh's original. Hence, the original need only resemble itself in order to be a The Starry Night painting, which it trivially does. It doesn't need to bear any resemblance relation to any other painting, in order to be what it is. Likewise, if the Good really is the paradigm good, then the relation R that good things bear to the Good would appear to be the resemblance relation.Footnote 11 In that case, the Good need only resemble itself in order to be good, and thus is good ‘through itself’ in this sense. Hence, the independence of the Good with respect to its goodness would not at all constitute an arbitrary exception to the rule that the goodness of ordinary good things consists in their standing in some relation to a further thing.

If the arbitrariness is removed, so are the problems associated with it. For one thing, the independence of the Good with respect to its goodness gives us no grounds for suspecting that other good things might also be independent in that way, any more than the independence of Van Gogh's original The Starry Night painting with respect to its ‘starry-night-ness’ casts doubt on the dependence of copies of The Starry Night with respect to their starry-night-ness. For another, the ‘third man’ regress is stopped dead in its tracks, since once again, a paradigm good thing need only resemble itself in order to be good, just as the original The Starry Night need only resemble itself in order to be what it is.

Conclusion: the Good, if good at all, is supremely good

I am not aware of any other way of characterising the Good, in such a way that would solve the arbitrariness problem. If no such alternative exists, we have strong grounds for believing that the Good, if it exists, is a paradigm good thing.

If the Good is the paradigm good, ordinary good things are good to the extent that they resemble the Good. As with the painting, some will do this more successfully than others. But none could possibly be greater than the Good itself, since this would amount to resembling the Good more than the Good resembles itself, which is absurd. It follows that the Good, if it is good at all, must be supremely good, given how I have characterized supreme goodness earlier.

This ends my discussion of the argument for premise (II) of the Monologion proof. I will now consider objections to both premises of my argument.

Objections to (1) The Good must itself be good

(1) is absurd

A first, very natural objection consists merely in dismissing (1) as an absurd proposition. Goodness cannot itself be good, one might think, any more than ‘dogness’ can itself be a dog. To say that it is is to commit a serious category error.

(1) would perhaps be absurd, if ‘the Good’ referred to a universal, standing in a relation of exemplification to particular good things.Footnote 12 But the argument I have defended is an argument to the effect that the Good is a paradigm good thing, a paradigmatic particular, rather than a universal.Footnote 13 As we have seen, there is nothing absurd about the claim that a paradigmatic good thing is itself good.

Thus, and as much as we may sympathize with the intuitive incredulity from which it springs, the objection in its current form seems simply to beg the question against my argument, by assuming that the Good, if it exists at all, must be a universal. A stronger objection would instead advance reasons for denying that the Good (if it exists) could be a good particular. The next objections will attempt to do precisely that.

(1) is question-begging

Recall that one of the motivations for (1) was the UG principle, which stated that ‘everything that exists is good to some degree’. Since the Good exists, I argued, it follows that it must be good to some degree.

It may be thought that such a principle, if true at all, is only true of particulars, and that universals, in contrast, need not be good to any degree in order to exist. If this were correct, then it would seem that my case for (1) begs the question against the view that the Good is a universal, since it involves applying UG to the case of the Good, thereby presupposing that the Good is not a universal.

However, I am not aware of any good reason to restrict the UG principle to particulars. Recall the mini-argument offered in defence of UG:

  1. (i) Every existing thing instantiates properties.

  2. (ii) It is good to instantiate properties.

  3. (iii) Therefore, every existing thing is good.

Whatever one may think of this argument, it is well recognized that universals, if they exist, instantiate properties, such as the property of being abstract (or concrete). In that case it is clear that ‘every existing thing’ in (i) and (iii) must include universals. Since (iii) simply states UG, it follows that UG would apply to universals as well as particulars.

In any case, I have offered a second motivation in defence of (1), which did not appeal to UG. I indeed argued that the Good (if it exists), whatever other properties it might have, is the sort of thing that can enable good things to exist, and that this is surely a great good. Here again, I am not aware of any reason why the latter could only be true if the Good is a particular, and not a universal. In either case, the Good is that without which no good thing could exist, which is surely a positive property if there ever was one. It would seem arbitrary to say that this property could only be positive if a particular, and not a universal, bears it.

Objections to (2) If the Good is itself good, it must be supremely good.

Things that cannot resemble the Good

I motivated (2) by arguing that the Good must be the paradigm good. If so, I argued, to be good is to resemble the Good to some degree. A natural response is to point to entities which seemingly cannot resemble a supremely good thing at all. One could mention, for instance, purportedly abstract entities like numbers, times, possible worlds, or transcendent universals, to name a few. The nature of these entities may seem to preclude them from resembling the Good in any way.

One could deny that such things are good to any degree. But once again, I motivated (1) with a principle (UG) such that all things that exist are good – and we have seen good reasons not to restrict this principle to concrete particulars.

Fortunately, this objection may still be swiftly dispatched. For all their inherent strangeness, abstracta (along with all other existing things) instantiate properties. The Good, we have seen, also instantiates properties. Hence, even the strangest possible existing things will always resemble the Good, if only by having the higher-order property of instantiating properties.

Another regress?

I mentioned the famous ‘Third Man’ regress earlier, and argued that it does not arise if we take the Good to be the paradigm good. But it may be thought that doing so gives rise to another, potentially vicious, regress.

Suppose, once again, that to be good is to resemble the Good. This presumably includes resemblances (i.e. instances of resemblance), which, if they exist (and given UG) are good to some degree. So, if some thing – call it ‘Gary’ – is good, there is a resemblance r which relates Gary and the Good, and r is also good. But for r to be good, there must be some resemblance r′ relating r and the Good. But r′ will also be good, and will thus also need to be related to the Good by some resemblance r″ – and so on ad infinitum.

I have two replies to this objection. First, it is not clear why this regress should be vicious. The regress shows that if the Good is the paradigm good, there is an infinite number of resemblances. But this, in and of itself, does not seem like a serious defect. Indeed, the fact that mathematical and modal platonists are committed to the existence of an infinite number of abstract entities (one for each number, or one for each possible world) isn't usually held against them.

But is there some other feature of the regress, by virtue of which it is vicious? A general account of when infinite regresses are vicious is well beyond the scope of this article. But notice that there is a significant difference between the regress at hand, and the ‘Third Man’ regress described earlier. For the latter, and not the former, implies that the Good fails to explain what it was postulated to explain, namely the fact that numerically different things can all be ‘good’. If the Good is itself good, and its goodness is grounded in the fact that it bears some relation to some further thing, then it is not true that good things are good by virtue of relating to the Good (and we will of course face the same problem when we ask whether this ‘further thing’ can do what the Good couldn't).Footnote 14

By contrast, an infinite number of resemblances all themselves bearing resemblance relations to the Good would not show that the Good is not up to the task given to it. For each resemblance, its goodness is metaphysically explained by the fact that it resembles the Good. This difference between the two regresses is not insignificant: on one influential view, regresses are vicious when they show that some proposed explanatory account of some general fact (e.g. ‘There are Fs’) fails to explain said fact (cf. Bliss (Reference Bliss2013)).

My second reply is that, whether or not the regress at hand is vicious, it is not clear that identifying the Good with a universal (rather than a supremely good particular) would be advantageous in this respect. For if we take R to be the exemplification relation (rather than the resemblance relation), we quickly find that instances of exemplification are no less prone to proliferation. If Gary exemplifies Goodness, an exemplification e conjoins Gary and Goodness. But e itself exemplifies R (i.e. the exemplification relation). Hence, e and R are conjoined by an exemplification e’, which also exemplifies R, and the regress continues.Footnote 15

The objector may perhaps protest that there really is no such thing as a particular exemplification like e and e′ – there is just the universal ‘exemplification’, which bears itself to itself. But if this is an acceptable response, it is surely also acceptable to respond to the original regress with the claim that there are no particular resemblances like r and r′, and that there is only the ‘resemblance’ universal, which bears itself to itself.

There is perhaps some difference between the two regresses, such that the former is vicious and the latter is not. Until I am made aware of one, I will assume that the kind of regress discussed in this section does not uniquely threaten my position, if it threatens it at all.

The greatest existing good

I have argued that the Good must be ‘supremely’ Good, in the sense that nothing could be better than it is. One could object that my arguments instead motivate the weaker claim that the Good must be the best actually existing thing. Since the Good serves the role of a paradigm good thing, could this role not be served by different things in different possible worlds, containing different combinations of good things? Perhaps the paradigm good thing of any world is whatever happens to the best thing in that world, rather than the best possible thing, in which case the existence of the Good does not imply the existence of a supremely good being.

The analogy used earlier to explicate the relevant concept of a ‘paradigm’ indicates that this suggestion is implausible. Once again, Van Gogh's original painting serves as a paradigm The Starry Night, insofar as any painting logically must resemble it in order to be a The Starry Night painting.Footnote 16 Consider a nearby world in which Van Gogh's original had been destroyed, rather than being on display in New York's Museum of Modern Art. In such a world, would the best existing copy C of the original constitute the paradigm The Starry Night? Surely not. Intuitively, the ‘starry-night-ness’ of paintings in that world still depends on how closely they resemble the (no longer existing) original, or perhaps on how closely they would resemble the original if it still existed. The fact that some painting in that world P is an excellent copy of The Starry Night is still grounded by its resemblance to the original, not by its resemblance to C. Moreover, if someone in that world produces a painting C′ which even more closely resembles the original than C, we would say that C′ is a better The Starry Night painting than C, even though C a fortiori resembles itself more than C′ resembles C.

This suggests a serious problem for the objection: if the paradigm Good is simply taken to be some object which happens to be better than all other actually existing objects, it is false to say that to be ‘good’ just is to resemble the Good. For it would be true in our world that some object O could come into existence and be better than the Good, even though O resembles the Good less than the Good resembles itself. If so, it is false that to be ‘good’ just is to resemble the Good (the Good is simply a yet-unmatched exemplar of goodness). But in that case, the arbitrariness problem – which my ‘paradigm Good’ theory was supposed to solve – rears its ugly head once more. Indeed, if the goodness of the Good does not consist in its resemblance to itself (as in my account), then there is no reason why the Good, unlike other good things, should be good ‘through itself’, that is, not by virtue of standing in some relation R to some other thing, like other good things. Its independence with respect to goodness is completely arbitrary, which is precisely what we were trying to avoid, and gives rise to the worries described earlier in connection to the arbitrariness problem.

Nor would it help to argue that to be good is to resemble paradigm G1 in world W1 or G2 in W2, or G3 in W3, etc. For it seems obviously false to say that if our world contained no better thing than Nero, then it would be true in our world to say that to be good just is to resemble Nero.

I conclude that the paradigm Good cannot merely be the best actually existing thing in order to serve the purpose set out for it, and thus that the objection fails.

The properties of the paradigm Good (and divine simplicity)

My case for (1) contained an inference from the fact that the Good instantiates certain properties, to the conclusion that the Good must itself be good. One might take this to mean that the Good derives its goodness from something other than itself, namely, the particular properties that it instantiates. This in turn suggests that the Good and other good things which also have these properties will each be good in virtue of possessing said properties.

This seems inconsistent with the account of goodness sketched out in defence of (2), whereby the Good is not good in virtue of standing in some relation to some other thing, as in the case of other good things: rather, it is good ‘through itself’, since its goodness consists in its (trivial) resemblance to itself. But if the goodness of the Good, and of all other good things, instead consists in the instantiation of (at least some) particular properties, it would appear to follow that the Good is ‘good through another’, just like every other good thing, where ‘another’ refers to the shared properties.

Can this tension between the arguments for (1) and (2) be resolved? I submit that it can. Note first that to infer the goodness of the Good from the fact that it instantiates particular properties is not to say its instantiation of these properties is what makes it good. For it could instead be the other way around: perhaps, the Good has the particular properties that it has in virtue of being good.

This second option is in fact what is apparently implied by the claim that to be good just is to resemble the paradigm Good. On this model, the goodness of the Good consists in its self-resemblance, which trivially obtains in virtue of its (equally trivial) self-identity. Now, it seems intuitively wrong to say that an object is identical to itself and thus resembles itself, in virtue of having the particular properties that it has (P, Q, etc.). For the former remains true, regardless of what the object's properties are. The converse seems more plausible: an object o has the properties had by an object o′, in virtue of the fact that o = o′, and thus that o perfectly resembles o′. Thus, it seems more plausible to say that the Good has the particular properties that it has in virtue of its goodness (which just is its self-resemblance), and not vice versa, in which case the Good is not good in virtue of instantiating particular properties.

I will later offer a slightly more complex account of goodness, such that to be good is either to be identical to the Good, or to ‘imitate’ the Good (in a sense that will be explicated shortly). On this account, the answer to the objection at hand is simpler: the goodness of the Good consists merely in its self-identity, not in its instantiation of any particular property.

I conclude that, on either account of goodness, the objection is unsuccessful. But talk of the Good's properties admittedly raises concerns for advocates of divine simplicity, who typically balk at the suggestion that God has properties. It may be asked whether my argument can by adopted by said advocates. But notice that my theistic argument is hardly unique in this respect – on the contrary, most (if not all) theistic arguments involve the ascription of properties to God, be it necessity (as in many cosmological arguments), intelligence (as in design arguments), or absolute perfection (as in ontological arguments). The question is whether it can be maintained that these properties are all identical to one another, and to God. If it can, advocates of divine simplicity should have no particular difficulty with my argument. If it cannot, then divine simplicity is false, and the fault lies with divine simplicity, not with my argument.

The Supreme Dog (and other parodies)

Parodies of arguments for the existence of a supremely good being have existed at least since Gaunilo's famous ‘lost island’ parody of the Proslogion proof, and continue to prove popular (cf. Law Reference Law2010, Nagasawa Reference Nagasawa2010). Why should my argument be an exception?Footnote 17

Consider the following argument:

  • (1′) D is itself a dog.

  • (2′) If D is a dog, it must be the doggiest of all possible dogs.

  • (3′) Therefore, D is the doggiest of all possible dogs.

Take D to be an entity such that to be a dog is to bear some relation R′ to D. For this argument to be an effective parody of mine, it must be that both (1′) and (2′) are just as plausible as (1) and (2).

To reiterate the motivation for (1) once more, I argued that the Good must itself be good because (a) all existing things are good and (b) is the sort of thing that can enable good things to exist, which is surely a positive property. These considerations show that D is also a good thing, whatever else it is supposed to be: it exists (we assume), and enabling dogs to exist is also (plausibly) a positive property.

But (1′) states that D is a dog, not that D is a good thing. And it is clear that there is no parallel case for D being a dog. There is obviously no true principle to the effect that all existing things must be dogs. And one can make it logically possible for dogs to exist without being oneself a dog (indeed, matter performs that job insofar as dogs are essentially material, and matter is not a dog).

The above argument fails as a parody, because the motivations for (1) do not likewise motivate (1′). Here is another candidate:

  • (1*) The Bad is itself bad.

  • (2*) If the Bad is bad, it is supremely bad.

  • (3*) Therefore, the bad is supremely bad.

Take ‘the Bad’ to be an entity such to be bad is to bear some relation R* to it. A thing is ‘bad’ to the extent that it instantiates ‘negative properties’, that is, properties that make a thing worse than it otherwise would be. A supremely bad thing is one that could not possibly be worse than it is. ‘Bad’ here is taken in a very broad sense, including but not exhausted by moral badness.

This argument seems more promising as a parody. Its first premise (1*) may receive a motivation similar to that of (1): the property of enabling bad things to exist surely is a negative property. Hence, whatever else it is, the Bad must be bad to some degree.

What of (2*)? A parallel case for (2*) would require one to argue that the Bad is the ‘paradigm bad’, and that to be bad just is to resemble the Bad to some degree. But what would a paradigm bad look like? It could evidently not be the radical opposite of the paradigm good, in the sense of lacking anything good at all. For if UG is true, mere existence is sufficient to being good to some degree. Moreover, if it is to instantiate properties like wickedness and cruelty, the paradigm evil will be logically required to instantiate some positive properties like consciousness and knowledge of other minds, without which wickedness and cruelty are impossible.

It should be clear that if privation theory of badness is true, and to be bad just is to be deprived of some good, a paradigm theory of evil would be very implausible. Consider again our earlier analogy: if (as is plausible) to be a bad copy of The Starry Night just is to be deprived of ‘starry-night-ness’, then it seems absurd to say that what makes this copy worse than another is that it more closely resembles some paradigm bad painting. More plausibly, what makes the copy worse is that it less closely resembles Van Gogh's original. Similarly, on privation theory, for a thing to be worse than another just is for that thing to less closely resemble the paradigm good, not for it to more closely resemble a paradigm bad thing.

Here is not the place to defend or critique privation theory,Footnote 18 though it is clear that at least some of the ways of being which we call ‘bad’ are mere privations of goodness (e.g. being unempathetic or unkind). Nevertheless, an upshot of the above paragraph is that the ‘badness’ that resemblance to the paradigm bad is supposed to explain can only be the badness that does not consist in mere privation of goodness, if such badness exists. Plausible candidates include wickedness and cruelty.

A paradigm bad, then, would be a supremely wicked and cruel thing. Suppose that privation theory is false, and that there is no less reason to believe in a paradigm bad than in the paradigm good. Would this show that something must be wrong with my case for (2)? I do not see why it should. At most, it could be thought to show that, pace Augustine and the classical theist tradition, the Manichaeans were correct to postulate a supremely evil principle, ontologically on a par with the Good. But even this is unclear, as the Bad would still need to depend on the Good in a way that the Good need not depend on the Bad: once again and given UG, the Bad necessarily has some goodness qua existing thing. The Good in contrast need not be wicked or cruel (or whatever else requires resemblance to the paradigm bad); more than this, some of its positive properties (e.g. love, kindness) rule this out.Footnote 19

One may of course charge that a supremely good thing could not possibly allow a supremely wicked thing to exist. In that case, and if the arguments for a supremely good thing and a supremely bad thing stand and fall together, it would follow that they both fail, since their conclusions cannot both be true. But this objection only succeeds on the assumption that there are no good responses to the problem of evil, and this of course is hotly contested.Footnote 20

Admittedly, arguments from evil don't typically charge that a supremely bad thing exists, and that this is impossible or unlikely given theism. Rather, they make much weaker claims about the bads that exist. In consequence, it may be thought that the usual theistic responses to the standard problem of evil are ill-equipped to neutralize the objection at hand.

But it is far from clear that the existence of a supreme Bad would pose a special problem for theism. For suppose that the theist has a good explanation why a perfect being could justifiably allow exceedingly cruel and wicked human beings like Nero and Pol Pot to exist (which is one of the states of affairs that standard theodicies purport to explain). If so, it would be odd and arbitrary for the critic to insist that a perfect being can legitimately tolerate the existence of vicious human tyrants, but not that of a maximally malicious devil (cf. note 18). The onus is on the critic to show why the latter, and not the former, would be outside the sphere of acceptable divine behaviour.Footnote 21

I conclude that it is unclear whether this second parody argument undermines the argument for (II).

An alternative to resemblance

In arguing that the Good (given that it exists) must be supremely good, I argued that it must be a paradigm good, and the relation R that good things ought to bear to the Good is the resemblance relation.

In their critique of the Monologion proof, Visser and Williams (Reference Visser and Williams2008) argue that the case for (I) – which states the existence of the Good – is plausible only if the relation R that is supposed to hold between the Good and good things is instead the exemplification relation. The motivation for (I), the authors claim, is the need for an ontological basis for our predicating ‘is good’ of good things. They then contend that only the exemplification of the Good by such things can constitute said basis. Since it is impossible to exemplify a supremely good thing, it follows that the Good is not that.

While the authors do not tell us why the resemblance relation is not up to the job, it is easy to see why philosophers of a platonic temperament should think it is not. Such philosophers may protest that the whole purpose of postulating something like the Good is to give an explanation of resemblance, which would otherwise be brute. For example, Gould (Reference Gould2012) contends that the need for an entity like the Good stems from the need to answer the question ‘what explains resemblance facts’. And Armstrong (Reference Armstrong1978, 50) writes that it seems ‘obvious’ that there ought to be a ‘ground’ for resemblance facts, including presumably resemblances with respect to goodness. As he notes, while ‘[it] is natural to assert that things resemble because they have something in common’, it is ‘counterintuitive to say that they have something in common because they resemble each other’.

Accordingly, one could accuse me of getting the order of explanation wrong: things are not good because they resemble the Good, or anything else. Rather, they resemble the Good because they are good. To invert this order, one could argue, is to commit the error of resemblance nominalists.Footnote 22

I would perhaps be within my rights to respond that since my argument for the proposition that the Good is the paradigm good is sound, it simply must be the case that resemblance facts explain facts about the goodness of good things. Equally, the critic may insist that my argument cannot be sound, because resemblance facts cannot explain facts about the goodness of good things.

Is there a way to break this unsatisfying stand-off? I would like to suggest that there is. The chief analogy used to characterize the Good's relationship to good things offers a clue: on reflection, it appears that resembling Van Gogh's original is not sufficient to being a copy of The Starry Night. For if, by a freak accident, a chimpanzee throwing blobs of paint at a blank canvas produced something that resembled Van Gogh's original, I don't imagine that we could call it a The Starry Night painting. It seems that some additional condition is required, namely that painting be an imitation of van Gogh's original, where ‘imitation’ is a kind of causal relation. For some thing a to be an imitation of some other thing b, it must at least be the case that a and b causally interact, such as to bring it about that a resembles b as a result of this interaction. In other words, a is modelled after b: whoever produced a did so in view producing something that resembles b.

That imitation and resemblance are not identical should be manifest, if only because the latter is essentially symmetrical, and the former isn't. A painting cannot possibly resemble another, unless the second resembles the first as well. Conversely, the first may have been modelled on the second, while the second was not modelled on the first. Importantly, the fact that the first painting is an imitation of the second explains the fact that they resemble each other.

Suppose, then, that R is the imitation relation, and that ordinary good things are good to the extent that they imitate (or ‘copy’) the Good. This scenario is admittedly complicated by the fact that imitation, unlike resemblance, does not seem reflexive – the Good cannot be an imitation of itself, just as Van Gogh's original painting is not modelled after itself. The goodness of the Good must instead consist in its identity with itself, just as the original painting's ‘starry-night-ness’ consists in the fact that it just is Van Gogh's The Starry Night. Thus, to be good on this view is either to be identical to the Good, or to be an imitation of the Good.Footnote 23

The view that ordinary good things owe their goodness to being imitations of a supremely good thing is not without precedent in the history of philosophy. It is indeed a common theme in Neoplatonic writings (Robert (Reference Robert2018), 102), which echo the suggestion in Plato's Timaeus that living things were ‘modelled’ after an eternal paradigm (Gerson (Reference Gerson2005), 82). Leibniz writes in his Discourse on Metaphysics that ‘the essences of our souls are certain expressions, imitations or images of the divine essence' (Taylor (Reference Taylor2011), 441) and that this imitation is maintained through continuous divine conservation.

Most significantly for our purposes, this model lacks the unsavoury implication that ordinary good things are good as a result of the resemblance relations in which they stand. Rather, their goodness, which consists in their being modelled on the Good, is what explains those resemblance facts. To say that good things are good because they are all modelled on the same thing is significantly less counterintuitive than to say that they are good because they all resemble the same thing.

I'm not sure whether this alternative picture of the paradigm good would fully satisfy the critic.Footnote 24 But it at least avoids the specific worry associated with the resemblance relation, and will hopefully make my argument more attractive to philosophers with platonic instincts

Conclusion: the other ontological argument?

The Monologion proof infers the existence of God from the existence of the Good, which, it holds, must itself be supremely good, if it exists at all. I have presented and defended an argument for the latter contention. It is my hope that doing so will draw more attention to this neglected Anselmian argument.Footnote 25

Should the Monologion proof be regarded as a type of ontological argument, like its Proslogion counterpart? The relevant Stanford Encyclopaedia of Philosophy article defines such arguments as arguments ‘for the conclusion that God exists, from premises which are supposed to derive from some source other than observation of the world – e.g., from reason alone’ (Oppy (Reference Oppy and Zalta2014)). If this is correct, my argument seems to qualify. All three premises, if they are true, seem to be knowable a priori. This includes the argument's first premise (I), which states the existence of the Good. I may infer this from the existence of at least one good thing – namely, necessary abstracta such as numbers and possible worlds, or possibly myself – which I can know to exist a priori. Alternatively, I may infer it from my a priori knowledge that there is no such thing as an empty world,Footnote 26 and thus (by UG) that there must be at least some goodness in the actual world.

On the other hand, some might argue that there is more to an ontological argument than simply being a priori. For example, moral arguments are also plausibly a priori (at least if moral properties are knowable a priori), but they are not referred to as ‘ontological’ arguments. If so, my argument may be better characterized as an axiological argument.

In any event, those dissatisfied by arguments derived from the Proslogion proof may now avail themselves of a different kind of a priori argument, which traces its roots to Anselm's lesser-known proof.

Footnotes

1. Brower (Reference Brower2019) reconstructs the argument in a similar way, with some minor differences.

2. All Monologion quotes are taken from Hopkins and Richardson (Reference Hopkins and Richardson2000).

3. Similarly, Adams (Reference Adams1999, 14) identifies goodness with ‘excellence’, and with ‘that which is worthy of love or admiration’.

4. I say ‘almost all’ because as we will see, there is one kind of resemblance nominalism which is consistent with the existence the Good, given that the Good is a paradigm good thing, and that R is the resemblance relation.

5. For instance, one might hold that fundamental physical properties (which do not include ‘goodness’) are the only universals (cf. Armstrong (Reference Armstrong1978)).

6. Cf. Speaks (Reference Speaks2018) for a more recent challenge to perfect being theology.

7. Thus, Vallicella (Reference Vallicella2002, 181) notes that even the so-called ‘bare’ or ‘thin’ particulars that populate some ontologies ‘cannot exist without instantiating properties’. What makes them ‘bare’ isn't that they lack properties, but rather that they ‘have their properties by being externally related to them rather than having them intrinsically’ (ibid., 173)

8. I add this caveat in recognition that some particularly ‘hellish’ worlds, full of extreme suffering and devoid of great goods, may well be objectively worse than the empty world.

9. I am inclined to agree with Goodman (Reference Goodman1971, 4) that resemblance is a reflexive relation.

10. Lloyd Gerson (Reference Gerson2005, 225) notes that the Neoplatonists identified the Forms with ‘paradigmatic causes’. For a more modern example, see Adams (Reference Adams2002). Though the account of the Good that I defend in this section is quite similar to that of Adams, his arguments for this account are quite different from the one I motivate here.

11. Though I will consider an alternative relation later.

12. However, proponents of universals must grant that at least some universals are self-exemplifying. For instance, if universals are abstract, ‘abstractness’ exemplifies itself (and if universals are instead concrete, ‘concreteness’ exemplifies itself). We would thus be owed an explanation why ‘goodness’ couldn't likewise exemplify itself.

13. Note, however, that the argument is consistent with there being some universals, perhaps such as ‘dogness’, even if the Good is not one of them.

14. Indeed, a common interpretation of the threat that the Third Man regress is supposed to pose, is that it points to the explanatory failure of the Forms (cf. Vlastos (Reference Vlastos1954), Fine (Reference Fine1993), 204).

15. I am not sure whether this counts as a version of the regress attributed to F. H. Bradley (cf. Cameron (Reference Cameron2008))

16. Though again, and as we will see, this is not a sufficient condition.

17. Parody arguments do not target particular premises of the arguments they parody, hence why I discuss this type of objection in its own section, rather than (say) in a section about objections to (2).

18. Cf. Grant (Reference Grant2015) for a defence.

19. The great majority of classical theists have believed in the existence of a supremely wicked thing that nevertheless owes the goodness that it has to a supremely good thing. For recent philosophical discussions of the doctrine of the Devil, cf. McCraw & Arp (Reference McCraw and Arp2015)).

20. Cf. Dougherty (Reference Dougherty2011) for a relatively recent survey of arguments from evil and their rejoinders.

21. It should also be noted that tolerating the existence of a supreme bad does not entail giving it free reign to wreak maximal havoc on the rest of creation. As we have just seen, the Bad would asymmetrically depend on the Good for whatever goodness it has, including its power. Thus, the Good could plausibly prevent the Bad from realizing its full potential.

Note also that my response in no way implies that, if there is such a thing as the Bad, God must of necessity allow it to exist. The existence of a supremely Bad thing might well depend on contingent facts, much like the existence of lesser bads is often thought to be by theists. For example, it may be thought that God has given one of his creatures the capacity to freely choose to become supremely evil, but whether this choice is made is an entirely contingent matter.

22. Indeed, some resemblance nominalists hold that all qualitative facts are grounded by the resemblance of particulars to suitable paradigms (cf. Cargile (Reference Cargile2003)).

23. An interesting upshot of this is that the Good is ‘good’ only in an analogous sense to that in which other things are ‘good’, since identity and imitation are two different relations that one can bear to the Good. This of course is what advocates of divine simplicity have typically argued. In contrast, if R = resemblance, the Good and other good things are ‘good’ in precisely the same sense, that is, in their resemblance to the Good.

24. One could for instance reply that the imitation relation is obscure, though it is not clear to me that it is any less obscure than its rivals, be they resemblance or exemplification. Moreover, the role of God/the Good as intentional Creator in traditional theism may shed more light on the nature of the relation: just as a painter might intentionally produce a painting that resembles Van Gogh's original The Starry Night, God might intentionally create substances after his own likeness, as we are told that He does in Genesis 1:26. Though this verse specifically refers to human creations, other passages suggest that non-human creations are also reflections of God, albeit to a lesser degree (e.g. Psalm 19:1, ‘The heavens declare the glory of God’).

25. Burns (Reference Burns, Walls and Dougherty2018) defends an argument similar to the Monologion proof, though she treats it as a ‘patched’ version of the Proslogion proof instead. Moreover, though it is argued that ‘maximal excellence’ must exist in all possible worlds in which there are degrees of goodness, we are not told why it would follow that a maximally excellence should itself be instantiated. This has been the chief task of this article.

26. Cf. E. J. Lowe's a priori argument against the possibility of an empty world (Lowe (Reference Lowe and Goldschmidt2013), 192).

References

Adams, RM (1999) Finite and Infinite Goods: A Framework for Ethics. Oxford: Oxford University Press.Google Scholar
Armstrong, DM (1978) Nominalism and Realism: Universals and Scientific Realism Volume I. Cambridge: Cambridge University Press.Google Scholar
Bliss, RL (2013) Viciousness and the structure of reality. Philosophical Studies 166(2), 399418.CrossRefGoogle Scholar
Brower, J (2019) Platonism about goodness: Anselm's proof in the Monologion. TheoLogica: An International Journal for Philosophy of Religion and Philosophical Theology 3(2), 128.CrossRefGoogle Scholar
Burns, E (2018) Patching Plantinga's ontological argument by making the Murdoch move. In Walls, J and Dougherty, T (eds), Two Dozen (or so) Arguments for God: The Plantinga Project. Oxford: Oxford University Press, pp. 124134.Google Scholar
Byerly, T (2019) From a necessary being to a perfect being. Analysis 79(1), 1017.CrossRefGoogle Scholar
Cameron, RP (2008) Turtles all the way down: regress, priority and fundamentality. Philosophical Quarterly 58(230), 114.Google Scholar
Cargile, J (2003) On Russell's argument against resemblance nominalism. Australasian Journal of Philosophy, 81(4), 549560.CrossRefGoogle Scholar
Dougherty, T (2011) Recent work on the problem of evil. Analysis 71(3), 560573.Google Scholar
Feser, E (2014) Scholastic Metaphysics: A Contemporary Introduction. Neunkirchen-Seelscheid: Editiones Scholasticae.Google Scholar
Fine, G (1993) On Ideas: Aristotle's Criticism of Plato's Theory of Forms. Oxford: Clarendon Press.Google Scholar
Floyd, S (2006) Aquinas’ moral philosophy. Internet Encyclopedia of Philosophy. Available at https://iep.utm.edu/aq-moral/ (accessed 15 January 2021).Google Scholar
Geach, PT (1956) The third man again. Philosophical Review 65(1), 7282.CrossRefGoogle Scholar
Gerson, LP (2005) Aristotle and Other Platonists. Ithaca: Cornell University Press.Google Scholar
Goodman, N (1971) Languages of art: an approach to a theory of symbols. British Journal for the Philosophy of Science 22(2), 187198.Google Scholar
Gould, P (2012) The problem of universals, realism, and god. Metaphysica 13(2), 183194.CrossRefGoogle Scholar
Grant, WM (2015) The privation account of moral evil. International Philosophical Quarterly 55(3), 271286.CrossRefGoogle Scholar
Hopkins, J and Richardson, H (2000) Complete Philosophical and Theological Treatises of Anselm of Canterbury. Minneapolis: A.J. Banning Press.Google Scholar
Law, S (2010) The evil-god challenge. Religious Studies 46(3), 353373.Google Scholar
Lowe, EJ (2013) Metaphysical nihilism revisited. In Goldschmidt, T (ed.), The Puzzle of Existence. New York: Routledge, pp. 182196.Google Scholar
Mackie, JL (1955) Evil and omnipotence. Mind 64(254), 200212.Google Scholar
Malcolm, J (1991) Plato on the Self-Predication of Forms: Early and Middle Dialogues. Oxford: Oxford University Press.Google Scholar
McCraw, BW and Arp, R (eds) (2015) Philosophical Approaches to the Devil. New York: Routledge.CrossRefGoogle Scholar
Nagasawa, Y (2010) The ontological argument and the devil. Philosophical Quarterly 60(238), 7291.CrossRefGoogle Scholar
Oppy, G (2014) Ontological arguments. In Zalta, EN (ed.), Stanford Encyclopaedia of Philosophy. Available at https://plato.stanford.edu/entries/ontological-arguments/ (accessed 15 January 2021).Google Scholar
Pruss, A and Rasmussen, J (2018) Necessary Existence. Oxford: Oxford University Press.CrossRefGoogle Scholar
Rasmussen, J (2009) From a necessary being to god. International Journal For Philosophy Of Religion 66(1), 113. doi: 10.1007/s11153-008-9191-8.CrossRefGoogle Scholar
Robert, G (2018) General Pre-Established Harmony: A Study of Leibniz on Substance and the Unity of the World. PhD thesis, King's College London.Google Scholar
Rodriguez-Pereyra, G (2002) Resemblance Nominalism: A Solution to the Problem of Universals. Oxford: Clarendon Press.CrossRefGoogle Scholar
Silverman, A (2014) Plato's middle period metaphysics and epistemology. In Zalta, EN (ed.), The Stanford Encyclopedia of Philosophy. Available at https://plato.stanford.edu/entries/plato-metaphysics/ (accessed 15 January 2021).Google Scholar
Speaks, J (2018) The Greatest Possible Being. Oxford: Oxford University Press.CrossRefGoogle Scholar
Taylor, R (2011) The Rationalists. New York: Anchor.Google Scholar
Vallicella, W (2002) A Paradigm Theory of Existence: Onto-Theology Vindicated. Dordrecht: Springer Science & Business Media.CrossRefGoogle Scholar
Visser, S and Williams, T (2008) Anselm. Oxford: Oxford University Press.CrossRefGoogle Scholar
Vlastos, G (1954) The third man argument in the Parmenides. Philosophical Review 63(3), 319349.CrossRefGoogle Scholar
Wedberg, A (1995) The theory of idea. In Wedberg, A (ed.), Plato's Philosophy of Mathematics. Stockholm: Almqvist & Wiksell, pp. 2644.Google Scholar