Book Review: Imaguire, G. Priority Nominalism (Springer Verlag, 2018, 171 pages.)

Imaguire, G.. Priority Nominalism (Springer Verlag, 2018, 171 pages.)


The present work is a review of Imaguire's book 'Priority Nominalism'. In the first part I present the fundamental idea of the book along general lines; successively, I report a resume of each chapter and I present in more details the view of the author and the dialectic of his arguments. In the final part, I highlight some strong points of the book and I attempt a formulation of a possible difficulty arising from Imaguire's proposal.

Nominalism; Problem of Universals; Grounding

In his most recent book 'Priority Nominalism' (2018, Springer Verlag), Guido Imaguire presents a new sort of nominalism considered both as a development and an enrichment of Quine's view on universals notoriously labeled by Armstrong Ostrich Nominalism: like the Ostrich that buries his head under the ground, the Quinean nominalist gets rid of universals by not taking predicates with the adequate ontological seriousness.

The basic idea of the book is that questions of existence must be answered by applying what Imaguire calls the criterion of Grounded Ontological Commitment. According to this criterion, Quine's criterion of ontological commitment must be applied not to all sentences composing the theories that we are open to accept as true, but only to sentences of the same theories - or suitable paraphrases - expressing fundamental facts, i.e. facts that are not grounded in any other fact. This criterion combined with the view that predication is fundamental, i.e. not grounded in any other fact about properties, classes, platonic forms, etc... - results in a strengthened version of Ostrich Nominalism: there are no universals for there are no sentences expressing fundamental facts in which expressions allegedly standing for universals occur in a position into which we may quantify. Thus the notion of metaphysical grounding represents the additional and crucial ingredient of Priority Nominalism that makes it a strengthened version of Quine's Ostrich Nominalism. Moreover, Priority Nominalism besides gaining more argumentative strength than Ostrich Nominalism is also wider in scope: not just properties, but also entities like classes, numbers, meanings, and word types can be explained away using the same strategy.

The book has also another purpose: to show that the attitude of the Ostrich Nominalist is not dismissive regarding ontological questions about universals when he is endowed with the theoretical tool of the notion of grounding. The ostrich nominalist does not reject the problem of the grounds of predication: he simply argues that predication is not grounded in anything else, that is fundamental, and thus he does have an answer. Moreover, Imaguire argues that even Quine's Ostrich Nominalism is not dismissive and consequently the label Ostrich is unfair: according to Imaguire, what is achieved with the introduction of the notion of metaphysical grounding is a way of making explicit some aspects of Quine's nominalism that many times are justified by appealing to ontological intuitions.

In the first chapter, Imaguire presents the Problem of Universals. According to him, the expression 'Problem of Universals' has been traditionally used to denote different issues and formulations. Imaguire lists five formulations: (1) The existence question, (2) The grounding of predication, (3) The One-Over-Many Problem, (4) The Many-Over-One Problem, and (5) the Similar-But-Different Problem. (1) is summarized by the question “Do universals exist?”; (2) is the problem of explaining predication, i.e. of specifying in virtue of what a certain particular a is F. Formulations (3), (4), and (5) are deeply related and amount to answering questions introduced by the “how is it possible” clause: (3) “How is it possible that two different particulars a and b are both F?”; (4) “How is it possible that the same particular a is both F and G?”; (5) “How is it possible that two distinct particulars a and b are similar - insofar as they are both F - and different at the same time?”. As the author remarks, many traditional solutions to the Problem of Universals deal with one particular formulation, while his proposal has the ambition of providing answers to all formulations (1)-(5). The author defends that the logical core of the Problem of Universals is the type-token problem: the problem of accepting the existence of types just because there are tokens of the same type. The type-token problem represents a generalization of the Problem of Universals, for it extends the problem of existence to other suspicious abstract entities that are not properties. In another section, Imaguire argues that the type-token problem is often confused with the sparse-abundant problem. The sparse-abundant problem in spite of being connected with the problem of universals (existence of universal is defended on the ground of non-arbitrary special sorts of similarities, properties, classes) is not its logical core.

The chapter ends with a list of the main solutions to the Problem of Universals so far proposed:

  • Trascendental realism

  • Immanent realism

  • Class nominalism

  • Predicate/concept nominalism

  • Trope theory

  • Priority nominalism

In chapter 2 friends and foes of Ostrich Nominalism are considered. Concerning the foes, after examining the main objections in the literature, the author concludes that the Ostrich nominalist is subject to four main charges: 1) he does not take the Problem of Universals as a genuine metaphysical problem, 2) he does not take predicates with ontological seriousness, 3) he does not offer an analysis of predication, 3) he does not offer an explanation for commonality of properties. On the other hand, the Ostrich has friends, namely authors that partially agree with some crucial aspects of Ostrich Nominalism: e.g. the fact that predication is fundamental (Van Cleve, Summerford) and the fact that not just properties are suspicious entities but also other abstract entities (Melia, Azzouni).

In chapter 3 it is discussed what kind of explanation the Problem of Universals demands. Three main candidates for the role of explanans are considered:

  • Ontological commitment

  • Grounding

  • Truthmaking

The priority nominalist offers a complex explanation based on the combination of ontological commitment and grounding.

Given that the Problem of Universals is an ontological problem, ontological commitment seems at first glance the best candidate. Moreover, the One-Over-Many Problem, when framed as an argument, is based on the criterion of ontological commitment. The argument may be briefly resumed as follows: from the fact that a is F and b is F we deduce that a and b have something in common; thus there is something that a and b have in common. Hence, the fact that a is F and b is F is committed to an entity that a and b have in common.

The Priority Nominalist does not frame his explanation in terms of the truthmaking relation for several reasons. Truthmaking is a relation from reality to language while ontological commitment goes in the opposite direction. Yet the problem of universals is the problem of accounting for the truth of predication, thus it goes from language to reality. In this sense ontological commitment seems to be a more adequate explanans than truthmaking.

Another problem of the truthmaking relation is that - differently from ontological commitment - it is non-factive: the fact that a sentence S is made true by something does not ensure that there is a unique truth-maker and does not say anything at all on what sort of entities all possible truth-makers of S might be. Thus from the fact that 'Fa' is true, we cannot conclude by invoking the truthmaking relation that there is a universal for which F stands.

Grounding also seems to be more adequate than truthmaking. The main reason the author offers is that to construct the ontological hierarchy that is required for the formulation of the problem by the Priority Nominalist, the transitivity of the relation between different ontological categories is required. Truthmaking is not transitive whereas grounding is.

The final part of the chapter is dedicated to introduce the notions that are crucial to the explanation offered by the Priority Nominalist. The notion of ontological categories as the most general categories of reality is introduced and ontological categories are divided into fundamental and derivative. A metaphysical theory is considered as a System of Ontological Categories. Four important claims are made regarding ontological categories:

  • Categories of the same level are pairwise disjoint.

  • To accept a range of entities as ontological category does not mean to accept it as a fundamental ontological category

  • The mere existence of instances of an ontological category does not imply that the category is fundamental

  • When at least one entity e of a category C is fundamental, then C is fundamental

With this conception of ontological category in mind the Priority Nominalist may state his position: properties, states of affairs, tropes are instantiated ontological categories, yet they are only derivative. The only fundamental ontological category is the category of concrete particulars.

In chapter 4 the author deals with the Problem of Predication, i.e. the problem of explaining in virtue of what a particular a is F. A solution to this problem is necessary to deal with the One-Over-Many Problem, for the One-Over-Many Problem is formulated in terms of multiple predications. The chapter has a negative purpose: to show that any view so far proposed according to which predication is not fundamental and thus any attempt to ground predication irremediably falls into an infinite regress.

The author starts by listing how the so-called Bradley's regress occurs with the main approaches to the Problem of Predication: Transcendental Realism, Immanent Realism, Class Nominalism, Concept Nominalism, Predicate Nominalism, Resemblance Nominalism, and Trope Theory. Exception made for Trope Theory, the structure of the reasoning that gives rise to the regress is almost the same.

Successively, Imaguire passes to consider some possible strategies to block Bradley's regress that have been proposed and points out their main flaws:

  • Identity of levels strategy: all levels of explanation are only apparently different. However, the author objects that each level amounts to the introduction of a different relation (e.g. relation of different order, different linguistic level) thus different levels of grounding correspond to different facts.

  • Quantificational Strategy: this is a strategy available only for the nominalist. The idea is that there is no need to quantify over the relation introduced to ground predication, thus there is no effective ontological commitment to such a relation. The Priority Nominalist replies that it is unclear why we should not take with ontological seriousness the relation introduced to ground predication while we should do the opposite with the property appearing at the initial level.

  • Formal Relations: the relation appearing at each level of explanation is a mere formal ontological relation, thus we are not ontologically committed to it. Yet - as the author remarks - which criterion do we have to distinguish between properties and relations that need to be grounded and a formal ontological relation?

  • Internal Relations: the relation between a particular and a universal (whatever it may taken to be) is an internal relation, and internal relations are given as ontological free lunch whenever the relata are given. However - the author objects - the notion of internal relation cannot be strictly defined without appealing to intrinsic features of the relata. As a consequence, the internal relation of e.g. instantiantion is grounded on the fact that a certain particular has certain properties. How could it possibly ground predication without begging the question?

  • Truthmakers: Armstrong proposed an argument to block the regress based on the notion of truthmaker. As Armstrong argues, all steps of explanation in Bradley's regress have the same truthmaker, thus the explanation may arrest at the first step. The author objects that in Armstrong's argument there is an illegitimate switch between the relation of truthmaking and that of grounding: why at the first level, i.e. the level of predication, we must ask for grounding and at the following levels we must ask for a truthmaker?

The conclusion Imaguire draws is that all attempts to ground predication so far proposed are unsatisfactory; albeit this fact does not represent a knock-down argument against the view that predication may be grounded, it supports the hypothesis that predication is fundamental. And precisely this is the position of the Priority Nominalist. Moreover, the author stresses that such a position does not amount to refuse to deal with the Problem of Predication, yet it corresponds just to a particular answer to this problem, i.e. that predication is not grounded in anything else.

In Chapter 5 a solution is offered to the One-Over-Many Problem and its variations (i.e. the Many-Over-One and the Similar-But-Different Problems). As previously mentioned, the One-Over-Many Problem may be formulated as an argument whose crucial point is the criterion of ontological commitment: the existence of universals is justified by the fact that we are allowed to quantify over what two particulars being both F have in common. Imaguire highlights that the principle of ontological commitment presents a fundamental difficulty which he calls the Paraphrase Symmetry Problem:

“suppose that sentence S commits us to the existence of entity E, but its paraphrase S* does not. Why should we conclude that the commitment of S to E is only apparent? What reason could we have to prefer S to S*? Since 'is a paraphrase of' is plausibly a symmetrical relation between sentences, one could also conclude that the non-commitment of S* to E is only apparent.” Imaguire (2018IMAGUIRE, G. Priority Nominalism, Springer Verlag, 2018.), p. 87

According to the Priority Nominalism, such a difficulty may be overcome by combining the criterion of ontological commitment with the notion of metaphysical grounding. In other words, given the two sentences S and S* of the quoted passage, the criterion of ontological commitment must be applied to the sentence (if any) that expresses a fundamental fact. The combination of ontological commitment with grounding results in the Criterion of Grounded Ontological Commitment which may be summarized by the motto:

“To be is to be a value of a bound variable of a fundamental truth.” Imaguire (2018IMAGUIRE, G. Priority Nominalism, Springer Verlag, 2018.), p. 89

The Criterion of Grounded Ontological Commitment is firstly used to analyze the One-Over-Many Problem. Imaguire considers a battery of sentences and the corresponding paraphrases that are relevant to the issue: for instance, he considers both the sentence 'a is F' and the sentence 'a has the property F''. The Priority Nominalist is willing to say that 'a is F' expresses a fact that is more fundamental than that expressed by the sentence 'a has the property F', and thus, given that in 'a is F' there is no expression allegedly standing for a universal that occurs in a position over which we may perform a first-order quantification, there is no grounded ontological commitment to universals. To achieve this goal Imaguire uses Fine's logical theory of the grounding relation and in particular Fine's treatment of two lambda operators: the predicate abstraction and the property abstraction operator. Thus Imaguire formalizes the aforementioned battery of sentences and their paraphrases using Fine's rules for the lambda operators and the immediate result is that 'a is F' (formalized using the predicate abstraction operator) grounds 'a has the property F' (formalized using the property abstraction operator). The same strategy is used to dissolve the apparent ontological commitment to universals in the Many-Over-One Problem and the Similar-But-Different Problem.

The remaining part of the chapter is dedicated to two important issues: the status of sentences apparently committed to abstract entities and the specification of a truthmaker for sentences of the form 'a is F'. Concerning sentences like 'a has the property F ', 'a and b have the property F in common', etc... the priority nominalist has a position that notably differs from many nominalistic views: many nominalists would say that the sentence 'a has the property F' is false or truthvalueless at best, for there are no such entities as properties; the priority nominalist holds that 'a has the property F ' is “a common but misleading manner of saying that things are in a certain way” (Imaguire (2018IMAGUIRE, G. Priority Nominalism, Springer Verlag, 2018.), p. 100), i.e that a is in the F-way. The same applies to other abstract terms, as in the case of numbers: sentences containing number terms are not false, they are true even if they do not express fundamental facts; they are just ontologically misleading insofar as they suggests that there are numbers. By proposing a hierarchical structure of reality in which derivative facts are included with a thin notion of existence, the Priority Nominalist does not have to pay the price of avoiding property talk, or number talk, or meaning talk, etc...

Concerning the problem of specifying a truthmaker for 'a is F', the Priority Nominalism invokes the notion of thick particular: what makes true 'a is F' is precisely the thick particular a with its being in a particular way expressed by the predicate F. In other words, the state of affairs corresponding to 'a is F' has as only constituent the thick particular a.

Chapter 6 is about second-order quantification. Imaguire distinguishes two different senses of second-order quantification: the metaphysical sense and the logical sense. A metaphysical second-order quantification is a quantification over properties that may be instantiated by particulars: 'There is a property that Napoleon and Julius Caesar have in common' is an example of this sort of quantification. Notice that from a strictly logical point of view, this sort of quantification corresponds to a first-order quantification, for expressions allegedly standing for properties are nominalized: 'There is an x such that x is a property and Napoleon and Julius Caesar have x in common'. A logical second-order quantification is a quantification into the position of first-order predicates, e.g. ' There is something that both Napoleon and Julius Caesar are'. It is crucial for the priority nominalist to explain away both logical and metaphysical second-order quantification, for if second-order existential quantified sentences were as fundamental as first-order ones, then there would be an unavoidable (grounded) ontological commitment to type entities.

The author considers three contexts of abstract reference to properties that allow for metaphysical second-order quantification: exemplification, intensional, and classificatory contexts. Exemplification and intensional contexts are easily dismissed, thus he concentrates on classificatory contexts and in particular to two examples: the sentences `Humility is a virtue' and 'Red is more similar to orange than blue'. The strategy Imaguire uses to paraphrase away abstract reference is based on the following guiding principle: every time we talk about a property F we are not really talking about F-ness but about F things. The one of the simplest examples of this kind is when we paraphrase the sentence 'the concept F is a subconcept of the concept G' as 'For every x, if x is F, then x is G'. Clearly, cases like 'Humility is a virtue' are far more complex and require additional theoretical tools. Imaguire uses the method of grounded paraphrases, i.e. a method of paraphrasing second-order sentences based on both Fine's logic of grounding (including the relation of partial grounding) and a sort of negative form of grounding that he calls despite operator.

The case of logical second-order quantification is treated differently. Imaguire argues that logical second-order quantification is not intelligible, for every attempted construction of a grammatical sentence in ordinary language translating the formal second-order quantification ends up altering the syntactic category of the quantified expressions. Moreover, even if an intelligible reading of second-order quantification were available, it could not result in an ontological commitment, for there would still be a difference between second and first-order quantification based on the different semantic behaviors between naming expressions and predicative expressions. Such a difference is explained in terms of Dudman's distinction between the representational and the semantic role conceptions of reference. Predicative expressions have reference in the sense that they fulfill a certain semantic role in the determination of the truth-value of an entire sentence and not in the sense that they stand for existing entities. On the contrary, proper names have reference in the sense that they stand for an existing possibly extra-linguistic entity: according to Imaguire's terminology, proper names have referents, predicates have references. The conclusion of the chapter is that provided that both metaphysical and logical second-order quantification may be respectively explained away and dismissed, intelligible second-order sentences express facts that are not fundamental for they are grounded in facts expressed by the correspondent first-order grounded paraphrases. As a consequence, according to the criterion of grounded ontological commitment, second-order sentences do not have any additional ontological import compared to their first-order paraphrases.

In the last chapter the author resumes his position by presenting the big picture of reality resulting from Priority Nominalism. Not just properties are dismissed as non-fundamental entities, but also word types, meaning, sets, numbers, etc... Even concrete particulars like mereological aggregates do not exist insofar as they are not fundamental: Priority Nominalism entails a form of mereological atomism. The chapter is also concerned with the contextualization of Priority Nominalism in the theoretical debate on the status of universals. Imaguire considers traditional realist and nominalist approaches to the Problem of Universals and remarks that most of them do not make explicit the distinctive features of Priority Nominalism, for the proposal of the book besides offering a new solution to the Problem of Universals, represents a relatively new way of understanding and formulating the problem itself. He argues that the approach the priority nominalist favors is what he calls the hierarchical approach. According to this approach, realists and nominalists disagree about the hierarchical structure of reality. The realist holds that properties are treated like objects, while the nominalist holds that they belong to a different level and only the level zero (i.e. the level at which we are allowed to quantify over in fundamental truths) is the level of existing entities. Thus the realist is accused of confusing different levels of the hierarchical structure, by reifying what does not belong to the level zero.

Finally the author lists the main advantages of Priority Nominalism:

  • Agreement with pre-theoretical intuitions: the apple is red is a fundamental fact, is not grounded in the existence of properties or classes, or mysterious relations of resemblance.

  • Few metaphysical assumptions: does not need modal realism, does not need universals, does not need sets.

  • Qualitatively and quantitatively economical: there is just one category of existence, i.e. particulars.

  • Provides an objectivist solution to the problem of universals: there are no abstract entities, yet there are objective truths about them.

'Priority Nominalism' is an excellent example of how a book may be concerned with vexed problems and vast topics in a relatively small number of pages. The author goes constantly straight to the point and avoids as much as possible any sort of digression; moreover, the purpose of book and the general view of the author on the matter are frequently resumed and re-proposed, so that the reader should not get lost in the dialectic of the arguments. At every crucial point of the book, a long list of examples facilitates the understanding; the style of writing is simple, direct, and pleasant.

The book is an original and interesting work in two senses: it contains a new solution to the Problem of Universals and represents a new formulation and understanding of the problem itself. For instance, in chapter 1 the reader may find a remarkably clear exposition of the Problem of Universals that is re-formulated in many versions according to fine and profound philosophical distinctions; even the reader who is not so familiar with the relevant literature may read the introductory parts of the book without big efforts.

The basic idea of the proposed view - the combination of grounding with ontological commitment - is simple and at first glance seems to be fruitful. However, the fact that complex arguments and notions are often resumed in the space of few pages may give the false impression that notions such as that of metaphysical grounding are less controversial than they actually are. Perhaps such an impression is given by the fact that while the author is extremely clear regarding the main difficulties and objections to Quine's criterion of ontogical commitment, he does not seem to do the same with the notion of metaphysical grounding which is definitely a controversial notion; in recent times almost any aspect of grounding has been questioned and put under debate: its modal status (Trogdon 2013), the formal properties of the grounding relation (Rodriguez-Pereyra 2015RODRIGUEZ-PEREYRA, G. Grounding is not a Strict Order, Journal of the American Philosophical Association 1 (3):517-534, 2015.), its theoretical role and indispensability (Wilson 2014WILSON, J. No Work for a Theory of Grounding, Inquiry: An Interdisciplinary Journal of Philosophy 57 (5-6):535-579, 2014.). Given that it is not clear from the book what is the author's position regarding the main problems of the notion of grounding, possible difficulties for Priority Nominalism may arise if grounding is understood in one way or the other. For the sake of clarity, I will try to sketch a problem for the priority nominalist that may arise from the controversial nature of the notion of grounding. The priority nominalist may be in a predicament engendered by the very strategy he uses to dismiss universals, i.e. the principle of grounded ontological commitment. Consider the sentences 'a is F' and 'a has the property F'; let A be the fact expressed by the former and B the fact the latter expresses. Consider now the sentence 'A grounds B': the priority nominalist is happy to say that 'A grounds B' is true. Let C be the fact expressed by 'A grounds B'. For the priority nominalist to say that C is a fundamental fact is not an option: for given that B is a fact included in C and given that C is fundamental, then B must also be fundamental (this is a version of what has been known as the collapse problem (Sider 2011SIDER, T. Writing the Book of the World, Oxford University Press, 2011.)). Yet if B is fundamental, then by the criterion of grounded ontological commitment there are properties. Thus the priority nominalist owes us an argument to the effect that C is not a fundamental fact and is grounded in another fact D not including B. Perhaps C is grounded on A (as suggested by adapting deRosset's strategy to avoid the collapse problem to the present case (deRosset 2013DEROSSET, L. Grounding Explanations, Philosophers' Imprint 13, 2013.)); nevertheless, the author does not say anything in the book about facts expressed by sentences of the form 'X grounds Y'.

In spite of possible controversies regarding Imaguire's proposal, 'Priority Nominalist' is a highly recommended reading for everyone who is interested in contemporary metaphysics. It is at the same time an excellent introduction to the Problem of Universals, a capillary survey of the recent literature on the issue, and an extremely interesting attempt of vindicating some ontological intuitions that are implicit in Quine's nominalism.


  • DEROSSET, L. Grounding Explanations, Philosophers' Imprint 13, 2013.
  • IMAGUIRE, G. Priority Nominalism, Springer Verlag, 2018.
  • RODRIGUEZ-PEREYRA, G. Grounding is not a Strict Order, Journal of the American Philosophical Association 1 (3):517-534, 2015.
  • SIDER, T. Writing the Book of the World, Oxford University Press, 2011.
  • WILSON, J. No Work for a Theory of Grounding, Inquiry: An Interdisciplinary Journal of Philosophy 57 (5-6):535-579, 2014.

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    CDD: 149.1

Publication Dates

  • Publication in this collection
    01 Apr 2019
  • Date of issue
    Apr-Jun 2019


  • Received
    07 Feb 2019
  • Accepted
    11 Feb 2019
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