Abstract
The core of the book is presented in this chapter. In it, I offer a solution to the One Over Many problem, which is usually considered the most perspicuous way to formulate the Problem of Universals. I also solve the two variants, the Many Over One and the Similar but Different problems. The last one is particularly interesting because it was exactly formulated in order to show that Old Ostrich Nominalism does not provide an adequate solution to the Problem of Universals. Basically, the solution consists in (i) analysing the ontological commitments of various statements about property distributions (objects sharing the same property, objects having different properties, and different objects that are similar with regard to some and different with regard to other properties), (ii) explaining how to use the notion of grounding to avoid a commitment to properties, and (iii) offering truthmakers and ‘possibilitators’ for such statements.
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Notes
- 1.
- 2.
For a different view, see Melia (2015:176): ‘In particular, the austere nominalist rejects the existence of natural properties, and thus, in one sense, the distinction between the natural and the unnatural properties’.
- 3.
This is, at least, how Donagan (1963) interprets Russell’s position. So, the use of the predicate ‘is identical to’ does not commit us to recognise the existence of the entity identity , because it is a formal term. And the use of the predicate ‘human’ does not commit us to accept the existence of the universal humanity, because it is not primitive (it can be reduced to, say, ‘rational animal’). But since ‘rational’ is a primitive predicate (let us suppose), we are compelled to accept the existence of the universal rationality. And, as strange as it may seem, even if no particular were rational, rationality would nevertheless exist, for the sentence ‘a is not rational’ would be true, in this case, for any a. In truth, if someone uses this criterion, he is very close to a trivial form of Realism , for this criterion for deciding if there is a corresponding universal is too easily satisfied. It can hardly be denied that we must use some irreducible predicates. Thus, the acceptance of the existence of universals becomes unavoidable.
- 4.
As in the previous footnote, we can conclude that if we adopt this criterion, Realism becomes unavoidable. It is evident that every theory has primitive predicates and that we need predicates for formulating the most fundamental scientific laws. Nobody would dare to defend the contrary.
- 5.
Note that the semantic ascent (from (a) and (b) to ‘(a)’ and ‘(b)’) is inevitable here, since the question is about ontological commitment, i.e. we must go from language to ontology. And by making this semantic ascent, we must suppose a high degree of transparency: the sentence ‘Barbara is 20 years old’ expresses the fact that Barbara is 20 years old, the sentence ‘Anne is 30 years old’ expresses the fact that Anne is 30 years old, and so on. Without supposing this transparency any analysis of the One Over Many, and not just the priority nominalist’s, would collapse.
- 6.
Williams (2012) defended a very similar claim in his ‘minimal metaphysics’. As Correia and Schneider (2012:33) succinctly summarised his view: ‘what [his] minimal metaphysics purports to describe … is what is fundamentally the case; if the metaphysics rejects the existence of numbers and heavenly bodies, it remains compatible with the view that it is the case, albeit derivatively, that 2 + 2 = 4 and that there are eight planets in orbit around the Sun’.
- 7.
Note again, as pointed out in footnote 56, that a semantic ascent is inevitable here, since the question is about ontological commitment, i.e. we must go from language to ontology. And in making this semantic ascent we must suppose high transparency: that ‘Fa’ expresses the fact that a is F, and that ‘a has the property F’ expresses the state of affairs that a has the property F, and so on. Without supposing this transparency, any analysis, not just the Ostrich’s, would collapse. And let’s remember that even the realist assumes in his One Over Many Argument that ‘there is something that a and b have in common’ must express transparently that there is something that a and b have in common, and so on.
- 8.
Remember that for Priority Nominalism, contrary to Resemblance Nominalism, the sentence that explicitly states the similarity between a and b, viz. ‘a and b are similar’, is also grounded in Fa and Fb: a and b are similar in virtue of both being F.
- 9.
A similar point was made by van Cleve (1994:587): ‘Could one hold that the specific predication ‘Tom is tall’ makes no commitment to universals, but that as soon as we are forced to generalise and say ‘∃F(Tom is F)’ we do recognise the existence of universals? That seems highly unlikely.’
- 10.
Curiously, for motivating the extensive description, instead of ‘the average mum has 2.4 children’, Melia (2005:225) writes: ‘Rather than include “the average mum has 2.4 children” into our best theory, why not count up how many mothers and offspring there are, write down the sentence which says how many there are of each, and include this sentence in our best theory?’ The curious aspect of this passage is the suggestion that we should ‘count up’ how many mothers and offspring there are. In practice, long before we say the average woman has 2.4 children, we have certainly already counted the number of mothers and offspring and, just based on these data, we calculate the number of children of the average mum.
- 11.
Supervenience and grounding are, of course, different relations. But I am pretty sure that Melia would extend his criticism to the idea that grounded entities are unreal. In a sense, we could say that Melia and the priority nominalism
- 12.
He compares these cases with the argument against the deflationist theory of truth, where one can say that ‘everything he said yesterday is true’ without being able to repeat what he said.
- 13.
For a similar view about properties as ways see Heil (2003:126).
- 14.
On a different option for the Ostrich, see Melia (2005) ‘Truthmaking Without Truthmakers’.
- 15.
- 16.
Let’s remember that this hyperintensional character for distinguishing co-extensive properties was Plato’s main purpose for introducing grounding. In Euthyphro’s dilemma, Socrates asks Euthyphro: ‘is the pious loved by the gods because it is pious, or is it pious because it is loved by the gods?’ (Euthyphro 10a).
- 17.
Indeed, this is Peacock’s line of reasoning for rejecting Ostrich Nominalism in his (P2009) paper.
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Imaguire, G. (2018). The One Over Many and Its Variations. In: Priority Nominalism. Synthese Library, vol 397. Springer, Cham. https://doi.org/10.1007/978-3-319-95004-4_5
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