Abstract
This chapter deals with one of the main arguments for Priority Nominalism: the regress argument against the possibility of finding an explanation for predication . Indeed, since the priority nominalist considers predication a fundamental ontological relation, regress arguments are one of his main weapons against all rivals. Accordingly, the main aim of this chapter will be to show that all strategies used for blocking a regress are faulty. These strategies are: the identity of level solution, the quantificational solution, the formal relation solution, the internal relation solution and the truthmaking and grounding solutions. The straightforward conclusion is: once you destroy the unity of a thick object (i.e. you separate the particular from its properties) then (as with Humpty Dumpty) you can never it back together again.
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Notes
- 1.
Strong arguments for a Bradleyan stance can also be found in Vallicella (2000, 2002). His main point (that states of affairs are best suited as truthmakers for simple predicative statements) can gladly be accepted by the priority nominalist. And, as we will see in the next chapter, this does not amount to accepting an ontology of states of affairs.
- 2.
- 3.
- 4.
As far as I can see, no one has proposed this interpretation, but it strikes me as an obvious option.
- 5.
This is e.g. the form in which Vallicella (2000: 239) constructs the Regress in Realism.
- 6.
Some contemporary authors have dealt with more radical alternatives, proposing e.g. that a regress is not really so bad. Reasons for considering regresses undesirable are offered by Nolan (2001) and in particular for the case of predication, Alvarado (2013), who argues that Bradley’s regress is not really damaging (2013: 42). Gaskin (2008) maintained that, concerning propositions, we should not treat Bradley’s regress as vicious, but instead regard it as providing the metaphysical condition of unity of propositions. Cameron (2008) gives a critical analysis of the general intuition that there must be a fundamental level in metaphysics.
- 7.
This argument is usually applied to stop the Object Regress in realism: a participates in F-ness and a participates in the participation of F-ness are fully identical facts, since the properties to participate in F-ness and to participate in the participation of F-ness are strictly speaking the same (even more than ‘just’ modally co-extensional, if you will). See Branquinho and Imaguire (2013).
- 8.
This strategy is, e.g. suggested by van Cleve (1994: 578) and discussed by Rodriguez-Pereyra (2002: 111). According to the latter, the Regress Argument begs the question, because in the case of Resemblance Nominalism , for instance, we do not need to infer from a resembles b that there is an entity like the type or token resemblance that holds between a and b.
- 9.
Since in Predicate /Concept Nominalism the ‘y’ on level 2 is a predicate, and a predicate is arguably a type , this kind of nominalism already faces a problem on this level. So, it would be better for Predicate/Concept Nominalism to take Fa as fundamental, for here there is no quantification over ‘F’. But then Predicate/Concept Nominalism would simply collapse into Priority Nominalism.
- 10.
This is similar to the question discussed in philosophy of logic about the distinction between ‘formal’ and ‘material concepts’. Tarski (especially 1936) made great contributions to understanding this topic, but in the end his general conclusion was somewhat disappointing, viz. that the demarcation between formal and material is relative to the theory. Probably something similar could be said in metaphysics: each theory has the right to fix its own distinction between ‘formal’ and ‘material concepts’, or between its ‘ideology’ and its ‘ontology’.
- 11.
Such a strategy is, e.g. found in Armstrong’s Fundamental Ideas and Axioms of Mathematics (1989), where he defends the view that some formal entities can belong to different categories. Thus, numbers can be objects (represented by numerals ‘1’, ‘2’, ‘3’…) or properties (represented by words ‘is one’, ‘are two’, ‘are three’…). Accordingly, the sentence ‘2 and 3 are two’ is true (it means something like ‘2 and 3 are two entities’), while ‘2 and 3 are 2’ is false (it means something like ‘2 plus 3 is 2’).
- 12.
- 13.
Daly (1997: 152) argued against the general idea that an internal relation, or a relation that supervenes on its relata, does not constitute an ontic addition over its relata. This could be a first line of argument against this strategy, but I will not pursue it here.
- 14.
- 15.
For a more detailed criticism of Maurin’s solution, see Briceño (2016).
- 16.
- 17.
For a criticism of the solution offered by the Trope Theory, see Briceño (2016).
- 18.
A similar view is also defended by Donald Mertz (1996).
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Imaguire, G. (2018). Predication and Regress: In Virtue of What is a F?. In: Priority Nominalism. Synthese Library, vol 397. Springer, Cham. https://doi.org/10.1007/978-3-319-95004-4_4
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