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Collective Essence and Monotonicity

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Abstract

This paper focuses on the concept of collective essence: that some truths are essential to many items taken together. For example, that it is essential to conjunction and negation that they are truth-functionally complete. The concept of collective essence is one of the main innovations of recent work on the theory of essence. In a sense, this innovation is natural, since we make all sorts of plural predications. It stands to reason that there should be a distinction between essential and accidental plural predications if there is a distinction among singular predications. In this paper I defend the view that the concept of collective essence is governed by the principle of Monotonicity: that something is essential to some items only if it is essential to any items to which they belong.

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Notes

  1. There are also accidental plural predications. For example, we may say of some people that they form a line, even though it is accidental to them that they form a line.

  2. Despite appearances, talk of pluralities is irreducibly plural: it is devoid of set theory and there are no distinctive items that are pluralities. See (Boolos 1984) and (Lewis 1991).

  3. We can form plural names using lists of singular names. For example, given that ‘Socrates’, ‘Plato’, and ‘Aristotle’ are singular names, ‘Socrates, Plato, and Aristotle’ is a plural name. We assume that pluralities are non-empty but that there may be a single item belonging to some. So we can say that for every x there are some X such that, for any yy belongs to X iff y is identical with x. In other words, there is a plurality unique to every individual item. This allows the singular cases to be subsumed under Monotonicity. For example, given that it is essential to Socrates that Socrates is human, Monotonicity says that it is essential to Socrates, Plato, Aristotle, and conjunction that Socrates is human.

  4. A few remarks. First, the way I characterized the variables in the introduction—as ranging over possible items and pluralities of possible items—makes clear that I am working within a necessitist framework. For interesting challenges to contingentist essentialism, see (Teitel 2017). Second, I deploy the concept of constitutive essence. However, some skepticism surrounds this concept; in particular, how to separate it from consequentialist essence (Fine 1994, 58). But if we heed the results of Fine’s ‘Essence and Modality’ then we are at least in possession of a concept of essence linked with real definition in the way described above. We should be able to work with this concept even if there are extant issues surrounding it.

  5. I adopt this terminology from (Correia 2006).

  6. I sometimes use expressions such as ‘what it is to be Socrates’. These are here treated as statements of objectual essence. But in general, statements of objectual essence are formed using a name-sentence operator, whereas statements of generic essence are formed using a predicate-predicate operator.

  7. There are other distinctions of essence, such as the distinction between mediate and immediate essence (Fine 1994). What divides mediate from immediate essence concerns dependence. For example, that it is part of the mediate essence of {Socrates} that Socrates is human but not part of its immediate essence (Fine 1995a). Although I will speak of dependence, the distinction between immediate and mediate essence is not really of concern.

  8. A few remarks. First, Correia (2000) develops a propositional fragment of Fine’s system using plural terms. Second, in giving his semantics for the logic of essence, Fine (2000) pronounces the essentialist operator roughly as “It is essential to some or allX that A”. This does not trivialize Monotoncitity. First, Fine (2000) is intending to provide a semantics for the system E5 of (Fine 1995b) for which the same pronunciation is not provided. Second, Monotonicity is given as an axiom in both (Fine 1995b) and (Fine 2000). Third, Monotonicity concerns pluralities in whichX is included, and not pluralities Xcontains. The “some or all” pronunciation of the operator fits only the containment model.

  9. If it is essential to X that A then we say that X are a source of ‘A’ (Fine 1994a). I adopt the source terminology here in the titles because Glazier uses this terminology.

  10. Glazier actually formulates the principle using singular variables only. However, he alludes to the case of collective essence which is only naturally extended in this way.

  11. On dependence, see (Correia 2008), (Fine 1994, 1995a), and (Tahko and Lowe 2016).

  12. What is more, this does not commit us to the contingency of what is accidental. For example, I accept that it is essential to conjunction and negation that they are truth-functionally complete. So it is necessary that they are so. But I think it is not essential to conjunction that conjunction and negation are truth-funcitonally complete. So, it is accidental to conjunction that it and negation are truth-functionally complete.

  13. If Sources are Constituents fails then how do we make sense of the fact that it is not essential to Socrates that Plato is a sophist or Plato is not a sophist, given that I am deploying the concept of constitutive essence? I take up this question in Sect. 4.1 below.

  14. Sources are Pertinent is inspired by (Fine 2000). See also (Correia 2000).

  15. The point about distinctness seems to generalize. For example, a pair of distinct points in a Euclidean Space are essentially distinct. Moreover, the essentiality of their distinctness has to do with their individual essences as tuples of real numbers.

  16. A few remarks. First, Dasgupta (2014, 4–5) discusses relevance for grounds and not sources. On his view, the concept of relevance is taken as primitive. What if the foe of Monotonicity took their concept of relevance as primitive? Might this sustain the argument lurking behind the incredulous stare? I do not think that it would. For the primitivist would have to provide us with some principles governing the primitive concept. For example, are only constituents relevant? Are only items in the closing of a statement relevant? But then either the primitivist faces the problems raised against Sources are Constituents and Sources are Pertinent or else they cannot provide us with anything that helps fix the concept of relevance they take as primitive. Second, consider the definition: x is relevant to ‘A\(\hbox {iff}_{df}\)x is a constituent of ‘A’ or is a constituent of some partial ground of ‘A’. Then consider Sources are Grounds: If it is essential to X that A then every x belonging to X is either a constituent of ‘A’ or a constituent of some partial ground of it. Sources are Grounds will not evade the objection to Sources are Pertinent, since New York City is neither a constituent of ‘Socrates is human’ nor a constituent of any partial ground of it.

  17. Some think that everything must go: that we should dispense with the idea that there is a plurality of everything (Spencer 2012). If they are right, the argument of this section still goes through. We simply would not talk about “outermost leaves”.

  18. N.B. Y properly belongs to X\(\hbox {iff}_{df}\) for every xx belongs to Y only if x belongs to X but for some yy belongs to X but does not belong to Y. For example, Socrates and Plato properly belong to Socrates, Plato, Aristotle, and conjunction.

  19. I deploy the concept of ground represented by the logic of strict ground and its tree-like semantics (deRosset 2014, 2015). See also (Fine 2012). N.B. The fact that essence is monotonic according to Monotonicity does not affect the non-monotonicity of ground.

  20. On this account of relevance, we can say that it is not essential to Socrates that Plato is a sophist or Plato is not a sophist because Socrates is not part of an ultimate source of ‘Plato is a sophist or not a sophist’.

  21. In this sense, I think we can recover Glazier’s results in the context of the present theory. We simply introduce the principle Ultimate Sources are Constituents. On this view, explanations of the form ‘A because X is an ultimate source of ‘A” can be ultimate and a distinctive kind of metaphysical explanation. However, there will be grounding explanations of the form ‘It is essential to X that A because it is essential to Y that A’.

  22. I want to construe grounding neutrally here between friends (Correia 2013, deRosset 2014, Dasgupta 2014, Fine (2012), etc.) and foes (Koslicki (2015), Wilson (2014), etc.). Whether grounding is the stitching together of small-g relations or something seamless, reality exhibits an explanatory structure. Whether we owe the explanatory structure of essential truths to grounding or to specific explanatory relations between sources should not affect the results of this paper.

  23. For a discussion of these modes of expression for essence, see (Fine 1994b).

  24. Also, (2) seems to hold in virtue of (5).

    1. (5)

      Socrates is essentially human,

    although ‘Socrates is essentially an X such that Socrates is human’ may sit between (2) and (5) within the explanatory structure if the view I proposed above is correct.

  25. The difference is attributable to the following. In the case of ‘Socrates and New York City are an X such that Socrates is human’ there is overlap between the subject of the sentence (i.e. Socrates and New York City) and the subject of the \(\lambda \)-abstract (i.e. Socrates). However, in the case of ‘New York City and Rome are an X such that Socrates is human’, there is no overlap. In general, it seems that if ‘A’ is not purely qualitative then Y are essentially an X such that A only if Y overlaps with the subject(s) of ‘A’: some x belongs both to Y and to the subject(s) of ‘A’. This is suggested in (Fine 1994a, 5–6).

References

  • Boolos, G. (1984). To be is to be a value of a variable (or to be some values of some variables). Journal of Philosophy, 81(8), 430–449.

    Article  Google Scholar 

  • Correia, F. (2000). Propositional logic of essence. Journal of Philosophical Logic, 29(3), 295–313.

    Article  Google Scholar 

  • Correia, F. (2006). Generic essence, objectual essence, and modality. Nous, 40(4), 753–767.

    Article  Google Scholar 

  • Correia, F. (2008). Ontological dependence. Philosophy Compass, 3, 1013–1032.

    Article  Google Scholar 

  • Correia, F. (2012). On the reduction of necessity to essence. Philosophy and Phenomenological Research, 84(3), 639–653.

    Article  Google Scholar 

  • Correia, F. (2013). Metaphysical grounds and essence. Basic philosophical concepts series. In M. Hoeltje, B. Schnieder, & A. Steinberg (Eds.), Varieties of dependence (pp. 271–96). Philosophia: Munchen.

    Google Scholar 

  • Correia, F., & Skiles, A. (2017). Grounding, essence, and identity. Philosophy and Phenomenological Research. https://doi.org/10.1111/phpr.12468.

    Article  Google Scholar 

  • Dasgupta, S. (2014) On the plurality of grounds. Philosophers’ Imprint, 14(20), 1–28.

  • Dasgupta, S. (2016). Metaphysical rationalism. Nous, 50(1), 1–40. https://doi.org/10.1111/nous.12082.

    Article  Google Scholar 

  • deRosset, L. (2014). On weak ground? Review of Symbolic Logic, 7(4), 713–744.

    Article  Google Scholar 

  • deRosset, L. (2015). Better semantics for the pure logic of ground. Analytic Philosophy, 56, 229–252.

    Article  Google Scholar 

  • Fine, K. (1994a). Essence and modality. In J. Tomberlin (Ed.), Philosophical perspectives 8: Logic and language (pp. 1–16). Atascadero: Ridgeview.

    Google Scholar 

  • Fine, K. (1994b). Senses of essence. In Walter Sinnott-Armstrong (Ed.), Modality, morality, and belief (pp. 53–73). New York: Cambridge University Press.

    Google Scholar 

  • Fine, K. (1995a). Ontological dependence. Proceedings of the Aristotelian Society, 95, 269–90.

    Article  Google Scholar 

  • Fine, K. (1995b). The logic of essence. Journal of Philosophical Logic, 24, 241–73.

    Article  Google Scholar 

  • Fine, K. (2000). Semantics for the logic of essence. Journal of Philosophical Logic, 29(6), 543–584.

    Article  Google Scholar 

  • Fine, K. (2001). The Question of Realism. Philosophers' Imprint, 1, 1–30.

  • Fine, K. (2012). A guide to ground. In F. Correia & B. Schnieder (Eds.), Metaphysical grounding: Understanding the structure of reality. Cambridge: Cambridge University Press.

    Google Scholar 

  • Fine, K. (2015). Unified foundations for essence and ground. Journal of the American Philosophical Association, 1(2), 296–311.

    Article  Google Scholar 

  • Fine, K. (XXXX). Truthmaker semantics. In Blackwell philosophy of language handbook (forthcoming).

  • Glazier, M. (2017). Essentialist explanation. Philosophical Studies, Philosophical Studies, 174, 2871–2889.

    Article  Google Scholar 

  • Koslicki, K. (2015). The coarse-grainedness of grounding. Oxford Studies in Metaphysics, 9, 304–344.

    Google Scholar 

  • Kripke, S. (1980). Naming and necessity. Cambridge: Harvard University Press.

    Google Scholar 

  • Lewis, D. (1991). Parts of classes. Oxford: Blackwell.

    Google Scholar 

  • Plantinga, A. (1978). The nature of necessity. Oxford: Clarendon Press.

    Book  Google Scholar 

  • Prior, A. N. (1971). Platonism and quantification. Objects of thought (pp. 31–47). Oxford: Oxford University Press.

    Chapter  Google Scholar 

  • Rosen, G. (2015). Real definition. Analytic Philosophy, 56(3), 189–209.

    Article  Google Scholar 

  • Schaffer, J. (2015). What Not to multiply without necessity. Australasian Journal of Philosophy, 93, 644–664.

    Article  Google Scholar 

  • Spencer, J. (2012). All things must pass away. Oxford Studies in Metaphysics, 7, 67.

    Article  Google Scholar 

  • Tahko, T., & Lowe, E. (2016). Ontological Dependence. In E. N. Zalta (ed.) The stanford encyclopedia of philosophy. https://plato.stanford.edu/archives/win2016/entries/dependence-ontological/, Winter (2016).

  • Teitel, T. (2017). Contingent existence and the reduction of modality to essence. Mind,. https://doi.org/10.1093/mind/fzx001.

    Article  Google Scholar 

  • Wilson, J. (2014). No work for a theory of grounding. Inquiry, 57(5), 537–79.

    Google Scholar 

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Acknowledgements

Thanks to Louis deRosset, Kathrin Koslicki, Mike Raven, Riin Sirkel, and to anonymous referees for helpful comments.

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Zylstra, J. Collective Essence and Monotonicity. Erkenn 84, 1087–1101 (2019). https://doi.org/10.1007/s10670-018-9996-5

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