, Volume 191, Issue 10, pp 2115–2145 | Cite as

Constructing formal semantics from an ontological perspective. The case of second-order logics

  • Thibaut Giraud


In a first part, I defend that formal semantics can be used as a guide to ontological commitment. Thus, if one endorses an ontological view \(O\) and wants to interpret a formal language \(L\), a thorough understanding of the relation between semantics and ontology will help us to construct a semantics for \(L\) in such a way that its ontological commitment will be in perfect accordance with \(O\). Basically, that is what I call constructing formal semantics from an ontological perspective. In the rest of the paper, I develop rigorously and put into practice such a method, especially concerning the interpretation of second-order quantification. I will define the notion of ontological framework: it is a set-theoretical structure from which one can construct semantics whose ontological commitments correspond exactly to a given ontological view. I will define five ontological frameworks corresponding respectively to: (i) predicate nominalism, (ii) resemblance nominalism, (iii) armstrongian realism, (iv) platonic realism, and (v) tropism. From those different frameworks, I will construct different semantics for first-order and second-order languages. Notably I will present different kinds of nominalist semantics for second-order languages, showing thus that we can perfectly quantify over properties and relations while being ontologically committed only to individuals. I will show in what extent those semantics differ from each other; it will make clear how the disagreements between the ontological views extend from ontology to logic, and thus why endorsing an ontological view should have an impact on the kind of logic one should use.


Ontology Semantics Truthmaker Ontological commitment Second-order logic Nominalism Realism Tropes 


  1. Armstrong, D. M. (2004). Truth and truthmakers. Cambridge: Cambridge University Press.Google Scholar
  2. Armstrong, D. M. (1984). A combinatorial theory of possibility. Cambridge: Cambridge University Press.Google Scholar
  3. Bacon, J. (1995). Universals and property instances: The alphabet of being. Oxford: Blackwell.Google Scholar
  4. Cameron, R. (2008). Truthmakers and ontological commitment: Or how to deal with complex objects and mathematical ontology without getting into trouble. Philosophical Studies, 140, 1–18.CrossRefGoogle Scholar
  5. Cameron, R. (2010). How to have a radically minimal ontology. Philosophical Studies, 151(2), 249–264.CrossRefGoogle Scholar
  6. Campbell, K. (1990). Abstract particulars. Oxford: Blackwell.Google Scholar
  7. Heil, J. (2003). From an ontological point of view. Oxford: Oxford University Press.CrossRefGoogle Scholar
  8. Mertz, D. W. (1996). Moderate realism and its logic. New Haven: Yale.Google Scholar
  9. Prior, A. (1971). Object of thought. Oxford: Clarendon Press.CrossRefGoogle Scholar
  10. Schneider, C. (2002). Relational tropes—a holistic definition. Metaphysica International Journal for Ontology and Metaphysics, 2, 97–112.Google Scholar
  11. Simons, P. (1997). Higher-order quantification and ontological commitment. Dialectica, 51(4), 255–271.CrossRefGoogle Scholar
  12. Williams, D. C. (1953). The elements of being. Review of Metaphysics, 7(3–18), 171–192.Google Scholar
  13. Zalta, E. N. (1988). Intensional logic and the metaphysics of intentionality. Cambridge, MA: A Bradford Book, The MIT Press.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Institut Jean Nicod – EHESS (Paris)ParisFrance

Personalised recommendations