What purpose does allowing for terms that do not denote any object serves in free logic?

Free logics may allow for terms that do not denote any object.

What exact purpose does that serve. Does it have any utility? It seems to only exist for the purpose of philosophizing about logic and ontology. I am not sure what other purpose it may serve.

  • 1
    It serves the same purpose as in the ordinary language, to be able to talk about objects whose existence is an open question or a useful fiction. For example, "magnetic monopole" may or may not denote an object, we just do not know yet, the same goes for "dark energy", "bigfoot", "Santa Clause", "unicorn" and so on. Most applications are very far from philosophizing, quantifying only over objects we are sure exist is often impractical.
    – Conifold
    Jun 5, 2021 at 7:40
  • @Conifold bigfoot/dark energy/santa claus/etc sounds more like counterfactual reasoning to me. Are you saying free logic is sufficient to model counterfactual reasoning?
    – causative
    Jun 5, 2021 at 9:39
  • Counterfactuals presuppose something contrary to fact, not necessarily non-existent objects, free logic covers such objects, but does not necessarily presuppose non-existence. There is no inclusion in either direction.
    – Conifold
    Jun 5, 2021 at 9:54
  • @Conifold Counterfactuals do not have to be contrary to fact. From plato.stanford.edu/entries/counterfactuals/#WhatCoun "Counterfactuals are not really conditionals with contrary-to-fact antecedents. For example (2) can be used as part of an argument that the antecedent is true (Anderson 1951):" ... "This entry will use counterfactual conditional and subjunctive conditional interchangeably, hoping to now have dispelled the suggestion that all counterfactuals, in that sense, have contrary-to-fact antecedents."
    – causative
    Jun 5, 2021 at 16:40

1 Answer 1


Indeed as you conceived such free logic may be just for the purpose of philosophizing according to reference here:

Karel Lambert wrote in 1967: "In fact, one may regard free logic... literally as a theory about singular existence, in the sense that it lays down certain minimum conditions for that concept."... So, Lambert argues, to reject his construction of free logic requires you to reject Quine's philosophy, which requires some argument and also means that whatever logic you develop is always accompanied by the stipulation that you must reject Quine to accept the logic. Likewise, if you reject Quine then you must reject free logic. This amounts to the contribution that free logic makes to ontology.

The point of free logic, though, is to have a formalism that implies no particular ontology, but that merely makes an interpretation of Quine both formally possible and simple. An advantage of this is that formalizing theories of singular existence in free logic brings out their implications for easy analysis. Lambert takes the example of the theory proposed by Wesley C. Salmon and George Nahknikian, which is that to exist is to be self-identical.

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