free logic a system of quantification theory, with or without identity, that allows for non-denoting singular terms. In classical quantification theory, all singular terms (free variables and individual constants) are assigned a denotation in all models. But this condition appears counterintuitive when such systems are applied to natural language, where many singular terms seem to be non-denoting (‘Pegasus’, ‘Sherlock Holmes’, and the like). Various solutions of this problem have been proposed, ranging from Frege’s chosen object theory (assign an arbitrary denotation to each non-denoting singular term) to Russell’s description theory (deny singular term status to most expressions used as such in natural language, and eliminate them from the ‘logical form’ of that language) to a weakening of the quantifiers’ ‘existential import,’ which allows for denotations to be possible, but not necessarily actual, objects. All these solutions preserve the structure of classical quantification theory and make adjustments at the level of application. Free logic is a more radical solution: it allows for legitimate singular terms to be denotationless, maintains the quantifiers’ existential import, but modifies both the proof theory and the semantics of first-order logic. Within proof theory, the main modification consists of eliminating the rule of existential generalization, which allows one to infer ‘There exists a flying horse’ from ‘Pegasus is a flying horse’. Within semantics, the main problem is giving truth conditions for sentences containing non-denoting singular terms, and there are various ways of accomplishing this. Conventional semantics assigns truth-values to atomic sentences containing non-denoting singular terms by convention, and then determines the truth-values of complex sentences as usual. Outer domain semantics divides the domain of interpretation into an inner and an outer part, using the inner part as the range of quantifiers and the outer part to provide for ‘denotations’ for non-denoting singular terms (which are then not literally denotationless, but rather left without an existing denotation). Supervaluational semantics, when considering a sentence A, assigns all possible combinations of truth-values to the atomic components of A containing non-denoting singular terms, evaluates A on the basis of each of those combinations, and then assigns to A the logical product of all such evaluations. (Thus both ‘Pegasus flies’ and ‘Pegasus does not fly’ turn out truth-valueless, but ‘Pegasus flies or Pegasus does not fly’ turns out true since whatever truth-value is assigned to its atomic component ‘Pegasus flies’ the truth-value for the whole sentence is true.) A free logic is inclusive if it allows for the possibility that the range of quantifiers be empty (that there exists nothing at all); it is exclusive otherwise. See also FORMAL SEMANTICS , PROOF THE- ORY , QUANTIFICATIO. E.Ben. free rider, a person who benefits from a social arrangement without bearing an appropriate share of the burdens of maintaining that arrangement, e.g. one who benefits from government services without paying one’s taxes that support them. The arrangements from which a free rider benefits may be either formal or informal. Cooperative arrangements that permit free riders are likely to be unstable; parties to the arrangement are unlikely to continue to bear the burdens of maintaining it if others are able to benefit without doing their part. As a result, it is common for cooperative arrangements to include mechanisms to discourage free riders, e.g. legal punishment, or in cases of informal conventions the mere disapproval of one’s peers. It is a matter of some controversy as to whether it is always morally wrong to benefit from an arrangement without contributing to its maintenance. See also JUSTICE , SOCIAL CHOICE THE- ORY , UTILITARIANIS. W.T.