Actualists who believe in possible worlds typically regard them as "abstract" objects of some special sort. For example, Alvin Plantinga takes worlds to be maximal possible states-of-affairs, all of which "exist", as actualism requires, but only one of which "obtains". Views like Plantinga's run into difficulty in the interpretation of statements of "iterated" modality, statements about what is "possible" for individuals that "could" exist but that do not actually exist. These statements seem to require the existence of "singular" states-Of-affairs that (...) have nonactual individuals as constituents, a requirement that is incompatible with actualism. One can try to avoid the troublesome singular states-of-affairs by introducing "unexemplified individual essences" and maintaining that these are the true constituents of the required states-of-affairs, rather than the nonactual possibles themselves. However, serious arguments are raised against this employment of individual essences. (shrink)

The authors develop an axiomatic theory of nonexistent objects and and give a formal semantics for the language of the theory.

Recently Saul Kripke has drawn attention to a puzzle about belief and proper names, a puzzle of which philosophers have been aware for a long time, but which has never been completely resolved. Kripke gives a new, bilingual illustration of the puzzle:1 Pierre, while living in his native France, learns much about the city of London, which he calls ‘Londres,’ and comes to believe something which he would express in French with the words, ‘Londres est jolie.’ Using standard principle of (...) translation, it seems correct for us to say, ‘Pierre believes that London is pretty.’ Suppose however that Pierre learns English, travels to London, learns that the name of the city he is in is ‘London,’ and sincerely and comprehendingly asserts, ‘London is not pretty.’ On the basis of his assertion, it seems correct for us to say, ‘Pierre believes that London is not pretty.’ But suppose he does not realize that ‘Londres’ is also a name for the city he is in, so he retains the belief which he would express with the French words, ‘Londres est jolie.’ Then, by the same principles of translation as before, it seems that we are still justified in saying, ‘Pierre believes that London is pretty.’ But now we have attributed to Pierre contradictory beliefs, and that does not seem acceptable, since Pierre has committed no logical oversight.Kripke believes that this is the same puzzle as one that arises in older, monolingual examples, such as that used by Quine: suppose Tom believes that Cicero denounced Cataline. Since ‘Tully’ is another name for Cicero, it seems acceptable to paraphrase his belief and say, ‘Tom believes that Tully denounced Cataline.’ But suppose Tom does not realize that Cicero and Tully are the same person, and suppose, in fact, that he sincerely and comprehendingly asserts, ‘Tully did not denounce Cataline.’ Then it also seems acceptable to say, on the basis of Tom’s assertion, ‘Tom believes that Tully did not denounce Cataline.’ But now we have attributed to Tom contradictory beliefs, and, as in the Pierre example, that does not seem acceptable. (shrink)

Recently Saul Kripke has drawn attention to a puzzle about belief and proper names, a puzzle of which philosophers have been aware for a long time, but which has never been completely resolved. Kripke gives a new, bilingual illustration of the puzzle:1 Pierre, while living in his native France, learns much about the city of London, which he calls ‘Londres,’ and comes to believe something which he would express in French with the words, ‘Londres est jolie.’ Using standard principle of (...) translation, it seems correct for us to say, ‘Pierre believes that London is pretty.’ Suppose however that Pierre learns English, travels to London, learns that the name of the city he is in is ‘London,’ and sincerely and comprehendingly asserts, ‘London is not pretty.’ On the basis of his assertion, it seems correct for us to say, ‘Pierre believes that London is not pretty.’ But suppose he does not realize that ‘Londres’ is also a name for the city he is in, so he retains the belief which he would express with the French words, ‘Londres est jolie.’ Then, by the same principles of translation as before, it seems that we are still justified in saying, ‘Pierre believes that London is pretty.’ But now we have attributed to Pierre contradictory beliefs, and that does not seem acceptable, since Pierre has committed no logical oversight.Kripke believes that this is the same puzzle as one that arises in older, monolingual examples, such as that used by Quine: suppose Tom believes that Cicero denounced Cataline. Since ‘Tully’ is another name for Cicero, it seems acceptable to paraphrase his belief and say, ‘Tom believes that Tully denounced Cataline.’ But suppose Tom does not realize that Cicero and Tully are the same person, and suppose, in fact, that he sincerely and comprehendingly asserts, ‘Tully did not denounce Cataline.’ Then it also seems acceptable to say, on the basis of Tom’s assertion, ‘Tom believes that Tully did not denounce Cataline.’ But now we have attributed to Tom contradictory beliefs, and, as in the Pierre example, that does not seem acceptable. (shrink)

The use of a concept called "explicativity", for (provisionally) accepting a theory or Hypothesis H, has previously been discussed. That previous discussion took into account the prior probability of H, and hence implicitly its theoretical simplicity. We here suggest that a modification of explicativity is required to allow for what may be called the pragmatic simplicity of H, that is, the simplicity of using H in applications as distinct from the simplicity of the description of H.

A frege-Russell cardinal number is a maximal class of equinumerous classes. Since anything can be numbered, A frege-Russell cardinal should contain classes whose members are cardinal numbers. This is not possible in standard set theories, Since it entails that some classes are members of members of themselves. However, A consistent set theory can be constructed in which such membership circles are allowed and in which, Consequently, Genuine frege-Russell cardinals can be defined.