 Problems: Logical atomism is not easy to sustain and has rarely been held in a pure form. Among its difficulties are the following: (a) What, exactly, are the elementary truthbearers? How are they determined? (b) There are molecular truthbearers, such as subjunctives and counterfactuals, that tend to provoke the funny-fact objection but cannot be handled by simple truth-conditional clauses, because their truth-values do not seem to be determined by the truth-values of their elementary constituents. (c) Are there universal facts corresponding to true universal generalizations? Wittgenstein (1921) disapproves of universal facts; apparently, he wants to re-analyze universal generalizations as infinite conjunctions of their instances. Russell (1918) and Armstrong (1997, 2004) reject this analysis; they admit universal facts. (d) Negative truths are the most notorious problem case, because they clash with an appealing principle, the “truthmaker principle” (cf. Section 8.5), which says that for every truth there must be something in the world that makes it true, i.e., every true truthbearer must have a truthmaker. Suppose ‘p’ is elementary. On the account given above, ‘not-p’ is true iff ‘p’ is false iff ‘p’ does not correspond to any fact; hence, ‘not-p’, if true, is not made true by any fact: it does not seem to have a truthmaker. Russell finds himself driven to admit negative facts, regarded by many as paradigmatically disreputable portions of reality. Wittgenstein sometimes talks of atomic facts that do not exist and calls their very nonexistence a negative fact (cf. 1921, 2.06)—but this is hardly an atomic fact itself. Armstrong (1997, chap. 8.7; 2004, chaps. 5-6) holds that negative truths are made true by a second-order “totality fact” which says of all the (positive) first-order facts that they are all the first-order facts.