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This is the first comprehensive textbook on higher-order logic that is written specifically to introduce the subject matter to graduate students in philosophy. The book covers both the formal aspects of higher-order languages-their model theory and proof theory, the theory of λ-abstraction and its generalizations-and their philosophical applications, especially to the topics of modality and propositional granularity. The book has a strong focus on non-extensional higher-order logics, making it more appropriate for foundational metaphysics than other introductions to the subject from computer science, mathematics, and linguistics.　A Philosophical Introduction to Higher-order Logics assumes only that readers have a basic knowledge of first-order logic. With an emphasis on exercises, it can be used as a textbook though is also ideal for self-study.

Logic --- Logic, Symbolic and mathematical --- Logique --- Logique mathématique. --- Philosophie. --- Logique mathématique.

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The canonical difference-in-differences (DD) model contains two time periods, "pre" and "post", and two groups, "treatment" and "control". Most DD applications, however, exploit variation across groups of units that receive treatment at different times. This paper derives an expression for this general DD estimator, and shows that it is a weighted average of all possible two-group/two-period DD estimators in the data. This result provides detailed guidance about how to use regression DD in practice. I define the DD estimand and show how it averages treatment effect heterogeneity and that it is biased when effects change over time. I propose a new balance test derived from a unified definition of common trends. I show how to decompose the difference between two specifications, and I apply it to models that drop untreated units, weight, disaggregate time fixed effects, control for unit-specific time trends, or exploit a third difference.

Zonder onderwerpscode: economie

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This paper uses the rollout of the first Community Health Centers (CHCs) to study the longer-term health effects of increasing access to primary care. Within ten years, CHCs are associated with a reduction in age-adjusted mortality rates of 2 percent among those 50 and older. The implied 7 to 13 percent decrease in one-year mortality risk among beneficiaries amounts to 20 to 40 percent of the 1966 poor/non-poor mortality gap for this age group. Large effects for those 65 and older suggest that increased access to primary care has longer-term benefits, even for populations with near universal health insurance.

Zonder onderwerpscode: economie