I reject the contention that an important theoretical difference exists between formal and natural languages.

It has been maintained that we need not tolerate such entities as pains, events, tasks, and obligations. They are indeed not required in connection with sentences like ‘Jones has a pain’, ‘the event of the sun’s rising occurred at eight’, ‘Jones performed at eight the task of lifting a stone’, or ‘Jones has the obligation to give Smith a horse’, which can be paraphrased without reference to the entities in question—for instance, in the case of the second example, as ‘the (...) sun rose at eight’. (shrink)

Logic: Techniques of Formal Reasoning, 2/e is an introductory volume that teaches students to recognize and construct correct deductions. It takes students through all logical steps--from premise to conclusion--and presents appropriate symbols and terms, while giving examples to clarify principles. Logic, 2/e uses models to establish the invalidity of arguments, and includes exercise sets throughout, ranging from easy to challenging. Solutions are provided to selected exercises, and historical remarks discuss major contributions to the theories covered.

Hempel and Oppenheim, in their paper 'The Logic of Explanation', have offered an analysis of the notion of scientific explanation. The present paper advances considerations in the light of which their analysis seems inadequate. In particular, several theorems are proved with roughly the following content: between almost any theory and almost any singular sentence, certain relations of explainability hold.

Some philosophers, for example Quine, doubt the possibility of jointly using modalities and quantification. Simple model-theoretic considerations, however, lead to a reconciliation of quantifiers with such modal concepts as logical, physical, and ethical necessity, and suggest a general class of modalities of which these are instances. A simple axiom system, analogous to the Lewis systems S1 —S5, is considered in connection with this class of modalities. The system proves to be complete, and its class of theorems decidable.