A Mathematical Introduction to Logic, Second Edition, offers increased flexibility with topic coverage, allowing for choice in how to utilize the textbook in a course. The author has made this edition more accessible to better meet the needs of today's undergraduate mathematics and philosophy students. It is intended for the reader who has not studied logic previously, but who has some experience in mathematical reasoning. Material is presented on computer science issues such as computational complexity and database queries, with additional (...) coverage of introductory material such as sets. Increased flexibility of the text, allowing instructors more choice in how they use the textbook in courses. Reduced mathematical rigour to fit the needs of undergraduate students. (shrink)

The thesis of the conventionality of simultaneity in the special theory of relativity has been the subject of controversy for over fifty years Unfortunately, debates about this thesis have sometimes been marred by a failure to clearly distinguish different conventionalist theories. In my dissertation I evaluate, clarify, and carefully distinguish a number of different conventionalist theories, and thus clear up some of the confusion surrounding the thesis of the conventionality of simultaneity . In particular, I examine the following conventionalist theories. (...) ;According to the definitional theory of principles, there are some important scientific "laws" which apparently state facts, but which in reality are true by definition. I show that the most notable attempts, to establish that some important scientific laws were actually "definitions in disguise" were not successful. ;According to the theory of conventional reference, there are some words which have meanings which do not uniquely determine their respective references. For example, Reichenbach claimed that the meaning of "simultaneity" did not uniquely determine its reference. I show in my dissertation that if Reichenbach were correct about the meaning of "simultaneity" then his argument would be sound, but that there are good reasons for doubting the correctness of Reichenbach's views about the meaning of "simultaneity". ;Closely related to the theory of conventional reference was Reichenbach's theory of coordinative definitions. According to the theory of coordinative definitions, if a word's meaning failed to uniquely determine its reference, some sentences in the theory must be used solely to fix the reference of the word. Reichenbach proposed a coordinative definition of "simultaneity", but I argue in my dissertation that even if one accepts Reichenbach's views about the meaning of "simultaneity", his views about the coordinative definition of "simultaneity" are not substantiated. ;According to the theory of intertranslatability, there are apparently incompatible scientific theories which nonetheless "say the same thing", in some intuitive sense. Such theories are said to be intertranslatable. For example, according to Winnie there are theories which seem to be incompatible with the standard version of the special theory of relativity, but which are actually intertranslatable with it. After examining a number of proposed criteria for intertranslatability, I select an adequate one. I use this criterion to show that Winnie's claim is true, but trivial, since the proposed "alternatives" to the standard version of the special theory of relativity are merely the same covariant theory expressed in different coordinate systems. ;Finally, according to the theory of conventional relations, there are some relations which are conventional because they are not intrinsic . Malament demonstrated that if symmetric causal connectability is the only intrinsic spacetime relation, then standard simultaneity is not a conventional relation, but every non-standard simultaneity relation is conventional. I demonstrate that if an asymmetric causal connectability relation is intrinsic, then not only is standard simultaneity not conventional, there are also an infinitude of non-conventional non-standard simultaneity relations. (shrink)