Approximate truth and causal strength in science
In Chapter One I motivate the search for an account of approximate truth as being the way to make sense of how our best scientific theories are simultaneously false but useful, and of how the same theory (even a true one) varies in its usefulness depending on context. I evaluate existing approaches and find that they fail - among other reasons - because they are unable to accommodate how two errors of similar logical seriousness nevertheless may have greatly different implications for approximate truth. The only way round this is some form of weighting scheme across logical statements that is motivated by extra-logical criteria. The little existing work along these lines suffers from insufficient generality, and I suggest instead a weighting scheme based on the notion of causal strength. In Chapter Two I develop the details of following such a prescription. It turns out to be crucial to highlight a hitherto underappreciated dichotomy between what I label the 'ontological' and 'empirical' senses of approximate truth. After outlining the practical advantages of my approach I discuss a number of technicalities, including several that confound all previous approaches. (I also outline an exact formal definition in an appendix.) Finally, I tackle the vexed issue of comparing two models with incommensurable ontologies. One of the results of the complicated discussion is that no sense can be made of science in general getting nearer the truth, only sense made of particular models getting nearer the truth of particular explananda. In Chapter Three I flesh out the notion - key for my scheme - of causal strength, giving a formal definition and sorting through the numerous necessary technicalities. I also explain how straightforward sense can be made of causal strengths even in cases of interactive effects and also even in cases where two causes are apparently incommensurable.