It is easy to make a system simple by sacrificing strength: have just the axiom that 2 + 2 = 4.) According to Lewis (1973, 73), the laws of nature belong to all the true deductive systems with a best combination of simplicity and strength. (It is easy to make a system stronger by sacrificing simplicity: include all the truths as axioms. These two virtues, strength and simplicity, compete. Some true deductive systems will be stronger than others some will be simpler than others. The logical consequences of the axioms are the theorems. Deductive systems are individuated by their axioms. The idea dates back to John Stuart Mill (1947 ), but has been defended in one form or another by Frank Ramsey (1978 ), Lewis (1973, 1983, 1986, 1994), John Earman (1984) and Barry Loewer (1996). One popular answer ties being a law to deductive systems. What makes the difference? What makes the former an accidental generalization and the latter a law? The latter is not nearly so accidental as the first, since uranium's critical mass is such as to guarantee that such a large sphere will never exist (van Fraassen 1989, 27). Though the former is not a law, the latter arguably is. The perplexing nature of the puzzle is clearly revealed when the gold-sphere generalization is paired with a remarkably similar generalization about uranium spheres:Īll gold spheres are less than a mile in diameter.Īll uranium spheres are less than a mile in diameter. Galileo's law of free fall is the generalization that, on Earth, free-falling bodies accelerate at a rate of 9.8 meters per second squared. There also appear to be generalizations that could express laws that are restricted. There are no gold spheres that size and in all likelihood there never will be, but this is still not a law. Consider the unrestricted generalization that all gold spheres are less than one mile in diameter. There are true nonlaws that are not spatially restricted. But that's not what makes the difference. So, it is easy to think that, unlike laws, accidentally true generalizations are about specific places. That everyone here is seated is spatially restricted in that it is about a specific place the principle of relativity is not similarly restricted. Einstein's principle that no signals travel faster than light is also a true generalization but, in contrast, it is thought to be a law it is not nearly so accidental. Though true, this generalization does not seem to be a law. Then, trivially, that everyone here is seated is true. Suppose that everyone here is seated (cf., Langford 1941, 67). So, some sympathetic to Goodman's idea come to the problem of laws as a result of their interest in the problem of induction. Third, Goodman famously suggested that there is a connection between lawhood and confirmability by an inductive inference. For example, sparked by the account of counterfactuals defended by Roderick Chisholm (1946, 1955) and Nelson Goodman (1947), and also prompted by Carl Hempel and Paul Oppenheim's (1948) deductive-nomological model of explanation, philosophers have wondered what makes counterfactual and explanatory claims true, have thought that laws must play some part, and so also have wondered what distinguishes laws from nonlaws. Second, laws are important to many other philosophical issues. Here are four reasons philosophers examine what it is to be a law of nature: First, laws at least appear to have a central role in scientific practice. The Basic Question: What is it to be a Law?
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