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Nagel - The Structure of Science The Logical Character of Scientific Laws
Laws have the form of generalized conditions: 'For any x, if x is A then x is B'
* fulfilment of this schema is not sufficient for something to be classed as a law
* thus the difference between lawlike universal statements and non-lawlike universal statements will underpin much of any explanation
Accidental and Nomic (i.e. lawlike) Universality
Scientists characterise many statements as laws, but there are divergent opinions
* is it a law if it refers to a particular object e.g. the sun?
* are statistical generalizations laws?
* can we ever make laws of uniform human behaviour e.g. economics?
If we use the schema 'For any x, if x is A then x is B' then we do not discriminate between accidental and nomic universality
* because of the rules of logic, if the antecedent is false, then the universal conditional is true irrespective of the content of its consequent - 'vacuously true' This is inadequate; laws express more than coincidental concomitance between objects
* in the case of nomic universality, we want to say that there is not, never has been, and never will be an x such that it is A but not B; that it is physically impossible. Thus we introduce physical necessitation
* we also want to extend to subjunctive and counterfactual conditionals
* the schema 'for any x, if x is A then x is B' cannot be extended to accidental universals e.g. 'For an x, if x were a screw in Smith's current car x would be rusty' because the accidental generalization does not necessitate screws being or becoming rusty 'A universal law "supports" a subjunctive conditional, while an accidental universal does not.' So how can we support subjunctive conditionals, given that they are not formalizable?
Are Laws Logically Necessary?
It seems that laws are necessary. But what kind of necessity?
* logical necessity has the benefit of clarity but faces grave difficulties
* we may claim the relevant necessity is unique and unanalyzable, but this is a last resort It is often claimed that genuine nomological laws could in principle be shown to be logically necessary, even if they haven't already been
* this is somewhat torpedoed by the fact that the formal denials of most laws are demonstrably not self contradictory
# so either these aren't really laws, or the proofs that show their denials not to be self-contradictory are mistaken
# also, if this is the case then why pursue empirical evidence for supposed laws?
* many 'laws' with broad explanatory and predictive powers are in no way logically necessary Some generalizations can be shown to be logically necessary definitionally, and hence trivially
* for example, to claim that 'all copper expands when heated' is logically necessary if a
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