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Nagel Laws Of Nature Notes

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Nagel - The Structure of Science The Logical Character of Scientific Laws
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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
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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?
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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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