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
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
