Falsifying universal statements

Statements in which only universal names and no individual names occur will here be called ‘strict’ or ‘pure’. Most important among them are the strictly universal statements which I have already discussed. In addition to these, I am especially interested in statements of the form ‘there are black ravens’, which may be taken to mean the same as ‘there exists at least one black raven’. Such statements will be called strictly or purely existential state­ments (or ‘there-is’ statements).

The negation of a strictly universal statement is always equivalent to a strictly existential statement and vice versa. For example, ‘not all ravens are black’ says the same thing as ‘there exists a raven which is not black’, or ‘there are non-black ravens’.

The theories of natural science, and especially what we call natural laws, have the logical form of strictly universal statements; thus they can be expressed in the form of negations of strictly existential statements or, as we may say, in the form of non-existence statements (or ‘there-is-not’ statements). For example, the law of the conservation of energy can be expressed in the form: ‘There is no perpetual motion machine’, or the hypothesis of the electrical elementary charge in the form: ‘There is no electrical charge other than a multiple of the electrical elementary charge’.

In this formulation we see that natural laws might be compared to ‘proscriptions’ or ‘prohibitions’. They do not assert that something exists or is the case; they deny it. They insist on the non-existence of certain things or states of affairs, proscribing or prohibiting, as it were, these things or states of affairs: they rule them out. And it is precisely because they do this that they are falsifiable. If we accept as true one singular statement which, as it were, infringes the prohibition by asserting the existence of a thing (or the occurrence of an event) ruled out by the law, then the law is refuted. [47-8]

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