Barriers to Implication

Implication barrier theses deny that one can derive sentences of one type from sentences of another. Hume’s Law is an implication barrier thesis; it denies that one can derive an ‘ought’ (a normative sentence) from an ‘is’ (a descriptive sentence). Though Hume’s Law is controversial, some barrier theses are philosophical platitudes; in his Lectures on Logical Atomism, Bertrand Russell claims: You can never arrive at a general proposition by inference particular propositions alone. You will always have to have at least one general proposition in your premises. (Russell, 1918, p. 206) We will refer to this claim—that one cannot derive general sentences from particular sentences—as Russell’s Law.1 A third barrier thesis claims that one cannot derive sentences about the future from sentences about the past or present. Hume’s endorsement of this barrier thesis is well-known: all inferences from experience suppose, as their foundation, that the future will resemble the past . . . if there be any suspicion that the course of nature may change, and that the past may be no rule for the future, all experience becomes useless, and can give rise to no inference or conclusion. It is impossible, therefore, that any argument from experience can prove this resemblance of the past to the future; since all these arguments are founded on the supposition of that resemblance. (Hume, EHU 4.21/37) We will refer to this barrier thesis as Hume’s Second Law. A fourth barrier thesis says that one cannot derive a necessary sentence from one about the actual world and we will refer to this last thesis Kant’s Law. Such implication barrier theses present a problem.
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