Nicod's Criterion: Subtler than You Think

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In a recent note, Horwich (1978) challenges the foundations of Hempel's classic paradox of confirmation by a clever example purporting to show that under Nicod's Criterion, data can be made to confirm a hypothesis with which they are logically incompatible. Specifically, Horwich observes that 'Pb' (i.e., 'object b has property P') is formally equivalent to '(x)(∼Px · ∼Pb ⊃ x ≠ b)'. The latter has form '(x)(ψx ⊃ ϕx)' with '∼P___ · ∼Pb' for 'Ψ' and '___ ≠ b' for 'ϕ', while the observation that distinct objects a and b both lack P, i.e. that —Pa · ∼Pb · a ≠ b, can be expressed as 'Ψa · ϕa' for these same instantiations of the predicate markers. Accordingly, if an uncertain generality '(x)(Ψx ⊃ Ψx)' were always to be confirmed by an observation of form 'Ψa · ϕa', as Nicod's Criterion has long been presumed to say, then we could confirm that b has P by observing that b and some other object both lack P—a flagrant absurdity.