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Correction to: Philosophy & Technology
The original version of this article unfortunately contains an unconverted data in footnotes 5, 9 and 13.
The correct presentation of data should be.
5Formally:
P1: (P ⊃ Q)
P2: ~Q
C: ∴ ~P (modus tollens rule of inference)
9Formally:
P1: (P ⊃ Q)
P2: ((Q.R) ⊃ S)
P3: R
C: ∴ (P ⊃ S)
Proof of validity:
1: (P ⊃ Q)
2: ((Q.R) ⊃ S)
3: R
(P ⊃ S) (block off conclusion and assume the negation of C)
4: asm: ~(P ⊃ S)
5: ∴ P (from 4)
6: ∴ ~S (from 4)
7: ∴ Q (from 1 and 5) (modus ponens)
8: ∴ (Q.R) (from 3 and 7)
9: ∴ S (from 2 and 8) (modus ponens)
10: ∴ (P ⊃ S) (from 4; 6 contradicts 9) (reductio ad absurdum) (QED)
13 Formally:
P1: (P ⊃ Q)
P2: (Q ⊃ R)
P3: (P ≡ S)
C: ∴ (S ⊃ R)
Proof of validity:
1: (P ⊃ Q)
2: (Q ⊃ R)
3: (P ≡ S)
(S ⊃ R) (block off conclusion and assume the negation of C)
4: asm: ~(S ⊃ R)
5: ∴ S (from 4)
6: ∴ ~R (from 4)
7: ∴ (P ⊃ R) (from 1 and 2) (hypothetical syllogism)
8: ∴ ~P (from 6 and 7) (modus tollens)
9: ∴ (S ⊃ P) (from 3)
10: ∴ ~S (from 8 and 9) (modus tollens)
11: ∴ (S ⊃ R) (from 4; 5 contradicts 10) (reductio ad absurdum) (QED)
The original article has been corrected.
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Chen, M. Correction to: A Tale of Two Deficits: Causality and Care in Medical AI. Philos. Technol. 32, 769–770 (2019). https://doi.org/10.1007/s13347-019-00375-6
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DOI: https://doi.org/10.1007/s13347-019-00375-6