Correction to: A Tale of Two Deficits: Causality and Care in Medical AI

Correction to: Philosophy & Technology

https://doi.org/10.1007/s13347-019-00359-6

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.