Dependency Lists Whenever you use PA in a proof, you need to include dependency lists.

Dependency Lists Whenever you use PA in a proof, you need to include dependency lists. Here is why they are necessary: 1) M>B A 2) M PA 3) B 1,2 >O

Dependency Lists Whenever you use PA in a proof, you need to include dependency lists. Here is why they are necessary: 1) M>B A 2) M PA 3) B 1,2 >O But the argument M>B | B is invalid!

We need a way to keep track of Provisional Assumptions. Dependency Lists Whenever you use PA in a proof, you need to include dependency lists. Here is why they are necessary: 1) M>B A 2) M PA 3) B 1,2 >O But the argument M>B | B is invalid! Moral: We need a way to keep track of Provisional Assumptions.

Moral: We need a way to keep track of Provisional Assumptions. Dependency Lists Whenever you use PA in a proof, you need to include dependency lists. Here is why they are necessary: 1) M>B A 2) M PA 3) B 1,2 >O But the argument M>B | B is invalid! Moral: We need a way to keep track of Provisional Assumptions.

Dependency Lists 1) C>M 2) M>J 3) C 4) M 5) J 6) C>J A PA 1,3 >O 2,4 >O 3-5 >I

Assumptions depend on themselves Dependency Lists 1 2 3 1) C>M 2) M>J 3) C 4) M 5) J 6) C>J A PA 1,3 >O 2,4 >O 3-5 >I Assumptions depend on themselves

Dependency Lists 1 2 3 1,3 1) C>M 2) M>J 3) C 4) M 5) J 6) C>J A PA 1,3 >O 2,4 >O 3-5 >I For >Out, &In, and &Out add together the dependency lists for the lines used.

Dependency Lists 1 2 3 1,3 1,2,3 1) C>M 2) M>J 3) C 4) M 5) J 6) C>J A PA 1,3 >O 2,4 >O 3-5 >I For >Out, &In, and &Out add together the dependency lists for the lines used.

Dependency Lists 1 2 3 1,3 1,2,3 1,2 1) C>M 2) M>J 3) C 4) M 6) C>J A PA 1,3 >O 2,4 >O 3-5 >I For >In, take the list for the consequent, and remove the number for the PA.

Dependency Lists 1 2 3 1,3 1,2,3 1,2 1) C>M 2) M>J 3) C 4) M 6) C>J A PA 1,3 >O 2,4 >O 3-5 >I For >In, take the list for the consequent, and remove the number for the PA. WHY DO YOU REMOVE THE PA NUMBER?

Dependency Lists 1 2 3 1,3 1,2,3 1,2 1) C>M 2) M>J 3) C 4) M 6) C>J A PA 1,3 >O 2,4 >O 3-5 >I For >In, take the list for the consequent, and remove the number for the PA. WHY DO YOU REMOVE THE PA NUMBER? A CONDITIONAL DOES NOT DEPEND ON ITS ANTECEDENT.

For more click here Dependency Lists Why this “proof” does not work: 1 1. M>B A 2 2. M PA 1,2 3. B 1,2 >O No proof is complete if the dependency list contains the number of a PA! For more click here