notes_7

# notes_7 - Notes for Week 7 of Confirmation Branden Fitelson...

This preview shows pages 1–2. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Notes for Week 7 of Confirmation 10/17/07 Branden Fitelson 1 Some Properties of Confirmation Relations Hempel (in his second installment) discusses various properties that confirmation relations might have. I will discuss a longer list of properties. Here are a bunch of properties that we’ll discuss today. We will assume throughout most of our discussion that all of our E ’s, H ’s, and K ’s are logically contingent. (M E ) If E confirms H relative to K , then E & E confirms H relative to K (provided that E does not contain any constant symbols not already contained in { H,E,K } ). (M K ) If E confirms H relative to K , then E confirms H relative to K & K (provided that K does not contain any constant symbols not already contained in { H,E,K } ). (NC) [ φ x & ψ x \ confirms [ ( ∀ y)(φy ⊃ ψy) \ relative to (some/all/specific) K . (SCC) If E confirms H relative to K and H K H , then E confirms H relative to K . (CCC) If E confirms H relative to K and H K H , then E confirms H relative to K . (CC) If E confirms H relative to K and E confirms H relative to K , then K ø ∼ (H & H ) . (CC ) If E confirms H relative to K and E confirms H relative to K , then K ø ∼ (H ≡ H ) . (EC) If E K H , then E confirms H relative to K . (CEC) If H K E , then E confirms H relative to K . (EQC E ) If E confirms H relative to K and K E ≡ E , then E confirms H relative to K . (EQC H ) If E confirms H relative to K and K H ≡ H , then E confirms H relative to K . (EQC K ) If E confirms H relative to K and K K , then E confirms H relative to K . (NT) For some E , H , and K , E confirms H relative to K . And, for every E / K , there exists an H such that E does not confirm H relative to K . (ST) If E confirms H relative to K and E confirms H relative to ∼ K , then E confirms H relative to > . As exercises, let’s think about some subsets of this large set of conditions. Consider the following triples: • (NT), (CEC), (SCC) – Inconsistent. Pick an E . Then, by (NT), E does not confirm (some) H relative to (some) K . But, by (CEC), E confirms H & E , relative to K . Then, by (SCC), E confirms H , relative to K . Contradiction. • (NT), (EC), (CCC) – Inconsistent. Pick an E . Then, by (NT), E does not confirm H relative to K . By (CCC), E does not confirm H ∨ E relative to K (if it did, then, by (CCC), it would also confirm the logically stronger H , contrary to our initial assumption). By (EC), E confirms H ∨ E relative to K . Contradiction. • (NT), (CCC), (SCC) – Inconsistent. By (NT), (some) E confirms (some) H relative to (some) K . By (CCC), E confirms H & H relative to K . By (SCC), E confirms H relative to K . But, H was arbitrary here. So, we have found an E / K such that, for all H , E confirms H relative to K , which contradicts (NT)....
View Full Document

## This note was uploaded on 08/01/2008 for the course PHIL 290 taught by Professor Fitelson during the Fall '06 term at Berkeley.

### Page1 / 6

notes_7 - Notes for Week 7 of Confirmation Branden Fitelson...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online