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The Meaning of 'Ought'Beyond Descriptivism and Expressivism in Metaethics$

Matthew Chrisman

Print publication date: 2015

Print ISBN-13: 9780199363001

Published to Oxford Scholarship Online: October 2015

DOI: 10.1093/acprof:oso/9780199363001.001.0001

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Proposed Semantic Rules for ‘Ought’

Proposed Semantic Rules for ‘Ought’

The Meaning of 'Ought'

Matthew Chrisman

Oxford University Press

  1. RIa. [ [ ought ] ]c=Ο:For all<xagent,yaction>,[ [ Ο(x,y) ] ]c=1iff the agentx relevant in c has an obligation to perform the actioy relevant in c.

  2. RIb. [ [ ought ] ]c=Ο:For all<xagent,yaction>,[ [ Ο(x,y) ] ]c=1iff the agentxrelevant in c would have a better overall life were she toperform the action y relevant in c.

  3. RIc. [ [ ought ] ]c=Ο:For all<xaction>,[ [ Ο(x,y) ] ]c=1iff xis the mosteffi-cient way to achieve the end most salient in c.

  4. RId. [ [ ought ] ]c=Ο:For all<xoutcome>,[ [ Ο(x) ] ]c=1iffit would be idealin the contextually determined way if x were true.

  5. RIe. [ [ ought ] ]c=Ο:For all<pproposition>,[ [ Ο(p) ] ]c=1iffproposition pislikely true given the body of evidence relevant in c.

  6. RIs.

    1. a. α‎ ought ϕ‎ = 1 iff α‎ is obligated to ϕ‎.

    2. b. α‎ ought ϕ‎ = 1 iff α‎’s life would go better if she ϕ‎ed.

    3. c. ought ϕ‎ = 1 iff ϕ‎ ing is the most efficient way to achieve e.

    4. d. ought x = 1 iff x would be ideal in some way k.

    5. e. ought p = 1 iff p is likely true.

  7. R2. [ [ ought ] ]c=Ο:For all<xsubject,yresponse>,[ [ Ο(x,y) ] ]c=1iff xhas areason to respond with y in the situation made rele-vantinc.

  8. R2'. [ [ ought ] ]c=Ο:For all<xsubject,yresponse>,[ [ Ο(x,y) ] ]c=1iff the sub-ject x relevant in c has a reason to give response ymade relevant in c to the situation made relevant in c.

  9. R2". [ [ ought ] ]c=Ο:For all<xsubject,yresponse>,[ [ Ο(x,y) ] ]c=1iff xhas aconclusive reason to respond with y in the situationmade relevant by c.

  10. R2s. oughtϕ=1 iff αhas conclusive reason to ϕ.

  11. (p.236) R3. [ [ ought ] ]c=Ο:For all<xoption>,[ [ Ο(x) ] ]c=1iffxisthe best optionin the way w determined by c among the set of rele-vant alternatives determined by c.

  12. R3.' [ [ ought ] ]c=Ο:For all<xstate-of-affairs>,[ [ Ο(x) ] ]c=1iffisthe bestimaginable state of affairs in the way w determinedby c among the set of relevant alternatives determinedby c.

  13. R3." [ [ ought ] ]c=Ο:For all<xproposition>,[ [ Ο(x) ] ]c=1iffxis,or is a neces-sary condition on the best possibility in the way de-termined by c among the set of possibilities deter-mined by c.

  14. R3s oughtx=1iffxis highest ranked possible state of affairs amongPc.

  15. R4. [ [ ought ] ]R,x;w=Ο:For all pproposition ,[ [ Ο(p) ] ]w=1 iff[ [ p ] ]w=1in allworlds R-accessible-relative-to-x from w.

  16. R4s oughtp=1iffp=1in all worlds Rc-accessible from w.

  17. R5. [ [ ought ] ]f,g;w=Ο:For all<pproposition>,[ [ Ο(p) ] ]c;w=1iff[ [ p ] ]c;w=1inall worldsνf(w),for which there is no νfsuch thatν<g(w)ν.

  18. R5s oughtp=1iffp=1inall f-worlds for which there are no betterworlds along the g-ordering.

  19. R6. [ [ ought ] ]f,g;w=Ο:For all<pproposition>,[ [ Ο(p) ] ]c;w=1iff[ [ p ] ]c;w=1inall worlds v in some maximal chain cf(w),which are at or above the relevant lower bound B ofthe ordering<g(w).

  20. R6s oughtp=1iff p = 1 in all of the f-worlds, along at least one maxi-mal chain, that are above the relevant lower bound onthe g-ordering.

  21. R7s oughtp=1iff p = 1 in all f-worlds for which there are no betterworlds along the g-ordering, where (a) p may be anynonagentive proposition, or (b) p may be the proposi-tionthat αbringsit about thatq,whereqisany nona-gentive proposition.

  22. (p.237) R8. [ [ ought ] ]f,g;w,α=Ο:For all<Pproposition>,[ [ Ο(πp) ] ]c;w=1iff[ [ p ] ]c;w=1in all world-agent pairsνf(w,α),forwhichthere is noνf(w,α)such thatν<g(w,α)ν.

  23. R8s oughtp=1iffp=1in all world-agent pairs f for which there areno better world-agent pairs along the g-ordering.

  24. R9.

    1. a. [ [ ought ] ]c;w=Οa:For all xagent,yaction ,[ [ Ο(x,y) ] ]c;w=1iff theagent x relevant in c is oughtness related to theaction y relevant in c.

    2. b. [ [ ought ] ]f,g;w=Οb:For all<Pproposition>,[ [ Ο(p) ] ]c;w=1iff [ [ p ] ]c;w=1in all worldsνf(w),for which there is noνfsuch thatν<g(w)ν.

  25. R9s

    1. a. αoughtϕ=1iffαΟaϕ

    2. b. oughtp=1iffp=1at all of the highest w in Pc.

  26. R10. [ [ ought ] ]f,g;w=Ο:For all<pproposition/practition>,[ [ Ο(P) ] ]c;w=1iff[ [ p ] ]c;w=1relative to all of the<w,n>compatible with the back-ground f(w), which are such that there is no <w,n>alsocompatible with the backgroundf(w)and higher rankedbyg(w).

  27. R10s oughtp=1iffp=1at all of the highest<w,n>inPfg.