ABSTRACT
If you refrain from believing A, you might believe that A is false or you might take no position on A. Here are some further translations:
You believe that you ought to do A Everyone believes that they ought to do A
You believe that if A then not-B If you believe A, then you don’t believe B
= =
= =
u:OAu (x)x:OAx
u:(A Ä ÀB) (u:A Ä Àu:B)
Since our belief logic generates norms prescribing consistency, it focuses on imperative belief formulas – which we express by underlining the small letter:
Believe that A is true = u:A
Don’t believe that A is true Believe that A is false
Don’t believe A and don’t believe not-A
= = =
Àu:A u:ÀA (Àu:A Â Àu:ÀA)
Believe that you ought to do A Let everyone believe that they ought to do A
= =
u:OAu (x)x:OAx
As before, we distinguish between if-then and don’t-combine forms:
If you in fact believe A, then don’t believe B Don’t combine believing A with believing B
= =
(u:A Ä Àu:B) À(u:A Â u:B)
Translate these sentences into wffs (use “u” for “you” and “G” for “There’s a God”).
