The Obligatory, the Supererogatory, and Two Moral Senses of ‘Ought’

This is an old post from the Powerblogs site, written a few years ago.  The points made still seem correct.

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Peter Lupu's version of the logical argument from evil (LAFE) is committed to a principle that I formulate as follows:

P. Necessarily, agent A ought to X iff A is morally obligated to X.

This principle initially appealed to me, but then I came to the conclusion (with the help of the enigmatic Phil Philologos or was it Seldom Seen Slim?) that the biconditional (P) is correct only in the right-to-left direction. That is, I came to the view that there are moral uses of 'ought' that do not impute moral obligations. But so far I have not convinced Peter. So now I will try a new argument, one that explores the connection between the obligatory-supererogatory distinction and the thesis that there are two moral senses of 'ought.' Here is the gist of the argument:

How to ‘Derive’ Ought from Is

I demanded an argument valid in point of logical form all of whose premises are purely factual but whose conclusion is categorically (as opposed to hypothetically or conditionally) normative.  Recall that a factual proposition is one which, whether true or false, purports to record a fact,  and that a purely factual proposition is a factual proposition containing no admixture of normativity. 

My demand is easily, if trivially, satisfied.

Ex contradictione quodlibet.  From a contradiction anything, any proposition, follows.  This is rigorously provable within the precincts of the PC (the propositional calculus).  As follows:

1. p & ~p 
2. p  (from 1 by Simplification)
3. p v q (from 2 by Addition)
4. ~p & p (from 1 by Commutation)
5. ~p (from 4 by Simplification)
6. q (from 3, 5 by Disjunctive Syllogism)

Now plug in 'Obama is a liar' for p and 'One ought to be kind to all sentient beings' for q.  The result is:

Obama is a liar 
Obama is not a liar
Ergo
One ought to be kind to all sentient beings.

My demands have been satisifed.  The above is an argument valid in point of logical form whose premises are all purely factual and whose conclusion is categorically normative.

I am demanding too little!