WARNING: Logic ahead!
Lot’s of folks have commented on van Inwagen’s “Free Will Remains a Mystery” (2000; Kane 2002) but most of the commentaries are about part 2: the rollback (or Mind or luck) argument against the libertarian agency theory. Almost nothing has been written about part 1, his revised version of the consequence argument. There is one notable replay that goes virtually unnoticed: Lynn Rudder Baker’s “The Irrelevance of the Consequence Argument,” Analysis 68.1 (2008): 13-22.
Recall that van Inwagen’s third argument was under attack because of a counterexample to transfer principle Beta: From Np, N(p --> q) derive Nq. (The counterexample is derived from McKay and Johnson 1996 and others.)
Suppose that a coin was not tossed though I was able to toss the coin. Let:
h = the coin landed heads
f = the coin was tossed (or flipped)
N~h = the coin did not land heads & no one is or ever was able to act so as to ensure that the coin landed heads = TRUE
N(~h --> ~f) = N(if the coin did not land heads, then the coin was not tossed) = TRUE
N(~f) = the coin was not tossed & no one is or ever was able to act so as to ensure that the coin was tossed = FALSE
Why is N(~h --> ~f) true, you might ask?
1. If the coin did not land heads, then the coin was not tossed = TRUE [for the coin was not tossed, so the consequence is true].
2. ~(If the coin did not land heads, then the coin was not tossed) = the coin was tossed and landed heads.
3. No one is or ever was able to act so as to ensure that the coin was tossed and landed heads = TRUE.
There are lots of different ways to fix the third argument in light of this counterexample. Crisp and Warfield (2000) suggest replacing Beta with:
Beta*: From Np, p entails q derive Nq (Widerker 1987).
McKay and Johnson suggested redefining the N-operator and van Inwagen follows this route. Van Inwagen’s definitions here are a bit complicated, so bear with me. First, he rephrases everything in terms of having access to various regions of logical space, where a region of logical space corresponds to a proposition (4-5). Intuitively, one has a choice about whether some true proposition is true provided that one is able to ensure that the proposition is false. (Remember, we’re working with classical free will here: the ability to do otherwise.) This leads to:
“Np” =df. “p and every region of logical space to which anyone has, or ever had, access overlaps p” (7).
Unfortunately, as the above counterexample indicates, this definition is inadequate. Van Inwagen: “I may, for example, be able to ensure that the dart hit the board, but unable to ensure with respect to any proper part of the board that it hit that proper part.” (5) I may also be able to toss a coin but not ensure that it lands heads.
Van Inwagen alters the definition in an attempt to get around this problem: “Np” =df. “p and every region to which anyone has, or ever had, exact access is a subregion of p” (8).
Suppose it would be good if you tossed a coin and it came up heads (think “No Country for Old Men”) but you don’t even toss the coin. Van Inwagen says: “You had a choice about whether the coin was tossed, and if you had tossed it, it might have landed ‘heads.’ What you are to blame for is not doing your best to bring it about that the coin landed ‘heads’.” (8) As McKay and Johnson note, by weakening from would-ability to might-ability, one actually strengthens the transfer principle and given this alteration Beta survives the above counterexample.
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