## Friday, August 22, 2014

### A criticism of some consequence arguments

The standard consequence argument for incompatibilism makes use of the operator Np which abbreviates "p and no one has or has ever had a choice about whether p". Abbreviating the second conjunct as N*p, we have Np equivalent to "p and N*p". The argument then makes use of a transfer principle, like:

• beta-2: If Np and p entails q, then Nq.
When I think about beta-2, it seems quite intuitive. The way I tend to think about it is this: "Well, if I have no choice about p, and p entails q, then how can I have a choice about q?" But this line of reasoning commits me not just to beta-2, but to the stronger principle:
• beta-2*: If N*p and p entails q, then N*q.
But beta-2* is simply false. For instance, let p be any necessary falsehood. Then clearly N*p. But if p is a necessary falsehood, then p entails q for every q, and so we conclude—without any assumptions about determinism, freedom and the like—that no one has a choice about anything. And that's unacceptable.

This may be what Mike Almeida is getting at in this interesting discussion which inspired this post.

Of course, this counterexample to beta-2* is not a counterexample to beta-2, since although we have N*p, we do not have Np, as we do not have p. But if the intuition driving one to beta-2 commits one also to beta-2*, then that undercuts the intuitive justification for beta-2. And that's a problem. One might still say: "Well, yes, we have a counterexample to beta-2*. But beta-2 captures most of the intuitive content of beta-2*, and is not subject to this counterexample." But I think such arguments are not very strong.

This is not, however, a problem if instead of accepting beta-2 on the basis of sheer intuition, one accepts it because it provably follows from a reasonable counterfactual rendering of the N*p operator.

Mark said...

I would like to examine the relation between the counter-example to beta-1 and Np.

Beta-1: [Np&N(p-->q]-->Nq.

Beta-1 (along with rule alpha) uncontroversially implies agglomeration.

Agglomeration: (Np&Nq)-->N(p&q).

My question is: given the definition of Np as "p and no one has a choice about whether p", is agglomeration invalid?

The counter-example to agglomeration about tossing an indeterministic coin is what has convinced most people that agglomeration is invalid.

I'll post the counter-example here. From "Incompatibilism Proved":

"But agglomeration is invalid. Suppose you actually won’t toss an indeterministic
coin but can. Let p be the proposition that the coin won’t land heads. Let q be
the proposition that the coin won’t land tails. Then N p, since p is true and you
have no choice about p, because there is nothing you could do to make p false—you
can’t make the coin land heads. Similarly, Nq. On the other hand N(p ∧ q) is false,
because you do have a choice about p ∧ q—if you toss the coin, the conjunction
p ∧ q will be false, since the coin will land either heads or tails."

But it strikes me that something is wrong here. It seems to me that given Np (and not N*p), the counter-example doesn't work.

Here's the tension between two propositions of the excerpt I quoted from your article:

(1) "Let p be the proposition that the coin won’t land heads."

AND

(2) "Then N p, since p is true and you

AND

(3) "Let q be
the proposition that the coin won’t land tails".

AND

(4) "Similarly, Nq".

(4) is equivalent to (5):

(5) "Then N q, since q is true and you

(5) and (2) make two explicit assumptions, namely:

(6) p is true, and q is true.

From (6), and (1), and (3), we get:

(7) "the coin won’t land heads" & "the coin won’t land tails".

The following is true:

(8) If the coin won't land heads, then it lands tails.

From (7) and (8), we get:

(9) "the coin lands tails" & "the coin won't land tails".

(9) is a contradiction (the landings of the coin are happening at the same time).

I believe the counter-example to agglomeration was based on N*p and not Np. Perhaps that's why the counter example began with "Suppose you actually won’t toss an indeterministic
coin but can."

-WH

Mark said...

Minor Correction:

I retract this statement:

"Here's the tension between two propositions of the excerpt I quoted from your article:"

And replace it with:

"Here's the tension I found in the excerpt I quoted from your article:"

Alexander R Pruss said...

(8) is false. If the coin won't land tails AND it is tossed, then it will land heads.

Mark said...
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