Peter van Inwagen An Argument for Incompatibilism

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Peter van Inwagen An Argument for Incompatibilism

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Title: Peter van Inwagen An Argument for Incompatibilism

1

Peter van Inwagen An Argument for
Incompatibilism
The agent-causation view is a form of
libertarianism, and libertarianism is a form of
incompatibilism. We didnt get any positive
argument for incompatibilism from Chisholm or
OConnor or Clarke. The closest we got was an
argument against compatibilism from Chisholm.
van Inwagen is going to provide a positive
argument for incompatibilism. The argument will
make use of a number of technical concepts
Propositions
A state of the entire physical world at an
instant
A law of nature
Determinism
s can render p false

1. Propositions these are abstract, non-mental
and non-linguistic bearers of truth and falsity
and the objects of belief. For example, these
sentences express the same proposition
Snow is white La neige est blanche Schnee
ist weiss
- The proposition expressed by these sentences
is not in any language - it is not in English or
French or German. Propositions are
non-linguistic.
- It is not in anyones mind - it is something
that all of us can grasp. Propositions are
non-mental.
- The proposition that snow is white is true if
and only if snow is white. This proposition is
the bearer of a truth-value.
- Suppose you and I both believe that snow is
white. What we believe is the proposition that
snow is white. Propositions are the objects of
belief.

van Inwagens 4 assumptions about propositions
(i) To every possible way the world could be,
there corresponds at least one proposition, a
proposition that is necessarily such that it is
true if and only if the world is that way.(39)
(ii) Every proposition is either true or
false.(40)
(iii) The conjunction of a true and a false
proposition is a false proposition.(40)
(iv) Propositions obey the law of
Contraposition with respect to entailment.(40)
Law of Contraposition w.r.t. entailment
If P entails Q, then not-Q entails not-P.
If P ? Q then not-Q ? not-P
P entails Q it is impossible for P to be true
and Q false.

van Inwagen brings up a certain view about what
propositions are.
Consider all the possible ways for the world to
be. Call any such way for the world to be a
possible world. The actual world is one such
possible world - it is the way the world actually
is.
Consider the proposition that GWB won the 2004
presidential election. This proposition is true
in some possible worlds and false in others. It
is false in possible worlds in which John Kerry
won, or worlds in which Al Sharpton won, or etc.
Proposal
ltGWB won the 2004 presidential electiongt w
GWB won the 2004 presidentical
election in w

the proposition that GWB won the 2004
presidential election
the set of possible worlds in which GWB won the
2004 presidential election
5

On this account of propositions, a proposition is
true iff it contains the actual world.
Let w the actual world
ltGWB won the 2004 presidential electiongt is true
iff w ? w GWB won the 2004
presidential election in w
P entails Q iff P is contained in Q, (i.e. P ? Q).

Q worlds
P entails Q iff it is impossible for P to be
true and Q false there is no possible world
that is a member of P and not a member of Q
P worlds
6

van Inwagen notes that there are serious problems
for this account of what propositions are - but
these problems will not affect his argument.
P is necessarily true P is true in all possible
worlds
P is possibly true P is true in at least one
possible world
P is impossible / necessarily false P is false
in all possible worlds
P is contingently true P is true and there is
at least one possible world in which P is false
1 1 2 xn yn zn has no non-zero integer
solutions when ngt2
(Fermats Last Theorem)

Both are necessarily true - true in all possible
worlds. So, on the possible worlds account of
propositions, these sentences express the same
proposition. Furthermore, if you believe that 1
1 2, then you must also believe Fermats Last
Theorem.
7

2. The state of the entire physical world at an
instant
(i) Our concept of state must be such that,
given that the world is in a certain state at a
certain instant, nothing follows about its state
at any other instant...(40)
- this means that no state of the world at
an instant t includes as part of its description
that the world will be such-and-such a way at an
instant after t
(ii) If there is some observable change in the
way things are - if a white cloth becomes blue, a
warm liquid cold, or if a man raises his hand -
this change must entail some change in the state
of the world.(40)
- if there is an observable difference
between states s1 and s2, then s1 and s2 are
different states

van Inwagen Let us say that a proposition
expresses the state of the world at t provided it
is a true proposition that asserts of some state
that, at t, the world is in that state.(41)
Let k the state of physical universe at 1115
am, Jan. 31, 2005.
P expresses the state of the world at 1115 am,
1/31/05 iff
(a) P asserts that the world is in a certain
state at 1115 am, 1/31/05
and
(b) P is true
So, in order for P to express the state of the
world at 1115 am, 1/31/05, P must assert that at
1115 am, 1/31/05, the world is in state k.
P w at 1115 am, 1/31/05, w is in state k

3. Law of nature
- laws of nature are true propositions
- by definition, no one can render a law of
nature false
Let Q the proposition that no one has ever
swallowed 100 gallons of water from the
Mississippi river in one day
Q is true, but Q is NOT a law of nature. If we
wanted to, we could walk out to the Mississippi
after class and render it false. Laws of nature
are not like this - even if we wanted to, we
couldnt render a law of nature false.
Let L the proposition that nothing ever travels
faster than the speed of light
L is a law of nature. It is impossible for us to
render L false.

This last claim has to be understood carefully.
It is not the claim that there is no possible
world in which we do things that are incompatible
with the truth of L.
L the proposition that nothing ever travels
faster than the speed of light
Consider a possible world in which L is not a law
of nature, i.e. in which it merely happens to be
true that nothing ever travels faster than light.
With respect to that world we would have it in
our power to do something that would render L
false, i.e. we could do something that it
incompatible with the truth of L.
van Inwagen is arguing for the following
principle about laws of nature
It is necessary that, for every person x and
proposition y, if y is a law of nature, then x
cannot render y false.(43)
In all possible worlds w, for every person x and
proposition y, if y is a law of nature in w then
x cannot render y false.

van Inwagen points out that this principle is
distinct from the trivial principle
It is impossible for there to be a person x and
proposition y such that x can bring it about that
y is a law of nature and false.(43)
There is no possible world w such that, for a
person x and proposition y,
x can bring it about that y is a law of nature
and false.

This is trivial because if something is a law of
nature then it must be true. There are obviously
no possible worlds in which a person makes
something both true and false. It is not
possible for anyone to make a proposition both
true and false.
12

s can render proposition p false def
It is within ss power to arrange or modify the
concrete objects that constitute his environment
in some way such that it is not possible in the
broadly logical sense that he arrange or modify
those objects in that way and the past have been
exactly as it in fact was and p be true.(48)
It is not logically possible for p to be true and
q false p logically entails q
p ? q
It is not logically possible for p to be true and
q to be true
p logically entails not-q
p ? not-q
...it is not possible in the broadly logical
sense that he arrange or modify those objects in
that way and the past have been exactly as it in
fact was and p be true...
(his arranging objects in that way the past
remains the same) ? not-p

L the proposition that nothing ever travels
faster than the speed of light.
I can render L false
there is some action a within my power such that
(I do a the past remains the same) ? it is not
the case that nothing ever travels
faster than the speed of light
Suppose a is I move my hand faster than the
speed of light. If I did a, then there would be
something that travels faster than light, i.e. my
hand. So, if a is within my power, then I can
render L false.
Remember van Inwagens claim about laws of
nature
It is necessary that, for every person x and
proposition y, if y is a law of nature, then x
cannot render y false.(43)
This implies that it is not within my power to do
a.
van Inwagen ...the laws of nature impose limits
on our abilities they are partly determinative
of what it is possible for us to do. (42)

a is within my power ? the proposition that I do
a is not logically incompatible
with any law of nature
Since the laws of nature can vary from world to
world, the actions that are within my power can
vary from world to world.
Van Inwagens point is that, with respect to any
possible world and the laws of nature in that
world, there is no action I can perform in that
possible world that would count as a
counterexample to any of those laws of nature.
It is necessary that, for every person x and
proposition y, if y is a law of nature, then x
cannot render y false.(43)
For all possible worlds w, for every person x and
proposition y, if y is a law of nature, then
there is no action a within xs power which is
such that, if x did a and the past remains the
same, then y would not be true.

Can I render these propositions false?
p no one has ever swallowed 100 gallons of
water from the Mississippi river in one day
YES - there is an action a, i.e. going out to the
river and swallowing 100 g of water, which is
such that
(I do a the past remains the same) ?
it is not the case that no one has ever
swallowed 100 gallons of Mississippi water in
one day
q that 5 7 12
NO - there is no arrangement or modification of
my environment a that I can perform which is such
that
(I do a the past remains the same) ? 5 7 ?
12
NOTE the fact that I cannot render a proposition
false does not imply that the proposition is a
law of nature.

r that Elvis did not meet Richard Nixon (r is
false)
YES (!) - Is there any action a within my power
such that
(I do a the past remains the same) ? it is not
the case that Elvis did not meet
Richard Nixon
? Elvis did meet Richard Nixon
Sure. Let a be the action of me raising my arm.
The implication will hold simply because
the past remains the same ? Elvis did meet
Richard Nixon
This is an odd consequence of van Inwagens
definition of can render false. It turns out
that if p is any false proposition about the
past, then I can render p false. This
consequence is not going to make any difference
to his argument, so he doesnt worry about it.

h the Spanish Armada was defeated in 1588.
Is there any action a within my power such that
(I do a the past remains the same) ? not-h
NO. There are no actions within my power that
can make it false that Spanish Armada was
defeated in 1588.
g the law of gravity, i.e. Fg G x m1m2 / r2
Is there any action a within my power to perform
which is such that
(I do a the past remains the same) ? not-g
NO. Since g is a law of nature, there is no such
action within my power.

4. Determinism
For every instant of time, there is a
proposition that expresses the state of the world
at that time.
and
If p and q are any propositions that express the
state of the world at some instants, the
conjunction of p with the laws of nature entails
q. (45)
Notice that the state of the world expressed by p
may occur at an instant after the state of the
world expressed by q.

19
L conjunction of the laws of nature

time
expresses
expresses
entails
p
q
L
time
expresses
expresses
entails
L
q
p
20

The argument for incompatibilism (finally)
Let us suppose that there was once a judge who
had only to raise his right hand at a certain
time, T, to prevent the execution of a sentence
of death upon a certain criminal, such a
hand-raising being the sign, according to the
conventions of the judges country, of a granting
of special clemency. Let us further suppose that
the judge - call him J - refrained from raising
his hand at T, and that this resulted in the
criminals being put to death.(49)
In addition, assume that J was unbound,
uninjured, rational, deliberative, etc. etc. etc.

T time at which J refrained from raising his
hand
P proposition expressing the state of the world
at T
T0 time prior to Js birth
P0 proposition expressing the state of the
world at T0
L conjunction of the laws of nature
If determinism is true, then the conjunction of
P0 and L entails P.
It is not possible that J have raised his hand at
T and P be true.
If (2) is true, then if J could have raised his
hand at T, J could have rendered P false.
If J could have rendered P false, and if the
conjunction of P0 and L entails P, then J could
have rendered the conjunction of P0 and L false.
If J could have rendered the conjunction of P0
and L false, the J could have rendered L false.
J could not have rendered L false.
(7) If determinism is true, J could not have
raised his hand at T.

T time at which J refrained from raising his
hand
P proposition expressing the state of the world
at T
T0 time prior to Js birth
P0 proposition expressing the state of the
world at T0
L conjunction of the laws of nature
If determinism is true, then the conjunction of
P0 and L entails P.
This follows directly from the definition of
determinism.
It is not possible that J have raised his hand at
T and P be true.
This is obvious, since in order for P to be true,
it must be the case that J did not raise his hand
at T.

T time at which J refrained from raising his
hand
P proposition expressing the state of the world
at T
T0 time prior to Js birth
P0 proposition expressing the state of the
world at T0
L conjunction of the laws of nature
It is not possible that J have raised his hand at
T and P be true.
(3) If (2) is true, then if J could have
raised his hand at T, J could have rendered P
false.
(J raises his hand at T the past remains the
same) ? not - P
So, if raising his hand at T was within Js
power, then J could have rendered P false.

T time at which J refrained from raising his
hand
P proposition expressing the state of the world
at T
T0 time prior to Js birth
P0 proposition expressing the state of the
world at T0
L conjunction of the laws of nature
If J could have rendered P false, and if the
conjunction of P0 and L entails P, then J could
have rendered the conjunction of P0 and L false.
J raises his hand at T ? not-P
(P0 L) ? P
not-P ? not (P0 L) Law of Contraposition
J raises his hand at T ? not-P
? not (P0 L)
So, if it was within Js power to raises his hand
at T, then J could have rendered (Po L) false.

T time at which J refrained from raising his
hand
P proposition expressing the state of the world
at T
T0 time prior to Js birth
P0 proposition expressing the state of the
world at T0
L conjunction of the laws of nature
(5) If J could have rendered the conjunction
of P0 and L false, the J could have rendered L
false.
If J could have rendered (P0 L) false, then
either J could have rendered P0 false or J could
have rendered L false.
P0 is a proposition expressing the state of the
world at some time prior to Js birth. So J
could not have rendered P0 false.
Therefore, if J could have rendered (P0 L)
false, then J could have rendered L false.

T time at which J refrained from raising his
hand
P proposition expressing the state of the world
at T
T0 time prior to Js birth
P0 proposition expressing the state of the
world at T0
L conjunction of the laws of nature
(6) J could not have rendered L false.
van Inwagen This premiss would seem to be an
obvious consequence of what we said about powers
with respect to laws of nature in Section
3.3.(53)
But van Inwagen is willing to put aside his
account of powers and can render false, and to
simply appeal to intuition to support (6). On
any reasonable reading of can render false, it
is intuitively not the case that anyone can
render a law of nature false.
Laws of nature are not within our power to
contradict.

If determinism is true, J could not have raised
his hand at T.
This follows from premises (1) - (6).
This conclusion is a statement of
incompatibilism.
J refrained from raising his hand at T. If this
action was done freely, then J could have done
otherwise, e.g. J could have raised his hand at
T.
But according to (7), if determinism is true,
then J could not have raised his hand at T.
Hence, if determinism is true, then J did not
freely refrain from raising his hand at T.

It is important not to get bogged down in the
details of all of this.
van Inwagen Consider any act that (logically)
someone might have performed. If it should turn
out that this act was incompatible with the state
of the world before that persons birth taken
together with the laws of nature, then it follows
that that person could not have performed that
act. Moreover, if determinism is true, then just
any deviation from the actual course of events
would be incompatible with any past state of the
world taken together with the laws of nature.
Therefore, if determinism is true, it never has
been within my power to deviate from the actual
course of events that has constituted my
history.(54)
The main idea of the argument is that if
determinism is true, then in order for me to act
freely, it must be that either I can change the
way the world was before my birth or I can do
something that violates a law of nature. Since I
cannot do either of these, if determinism is
true, then I never act freely.

David Lewis Are We Free to Break the Laws?
David Lewis (1941 - 2001)
Modal realism possible worlds are concrete
universes existing in other dimensions.
Counterpart theory each individual exists in
only one possible world, but each individual has
many counterparts in other possible worlds.
It is possible for me to have worn a red jacket
today.
There is a world in which a counterpart of me
is wearing a red jacket today.

Remember our classification of views
Compatibilism no conflict between determinism
and free will
Incompatibilism if determinism is true, there
is no free will
- Libertarianism determinism is false, we have
free will
- Determinism determinism is true, we have no
free will
Soft determinism compatibilism the view that
determinism is true
Hard determinism incompatibilism the view
that determinism is true

Compatibilism no conflict between determinism
and free will
- Soft determinism determinism is true we
have free will
- Soft indeterminism determinism is false we
have free will
- Soft determinist/anti-libertarian
determinism is true we have no free
will
- Soft indeterminist/anti-libertarian
determinism is false we have no
free will
Incompatibilism determinism is true if and only
if there is no free will
- Libertarianism determinism is false, we have
free will
- Hard determinism determinism is true, we
have no free will
Lewis (official view) soft indeterminism (I
think)
A compatibilist might well doubt soft
determinism because he doubts on physical grounds
that we are ever predetermined to act as we do,
or perhaps because he doubts on psychoanalytic
grounds that we ever act freely. I myself am a
compatibilist but no determinist...(122)
For the purposes of this paper, though, Lewis is
a soft determinist.

Soft determinism is a form of compatibilism. So,
Lewis is obliged to respond to van Inwagens
argument for incompatibilism.
H historical proposition about the state of the
world before my birth
L conjunction of the laws of nature
P the proposition that I lowered my hand at t
1. If determinism is true, then (H L) ? P
2. If I could have raised my hand at t, then I
could have rendered P false.
3. If I could have rendered P false, then, if (H
L) ? P, I could have rendered (H L) false.
4. I could not have rendered H false.
5. If I could have raised my hand at t, then I
could have rendered L false.
6. I could not have rendered L false.
If determinism is true, I could not have raised
my hand at t.

Lewis is willing to accept van Inwagens
definition of determinism.
Lewis thinks the problem with the argument has to
do with whether it is ever the case that someone
can render a law of nature false.
Can I render a law of nature false?
Recall that for van Inwagen, I could have
rendered L false means
there was some action a within my power such
that
(I did a the past remains the same) ? not-L

Premise 6 of van Inwagens argument is I could
not have rendered L false.
L a conjunction of all the laws of nature)
I could not have rendered L false
there was no action a within my power such that
(I did a the past (prior to the time of a)
remains the same) ? not-L
Lewis On this definition, Premise 6 simply says
that I could not have arranged things in any way
such that I was predetermined not to arrange
things in that way. It is uninstructive to learn
that the soft determinist is committed to denying
Premise 6 thus understood.(fn.5, p.127)
Let H a proposition expressing everything about
the past before the time of a
I could not have rendered L false
there was no action a within my power such that
(I did a H) ? not-L
L ? not-(I did a H)
(L H) ? not-I did a ...I was
predetermined not to arrange things in that
way....

The soft determinist (compatibilism
determinism) thinks that for many actions that I
was predetermined to perform, I could have done
otherwise, i.e. when I performed those actions I
had it in my power to do something else. In
other words, there are actions that I was
predetermined not to perform that I could have
performed.
Premise 6, using van Inwagens definition of
could have done otherwise, simply says that for
any action I was predetermined not to perform, I
could not have performed that action, i.e. it was
not within my power to perform that action.
So, using van Inwagens definition of could have
rendered false, Premise 6 of his argument
amounts to a simple denial of soft determinism.
Lewis It is uninstructive to learn that the
soft determinist is committed to denying Premise
6 thus understood.(fn.5, 127)
Lewis goes on to see if there is some other sense
of could have rendered false that will serve
for this argument.

Distinguish two different senses of s could have
rendered P false
Weak sense
s could have rendered P false
s was able to perform some action a such that
if s did a then P would have been falsified
Strong sense
s could have rendered P false
s was able to perform some action a such that
ss doing a, or something caused by ss doing a,
would have falsified P

L nothing ever travels faster than the speed of
light
Weak
I could have rendered L false
I was able to perform an action a such that if I
did a then L would have been false.
Strong
I could have rendered L false
I was able to perform an action a which itself
would have falsified L, or which would have
caused an event that would have falsified L.

Suppose I am able to move my arm faster than the
speed of light.
Then I am able to perform an action a which is
such that my doing a falsifies L.
L nothing ever travels faster than the speed of
light
a me moving my hand faster than the speed of
light
If I am able to do a then I am able to render L
false in the strong sense.
Suppose I am able to flick a pebble so hard that
the pebble flies off faster than the speed of
light. Then I am able to cause an event that
falsifies L.
f me flicking a pebble, thereby causing it to
fly faster than the speed of light
If I am able to do f, then I am able in the
strong sense to render L false. I can do
something that will cause an event that falsifies
the law.

As a soft determinist, Lewis denies that we are
ever able to render laws false in the strong
sense.
So, he accepts Premise 6 when understood in the
strong sense
Premise 6 I could not have rendered L false.
There was no action a which I could have
performed which itself would have falsified L or
which would have caused an event that would have
falsified L.
But, as a soft determinist, he rejects Premise 5
when understood in the strong sense
Premise 5 If I could have raised my hand at t,
then I could have rendered L false.
If I could have raised my hand at t, then I
could have performed some action that would
itself have falsified L or would have caused some
event that would have falsified L.
So, raising my hand at t must not be or cause an
event that falsifies L.

How about the weak sense of could have rendered
false?
Lewis denies Premise 6 when understood in the
weak sense.
Premise 6 I could not have rendered L false.
There was no action a that I was able to perform
such that if I did a then L would have been
false.
At t I lowered my arm, and the proposition that I
lowered my arm was logically entailed by H L.
But, according to Lewis, at t there was an action
I was able to perform which is such that if I did
it, then L would have been false.

41
I lower my hand

actual course of events

t
possible alternative course of events
I raise my hand
event that falsifies a law of nature
divergence miracle
t
42

Lewis accepts Premise 5 when understood in the
weak sense.
Premise 5 If I could have raised my hand at t,
then I could have rendered L false.
If I could have raised my hand at t, then there
was an action I was able to perform which is such
that if I performed it then L would have been
false.
If there is a possible course of events in which
I raised my hand at t, then there is a possible
course of events in which I was able to perform
an action which is such that if I performed it
then L would have been false.
The soft determinist thinks this is true. For
any given action you perform, even if it is
predetermined by history and laws, there are
possible courses of events in which you do
something else.

43
Lewis accept or reject?

Premise 5
Premise 6

strong
REJECT
ACCEPT
weak
strong
ACCEPT
weak
REJECT
44

Objection this is not a kind of free will worth
having.
Suppose a wall fell over at t, and this was
predetermined to happen by history and the laws
of nature.

wall falls over
actual course of events
t
There is possible alternative course of events in
which a divergence miracle occurs prior to t
and in which the wall doesnt fall over at t.
possible alternative course of events
wall doesnt fall over
t
divergence miracle
45

The objection is that, on Lewis account, the
sense in which for any given action I could have
raised my hand is no different than the sense in
which the wall could have remained standing.
To put it another way, for Lewis
I could have done otherwise
amounts to
There is a possible alternative course of events
in which I was predetermined to do something
other than what I was actually predetermined to
do.
And you might think that genuine freedom requires
something stronger than this.
NEXT WEEK an argument for compatibilism, P.F.
Strawson, Freedom and Resentment