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Counterfactuals and Dispositions
Counterfactual Conditionals
The Material Conditional
• When we discussed formal logic, we considered the material conditional, p → q. The material
conditional is just a simple truth-function. Its truth value is entirely determined by the truthvalues of its component sentences, as shown in the following truth-table.
p
T
T
F
F
q
T
F
T
F
p→q
T
F
T
T
• As we noted at the time, while this allows us to give a purely formal logic, it gives some pretty
counter-intuitive results if we treat it as a translation of the English ‘if ..., then ...’.
• These counter-intuitive results are together known as the paradoxes of material implication.
– Note that, whenever ‘p’ is false, ‘p → q’ is true. But that means that, if ‘→’ gives a good
translation of ‘if..., then ...’, then the following claims would be true:
1. If Margaret Thatcher is still alive, then she’s hiding in my basement.
2. If Margaret Thatcher is still alive, then Margaret Thatcher is not still alive.
· Given the definition of ‘→’, ‘p → ¬p’ is true if ‘p’ is false.
– Also, whenever ‘q’ is true, ‘p → q’ is true. But that means that, if ‘→’ gives a good
translation of ‘if..., then...’, then the following claims would be true:
3. If you don’t eat your vegetables, then Margaret Thatcher will die next week.
(said last week)
4. If the moon landing was faked, then Margaret Thatcher will die next week.
(said last week)
• Conclusion: the meaning of ‘if p, then q’ is not captured by the material conditional ‘p → q’.
Indicative and Subjunctive Conditionals
• When we have a sentence of English of the form
If p, then q.
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containing two sentences p and q in the indicative mood (eg, is, was, will be), call that an
indicative conditional.
• When we have a sentence of English of the form
If it were the case that p, then it would be the case that q.
call that a subjunctive conditional.
• Interestingly, indicative conditionals behave differently than subjunctive conditionals. For
instance,
5. If Shakespeare didn’t write Hamlet, then somebody else did.
6. If Shakespeare hadn’t written Hamlet, then somebody else would have.
• The indicative conditional 5 is talking about the actual world; whereas the subjunctive conditional 6 is talking about a non-actual, merely possible world.
• If the antecedent of a subjunctive conditional is false, then it is called a counterfactual conditional.
Counterfactuals in Science
– Some examples of counterfactual conditionals taken from some random science textbooks:
“If the measurement of En had not taken place, what would the probability
density for finding the particle at x = L/2 have been?” (Risenborough, Quantum Mechanics I)
“...a purely monetary change would not have real effects. All nominal quantities
(such as prices and wages stated in nominal terms) would move in proportion
to the change in money, and no real quantity would be affected.” (Romer,
Advanced Macroeconomics)
“If the charge on the proton differed from that on the electron by, say, one part
in a billion, then each hydrogen molecule would carry a charge of 2 · 10−9 e,
and the departure of the whole mass of hydrogen would alter the charge of the
tank by 1016 e, a gigantic effect.” (Purcell and Morin, Electricity and Magnetism)
– More mundane examples:
If this match were struck, then it would light.
If this salt were placed in water, then it would dissolve.
• Counterfactuals like these create a puzzle for the philosophy of science. What is it that makes
claims like these true or false? What does the world have to be like for these claims to be
correct?
– Since these are counterfactuals, their antecedents don’t actually obtain. How, then, could
there be facts about what would have happened, if their antecedents had actually obtained?
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Dispositions
• Science is also litter with claims about object’s or system’s dispositions. Here’s a sampling:
“The energy decreases with x and y, so the equilibrium is unstable.” (Purcell and
Morin)
“The larger the [intertemporal elasticity of substitution in labor supply], the more
responsive the labor supply is to technology and capital.” (Romer)
• To say that an equilibrium is unstable is not to say that the system every actually moves away
from equilibrium. It is rather just to say that it is disposed to move away from equilibrium, if
it is pushed away by any outside forces.
• To say that the labor supply is responsive to technology and capital is not to say that it actually
responds to technology and capital. It is rather to say that it is disposed to respond in a certain
way, if technology and capital change.
• More mundane examples:
This match is flammable.
This salt is water-soluble.
• Claims like these—claims about object’s dispositions—create a puzzle for the philosophy of
science. What is it that makes claims like these true or false?
– Since the system needn’t ever actually depart from its equilibrium, what makes it the case
that the equilibrium was unstable? Since the match wasn’t actually struck, what makes it
the case that it was flammable?
Goodman’s (Attempted) Account of Counterfactual Conditionals
• Some notation: write the counterfactual conditional ‘If ‘p’ were true, then ‘q’ would be true’ as
‘p € q’.
• Goodman considers the following counterfactual conditional:
If the match were struck, then it would have lit.
A€C
(where A = The match is struck and C = The match lights.)
• It doesn’t follow as a matter of logic alone that a struck match lights. Rather, it seems to have
something to do with the laws at our world.
– However, it’s not a consequence of the laws at our world that anytime a match is struck,
it lights (’cause the wind could be too strong, the match could be damp, etc). So we can’t
say that ‘A € C’ is true just in case A and the laws of nature deductively entail that C.
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– Goodman: Yes, but it’s true that it wasn’t too windy, and it’s true that the match wasn’t
damp, etc. Gather together all of these relevant ancillary conditions—call them ‘S ’. Then, it
should follow deductively from the laws of nature L, these relevant ancillary conditions
S , and the claim that the match is struck A that the match lights C.
• This gives us the following account of counterfactual conditionals.
– A counterfactual conditional A € C is true if and only if there is a set of relevant ancillary conditions S such that the conditions in S actually obtain and it is a consequence
of the laws of nature that, if A and S obtain, then C obtains.
∗ If we suppose that it’s a law of nature that whenever a match is struck and the match
is dry and it’s not too windy, ..., then the match lights, then this account tells us that
it’s true that, if the match were struck, it would have lit. That’s because A = the
match is struck and S = the match is dry and it’s not too windy, and ... lead by law to
C = the match lights, and the conditions in S actually obtain.
• Goodman: what can be included in the relevant ancillary conditions?
– Suppose that we say that anything can be included in the relevant ancillary conditions.
Then, we could reason as follows:
∗ Let A = the match is struck and let S ′ = it’s not too windy, and ..., and the match doesn’t
light (S ′ doesn’t include the condition that the match is dry, but does include the
condition that the match doesn’t light). Then, it’s true that A and S ′ lead by law to
the claim that the match isn’t dry. However, the counterfactual conditional
If the match were struck, then it wouldn’t have been dry.
is false, not true.
– So we can’t include just anything in the relevant ancillary conditions. We must hold
some things fixed, and not hold other things fixed, when we evaluate the counterfactual
conditions.
– The most that Goodman can come up with this: A and S must be cotenable.
∗ A and S are cotenable if it is not the case that, if A were true, then S would not be
true.
A and S are cotenable ↔ ¬(A € ¬S )
– But this definition includes a counterfactual conditional. So we haven’t given a noncircular account of the counterfactual conditional. We still don’t know what it takes for
counterfactual conditionals to be true in non-counterfactual terms.
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C.B. Martin and Finkish Dispositions
• Hypothesis: there’s a relationship between claims about dispositions and counterfactual conditionals.
Dispositions
The match is flammable / The match is disposed to light if struck
The salt is water soluble / the salt is disposed to dissolve if placed in water
Counterfactuals
The match would light if struck
The salt would dissolve if placed in water
• The hypothesized relationship is this:
x is disposed to r in conditions c
↔
if conditions c were realized, then x would r
• Martin argues that this can’t be right, since the counterfactual claim could true even while
the dispositional claim is false.
• He gives the following example: consider the dispositional property of a wire’s being live.
Suppose that what it is for a wire to be live is for it to be disposed to transfer electricity into
a conductor if the conductor touches it. (Take this as a stipulative definition of what Martin
means by live.)
– Suppose that we’ve got a device called an electrofink. An electrofink has the ability to
detect whether the wire is about to be touched by a conductor. If it is about to be
touched by a conductor, then the electrofink makes the wire live before it gets touched.
– Imagine that we’ve got a dead wire hooked up to an electrofink. Then, the counterfactual ‘if the wire were touched by a conductor, then electrical current would flow from the wire
to the conductor’. However, it is false that ‘the wire is live’.
– So, the hypothesized relationship between dispositions and counterfactuals turns out to
be false. The wire doesn’t have the disposition, even though the counterfactual claim is
true.
• So the truth of the counterfactual claim isn’t sufficient for the truth of the dispositional claim.
• Neither is the truth of the counterfactual necessary for the truth of the dispositional claim.
– For we could have a reverse elecrtro-fink. The reverse electro-fink makes the wire dead
if it is touched by a conductor. Then, it could be true that the wire is live but false that
if it were touched with a conductor, then electric current would flow from the wire to
the conductor.
• So the truth of the corresponding counterfactual is neither necessary nor sufficient for the
truth of the dispositional claim.
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