Philosophical Review
Possibility
Author(s): Ian Hacking
Source: The Philosophical Review, Vol. 76, No. 2 (Apr., 1967), pp. 143-168
Published by: Duke University Press on behalf of Philosophical Review
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POSSIBILITY
POSSIBILITY is in disreputeboth because it seems indefinable and because there seem to be no criteria for telling
when two apparently different possibilities are really the same.
This paper aims at defining one kind of possibility and at stating
principles of individuation for possibilities of that kind. The
inquiry will be conducted more in terms of the adjective "possible" than in terms of the noun "possibility."
Sections I and II state two traditional accounts of possibility
while III through VI give reasons for accepting something like
what Peirce called a nominalistic, and Moore called an epistemic,
analysis of the concept. Sections VII through XVI provide the
grammatical analysis essential to stating and defending a definition of "possible"; XVII treats of "possibility." Sections XVIII
through XX provide criteria of identity for possible things. Section XXI concludes with the modal logic of our kind of possibility.
I. LOGICALPOSSIBILITY
First we shall have to distinguish some historically famous
ideas of possibility from the account given below. Logicians
have often classified states of affairs as follows. Some states of
affairs, like those demonstrated to obtain in mathematics, obtain
of logical necessity; others are logically impossible; anything not
logically impossible is logically possible; anything logically possible and not logically necessary is contingent. Sometimes the
modifiers "logical" and "logically" are omitted, and often the
categories are applied to propositions rather than to states of
affairs. Logical possibility may be further subdivided. Some
logically possible states of affairs are causally possible-that is,
compatible with the regulative laws of the universe. Among the
causally possible, some are technically possible-that
achieved by the means at our disposal.
'43
is, can be
IAN HACKING
These elegant divisions are accompanied by Leibniz' attractive
picture of possible worlds. What is necessary obtains in every
possible world, while the logically impossible is found in none;
the logically possible holds in some possible world. It is well
known how this family of notions moves in a rather tight circle.
Russell observes in his study, The Philosophy of Leibniz, that "it
would seem that necessity is ultimate and indefinable. We may
say, if we choose, that a necessary proposition is one whose
contradictoryis impossible; but the impossible can only be defined
by the necessary, so this account would give no information as
to necessity" (p. 23). This does not prove that the concept of
necessity is idle, for it can be indicated by examples and circumscribed by axioms. But more recent criticism, which begins
with Quine's essays in From a Logical Point of View, shows that
there is nothing inescapable about this whole family of ideas.
II. RUSSELL'sKIND
OF POSSIBILITY
One of Aristotle's groups of distinctions relies on the contrast
between events of a sort that always happen, ones that usually
happen, ones that sometimeshappen, and ones that never happen.
Translations from the Greek sometimes express these categories
as the necessary, the probable, the possible, and the impossible,
although the same English words have been applied to other
Aristotelian concepts, and Aristotle at least once seems to reserve
necessity for what is not only universal but also essential.
Whatever Aristotle's doctrines may have been, Russell on
several occasions equated necessity with that which always happens. To begin with, he was offended by the sort of definition
Peirce wrote for Baldwin's Dictionary: "That is necessary which
not only is true, but would be true under all circumstances."
In The Principles of Mathematics,where he says that the theory of
necessity urged by Kant "appears radically vicious," Russell
assertsthat "there seems to be no true proposition of which there
is any sense in saying that it might have been false" (p. 454).
So on Peirce's definition, truth and necessity would coincide.
Russell's essay, "On the Notion of Cause," found in Mysticism
'44
POSSIBILITr
and Logic, begins by trouncing Peirce. Then follows a crisp definition of Russell's: the word necessary,he writes, shall be "a predicate of a propositional function, meaning that it is true for all
possible values of its argument or arguments." Hence the function, "x never encountered Pegasus," is necessary, since it is true
that (x) (x never encountered Pegasus).
A derived notion applies to propositions themselves. "A proposition is necessary with respect to a given constituent if it
remains true when that constituent is altered in any way compatible with the proposition remaining significant." In other
words, necessarypropositionsresult from substituting the relevant
constituent in a necessary propositional function. Relative to the
constituent Plato, the proposition that Plato never encountered
Pegasusis necessary,but the very same propositionis not necessary
with regard to the constituent Pegasus.
It seems right to define Russellian possibility, with respect to
a constituent, by saying that a possible proposition is one whose
negation is not necessary. Evidently this idea differs from that
of Leibniz. Russell's is relative to a constituent, but Leibniz' is
not. What is possible for Leibniz need not be possible for Russell.
The proposition that Plato encountered a flying horse, though
logically possible, is (with regard to the constituent Plato) not
possible in the sense I have drawn from Russell's analysis.
III.
POSSIBLEAND MAY
Another conception of possibility is voiced a good deal more
often than those of Russell and Leibniz. It is closely connected
with the auxiliary "may." If something is possible, in the sense
I have in mind, then it may be the case. That is a necessary,
though perhaps not a sufficient, condition for something to be
possible.
Evidently not all logical possibilities are possible. It is not
possible that there are two hundred armchairs in my room as
I write these notes, for I am sitting here in these cramped quarters
and can see perfectly well that there are only three or four chairs
altogether. It would be absurd to say to someone, as if I meant
'45
IAN HACKING
it, that there may be two hundred chairs in this room: not only
absurd, but also false. It would be equally silly to say that it is
possible that there are two hundred-or even a dozen-armchairs
in my room as I write these words. We have a logically possible
state of affairs that is not possible.
It looks as if "might have been" is a necessary condition for
"logically possible." It is logically possible that there should have
been a dozen chairs in this room as I write these words only if
there might have been a dozen chairs in this room as I write
these words. Traditionally, an untrue proposition is logically
possible only if it might have been true. We have just seen how
Russell agreed to this conditional, for he rejected the twin ideas
of logical possibility and necessity partly because he thought that
"there seems to be no true proposition of which there is any sense
in saying that it might have been false," and, hence, no false
one of which it makes sense to say that it might have been true.
This historical connection of logical possibility and "might have
been" is enough in itself to show that there is a conception of
possibility less expansive than that of logical possibility. Plainly,
"may" is no synonym for "might have been," and, plainly, there
is some sense of the word "possible" associated with the word
"may." Some readers will prefer this line of proof to my unduly
Moore-like assertion that it is not possible that there are a dozen
armchairs in my room as I write these words. We have even
better proofs at hand. The next one is due to Moore himself.
IV. MOORE'sGRAMMATICALCRITERION
Book Moore
Under the heading "possible" in his Commonplace
observed that if, at the time he was writing, he had said, "It's
possible that Hitler is now dead" or "Hitler may be dead," some
listener might have contradicted him by retorting, "I know
Hitler isn't dead." Yet this would be no contradiction of the
belief that Hitler's being dead is logically possible. If I know that
Byp, I cannot truly say that it is possible that p; nor, it seems,
will what I say be true if a communicative colleague knows that
,p.
146
POSSIBILITr
This fact about "possible" helps distinguish the logically possible from the possible. Since the indicative mood is seldom used
for what is known to be false, in speaking of logically or causally
possible states of affairsthat are known not to obtain, one is driven
to use the subjunctive. Adapting an example of Moore's, it is
logically and perhaps causally possible that I should have been
blind by now, but it is not possible that I am blind now, though
it is possible that I shall be blind tomorrow. Usually in stating
that a simple state of affairsis possible, we can use the indicative,
while in stating what is only logically or causally possible, we
have to employ the subjunctive.
Persistent philosophical worrying at the concept of logical
possibility has tended to distort this pattern. There is a passage
where Schlick's translatorsproduce the sentence, "It is logically
possible that rivers run uphill" even though they are translating
a German sentence in the subjunctive mood, whose force is, "It
is logically possible that rivers should run uphill." The use of
the indicative in the translation will have grated on some readers,
but not on all. I think, however, that there remains enough use
of the subjunctive/indicativedistinction even among philosophers
for the indicative to be a tentative marker of what is possible
and not only logically possible.
Though the indicative may indicate what is possible, the converse does not hold: use of the subjunctive need not show that
a mere logical possibility is in question. There are two reasons.
The first is trivial: the subjunctive is the mood not only of the
contrary to fact, but also of the doubted and the uncommitted;
if you very much doubt that p you will most often use the subjuctive when you admit that it is possible that p. The second
reason is more substantial. Take any possibility expressed by a
q." When
compound sentence, say of the logical form "p and
it is known that p is false, we can say, "It is possible that p and
lq," using the subjunctive throughout but not implying that
"p and '.' q" is a mere logical possibility. For example, take the
two sentences, "It is possible that the ballot boxes should have
been rifled without anyone knowing it," and "It is possible that
the ballot boxes were rifled without anyone knowing." Though
one of these uses the subjunctive, both acknowledge a real pos'47
IAN HACKING
sibility. But they mark out differentpossibilities.The first sentence
can be used to attack electoral procedureswithout implying that
there are crooks in parliament, while the second would be a
tentative smear on the whole election.
V.
EPISTEMIC POSSIBILITY
The two grammatical markers, may/might-have-been and indicative/subjunctive, show that there is some sense of the word
"possible" in which it does not mean logically possible or even
causally possible. But how is the sense to be defined? Moore
names this sense epistemic possibility. The very name suggests
the following analysis: it is epistemically possible that p within
a certain community of speakers if and only if no one in the
community knows that it is false that p. So much would tally
with the few facts we have ascertained, but plainly the conjectured analysis is mistaken. Something can fail to be possible
-in
the very sense Moore seems to have in mind-even
though
no one knows it is false.
Imagine a salvage crew searching for a ship that sank a long
time ago. The mate of the salvage ship works from an old log,
makes some mistakes in his calculations, and concludes that the
wreck may be in a certain bay. It is possible, he says, that the
hulk is in these waters. No one knows anything to the contrary.
But in fact, as it turns out later, it simply was not possible for
the vessel to be in that bay; more careful examination of the log
shows that the boat must have gone down at least thirty miles
further south. The mate said something false when he said, "It
is possible that we shall find the treasure here," but the falsehood
did not arise from what anyone actually knew at the time.
At most it seemed possible to the salvage crew that the wreck
was in the bay. When one starts collecting examples like this, it
begins to look as if, whenever it turns out to be false that p' we
say, of an earlier era, that in those times it may have seemed
possible that p, but it was not really possible at all. But such a
conjecture would be too strong. Consider a person who buys
a lottery ticket. At the time he buys his ticket we shall say it is
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POSSIBILITY
possible that he will win, though probably he will not. As expected, he loses. But retrospectivelyit would be absurd to report
that it only seemedpossible that the man would win. It was
perfectly possible that he would win. To see this clearly, consider
a slightly different case, in which the lottery is not above board;
it is rigged so that only the proprietors can win. Thus, however
it may have seemed to the gullible customer, it really was not
possible that he should win. It only seemed so. "Seemed possible"
and "was possible" both have work cut out for them.
VI. A
WORKING HYPOTHESIS
Why was the mate speaking falsely when he said, "It is possible
that the hulk is here"? Because one could have found out from
the data that the wreck took place a good deal further south.
He could positively have proved that the ship was not in his bay.
Likewise in the case of the crooked lottery. Some feasible investigations-not necessarily as easy as recomputing from a ship's
log-would have revealed the dishonesty, or so we like to believe.
Some practicable inquiries or espionage would have ended by
proving that the innocent bystander could not win the rigged
sweepstake. But if the sweepstakeis fair, no practicable tests (short
of waiting to see who actually wins) could ever disprove that the
ticket holder would win, even though these same tests would
show that any gain is very unlikely.
We now suggest a working hypothesis: a state of affairs is
possible if it is not known not to obtain, and no practicable
investigations would establish that it does not obtain.
Notice the force of the "practicable" here. We do not claim
that no conceivable test would disprove our proposition. If
determinism is true, and a Laplacian demon is conceivable, then
some conceivable investigation would show before the draw
exactly which ticket number would win. But no humanly practicable investigation could do that under the conditions of a fair
draw.
VII. ON
GRAMMAR
I shall urge that aside from technical senses of logical or causal
possibility, the word "possible" is not ambiguous; that is, no
'49
IAN HACKING
sentence with a determinate grammatical structure has several
meanings in virtue of different meanings of our word. It does
not follow that we shall be able to give a single account of the
meaning. We may need different accounts for different constructions. Consider the sentence
(i)
It is possible that I shall go
and its seeming transform
(2)
It is possible for me to go.
If these sentences attribute possibility to the same thing-namely,
my departure-you would expect the two sentences to mean the
same. But they do not. (2) can be true while (i) is false, an
observation that is reinforced by noting that whereas the sentence
(3) It is possible for me to go, but I won't
is entirely straightforward,there is nothing straightforwardabout
"It is possible that I shall go, but I won't." The latter displays
one of Moore's paradoxes, but (3) doesn't. (i) entails (2), but
not vice versa, which is a fact to be explained by any theory on
the meaning of "possible."
On first looking into the grammar of possibility one sees a good
many different constructions. Not only may "possible" occur
before "that" and "for" clauses, but also the word is found as
a complement, before infinitives, and before a wide range of noun
phrases. Yet I shall divide occurrences of our word into exactly
two classes. "Possible that" constructions are typical of the first,
and "possible for" of the second. Sentences of the former class
have been much studied by logicians, and sentences in the latter
class have provided subject matter for moralists. Since it will turn
out that this is no accident, I shall call my two classes L and M
after the two philosophical professions, and shall speak of
L- and M-occurrences of the word "possible." One account of
the meaning of "possible" will be geared to L-occurrences; a
related account will fit M-occurrences. By occurrences, I mean
only those places where the word is used and not mentioned.
The moralist thinks about things to do and to choose, and so
he has to reflect on sentences like "It is possible for me to go,"
"It is possible to go," even sentences like "This is a possible title
I50
POSSIBILITY
for your book" and phrases like "with all possible energy."
also has, by default, "It is possible for a kettle to come to
boil in three minutes flat." Writing as a logician I shall
little about the moralist's class of sentences, but even if we
only to put it aside, we must define the class rigorously.
VIII.
Two
He
the
say
are
CLASSESOF OCCURRENCE
In many sentences "probable" can replace "possible" without
destroying sentencehood. In this category we find "It is possible
that he will go," "His defeat is possible," and "He is a possible
winner." Occasionally, good sense (not grammar) inclines us to
insert not "probable" for "possible," but "the probable" for "a
possible." In other sentences "probable" will not go at all. As
examples, take "It is possible for him to go," "It is possible to
lose," "That is a possible course of action for you to take," and
"We shall come with all possible speed." The word "permissible"
does fit into each of the latter four sentences. Our rough line of
distinction is, then, that L-occurrences of "possible" are ones
where "probable" may be substituted for "possible," and Moccurrences are ones where "probable" does not go but "permissible" does. Evidently the latter class will include sentences
about what it is possible to do or to choose. It is pleasant that
the very words we use to effect our formal distinction are intimately related to our earlier hunch: it is no accident that "probable," which marks out the L-class, is a logician's word, while
"permissible," which can define the M-class, is a tool of the
moralist.
IX. GRAMMATICALAMBIGUITY
Unfortunately mere substitution in sentences is not enough to
define our two classes of occurrence, for some sentences employing
"possible" are grammatically ambiguous. Take the sentence
(4) I know a possible spy for Anne to take to the party.
This can be parsed in two ways. Parsed in one way we get a
sentence that means
I5'
IAN HACKING
(5) I know a spy whom it is possible for Anne to take to
the party.
But (4) can also mean, when parsed differently, that I know
someone, who may be a spy, whom Anne might bring, namely,
(6) I know a person, who is a possible spy, and who is a
person for Anne to take to the party.
"Probable" goes into (6) but not (5). Replacing "possible" in (4)
by "probable" gives a sentence of determinate structure-a sentence that transforms into a sentence like (6) but not into one
like (5). Now it is easy to construct conversations where (4) is
unambiguous: the discourse determines uniquely which sense we
attach to the sentence. Then in asking whether we have an
L-occurrence of "possible" in this discourse, we must ask whether
replacing "possible" by "probable" would alter the structure of
(4) as uniquely determined by this discourse. If not, then we have
an L-occurrence; otherwise, an M-occurrence. Where (4) is uttered ambiguously we have neither a strict L-occurrence nor a
strict M-occurrence.
We shall want to refer to a particular utterance of a sentence
which, in the context of utterance, is entirely free of grammatical
ambiguity. I shall call such an utterance a uniquelyparsed utterance.
Grammarians are by no means agreed on how the different
grammatical structures of (4) should be represented. Perhaps
parsing is to be defined by classes of transformations; then to
decide whether a uniquely parsed utterance is L or M we must
ask whether "probable" does as well as "possible" in a relevant
set of transformations of (4). Perhaps we should define parsing
in terms of generation from kernel sentences; then we must check
both that "probable" fits the kernels and that generation remains
valid under this substitution. It is not fitting for me to pass
judgment on these or other alternatives.
It is instructive to see what happens to (4) as we whittle away
at the subordinate clause. We end up with
(7) I know a possible spy.
(7) does not look ambiguous until one thinks of its alternative
antecedents.
I52
POSSIBILITY
X.
FIRST DEFINITIONS
Definition: An occurrence of the word "possible" in a uniquely
parsed utterance is an L-occurrence if and only if the word
"probable" may be substituted for it without either destroying
the sentencehood or altering the parsing of the utterance.
Definition: An occurrence of the word "possible" in a uniquely
parsed utterance is an M-occurrence if and only if it is not an
L-occurrence.
Conjecture:Any M-occurrence of the word "possible" in a
uniquely parsed utterance may be replaced by the word "permissible" without either destroying the sentencehood or altering
the parsing of the utterance.
Now we can add our working hypothesis about the meaning
of "possible" to this sequence of definitions.
Definition: "It is possible that p," where there is an L-occurrence
of "possible," means that p is not known to be false, nor would
any practicable investigations establish that it is false.
Definition: A sentence of the form "N is possible," where there
is an L-occurrence of "possible," means that it is not known that
N is not a fact, nor would any practicable investigations establish
that N is not a fact.
The second definition takes for granted that where "probable"
can replace "possible" in "N is possible," "a fact" may also be
substituted with good grace. His defeat is possible: his defeat is
a fact. Evidently our two definitions could be telescoped into one.
For "a fact" can replace "possible" in "It is possible that." (At
most the mood of the main verb will have to be changed.)
Something that can significantly be called a fact is possible if
and only if it is not known not to be a fact, nor would practicable
investigations establish that it is not a fact.
Our definitions can be accused of circularity on the ground
that "practicable" must itself be explained in terms of possibility.
But the question is not whether the definitions are circular, but
whether, to echo Russell, they furnish any information as to
possibility. Evidently they do, for the definitions may very well
turn out to be mistaken. Moreover, we do not have a strict circle,
I53
IAN HACKING
for practicability must be explained in terms of what it is possible
to do, which involves an M-occurrence of our word; we are now
defining only L-occurrences. There is nothing novel in this piecemeal attempts to do L before M. For example, the reader may
have noticed that the word "possible" occurs in Russell's definition of "necessary" which I quoted in Section II above. Had
that been an L-occurrence of our word, his definition of "necessary" would have been flagrantly circular. But it is only an
M-occurrence, and Russell's definition is innocent.
XI.
NOUNS CONTRACTED BY "POSSIBLE"
The word "possible" can modify nouns, as in the phrase
"possible winner." But it can modify nouns in two distinct ways,
and this difference leads us to a pair of complementary definitions
of "possible" as a prenominal adjective. To begin with, we say
that any prenominal adjective A contracts the noun N that it
modifies if the class of things that can truly be called AN is
necessarily contained in the class of things that can truly be called
N. So "red" contracts "barn" but not "herring." Aside from
idioms most adjectives contract the nouns they modify, but there
are exceptions. "Imitation" dislocates "pearl," for no imitation
pearls are pearls. "Alleged" creates an overlap. Not all alleged
criminals are criminals, nor are all criminals alleged to be criminals.
In front of most nouns "possible" is like "alleged": not all
possible winners are winners. Despite this, there are a few philosophically significant nouns which are contracted by "possible."
I have in mind things like the philosopher's word "proposition,"
and also "hypothesis," "theory," even "story." Outside philosophy, when one speaks of a possible hypothesis, one has in mind
a hypothesis that it is possible to hold, entertain, test, work with,
and so forth. That is an M-occurrence. But in philosophy "possible proposition" is an L-occurrence (it vies with "probable
proposition" on the scale of modes). Moreover, "possible" contracts "proposition" since in philosophy all possible propositions
are propositions, but not vice versa. The same sort of thing goes
for "hypothesis," "theory," and the like.
I54
POSSIBILITY
It is to be expected that "possible" modifies the nouns it
contracts differently from the way it modifies the other nouns
it can stand in front of. We record this in the following pair of
definitions.
Definition: In a uniquely parsed utterance where "possible" has
an L-occurrence as a prenominal adjective modifying the noun
phrase N, and where it contracts N, something is a possible N
if and only if it possible that the thing is a, or the, true or correct N.
Definition: In a uniquely parsed utterance where "possible" has
an L-occurrence as a prenominal adjective modifying the noun
phrase N, and where the word does not contract N, something
is a possible N if and only if it is possible that it is or will be
an, or the, N.
XII. WHY DOES POSSIBLEMODIFY So FEW NOUNS?
This question illustrates a fault in my last definition. We can
have possible winners, possible defects in a machine; a man can
be a possible spy and a warm day a possible sign of spring. There
are possible consequences of my actions and possible cases of
diphtheria. But "possible man," "possible cat," and "possible
road" are absurd unless as M-occurrences (a possible man for
the job, a possible cat to use in our experiments, or a possible
road to take to Vanderhoof). Why does our word "possible"
L-occur before so few nouns?
It is true that some philosophers are sufficiently schooled that
they admit "possible"in front of any noun whatsoever. Of a speck
on the horizon they will have us say, "That is a possible spire";
of a pile of wood and a pot of glue, "That is a possible table."
For most philosophers like this, possible men, goats, and Chevrolets hold out no terrors. For a few, of whom Quine is the most
notable, the terrorsare rightlyjudged to be great, but the absurd
"possible man" is thought no worse (it seems) than "possible
winner," and the whole of possibility is popped.
In English the philosopher's dialect is not rampant. Moreover,
even if one were to concede sense to "possible man," "probable
man" is crazy, so "possible man" is no L-occurrence. Relatively
'55
IAN HACKING
few nouns admit of prenominal, L-occurrence modification by
"possible." The explanation of this fact, though requiring many
distinctions, is of some elegance. And though it is essentially
grammatical, the explanation is relevant to philosophy, for a good
deal of potent metaphysics has been tied to the very facts that
furnish it.
XIII.
THREE CONJECTURES AND SOME METAPHYSICS
Speaking purely from a syntactic point of view, one expects
to find at least one "possible for" sentence corresponding to each
sentence in which the word "possible" is used. Here are a couple
of examples. The reader can add to them at will:
A decrease in unemployment is a possible result of the next
tax cut- It is possible for the next tax cut to result in
decreased unemployment.
It is possible
That is a possible site (for the new building)(for us) to choose that as the site of the new building.
ConjectureI: Every use of the word "possible" in an utterance
has associated with it at least one noun phrase and a verb phrase
(perhaps unuttered) that can serve as the subject and predicate
of a corresponding "possible for" construction.
Now we notice that winners win, spies spy or agree to spy,
results result, signs signify, and outcomes come out; consequences
ensue, states of affairs obtain, and cases of diphtheria occur. With
each noun is associated a verb, and the verb represents what
something has to do in order to be correctly described by the noun.
Now look at interpretation, origin, and translation. Something
is a winner if it wins, but something is not a translation if it
translates; rather, it is we who translate and so generate the
translation. Here the noun associated with the verb stands for
what we or someone or something else has to do in order for
there to be an application, an interpretation, a transformation.
This pattern, where the possible N' is not the subject of the
"possible for" construction, is not restricted to nominalizations.
Take "a possible origin of his mistake"; the verb "to originate"
is formed from the noun.
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POSSIBILITY
I shall say that verbs like "win," "result," and so forth parallel
the corresponding nouns. Where it is important to differentiate
between the two kinds of ways a verb can parallel a noun, one
could say the verb V directlyparallels the noun N if something
is an N if and only if it V. The verb indirectlyparallels the noun
if something is an N if and only if we, or someone else, or something else, V. In each case the mood of the verb is active, but
the tense is in some cases present, while in others is past or future.
When a noun is paralleled by a verb, noun phrases gotten by
qualifying the noun are generally paralleled by verb phrases
gotten by qualifying the verb. Thus a sign of spring signifies
spring; and there is a translation of Ovid if and only if someone
translates Ovid.
There is a special class of nouns for things to choose (which
I owe to H.-N. Castaneda). Something is the site of the new
chalet, the next mayor of the town, the time of the meeting, the
title of your next book, the location of the camp, if and only if
it is chosen or settled on as the site, next mayor, time, title, or
location. I shall extend the idea of indirect paralleling to these
cases; the verb phrase in each case comes from adding a phrase
to a verb like "choose"or "settle on" or "appoint to." Something
is the time of the meeting if and only if we, or someone else, or
something else, chooses (chose, will choose) it as the time of the
meeting.
II: Aside from noun phrases that are contracted by
Conjecture
"possible," the adjective L-occursas a prenominal adjective before
only those noun phrases which have as their principal noun a
noun that is paralleled by a verb.
III: When an L-occurrence of "possible" can preConjecture
nominally modify a noun phrase N which is not contracted by
"possible," the verb demanded by conjecture I is the verb which
parallels the noun phrase, and whose existence is asserted by
conjecture II.
If these conjectures are correct we have both defined the class
of entities which can prenominally be called possible, and explained why it does not make sense to talk of a possible man.
It makes sense to speak of a possible man (for [us to choose for]
the job); there we have an M-occurrence, and the verb for the
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IAN HACKING
"possible for" construction is evidently "choose." But it does not
make sense to talk of a possible man, with an L-occurrence of
"possible," because there is no verb covering what something
must do to be a man, or what must be done to make a man.
Our conjectures impinge on an ancient doctrine. There is a
metaphysical thesis to the effect that something is a possible
so-and-so if and only if it has the power, or potency, within itself
to become a so-and-so. Now presumably if something changes
through a power in itself, we ought to say so using a verb in
the active voice; if it changes only through being changed by
something else we must use the passive. Translating into a more
formal mode of speech, something is a possible N if and only
if there is an active verb form V such that the thing is an N
if and only if it V. This metaphysical thesis is the core of the
story we have been telling about L-occurrencesof "possible." The
metaphysical thesis is not peculiar to the English-speakingpeoples,
but nor are the grammaticalfacts about "possible." Less thorough
analysis than that of the present study indicates that similar
grammatical facts obtain in the languages of some other peoples
who have embraced doctrines of possibility. It is not fruitful to
speculate on whether the grammatical chicken preceded the
metaphysical egg.
XIV.
INDEFINITE DESCRIPTIONS
For the record we had better notice another L-occurrence of
"possible." Consider the sentence
(8) It is possible that a man of I20 should live to be I30.
This can be used to make two different statements. One is
existential: it is possible (though doubtful) that at least one man
of I20 should, sometime, live to be I30. The other statement
would express a regularity about men of I 20: for any typical man
of I20, it is possible that he should live to be I30. The situation
is the same with a sentence like "A hen's egg will boil soft in
three minutes." That can be used to assert that at least one hen's
egg will boil soft in three minutes, or else to state a regularity
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POSSIBILITr
about hens' eggs. In a study called "A Theory of Indefinite
Descriptions" I provide a general analysis of the class of sentences
which are systematically ambiguous in this way, and whose
ambiguity depends on the indefinite article. I state here without
proof that my definition of Section X for "possible that" constructions, plus a theory of indefinite descriptions, gives a plausible
analysis of (8).
One possible misconception must be stopped. It is notorious
that when "probable" replaces "possible" in (8) we get a statement which philosophers often construe in terms of frequency.
With similar motivation they might falsely urge that (8) means
that some men of I20 live to I30, or will live to I 30. As noted
in Section II, there is an Aristotelianprecedent for this translation.
But it is wrong. According to the GuinnessBookof Records,no man
of I 20 has ever lived to I30; one cannot assertwith any confidence
that any man of I20 ever will live to I30, still less that some
will. Yet one can confidently assert (8).
XV.
M-OCCURRENCES
I have learned a good deal from work by D. G. Brown on what
I call M-occurrences of the word "possible." Some of this will
appear in Brown's book, Action,and other publications. In the
present paper it is proper to say only that the central "possible
for" construction can probably be analyzed along the lines of
the preceding sections, but that there are fierce complications
owing to the elaborate network of moral concepts surrounding
what it is possible for an agent to do. Yet in the final analysis
there may be simplifications, since my theory on L-occurrences
may follow from a correct view of the fundamental construction,
"possible for."
XVI.
HAS "POSSIBLE" SEVERAL MEANINGS?
One should give two accounts of the meaning of "possible."
One of them applies to L-occurrencesof the word, and although
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IAN HACKING
the account is broken up for different constructions, each part
of the account can be defined in terms of our definition for
"possible that." A second account, which at present I attribute
to Brown, should fit "possible for." Even if the two can be
combined in a nontrivial way, I think that at this stage of inquiry
it is better to keep the two accounts distinct. Does this show that
"possible"has two meanings? To say so would be to suggest that,
after all grammatical ambiguities are removed, there could still
be ambiguities. That I deny. So I say, not that "possible" has
two meanings, but that one can give an account of the meaning
of the word in L-occurrences, and an account of its meaning in
M-occurrences. There are grammatical ambiguities of the sort
illustrated in Section IX, but none of what one might call semantical ambiguities, unless they hinge on a careless dropping of the
adverb "logically" or "causally" from the technical expressions
"logically possible" or "causally possible."
Many readers will disagree, and suspect that my definitions
ignore other meanings of the word. We can test this suspicion
by using Malcolm's essay, "The Verification Argument," now in
Knowledgeand Certainty.Malcolm distinguishes five meanings of
"possible," or at least five of what he sometimes calls different
meanings and more often calls different uses. Two of these relate
to logical possibility, but what of the other three? The last of
the five tallies with my definition. Do the other two represent
meanings of the word which I have ignored? I shall argue not:
they do represent legitimate uses of our word, but do not prove
that the word has meanings beyond my definition.
In Malcolm's use (iii), a man says it is possible that p in order
to convey the fact that there is some reason to expect p to be
true; in use (iv) to inform his listeners that there is no reason
to believe Up, and in use (v) to indicate that the grounds for
believing Up are not absolutely conclusive. Evidently (v) is close
enough to my definition to occasion no argument here.
It also looks as if "possible" could mean exactly what I say
it means, and yet be put to uses (iii) and (iv). Let us try this
on Malcolm's own example for use (iii). You and I are discussing
plans for the evening. A certain Mrs. Jones comes up for the first
time in this fatuous bit of conversation:
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POSSIBILITr
(Ha) It is possible that Mrs. Jones will pop in later on.
(T) Why do you say that?
(Hb) Well, it's perfectly possible, isn't? After all, we know
nothing to the contrary.
We can agree that if I say (Ha), I show that (in my opinion)
there is some reason to expect Mrs. Jones, that in saying (T)
you ask for such a reason, and that (Hb) is unsatisfactory, and
shows that I ought not to have said (Ha). But Malcolm and I
give different explanations of these agreed phenomena.
According to Malcolm, (Ha) means, "There is some reason
to expect Mrs. Jones to pop in." Then (T) asks for that reason,
and (Hb) shows that I have no reason. Hence (Ha) is unwarranted and probably false. That, Malcolm would say, is why
I ought not to have said (Ha).
But there is another explanation which does not demand a
special sense of "possible." Suppose the word means just what
my definition says. When I utter (Ha) you infer that there is
some point to my mentioning a possible visit, and hence think
I have some reason to expect a visit. Why else bring up the
possibility? With (T) you ask why I expect a visit, and learn
from (Hb) that I have no reason. Now (Hb) does not show (Ha)
false. It shows that (Ha) is probably true. It shows also that (Ha)
was irrelevant. That is why (Hb) is an unsatisfactory terminus
to the conversation.
Thus in my view the following two propositions are entirely
consistent. Aside from logical possibility, "possible" has a single
meaning in the "possible that" construction; and "possible" has
all the uses discovered by Malcolm, and a good many more
besides. His different uses do not prove difference in meaning.
Malcolm has another and more potent argument. We say, for
example, "very possible" and "barely possible." Malcolm supposes that these modifiersshow that in at least one sense the word
is susceptible of degrees; he links this to his use (iii) and concludes
that we have a new meaning of the word "possible" in which
"very possible" means "considerable reason to expect" and
"barely possible" means "slight reason to expect."
We brush aside the fact that some manuals of English rule "very
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IAN HACKING
possible" out of order. They are pedantic. But we cannot forget
that if Malcolm were right, and "possible" admits of degrees,
we ought to be able to say, for example, "His defeat is more
possible than his victory." That is no English sentence. Since we
cannot say "more possible," it seems to follow that there is no
sense in which "possible" admits of degrees.
What then of "very," "barely," and the rest? "Very" itself
does not prove existence of degrees: we say that father and son
were born on the very same day of the month; we do not thereby
imply that sameness of day admits of degrees. We say of a man
that he was barely top of his class, not meaning that being top
can come in low degree, but meaning that the man barely made
the top. Likewise, some imagined state of affairs can be barely
possible, not because it has a low degree of possibility (whatever
that would be) but because it only barely makes the grade of
being possible.
It is notable that the permissible modifiers of "possible that"
fit the matrix, "It is . . . the case that," with the exception of
"very," which transformsto "very much." The rest, like "hardly,"
"seldom," "barely," "always," seem to fit nicely. So I would use
that matrix in defining modifications of "possible that," and
conclude that "possible" does not have a sense in which it admits
of degrees.
XVII.
POSSIBILITY
In the matter of degrees, the noun "possibility" looks more
embarrassing than the adjective "possible." Though the noun is
not our chief topic, we had better face up to the difficulty.
Malcolm observes that we can speak of a strong possibility, and
can say that
(g) There is a slight possibility that the Smiths are in Paris
this week, but a greater possibility that they are in Rome.
(Some scrupulous speakers balk at saying [9], but many find it
natural enough.) Do these examples show that possibility admits
of degrees? I doubt it, but do not know for sure. For one thing,
despite (9), it is odd to say there is more possibility of one event
than another. Why, if possibility can admit of degrees?
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POSSIBILITY
Resemblances between "probability" and "possibility" confuse
the issue. Malcolm's examples suggest that the words have rather
similar grammaticalroles, or at least that "probability" can define
an L-class of "possibility" just as "probable" defines an L-class
of "possible." But whereas "possible" goes into all but a few
constructionswhere "probable" occurs, "possibility"fits few probability utterances. We can have a high probability, but what is
a high possibility? "In all probability" is common enough, but
"in all possibility" is never heard. We can ask, "What is the
probability of X?" but not "What is the possibilityof X?" "That
tale has some probability," or so we say, but never "That tale
has some possibility." Most of these disparities hinge on the fact
that probability admits of degrees while possibility does not.
What then of Malcolm's example (9), with great and little
possibilities? Perhaps it can be understood in the light of the
following observations. A terrible dog is not terribly doggy but
a dog that is terrible in the way dogs can be. Likewise, a terrible
possibility is not terribly possible but a possibility that is terrible
in the way possibilities can be. A well-supported possibility is one
which is well supported in the way possibilities can be (the
possibility that I shall come is well supported if there is good
evidence that I shall come). A strong dog is not a dog that is
strongly doggy but a dog that is strong in the way dogs can be.
So I wonder if a strong possibility is not something that is strongly
possible, but a possibility that is strong in the way that possibilities
can be-namely, well supported. Likewise for the great and slight
possibilities of (9). (The parsing of "bare possibility," on the
other hand, is like that of "mere possibility.")
If that speculation about "strong possibility" is not correct, we
shall have to admit that "strong possibility" is an idiom common
to some but not all English dialects, and meaning something like
"strong probability." If we make this admission, we must notice
that the evidence proves such usage is strictly idiomatic-that
is, that although some people say "strong" and "slight" in front
of "possibility," this usage does not infect other regularities about
"possibility." In particular, aside from those few idioms where
"possibility"has been gratuitously slurredinto "probability," the
word "possibility" is not used as if possibility admits of degrees.
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IAN HACKING
No one asks, "What is the possibility of that?" or says, "That
tale has some possibility."
Hence, aside from a few idioms, it seems that the definition
of "possibility" must go along the following lines. There are two
kinds of possibility. They correspond to L- and M-occurrences
of "possible." A possibility is either a possible state of affairs
(L-occurrence) or something that it is possible to do (M-occurrence).
XVIII.
IDENTITY
It requires some temerity to speak of possibilities and possible
winners after Quine's scathing questionsin the famous paper, "On
What There Is," now in his book, Froma LogicalPoint of View.
"Take the possible fat man in that doorway," he invites us, "and,
again, the possible bald man in that doorway.Are they the same
possible man, or two possible men ?" And so on. No use to protest
that in English it is odd to speak of a possible fat man, because
"fat man" is paralleled by no verb. Quine is challenging. If we
can speak of possibilitiesand use the construction "a possible At,"
we must give criteria for recognizing when apparently different
possibilities are the same, and for distinguishing among possible
N's. We shall firstexamine the case of possibilitiesthat are possible
states of affairs, and then include this treatment under a general
rule of possible N's.
Consider the possibility that a certain man will arrive late for
dinner, and the possibility that he will arrive in black tie and
dinner suit. These seem different possibilities. There are, as we
may say, two possibilities-that he should arrive late, and that
he should arrive in a dinner suit.
Next consider the possibility that I should meet the Canadian
Prime Minister in town this afternoon, and the possibility that
I should meet Mr. L. B. Pearson in town this afternoon. These
are surely one and the same possibility. Why? Because at the
time of writing it is not possible that I should meet Mr. Pearson
without meeting the Canadian Prime Minister, and vice versa
(a modest knowledge of constitutional law is involved in this blunt
assertion; it is possible that Pearson should die before this afterI64
POSSIBILITY
noon, but not possible another Prime Minister be appointed in
his place and sworn in by that time; it is possible that Pearson
should offer to resign before this afternoon, but not possible that
he should have resigned by this afternoon, for it is not possible
that his resignation should be accepted so soon).
We therefore propose the following criterion of identity for
possibilities that are possible states of affairs. Two possible states
of affairs are the same if it is not possible that one should obtain
without the other obtaining.
The criterion works well on the example of coming late, or
in a dinner suit. As so far described, the case is one in which it
is possible to come late and not in a dinner suit, so these
possibilities are distinct. But we could conceive of a case and a
man such that the man will be late if and only if he comes in
a dinner suit (tying a bow tie delays him inordinately). In that
event there would hardly be two distinct possibilities, but only
one, coming late, in a dinner suit.
XIX.
COUNTING POSSIBILITIES
Quine invited us not only to distinguish between possibilities
but also to count them. Before satisfying him, we must first warn
that possibilities can be contained in other possibilities. Thus the
possibility that I meet the Canadian Prime Minister is contained
in the possibility that I meet some Prime Minister or other. On
my criterion these possibilities differ. Yet just because one is contained in the other, we should hardly call these two possibilities.
We can count only disjoint possibilities.
Even when possibilities are disjoint we usually count them on
the primitive scale of One, Two, Many. In general our knowledge
is so poor that there are too many possibilities for them to be
matched with any definite cardinal number. Only when we
know a great deal, as in a quasi-mathematical problem, may
we be bold enough to say: there are exactly eleven possibilities
here.
Aside from the fact that one possibility may be contained in
another, my principle of individuation is strange. Normally if it
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IAN HACKING
is true to say, at time t, that two particulars-at-time-t* are
identical, it is not true to say, at time t', that the two particularsat-time-t* differ. Yet this can happen with possibilities. Suppose
at time t it is possible that at time t* I shall travel in a helicopter,
and possible that at time t* I shall be en route to Revelstoke.
These are different possibilities. But at time t' just short of t*,
I am in a train which is caught in a totally unpredictable but
rather permanent snow slide in Kicking Horse Pass. The passengers are being taken by helicopter to Revelstoke. Now it is
not possible that I should have a helicopter ride at t* unless I
am en route, in the helicopter, to Revelstoke; nor is it possible
that I should be en route to Revelstoke at t*, unless I take the
helicopter. The possibilities, formerly distinct, are now identical.
XX.
IDENTIFYING POSSIBLE THINGS
Quine's problem about possible things can be put in the
following form. Suppose we have two different descriptionsd and
e, using each of which we may say in turn that d is a possible
N, that e is a possible N. Suppose that we have L-occurrences
of "possible." When are d and e the same possible N, and when
different? The question is not limited to descriptions; d and e
might be demonstratives.
Generalizing our conjecture for possible states of affairs, we
propose that d and e are different possible N's if (a) it is possible
that d should be an (or the) N, while e is not, or vice versa, and
(b) it is possible that d and e should both turn out to be N, but
turn out to be different N's.
The two clauses (a) and (b) need a little explanation. I say
"an (or the)" in clause (a) because for some nouns N, "an N"
is wrong: one says not that such and such is a state of affairs,
but that it is the state of affairs. Clause (b) is needed because
two differenthorsesmight both be possiblewinners (with reference
to some day at the race track) and they might not be differentiated
by clause (a), though they would plainly be different possible
winners. Clause (b) does the trick. Clause (b) is redundant for
those nouns for which we have to say "the" in clause (a); thus
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POSSIBILITT
for states of affairs our criterion reduces to the criterion of the
preceding section.
XXI.
MODAL LOGIC
Lewis' modal systemscalled Si to S5 are a good guide to modal
concepts. They were intended to cover traditional logical possibility and necessity, but the systems are open to many other
interpretations. The most interesting systems are S4 and S5, here
presented in a form due to von Wright. The operator "It is
possible that" is written M. To a classical propositional calculus
we add the rules:
From A to infer EMMA.
B to infer MAEEMB.
FromA
Then add two axioms:
p D Mp.
M(p v
=)
(Mp v Mq).
To get up to S4 add:
MMp D Mp.
While for S5 add instead:
MrMP D AMp.
Many students have debated whether traditional logical possibility fits S4 or S5. Personally, I think that those who advocate
S5 win the day, but that is only an opinion. The fact that there
is no consensus on this question may indicate an over-all incoherence in traditional logical possibility. Possibility, as defined
in the present paper, is better off, so long as we make the idealizations usual in formal logic.
We can to some extent iterate "possibles": it makes sense to
say it is possible that it is possible that he will come. Let us
idealize to allow of unbounded iteration, incidentally idealizing
the English sentence, pretending there is no upper bound to its
length. Say also that we can investigate a long disjunction as
readily as the disjunct that is hardest to investigate. Then possibility as defined in the present paper satisfies the crucial axiom
for S4, but not the one for S5.
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IAN HACKING
S4: MMp D Mp. Suppose rMp. Then, according to my definition, practicable investigations can establish that U.p. Those very
investigations prove, by counterexample, that Mp is false. So, by
my definition, ,MMp. To sum up, ,Mp D ,MMp, and hence
MMp D Mp.
S5: M Mp D -Mp. Counterexamples to this assertion come
easily. We need to find ap such that Mp is consistentwith M -Mp.
Let p be any deep and controversial proposition like "The big
bang theory of the universeis substantiallycorrect."Now consider
two more assertions. (a) No practicable investigations would
establish that p is false; in brief,p is in practice irrefutable. (b) No
practicable investigations would establish (a), namely, that p is
in practice irrefutable. Plainly (a) and (b) are compatible, for
there might be no way of refuting something, yet no way of
showing that there is no way of refuting it. Now according to
my definition (a) is Mp, while (b) works out at M --Mp. Hence
r-Mp does not follow from M iMp, and possibility fails to satisfy
S5.
IAN HACKING
Universityof BritishColumbia
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