In the following introductory chapter I will present the expositions of logical
possibility found in Hospers (1990), Bradley and Swartz (1977). I will show
that logical possibility rests upon an argument for constructing cases, with
definitions and claims about states of affairs, to see if there are any
contradictions entailed. So, the usual claim about logical possibility is:
whatever can be noncontradictorily asserted about a state of affairs and
definitions of the terms involved is logically possible. For instance, John
Hospers has claimed that there is nothing logically impossible in either of the
following claims:
(1). That a cat gives birth to pups; or,
(2). That a solid iron bar floats on water.
They do not ever happen in the world, are physical impossibilities, but they can still happen in other worlds where the laws of nature are different. The presupposition of logical possibility is the belief that what does not entail a contradiction is possible. In philosophy, logically possible examples are used to cast suspicion on empirically based claims, since the opposite of any claim based on the actual world is not contradictory it is said to be somehow possible. In the introduction we will be looking at how such logical possibilities are constructed.
Here I will use the more rigorous discussion of R. Bradley and N. Swartz' s
work Possible Worlds to make
clear the usual distinction between the logical and empirical realms. Bradley and Swartz first point out that
logical possibility should not be confused with `conceivability', taken as
imaginability; conceivability in this sense is not necessary for logical possibility since one's inability to
conceive of a state of affairs doesn't mean that it is not possible (such as
the `round' earth example). One could have very poor powers of imagination. But
Bradley and Swartz contend that neither is conceivability sufficient for logical possibility since
our ability to conceive of a certain state of affairs does not make it a
possible state of affairs (e.g. an MC Escher picture). The real test for
logical possibility is whether the statement (or statements) describing a state
of affairs is contradictory or not. If a statement is contradictory then it is
not logically possible--- not true in any world; but if a statement is not
contradictory then the state of affairs it signifies is logically possible, and
so true in some world.
Of course, how exactly we decide what is logically possible might lead us to
think that conceivability plays an important perhaps sufficient role. Some
adherents to logically possible examples do rely on conceivability regarding
what claims are compossible with certain definitions.
Since what is logically possible is taken to be what is true in at least one
world, it can be instructive to use possible worlds terminology. Following
Bradley and Swartz I will call constituents of possible worlds "items". These
are the sort of things we would have to mention in giving a description of a
possible world (Bradley and Swartz p. 7). These items have `attributes', which
are properties or relations. For example,
the Eiffel tower is an item and its location or colour are attributes.
So, in describing a possible world, any of the following might arise:
(3). That non-actual but logically possible worlds contain actual worldly items with different attributes;
(4). That non-actual but logically possible worlds contain certain items that do not exist in this world;
(5). That non-actual but logically possible worlds lack certain items that exist in this world.
Another world may lack certain actual world items, such as Richard Nixon; certain other non-actual items, such as Sherlock Holmes, could exist in these other worlds. And some other worlds include actual items with different attributes, such as a purple Eiffel tower. But all of these possible worlds or states of affairs can be subsumed under the class of logical possibilities. All that logical possibility requires is that the statement under consideration not imply a contradiction (we will soon discuss how this is `tested'). So, even statements that deny the natural laws of this world are possible in the logical sense; of course the denial of the applicability of natural laws on earth describes a physical (or empirical) impossibility, but this is not to say that such claims are contradictory since there is no logical contradiction involved in denying the physical laws of this world.
Given the above account of logical possibility, we can see that propositions
can have the following modal properties: Possibly true; Possibly false;
Necessarily true; and Necessarily false. Logical
truths are true in all possible worlds, while logical falsehoods are false in all
possible worlds. Logical possibilities
are true in at least one world. Logically
contingent statements are neither logically true or logically false,
i.e. they are true in at least one world and false in at least one world. The
following proposition, borrowed from Swartz and Bradley (p. 13), is logically
contingent:
(6). Woodrow Wilson was President in 1917.
This statement is true in this world, but may be false in another world where Wilson did not enter politics, but became a baker instead.
Claims about natural laws and essences are also supposedly in this category, since it could be true in this world that
(7). Elephants give birth to baby
elephants
but could be false in another world where this kind of animal gives birth to kittens. The truth of these propositions is world-relative; this world's laws are contingent, but so are the laws that would hold in each other world. Hence the facts can be said to be contingently this way or that way in this world or another. Rip van Winkle can sleep for twenty years in his world and wake, but this would not happen in our world given the laws of thermodynamics; Mr. Winkle would reach an equilibrium with his environment (that is, die) quite quickly in our world. But it is still meaningful, it is claimed, to speak of his world since there is no logical contradiction in saying that he slept for twenty years and awoke. The true litmus test for logical truth is what holds true for all worlds, viz., if the denial of a proposition entails a contradiction; and for logical possibility what is non-contradictory is possible.
Propositions that entail contradictions are said to be necessarily false. A
proposition that is true in all possible worlds is a necessary truth. Such a
necessary truth could have the form of an identity statement or
analytic definition, such as A is A, or AB is B respectively[i].
When we have given the true definition of a thing then we are said to have
given an analytic statement. Of course, a logical truth need not be in the form
of an identity claim, since any proposition that is true simply by its form
would count as a logical truth. Some examples are as follows:
(8). No unmarried man is married.
(9). If Molly is taller than Judi then it is not the case that Judi is taller than Molly (ibid p.21).
The first statement seems a suitable example, since it is true because of its logical particles. As Quine notes:
The relevant feature of this example [(8)] is that it not merely is true as it stands, but remains true under any and all reinterpretations of `man' and `married.' If we suppose a prior inventory of logical particles, comprising `no,' `un,' `not,' `if', `then', `and', etc., then in general a logical truth is a statement which is true and remains true under all reinterpretations of its components other than the logical particles (1953 pp. 22-3).
The second proposition supposedly holds as true in all possible worlds since we need only look at the form of the proposition,
(9.1) If x is taller than y then it is not the case that y is taller than
x.
Swartz and Bradley claim that the truth of this statement is a function of its form, not its content (p. 21). But the necessity depends upon the content of `taller than' as they note; the logical relation would have to take `taller than' as anti-symmetric. So, for (9) we get:
(9.2) xRy e ¬ yRx
And this is only necessary if the content of R makes it clear that it is anti-symmetric. So we are required to look at the content, not just the form. But the following claim is true since it depends only on the form:
(10). A & B | B
No matter what world we can imagine there cannot be a world where this statement is false, since its truth is a function of its valid logical form. Similarly, a necessarily false proposition is one that is contradictory, hence cannot be true in any possible world. But there still remains the problem of how exactly we decide what is contradictory and what is not. But given (9) above, the formality of logical truths cannot be the whole story, since often the content of a proposition, such as a definition, is important.
The person who espouses logically possible examples is committed, if this
analysis is correct, to holding that a set of definitions and claims is
logically possible iff there is no contradiction implied by this set. If there
is a contradiction implied by the set and the claims made about it then the
state of affairs described is inconsistent, or logically impossible. As we saw
above, a strictly formalized set of claims will not do since the content of the
proposition needs to be included. So,
a set of formal sentences, S, cannot satisfy our requirement, viz., that S is logically consistent iff S does not imply A & ¬A.
But in order to accomplish this we need to include the definitions into the analysis. So,
if S is the set of sentences and D is the representation of statements which give the definitions of the non-logical terms in S, then S is consistent iff S c D does not imply A & ¬ A.
Similarly for physical possibilities we could say:
If P is the symbolization of the true laws of nature, and D' the definitions of the terms in P, then S is physically impossible iff P c D' c S c D | A & ¬ A.
So, given the above outline of necessity and possibility we can see how logical possibility works. The essence or nature of a kind of thing is not taken to be part of the definition of that kind. Cats are said to be distinguishable by their appearance, hence are defined by these descriptions. An actual definition of `cat' would take into account its natural kindso that a creature with this underlying structure must give birth to a same sort of creature[ii]. Yet, take as an example of logical possibility, Hospers claim regarding a cat giving birth to pups:
Cats are distinguished from dogs by their general appearance, and it is logically possible for something with all the feline appearances to give birth to something with all the canine appearances. That nature does operate in this way, that like produces like, is a fact of nature, not a logical necessity (p. 134).
Regarding the facts of nature we can tell a different story from the way things actually happen; a logical necessity is one that holds true in all worlds by its form and its definitional content. But if a story can be told about a world where cats give birth to pups then this is said to be a logical possibility. This is not a case of resting logical possibility on imagination, but on what is said to be contained in the definitions of terms involved and in the description of the situation. There is no contradiction in asserting the definition of cat and in claiming that cats give birth to pups in some situation. Only if we made up a situation where what we said of `cats' was not compossible with its definition, would we be framing a logically impossible situation. Hence, Hospers claims:
When you describe a state-of-affairs, and its description involves you in a contradiction, that state -of -affairs is said to be logically impossible; all other states- of-affairs are logically possible, no matter how absurd they may be, such as a wasp turning into a dragon (p. 132).
And the test for the coherence of a story, or the compossibility of predicates, is based on definitions. We can say that it is logically possible that a stone thrown into the air will continue to rise, but we can not say that it is logically possible that a stone falls upward (p. 132)[iii]. This latter case is false by definition: things always fall downwards. To say that there could be a possible world where things fall upwards is not to have understood the meanings of `fall' and `upward'. We cannot predicate both terms at the same time and in the same respect of an object and not produce a contradiction.
In order to more fully explore the use of logical possibility we will now look
at two well-known examples: the first is the claim that time travel is
logically possible. The second is P.F.
Strawson's claim that it is possible that a single visual experience, usually
ascribed to one person, could depend on more than this person's own faculties
and spatial position. We will see in a later chapter how these examples can be
confuted.
If there is a notion that seems prima facie logically possible it is time
travel. After all, many books have been written that claim that it is possible
for persons to travel backwards and forwards in time. If these books have been
written, is it not possible that such things can happen? Has it not been
imagined, or conceived? But as Hospers argues, exactly how time travel has been
imagined is dubious; for instance, to say that we move forward and backward in
time is to use spatial terms that, while giving the appearance of movement
through time, land us in contradictions. It is contradictory to say that the
population of the Earth was 10 billion and not 10 billion; but the person who
`travels' back in time is committed to saying that the population was 10
billion persons yesterday and ten billion and one when he returns to yesterday.
It would seem, unsurprisingly, that by definition the past cannot be changed
since it has already happened.
But Arthur Collins has argued that we can tell a logically possible story about
time travel if we can be said to
imagine it (p. 51). His argument, which is not meant to be a defense of logical
possibility but, rather, a way of pointing out problems with it, is as follows:
A time machine on his account is just a windowless flying saucer- type craft.
One enters the craft then sets the controls and ends up in the past; but is
there a contradiction in this story, as Hospers has claimed? Collins claims
that it might seem so for:
I enter the time machine. Then, later in time, I set the controls; later still in time, it is the fifth century B. C. which is earlier in time. Therefore, my story involves a time which is both later than and earlier than another time and, consequently, I cannot really imagine my time machine at all (p. 51).
The reply to this which he gives helps us to understand the slippery nature of
logical possibility. If Collins' story has no contradictions then it is
logically possible. In order to get rid of the objection that the story is
contradictory all that he need do (he says) is to stipulate that he never says
that he enters his time machine and then later
in time visits the past which is earlier in time. Rather, he enters the time
machine and then, later in the story but not later in time, sets the controls
and then, later in the story but not time, is in the past. In such a way
contradictions -- at least for the time being-- are weeded out. This example
shows how thought experiments can be constructed which seem to show that claims
which do involve a contradiction can be reimagined not to involve one.
P.F. Strawson, in his book Individuals, argues
that an experience is only contingently dependent on one person for its
existence. He states that perceptual experience, for instance, is dependent on
three different kinds of facts: Firstly, there is the group of "empirical facts
of which the most familiar is that if the eyelids of that body are closed, the
person sees nothing" (p. 90). Secondly, is the fact that what a person sees is
dependent upon the orientation of his eyes, on the direction his head is
turned, etc. Thirdly, there is the fact that what can be seen depends upon the
person's field of vision, where his head is located. All of these visual facts
are seemingly dependent upon one body, since it requires a single body to have
a unity of experience. But Strawson argues that it "is a contingent fact that
it is the same body" (p. 90). He continues:
For it is possible to imagine the following case. There is a subject of visual experience, S, and there are three different relevant bodies: A, B, and C. (1) Whether the eyelids of B and C are open or not is causally irrelevant to whether S sees; but S see only if the eyelids of A are open....(2) Where A and B may be, however, is quite irrelevant to where S sees from, i.e., to what his possible field of vision is. This is determined only by where C is. So long as C is in the drawing room and the curtains are drawn, S can see only what is in the drawing room.... But (3) the direction in which the heads and eyeballs of A and C are turned is quite irrelevant to what S sees. Given the station of C, then which of all the views which are possible from this position is the view seen by S, depends on the direction in which the head and eyeballs of B are turned, wherever B may find himself (pp. 90-1).
Here Strawson claims to have described a situation where the visual experience of one person, S, is dependent in three different ways on the state or position of each of the bodies A, B and C (p. 91). The fact that visual experiences are dependent on the three kinds of facts above the operation, orientation, and location does not mean that these facts depend on a single body. Because Strawson can imagine that the visual experience is not dependent on a single body but on three, he concludes that the dependency for experience on a single body is contingent. He has not contradicted himself since he tells a story that utilizes the three sets of facts of a single experience spread over three different bodies. There is nothing in the set of three preconditions of a single experience, that contains the notion of belonging to a single body.[iv]
We have seen that logical possibility admits of many odd sounding
`possibilities'. But one wonders how useful the notion is for philosophical
investigation. George Seddon claims that logical possibility has become a
debilitating notion that blurs the distinction between science and
pseudo-science, which makes it more like science fiction than a useful
procedure for testing claims (p. 481). Any non-contradictory counterexample can
be dreamed up, as we saw with the authors above, to refute, or at least show
contingent, a seemingly plausible theory. But if we can show that essential
properties have a necessity of their own, hold true in all the worlds that have
these properties, then it is not possible to construct a counterexample that
denies such essential characteristics. We will not have to show regarding the
denial of a thing's nature that there is a logical contradiction involved
(Seddon p. 481), but only that there is an essential contradiction involved in
the claim that a solid iron bar float on water.
The ability to `imagine' a certain state of affairs by saying that it is logically
possible, is to tell a story that contains no contradictions— that is to say,
none of the items or attributes talked about seem to contradict any of the
relevant definitions. That iron bars float on water, rabbits are carnivorous,
or that elephants give birth to kittens, are clearly contrary to our experience. What I shall argue is that there
is a deeper problem with such claims: they are inconsistent with the natures of
things. In chapter two I will outline the Kripke- Putnam case for the view that
natural kind (NK) terms are rigid designators, and the essentialist
consequences they draw from it. While there is much debate about essences,
which I will touch upon, the theory of rigid designation cuts through the
description notion of things; a name or NK term does not stand for a set of
descriptions, but possibly designates an essential property. So, `water is H2O'
is an identity statement that holds true in every possible world. In worlds
where there is an item with all of the descriptive properties of water (cool,
refreshing, liquid, blue) but lacking in the essential property (being H2O), we
would have to say that this item is not water.
Of course it will be replied that the essences are contingent; can we not
imagine worlds, or situations, where essences are otherwise? How can I say that
the essences that provide a ground for rigid designation must be as they are? In chapter three I
will argue that, while I cannot show that the world must be as it is, it can be
said that given the essential properties of things, they cannot be different
(with respect to these properties) in any other world and still be the kinds of
things that they are. So, even though we can imagine that the world was
composed a different way, in no interesting sense does this make essences
contingent. We will be able to say that
there is a certain sort of
contradiction involved in the claim that, ceteris paribus, an iron bar
floats on water since the essence, or micro- composition, forbids it. With
essences we can expand the notion of iron bar, in that it is not just a bunch
of descriptions, so that it includes `sinking in water' as a necessary feature
or disposition. Given our definitions of logical and physical necessity above,
we can see that essential necessity will be a set which includes essential
properties and certain claims. If the set is essentially inconsistent, then it
describes an essentially impossible state of affairs. A claim is essentially
impossible iff,
the symbolization of true essential properties E combined with the explanation or definition of those properties, D', combined with set of claims S, and the definitions of terms in S, D, lead to a contradiction ( E c D' c S c D | A & ¬ A ).
I will argue that it is this notion of essential necessity which is most often relevant for philosophical investigations; there may be logically possible worlds such that solid iron can be said to float on water, but there is no essentially possible world where iron is iron and water is water and a solid iron bar floats on water. We must have imagined a world where something with many of the descriptive properties of an iron bar floats on water— but not a real iron bar.
It would seem that the often prevailing opinion is that logical necessity
trumps any other kind of empirically based necessities, hence logical necessity
seems stronger. Of course, using the term `stronger' to refer to logical
necessity could be misleading since it gives credence to the view that logical
necessity trumps any other kind of necessity, making them seem contingent by
comparison. Karl Popper claimed, regarding William Kneale's assertion that
logical and physical necessities were similar, that "[c]ompared with logical
tautologies, laws of nature have a contingent, an accidental character....For
there may be structurally different worlds
—worlds with different natural laws" (quoted in Fisk p.27). While I am not sure
that the necessities are comparable, I would like to suggest that we not take
logical necessity to be synonymous with necessity itself. The point of the
following essay is to show that essences restrict possibilities in a strong and
interesting way— one that ought to inform the making of philosophical
counterexamples. As A. H. Dunlop says:
To predicate a property essentially of a thing is to imply that it is somehow inconceivable that it could have lacked that property. So essential properties impose some sort of constraint on our thought about the things that have them (p. 76).
The burden of proof then will be on the person who appeals to logical possibility to show a certain claim to be contingent; simply showing that there is a logically possible state of affairs a state of affairs that can be constructed in a coherent fashion-- will not be sufficient to show an essential claim's contingency in an interesting way. What the adherent of logical possibility must show is that logically possible counterexamples that contradict certain a posteriori necessities perform some useful philosophical function. This will require more than showing that, on the usual account of logical possibility, essences are contingent.
[i] By saying that an analytic proposition has the form `AB=B' I mean simply what Kant says: that these propositions do not extend our knowledge, but merely explicate our concepts. So, the predicate B is covertly contained in the subject A to begin with.
[ii] It might seem to be good here in opposition to Hospers to offer a real definition of `cat'. Such a definition would need to be based on the underlying structure of the creaturewhich is a scientific question. As a foreshadowing of the argument in the next chapter, let us look at what Putnam says in this regard:
The reason we don't use `cat' as synonymous with a description is surely that we know enough about cats to know that they have a hidden structure, and it is good scientific methodology to use the name to refer rigidly to the things that possess that hidden structure, and not to whatever happens to satisfy some description. Of course, if we knew the hidden structure we could frame a description in terms of it; but we don't at this point. In this sense the use of natural-kind words reflects an important fact about our relation to the world: we know that there are kinds of things with common hidden structure, but we don't yet have the knowledge to describe all those hidden structures (Putnam p. 244).
I will argue that natural kind termsif they signify anything at allsignify the same kind of thing in all possible worlds.
[iii] Also compare another textbook's explanation of logical possibility:
...[W]e may distinguish between practical and logical possibility. For example, it is impossible in practice for a man to lift a one-ton block of stone. But it is not logically impossible— there is no contradiction in saying that a man lifts a one-ton stone. On the other hand, it is logically impossible for a man to lift a spherical cube of stone, because the notion of a cube which is also a sphere is a self- contradictory notion (Gorovitz and Williams p.40).
[iv] Mason notes that GE Moore said, in his Common-place Book, that it was logically possible that he be seeing what he was seeing, but that he had no eyes (p. 12).