What exactly does it mean for something to be contingent?

Question

X being contingent means that X could have been otherwise. But what exactly do people mean when they say this and why is this significant?

For example, I can certainly imagine my cup to not be on my table. But why does this imply that the cup could not have been on the table? What if we live in a deterministic universe where given the initial conditions of the universe, the cup could have not failed to be on the table that it is.

If contingency purely means “I can imagine it to be otherwise”, what is the practical significance of this? Sure, I can imagine the cup not being on my table, but I can also imagine the cup to suddenly grow wings and start flying.

So what exactly does it mean for X to be contingent and why is this significant?

Answer 1

There is the "possible world semantics," according to which we imagine a set of all "possible worlds," and say an event is contingent if it happens in at least one of them but not in some other.

But this leaves a huge open question. Which worlds are possible? It's just kicking the can down the road; we haven't really said anything about which propositions are possible, we've only transformed it into an even more unanswerable question about which worlds are possible.

In colloquial usage, we say something is "possible" if we can't rule it out at the moment with the information available to us. Say a police detective wants to track down a suspect. At first he says it's possible the suspect could have gone north along route 8, and it's possible the suspect could have gone south along route 8. Then a report surfaces that the suspect was spotted at a gas station north of the crime scene along route 8. So now the detective rules out that the suspect went south, and says it's only possible the suspect went north.

But nothing about the state of affairs regarding the suspect changed; the only change was what information was available to the detective. Possible world semantics cannot deal with this. In possible world semantics, whether an event is possible or not is an objective fact independent of what anyone thinks about it. That does not reflect the detective's situation or other colloquial usages of the word.

In colloquial usage, when not talking about the practically useless "possible world" formalism, we mostly use the word "contingent" when making future plans based on uncertain events (contingencies). A contingency is a future event we can neither rule out nor confirm at the moment with the information available to us. So we might make a plan for if it happens, and another plan for if it doesn't happen, so we would be prepared in either case.

Note that whether we can "rule out" or "confirm" an event is always a matter of degree. There is always a chance that an event could happen, or fail to happen; we can never reach warranted 100% certainty about any future event. (The suspect on route 8 could have changed direction after the gas station, or the person spotted at the gas station could have been someone else who just coincidentally looked like the suspect). So we say an event is contingent if our confidence that it will happen fails to reach an ambiguous threshold, and if our confidence that it will not happen also fails to reach that ambiguous threshold.

Answer 2

To @causative's point, in philosophy the term "contingent" is a modal term indicating whatever is "contingent" was not necessary - the world could have been otherwise.

For example, I'm walking in a forest and stub my toe on a thorn. I can imagine a world where, for various reasons, I did not step on the thorn - hence my stepping on the thorn is contingent: none of those scenarios appear to be impossible, hence we say my stepping on the thorn was contingent.

Contrast that with necessary things - there are no other possibilities or ways things could have turned out (on pain of contradiction usually).

The extent to which possible worlds are really "out there" is a controversial thing. For example, how do we resolve the following?

1. Objective randomness: Is there true indeterminism in the world. Some events may have statistical connections but they are not deterministic, and hence nature could have come out differently (e.g., maybe quantum phenomena).

2. Principle of plentitude: Is there a reason to think reality is limited to one instantiation of a world? What is stopping the universe (writ large) from exploring every possible avenue as a matter of necessity?

We arrive at different conclusions depending on if we accept/reject each of these.

Reject 1, Reject 2: This is the classical determinist view. At rock bottom we are forced to posit a brute necessity (God, initial conditions). Possible worlds are only linguistic tools for expressing inability to rule it out (per @Causitive).

Reject 1, Accept 2: Modal realism (ala Lewis). The ultimate expression of the "Copernican Principle" that humanity is not privileged. Nature/reality cannot be constrained to just one world - the fullness of reality is literally everything. It's not even clear that conceivability or adherence to classical logic is sufficient, because our logical sense evolved from living in this world.

The huge benefit here is (a) we don't need spooky randomness in the world and (b) no brute necessities -- existence exists necessarily and everything else follows from that - so highly explanatory from a few assumptions. Some say its not parsimonious but they mistake "number of entities" from what I think is the more important thing, which is "number of commitments." What appears as randomness is really epistemic: there are a number of worlds "close" the the one we are actually in and we don't know which one we are in with the given information, but science has been able to learn some of the tendencies (at least in our neck of total reality).

Big downside: We cannot (nor likely will we ever) be able to empirically support this (except tangentially if we find evidence of colliding universes .. but still not a "world" in the philosophical sense of independent and non-interacting).

Accept 1, Reject 2: Some kind of "fluctuation metaphysics" that says our world came from an indeterministic initial state. How things worked out so well (or even if they did) to allow life is an open question here.

Accept 1, Accept 2*: I would say this is actually no different than modal realism, since each way the world could be would also be -- not sure in what sense there is objective changes.

Anyway, one way to summarize. Hope this helps.

Answer 3

1. There might not be a strong correspondence between probability and possibility. If "probable" and "improbable" went with "possible" and "impossible," then "contingent" would go with "probably not" and "necessary" would go with "not probably not." The Aristotelian sense of "contingent," here, was, "Possibly A and possibly not A," but that doesn't fit, "Probably A and probably not A." The one is not a contradiction, the other is^U when, "Probably A," is shorthand for, "The majority chances are that A," since then the latter would come out to, "The majority chance is that A and the majority chance is that not A." (If "probably" is used for an exactly 50% chance of A, then the combined statement would be, "There is a 50% chance that A and a 50% chance that not A," which is not contradictory, though.)

2. Although in basic modal logic we use the box and the diamond as unary operators (on sentences/propositions), we also have expressions like, "A necessitates B," which make the modalities into binary operators. Since necessity and contingency enter into a mathematical duality with each other, we can say that something A is necessary if(f) ∃x(xNA), i.e. something A is necessary if(f) something x necessitates it; then contingency is this relation read in the other direction: A is contingent on x if(f) xNA but not ANx. (This is just a choice of wording, though, since for reasons of formal triviality, we could just as well say that something necessitating itself is then contingent upon itself. This would negate some of the opposition between necessity and contingency, though other contrariety would remain.)

3. "Possibly imagined" and "possibly existed" are not identical. Ability-talk is an internal way of telling when the ability to imagine something indicates the possibility of that thing, e.g. if I recognize my ability to blink, and can imagine either blinking or not blinking (or blinking at different rates), then I have some sense that it is possible for me to blink and possible for me to refrain from blinking (for a while). Or if I have the ability to imagine a red cube, I might recognize that it is possible for me to imagine a red cube, and possible for me to imagine something else (or nothing at all, as when I let my mind "go blank").

4. So if it is possible that everything is necessary, then either iterating modal operators is superfluous or not, so either everything would just be necessary, or it would be contingent that everything is necessary. Why would being able to imagine everything as determined prove that everything is possibly determined unless the able-to-be-imagined/able-to-exist pipeline were stronger and wider than it seems to be, anyway, though?

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^UAlternatively, we would be dealing with a violation of unitarity: if it was, say, 75% probable that A would happen and 75% probable that A would not happen, then the probability space as a whole would exceed 100%. For reasons of the theory of division, we don't usually expect this to be so, though when it comes to applying the theory of division to infinity, some complications arise (to be more precise: more complications arise w.r.t. the theory of division applied to transfinite cardinal numbers, than arise when dividing transfinite surreal numbers).

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ADDENDUM: the Aristotelian theory

From a (neo-)Aristotelian point of view, there is a special correspondence between talk of essential and accidental properties on the one hand, and necessity/contingency talk on the other. A necessary truth is one based on essential properties (as the objects of the predicates in the truth); of course this is not perfectly stable, though, for there are problems like that of accidental intrinsics (we would usually expect that an intrinsic property was an essential one, but perhaps not quite that every essential property was intrinsic; but here, not even the first principle holds). There is no effective difference, in this context, between logical and metaphysical necessity: a property F is essential to something X if the proposition, "X isn't F," is somehow "self-contradictory" or "violates the law of identity applied to X."

This is where Anselm and Aquinas diverged, then: Aquinas could agree that the divine nature was supposed to be something for which the essence/existence distinction was effaced in that Its essence is to exist, but he did not think, like Anselm, that, "God doesn't exist," was self-contradictory in the specific way that it would have to be for us to know God through the ontological argument.

Leibniz would later turn things much upside down by reasoning that every property of any being whatsoever was effectively essential, and that an infinite conceptual analysis of any monadic being would establish the conceptual necessity of that being and all the states it enters into. He (apparently) would attribute the ability to conduct such an infinite conceptual analysis to God alone, however.

ADDENDUM 2: there also seems to be some confusion regarding the role of the modifier "possible" in the phrase "possible worlds." Possibility is no more a material property than existence is, so it is not a material property of worlds and the phrase "possible worlds" is interchangeable with "worlds containing possibilities." Assuming that worlds do not contain themselves, they are not "modality-apt" as such (this opinion is called "amodalism"/the denial of a proper "modal profile" to worlds, and in Forster's criticism it is the problem of the modal ether).

Answer 4

1. A state of affairs “S” is contingent when there is at least one possible world where “S” is a fact, and at least one possible world, where “S” is not a fact.

   Analogously “S” is necessary when “S” is a fact in all possible worlds. That’s a precise formal definition.

2. But it opens up at once the following question: How to ensure that “S” is the same state of affairs in different possible worlds? That’s necessary to compare it in diferrent possible worlds.

   The concept of possible worlds may sound rather intuitive. But it is a difficult and involved task to make it precise, see possible worlds.

Answer 5

In simple terms, something is contingent if it is neither necessarily the case nor necessarily not the case. But there are many different kinds of modality, e.g. logical, physical, epistemic, deontic, nomic, metaphysical, etc. Hence there are correspondingly many different kinds of contingency.

• A proposition is logically contingent if it is neither a logical truth nor a contradiction.
• A belief is epistemically contingent for me if it may or may not be true consistently with what I know.
• An action is legally contingent if it is neither absolutely mandatory nor unlawful.
• An event is physically contingent if it neither certain to happen nor certain not to happen.
• Etc.

Physical determinism is one kind of modal necessity. In practice it is somewhat more complicated to spell out exactly what determinism means and how it relates to certainty. But if you believe the universe is deterministic and that every event either happens or does not happen of necessity then you would not believe that events in the universe are contingent in that specific sense.

As to why contingency is significant... Possibilities and necessities have an important impact on our reasoning and decision making. When we reason we need to understand what is logically possible and impossible. When we design and build things we need to understand what is possible and impossible within the bounds of scientific laws. When we make plans for the future we need to take into account what might or might not happen: even if the universe is deterministic we don't know the future so there are epistemic contingencies.

Even when we know some proposition to be true, there is value in considering its contingency. I might narrowly escape some misfortune and consider that if things had been slightly different the outcome would have been disastrous for me. That fact provides an incentive to be better prepared against that contingency in future.

Answer 6

You ask:

What exactly does it mean for something to be contingent?

That all depends on the language community or language user's intention when using that particular token as a tool in discourse. The general dictionary definitions provided by MW provide 5 definitions! From MW:

1 : dependent on or conditioned by something else Payment is contingent on fulfillment of certain conditions. a plan contingent on the weather
2 : likely but not certain to happen : possible 3 : not logically necessary especially : empirical
4 a : happening by chance or unforeseen causes b : subject to chance or unseen effects : unpredictable c : intended for use in circumstances not completely foreseen contingent funds
5 : not necessitated : determined by free choice

And those are just the use of the term in venacular English. I can only imagine how much ink and how many bytes have been dedicated to the cause of dealing with the topic "exactly". We can see that contingency circulates around some important concepts: 1) possibility 2) probability 3) chance 4) dependency. Rather than responding in detail as these other contributors have bravely elected to do, I simply suggest that you reference a number of articles in the SEP:

1. The Epistemology of Modality (SEP)
2. Possible Objects (SEP)
3. Modal Logic (SEP)
4. Possible Worlds (SEP)
5. Inductive Logic (SEP)

Modality and logic are primarily the study of contingency in various contexts. A learned man one said that logic is the study of what follows from what. And in this sense necessity, possibility, and probability are very much the core of what it means to study logic itself, so the idea that you'll get an "exact" answer is a bad way of thinking about how language is used. So, exactly what contingency means in philosophical language communities is like asking what does it mean to use the term 'logic' or 'necessity' or 'inference'. It might even be an essentially contested concept.

Answer 7

From Conifold:

It means nothing "exactly", as with "necessary" or "possible", until one specifies what kind of modality (imaginative, practical, normative, physical, nomic, metaphysical, conceptual, logical, etc.) they have in mind or the context makes it clear. Practical significance, if any, depends on that specification. It is controversial whether imaginability or conceivability imply logical possibility, for example, see SEP.