What is puzzling, philosophically, about possibility and necessity?

There is a problem which all philosophers must face—that of possibility and necessity.  “What problem,” you may ask, “I see no problem.  Some things are possible, like what color shoes I wore today, and some things are necessary, like 2 plus 2 is four.  What more do I need to know?” Ahh, there lies one problem: what do we know about possibility and necessity, because it seems that we know a lot about them.  That is the epistemological problem.  Another problem is the metaphysical one: what is the nature of possibility and necessity?

We will first tackle the epistemological problem.

Consider the following statement:

Donald Trump could have lost the election.

“But he didn’t,” you might respond right away, “Who care if he could have lost, he won.”

Yes, he did win.  We know that is exactly, or actually, what happened. We know this and believe it, because we observed it happen.   We can easily justify beliefs that we actually observe happen, because we saw it actually happen.  And by justify or justifiable I mean something that can be defended or confirmed; we usually confirm our beliefs by observing them.   But what actually happens isn’t the only kinds of beliefs bobbling around in our heads.  We also justify all kinds of possibilities that we never actually observed.  How could we have held the belief that Trump might have lost if we never actually observed that happen? Our problem should be becoming clearer.

We have justifiable beliefs of possible things even though we have only observed what actually has happened.   How is this possible?

Think of these other examples:

The Russians might have landed on the moon first.  How can we know this if in actuality the USA landed on the moon first?

The dice could have landed on seven.  How can we know this if in actuality the dice landed on twelve?

Regardless of what actually occurs we still have justifiable beliefs about possible outcomes.  We talk about them, we debate then, we may even try to prove them, but this doesn’t explain why we believe in them even though our experience tells us otherwise.

We’ve talked about how having beliefs about possible outcomes is puzzling, now let’s look at our equally puzzling beliefs about necessity.

We believe that some things that happen, happen necessarily, or that they must happen; for example, we believe that 2+2 necessary equals 4.  When we have two objects and then get two more we know that necessarily we must have four objects.  So far, so good.  But where in the addition sentence 2+2 is it observed that it necessary must equal 4?  Where do we observe the necessity?  Our problem gets clearer still because when looking for necessity we don’t directly observe it, but we still believe in necessary facts and scientists build theories around them.  How do we believe in necessary facts?

Consider another example, credited to David Hume’s arguments on causation: Drop something, like your book.  You observe that once the book leaves your hand it falls to the ground and lands. But you don’t observe anywhere in the book, the fall, or the ground, the necessity that it must fall.  You can drop the book over and over again, but will never see the necessity, only the repeating patterns of a book falling and landing. This is the same with 2+2=4.  You can write out the addition sentence over and over looking for the necessity, but you will only observe a repeating pattern.

Now we have more to think about:

Not only do we believe that possible things could have occurred, even though we never directly observed them happening, we also believe in necessary truths even though we have never directly observed that something is necessary. 

“Okay,” you say after considering all of what I’ve told you, “So I have beliefs which I believe are true, regardless of me observing them.  Who cares?  I’ve done just fine believing in all sorts of things which I can’t justify and I’ve done just fine.”

You are correct when you say that you do just fine with all kinds of beliefs which you don’t bother to prove.  Many people do care, though.  Philosophers and scientists and theologians (oh my!) care because their jobs depend on being able to prove, or at least justify, their beliefs.  These people want to know about out world.  For them, they figure if you can’t even know about possibility and necessity, how can you get to the point of learning about them.

When we want to claim we know something, as in we truly have the knowledge of something, we need to be able to explain why our knowledge is creditable and how we arrived at it.  There are numerous ways philosophers and scientists have tried to tackle this question, and while the discussion would be stimulating, I can’t go into the details here.  Instead I want to make good on my promise in the beginning.  I promised that we would be talking the puzzling problems about possibility and necessity, and about here we are getting into the great problems of epistemology.  We haven’t even touched on the metaphysical problems.

So, let’s talk metaphysics.

So far we have been thinking about what we know about possibility and necessity, which is an epistemological problem.  The metaphysical problem is not concerned about what we know, it is concerned about the nature of something or what something is.  When thinking about possibility and necessity, the metaphysician wants to understand what kind of things, or entities, or facts, they are.  What kind of thing is possibility and necessity?  Bingo, we’ve finally hit the metaphysical question.

Let’s first think about possibility.  We’ve learned that we believe things that are possible, even though we haven’t directly observed them; for example, we believe that we should wear our seat belts because it is possible that we could get into an accident.  But assuming when we drive somewhere and in actually we arrive safely what happens to that possible belief we had?

Was it some ghostly entity that floated around in our reality until the actual event occurred?  Maybe there is a ghostly world of all possible things and then the actual world that we live in.

What about necessity?  Is necessity something that doesn’t really exist?  Hume suggests that necessity is never in things, we can never observe it, and that the only place for it to exist is in our minds.  And if necessity is actual, even though we don’t or can’t observe it, who makes up the rules for what is necessary?  Rules suggest that someone wrote them; for example, God or some supreme being, wrote them.

“Who cares if possibility and necessity actually exist?” you might ask.

Besides philosophers, scientists (and possibly theologians) care about the reality of necessary things.  Theories are made up of necessary truths and a scientist’s job is to find out what the reality of theories actually are.  We learn more about our world that way.

There is a lot to think about when you consider possibility and necessity.  I have tried to present the problem these terms have for philosophers in a way non-philosophers could understand.  Now that you have some idea of the problem:

Why do you think that the average person should care, or shouldn’t care, about possibility and necessity?



Sider, Theodore.  “Possibility and Necessity”. Riddles of Existence, edited by Conee and Sider, 2005, pages 181-184.

Yalcin, Seth. “Modality”. Metaphysics, University of California, Berkeley, Spring 2011, Berkeley, CA. Lecture.

Hume, David.  Treatise Concerning Human Nature. 2nd Edition.,Revised by P.H. Nidditch, Oxford UP, 1978.

Further Reading:


Updated 12 July 2018

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