Critical Thinking Toolkit: Necessity and Contingency

In moments of deeper thought, have you ever noticed that there seem to be certain features of the world that are quite arbitrary or random, while other things seem like there isn’t really any other way things could be? Have you ever wondered at why things are the way they are, instead of some other way? This is the topic of this post, since these kinds of questions are taken quite seriously in philosophy. In fact, there is even a name for many of the deep considerations of this sort – we call them modal.

What is Modality?

Modal reasoning is an extension of normal logic. In order to understand what this extension is, it is worthwhile to review what logic normally is first.

Standard Deductive Logic

Logic is essentially the study of the different ways we can learn new information from previous knowledge. Here, we are concerned with deductive logic, which for our purposes means the type of logic that, if our starting point known, then the conclusion is in a sense forced upon us. Consider, for example, this argument:

  1. All men are mortal.
  2. Steve is a man.
  3. Therefore, Steve is mortal.

Notice that, if you accept both 1 and 2, you have to also accept 3. This may seem rather silly, and I’d say it does seem a bit silly to give a fancy name like ‘deductive logic’ to something that doesn’t look all that fancy. The reason why this actually isn’t silly is because of how few basic principles there are that are like this. There are just nine rules of deductive logic, along with two even more basic starting principles. The two basic principles are the law of non-contradiction, which says that nothing can be both true and false at the same time, and the law of the excluded middle, which says that any matter-of-fact claim is either true or false (there is no third alternative ‘in the middle’ of the two). The nine rules are all as simple as the rule used in the above example, which is the general pattern

  1. If X, then Y.
  2. X.
  3. Therefore, Y.

Other rules explain more about ‘if…then’ forms of thinking, some talk about how to treat sentences like ‘X and Y’ and ‘X or Y’. We don’t really need to go over all the rules – our main point is that the rules don’t deal with any language more complicated than and, or, not, and if…then.

The Additions in Modal Logic

Modal logic uses standard logic as its starting point and expands the language we can use. There are four key words we are adding to our logical language – necessary, possible, impossible, and contingent.

The word possible means pretty much what we normally mean when say use it. To say that something is possible means something like ‘it could potentially have happened’. To say something is impossible just means it is not possible. A square circle is a common example of something impossible – a shape can’t be both a square and a circle at the same time. That makes no sense – it is impossible. Another common example of an impossibility is a married bachelor – a married unmarried person. That is impossible – you can’t be both married and not married at the same time!

By contrasting against impossible things, we can better understand what counts as possible. For example, it is possible that there is a planet in our solar system we haven’t found yet. Notice that this doesn’t mean that there is a planet, and it also doesn’t mean there isn’t a planet. It just means the presence of such a planet isn’t utter nonsense like the idea of a square circle. It is also possible that the Baltimore Ravens win the Super Bowl next year, or that any other football team does for that matter. There are some teams that very likely won’t win, but unlikely things are still possible. We can proliferate different possibilities endlessly. Pretty much everything falls into things category.

The third category is a much stronger idea. This is the idea of a necessary thing. Something would be called necessary if it has to be the way it is – if it literally can’t be any other way. The easiest examples of necessary truths are things like “if it is raining, then there is currently water falling down to the ground from clouds”. This statement is necessarily true because the second part of the sentence just is what it means to be raining, so all I really said is “if it is raining, then it is raining”. It is literally impossible that “if it is raining, then it is raining” could be false. “All husbands are married” is another example of a necessary truth – being married is part of what it means to be a husband.

There is a fourth word that can also be important – contingent. Contingent is a label for anything that is neither necessary nor impossible. In possible world semantics, X is contingent if some possible worlds have X and others do not have X. For example, your birth is contingent. There is definitely a possible world in which you are born – you really have been born! But, had your parents not met (which certainly seems at least possible), then you wouldn’t have been born.

Now, a philosopher might now ask how these ideas work on the logical level – what sorts of logical rules do they follow? Studying the types of logical rules we can formulate using the terms necessary, possible, and impossible is called modal logic.

To give an example of one of the rules of modal logic, consider the following format similar to the bit of standard logic I wrote out earlier:

  1. Necessarily, if X then Y.
  2. Necessarily, X.
  3. Therefore, necessarily Y.

Now, lets think this through. Statement 1 says that if X happens, then Y must happen. It is unavoidable. Statement 2 says that X must happen. So, Statement 3 follows by stringing these together – since X must happen, Y must happen. This is one of the main rules of modal logic. There are plenty more rules, and they will often look very similar to the rules of standard logic with extra words added in. But, as we shall see later, you can’t throw in these words anywhere you want and wind up with good logic – sometimes things don’t work.

Possible World Semantics

I want to introduce here one of the common ways philosophers express modal styles of thinking in words. This style is called possible world semantics. In possible world semantics, the key concept is a possible world. A possible world is just some way that reality might have been. So, when I said earlier that it is possible that we haven’t found one of the plants orbiting our Sun yet, in possible world semantics we would say “there is a possible world in which there is an undiscovered planet orbiting the Sun”. If you wanted to say some situation is impossible, you can say that there is no possible world in which it is true. If you want to say something is necessary, you can say it is true in all possible worlds.

This can be a bit confusing sometimes because of the use of the word ‘world’. The confusion is quite understandable, because it makes it sound like the speaker actually think these possible worlds exist in some sense. But this need not be so. Possible world semantics is called semantics for a reason – it is nothing more than a helpful wording (a semantic device) that can be discarded if it is too confusing to be helpful. We have phrases like this in English – like the rising and setting of the Sun – that are merely semantic devices. We don’t necessarily mean the Sun is moving around the Earth when we use those phrases, but it is a helpful way of speaking and everyone understands what we mean, so we continue using this language.

So it is with possible world semantics. If imagining a ‘fake universe’ in which so-and-so is true helps you understand what ‘so-and-so is possible’ means, then great – use this way of phrasing things. If it isn’t helpful, that’s fine too. Ignore this bit, and if you hear someone using possible world language in a confusing way, just ask for clarification in different words.

Why it Matters

This will likely seem quite abstract, and perhaps to some it may even border on meaninglessness. But in philosophy, modality is very important – in fact there are debates about theories of modality, about how to correctly understand these distinctions, because they do in fact matter quite a lot.

Understanding Fundamental Reality

When we ask the ‘Big Questions’ so to speak, often we need to be able to use modal language in our answers – sometimes we even use modal language in the question itself! Instead of trying to convince you in an abstract way of the importance of modality in the Big Questions, I’ll just list out some Big Questions and emphasize the role of modal terms.

  • Do humans have free will? In other words, are all of our actions necessary, or do we have some possibility of choosing our own path?
  • Why does anything exist at all? Did the universe have to exist this way, or could it have been some other way? Is there a fundamental, necessary reason that explains why the universe exists?
  • Is it possible that our senses are misleading us? How do we know whether the world around us exists if our senses are deceiving us?
  • Is it possible that our cybersecurity algorithms are flawed, or is our encrypted data permanently safe?
  • Does human society always progress towards better morals over time, or towards worse morals, or do we have ebbs and flows?
  • If something doesn’t have to exist, then shouldn’t there be an explanation/cause of why it does exist? If not, why not?
  • Is a perfect society possible? If so, what does that look like and how do we try to get there?
  • Are mathematical statements like 2+2=4 necessarily true, or did we just invent them to help us keep things organized?

I hope that list will convince any reader of the importance of modal language in the most important questions of life. And if these words are important in the questions themselves, of course they will also be important in any attempts to answer them. And this leads to the next main point.

A Common Fallacy in Modal Logic

Earlier, I defined deductive logic as any method of thinking where, if you take for granted your starting point, then the conclusion if forced on you. This way of thinking about deductive logic makes it easy to define logical fallacies – these are forms of thinking that, at least some of the time, violate this condition. That is, a logical fallacy is a pattern of thinking that, at least some of the time, leads you to a wrong conclusion even if your starting points are true.

Modal logic has fallacies, just as we have fallacies in regular logic. However, very often fallacies in modal logic are harder to spot, because they are less obvious. In fact, they sometimes even have so much intuitive appeal that people use them casually and don’t even consider the possibility that this method is incorrect.

Let me give you an example. Consider the following logical form.

  1. Necessarily, if X, then Y.
  2. X.
  3. Therefore, necessarily Y.

This is a fallacy in modal logic. Let’s use one of our earlier examples involving bachelors to show how this fails.

  1. Necessarily, if Will is unmarried then Will is a bachelor.
  2. Will is unmarried.
  3. Therefore, Will is necessarily a bachelor.

This argument takes the form I wrote out, but is obviously wrong – I’m getting married later this year! So of course I don’t have to be a bachelor. But, both 1 and 2 are true about me right now. This conclusively shows that, just because we know 1 and 2 doesn’t mean 3 is true too.

This all seems rather obvious, but this logical fallacy is the very heart of why most people think God knowing the future is incompatible with free will. This theological argument normally comes in this form.

  1. Necessarily, if God knows you will do X tomorrow, then you will do X tomorrow,
  2. God knows you will do X tomorrow,
  3. Therefore, necessarily you will do X tomorrow.

The goal of this argument is to answer the Big Question about free will as a resounding ‘no’ by showing all of our actions are necessary if God knows the future. But, the entire argument rests on a logical fallacy! This means we don’t have to take it seriously. In order for modal logic to work here, you need to replace 2 with “Necessarily, God knows you will do X tomorrow.” But I’m thoroughly convinced that the theological doctrine of Molinism (which is held by many but not all Christians) conclusively proves that this modified version of 2 is false. Molinism takes too long to explain, so I won’t do so here, but my main point is just to show how much an understanding of modal logic really can matter.

The Ontological Argument for God

Ever since the medieval theologian and philosopher Anselm, there has been a detailed and interesting dialogue about a particular approach to a philosophical argument that God exist, called the ontological argument. As weird as it sounds, this argument basically makes the point that if God even might exist, then God does exist! I know, it sounds bizarre. But modal logic makes much clearer what we mean. Allow me to explain.

Part of what we normally mean by God is that God has always existed and cannot be destroyed – He is the greatest thing that exists. In more precise philosophical words, one of the things meant by such expressions is that God necessarily exists. Now, this is a modal word, so we should start thinking in modal terms. Now, by definition, God a being that exists necessarily (if He exists). This means that contingency isn’t applicable to the question or whether God exists or not – the only options available to us are necessity and impossibility. All else is ruled out by this definition of God. So, if you can disprove one of the two options, then you prove the other. There are a lot of different versions of ontological arguments, but all of them focus centrally on modal logic and the idea of God necessarily existing.

Conclusion

Modal logic may not come up incredibly often, but it is nonetheless important. It can be tricky to avoid tripping up sometimes when working in the weird world of modal logic, so some care is needed to minimize our mistakes. But, when it does come up, it is an indispensible tool that we can use to great effect and to understand the world in which we live better.

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