The Problem of Omnipotence

Watch the video here.

Imagine yourself relaxing at home one day when you suddenly hear a knock at the front door. To your amazement, it appears to be none other than John DeLancie himself, standing on your doorstep.

"Hello.” he says. “My name is Q, from the Q continuum. Just stopping by to let you know that I’m an omnipotent god. You should probably start bowing before me or else I might get really upset."

"That's cool," you think. You've never met an omnipotent being before. But hey, he seems like a pretty honest guy, and you're probably not very keen on the idea of getting turned into a frog right now. So naturally, you take him completely at his word and start bowing right that second, am I right?

No, of course not! You’re skeptical. Maybe this person is telling you the truth, or maybe this person is just some weirdo pulling your leg. So you demand some basic empirical evidence to show that this being really is what he says he is. 

“All right,” he says.  “You want proof?  You got it."

The next thing you know, Mr. Q snaps his fingers, and, in a brilliant flash of light, your car is suddenly transformed into a giant pile of squirrels. It’s a very impressive trick to be sure and maybe even enough to warrant sincere placation of this being. However, we’re all hard-nosed philosophers around here, and we want to be as sure as we possibly can. So let’s put this guy to the test and see whether or not he truly deserves the title of omnipotent, rather than, say, really-really awesome and powerful.

You might be forgiven for thinking that this was a perfectly straightforward question to ask, and in any other context it probably would be. But religious philosophy has a really funny habit of tripping all over itself whenever questions like this crop up. Because as simple and intuitive as this problem may seem, most religious philosophers cannot for the life of themselves seem to answer it coherently. It’s an elegant little thought experiment that perfectly captures the bizarre mental gymnastics of Christian apologetics, as well as some of the foundational failings of their entire philosophical world. It’s also a really fun exercise in basic critical thinking skill that takes us over a surprisingly broad spectrum of interesting philosophical subjects. That's why I personally find this question to be so strangely fascinating and why I think you'll enjoy following me down the looming rabbit hole that it represents.

To begin our analysis, let's frame the question in terms of something a little more mundane. Rather than claim to be a full-on omnipotent deity, suppose instead that our stranger merely claims to be a reasonably competent automobile mechanic. It's basically the exact same situation as before, but now framed in a completely nonreligious context. So ask yourself now: How exactly should we go about verifying this claim?After all, it’s not like we just take random people completely at their word for this stuff. There’s real money at stake here, plus the functionality of our cars. Surely there must be some sort of test we can offer before honoring him with such a title, right?

Obviously, the answer is yes, and it works like this. Go get out a piece of paper and write the following words that the top:

Things that a Competent Automobile

Mechanic Should be Able to Do

After that, you just enumerate the list with a collection of pertinent challenges. For example:

• Change a tire.
• Change oil. 
• Flush coolant.
• ... 

and so on until you’ve completely populated the list. Once finished, you can then issue your challenge in the following fashion:

Dear Mr. Stranger.

Given the proper tools, work space, assistance, etc, I challenge you to complete each of these items on my list within a reasonable amount of time. Or, if the list is infinite in length, then at least complete a reasonable sampling of items until I'm satisfied.

There, done. If our subject is successful, then great. He has officially earned himself the title of competent automobile mechanic. And if not, then oh well. Maybe he's just pretty good with cars or perhaps halfway decent. That’s fine, too. They're just words and labels.

Now to be fair, this isn’t exactly how we all go about our daily lives, but it does illustrate an important philosophical aspect over the nature of language. Doctors, lawyers, presidents, squirrels, rocks, potatoes---they're all just labels that we define and assign in accordance with a distinct set of empirically verifiable properties. Anything that demonstrates the properties of a given list may officially earn the corresponding title, while things which fail to satisfy those properties are simply not referred to as such. It’s basically a form of philosophical verificationism, and it represents a foundational pillar on which human language operates.

With that in mind, let’s go back to our supposedly omnipotent friend, Mr. Q. Start by getting out a piece of paper and writing the following words that the top:

Things That an Omnipotent Being Should Be Able to Do

What items go on the list now? The answer, it turns out, depends a lot on who you ask. For example, according to one school of thought, the answer is pretty simple: Anything. Literally anything you can think of goes on the list.

• Make it rain frogs? Check!
• Create a married bachelor? You got it!
• Flargle a snuffin? Sure, why not?
• ...

This is a naïve form of omnipotence commonly referred to as absolutism, or absolute omnipotence. Rene Descartes was a famous defender of this position, and even some modern philosophers have periodically defended it as well [1]. It’s actually pretty easy to see where this idea comes from, given that the Bible itself practically screams this interpretation at you. For instance,

• Matthew 19:26---With man this is impossible, but with God all things are possible.
• Mark 10:27---With man it is impossible, but not with God. For all things are possible with God.
• Luke 1:37---For nothing will be impossible with God.
• Job 42:2---I know that you [God] can do all things, and that no purpose of yours can be thwarted. 
• Philippians 4:13---I can do all things through Christ which strengtheneth me

Despite its intuitive basis on Christian scripture, the idea of absolutism is clearly riddled with problems. For example, take the challenge of Flargling a Snuffin. According to absolutism, Mr. Q here should be perfectly capable of doing exactly that without a second thought. Yet, as should be obvious by now, flargle and snuffin are just gibberish words I made up out of nothing---they have no established definition. So pray tell, what exactly could our subject ever do that would satisfy the challenge?

Bear in mind now that this is not a limitation on our subject per se, but a simple problem of language. It’s like mashing my keyboard with random characters and saying “here, do this!” There’s simply nothing to do. I may as well just stand there in silence, or perhaps shrug my shoulders and grunt. Mr. Q cannot ever hope to fulfill a challenge if no coherent challenge was actually given.

Notice that a similar argument also applies to the challenge of creating a married bachelor. By definition, a bachelor is an unmarried man, which means the creation of a married bachelor is the same thing as creating a married man who is also not married---a logical contradiction. The set of all things that are married is mutually exclusive to the set of all things that are not married. It therefore doesn’t matter what Mr. Q ever presents to me because the rules of logic forbid me from ever recognizing a successful outcome. Again, that’s not a limitation on our subject, but another limitation on language itself. The very words used to formulate the challenge are simply put together wrongly.

This is exactly why absolutism is generally regarded as a pretty terrible form of omnipotence. Nevertheless, it is important to recognize that the death of absolutism does necessarily imply the death of God. All it says is that, whatever things are out there for us to give labels to, none of them will ever be able to demonstrate omnipotence to any rational satisfaction. And since no being can ever possibly earn itself such a title (even in principle), the title itself is essentially meaningless. If, however, we simply redefine omnipotence to mean something slightly different, then all of the problems we just talked about would immediately vanish in a puff of logic.

Remember now that all we’re trying to do here at the end of the day is define a word. If that word is coherent, logical, and verifiable, then great. We can use it to describe various entities in our environment, if and when we ever happen to encounter them. But if the word is incoherent or logically inconsistent, then oh well. It’s not like the universe cares one way or the other. All it means is that we can't use the word to meaningfully describe stuff. Time to go back to the drawing board and see if we can’t think of something better.

Much to the credit of religious philosophers today, that seems to be exactly what happened. Rather than literally be capable of doing anything, a far more common view of omnipotence is the ability to do all that is logically possible [2]. It’s a perfectly straightforward revision that specifically seeks to avoid the incoherence of absolutism while still preserving the totality of power we've come to expect. And that’s a good thing! So let’s all get out a piece of paper and write the following words at the top:

Logically Possible Actions

What exactly does this mean? How do we determine whether or not some particular task should go on the list?

Here’s how I interpret it:

Consider a simple challenge like “eat a taco.” If I can imagine some logically possible world wherein that task is being performed by some agent, then good. It goes on the list. For example, I can imagine a logically possible world where it is true that the President of the United States is eating a taco. Therefore, it seems to me, it must be logically possible to eat a taco. It is officially something that can be done, and therefore it must go on the list. Anything that wishes to call itself omnipotent must therefore be able to replicate that feat.

That was easy enough. So let's shake things up a bit by asking a very simple question: Is it, or is it not, logically possible to tell a lie?

Obviously, the answer has to be yes, because people around the world tell lies all the time. Therefore, by modal axiom B [3], it must be logically possible to tell a lie. Therefore, by the definition of omnipotence, all omnipotent beings must be able to tell lies. Strangely enough, however, the Holy Christian Bible says outright that lying is something God cannot do; not just something God doesn’t do or chooses not to do, but literally cannot do.

• Titus 1:2 “[I]n hope of eternal life which God, who cannot lie, promised before time began.”
• Hebrews 6:18---“[I]t is impossible for God to lie.”

So right off the bat, the very definition offered by professional Christian philosophers themselves has immediately precluded their very own God from being omnipotent! Isn't that funny? But let's ignore that little problem anyway and see what else can we find wrong with this definition.

How about this? Go outside and start collecting rocks into a giant pile. Keep piling up rocks until the pile is so heavy that you cannot ever hope to lift them. Congratulations! You have just created a finite pile of rocks that officially satisfies the description of being unliftable by its own maker. Therefore, it must be logically possible to create a pile of rocks, or even a single rock, that satisfies the description of being unliftable by its own maker. Therefore, all omnipotent beings must be able to replicate this task. So let’s pose the challenge.

Dear Mr. Q,

I challenge you to create a finite rock such that its own maker cannot lift it. Go.

So far so good, right? But what happens if Mr. Q actually succeeds in this challenge? After all, last time I checked, it is always logically possible to lift a finite rock.

Notice that this is just a simple variation on the paradox of the stone---Can God create a rock so heavy that even God Himself cannot lift it. It’s a famous philosophical challenge to the idea of omnipotence because it logically prevents any being from ever demonstrating such a property. By definition, all omnipotent beings must, at any given moment, possess the power to both create rocks and to lift rocks subject to specifications. Yet the moment our subject creates a rock he cannot lift, he cannot possibly satisfy the definition of omnipotence any more. That means no being can ever possibly earn the title of omnipotence because the very act of proving it requires them to not have it.

Notice also that we could just as easily frame this exact same problem any number of ways. For example, one of my personal favorites is to stand before a podium and truthfully speak the words “I am not omnipotent.” Again, it’s a perfectly logical task, in that I can imagine a logically possible world where this is taking place. Therefore, at any given moment, an omnipotent being must, by definition, be able to replicate that task---stand before a podium and truthfully speak the words “I am not omnipotent.” Unfortunately, the only way to actually possess such a power is by not being omnipotent!

Bear in mind now that this is not some clever philosophical trick, but a fundamental property of binary propositional logic. Self-referential propositions, when coupled with logical negations, tend to produce really nasty inconsistencies. It's the exact same reason why we have so many other famous paradoxes as well. For example, the Liar’s Paradox, Russel’s Paradox, the Halting Problem, and even Godel’s Incompleteness Theorems are all just similar manifestations of self-referential negation. So it’s not like I’m just making this stuff up, because philosophers, logicians, and mathematicians have been studying this exact same phenomenon for centuries. We therefore must conclude that the capacity to do all that is logically possible is, ironically, not a logical possibility. You can either be complete, or you can be consistent, but you cannot have both simultaneously.

At this point, you would think that most Christians would simply say something like, “why yes, that seems to be a bit of an issue. Perhaps my conception of omnipotence is just a little bit too greedy. Let’s maybe learn from the last 100 years of mathematical logic and see if we can’t find something a little less contradictory.” But of course, the exact opposite is generally true, with hack philosophers around the world dogmatically clinging to their precious definition anyway.

For instance, one complaint that you might hear is how the challenge itself is inherently ambiguous. When I create a rock, the word "maker" refers to myself, the person speaking to you right now. Yet when someone else performs the same task, the meaning of “maker” suddenly changes. On other words, the challenge shares the same type of proposition, but not the same token [4]. Thus, in order for the challenge to be comparable, Mr. Q would not need to create a rock that he cannot lift, but only create a rock that I cannot lift.

This may sound like a somewhat reasonable point at first, but quickly falls apart the moment you actually stop and think about it. For starters, we don’t have to use the word “maker” if we don’t want to. We could have challenged our subject to create a rock so heavy that no being in the universe can lift it. Or better yet, stand before a podium and truthfully state the proposition that “There are no omnipotent beings.” They’re still logically possible actions in some logically possible world, which means they still have to go on the list.

The real problem, however, is that all actions are inherently self-referential. To see why, simply imagine what would happen if I challenged you, right now, to eat a taco. Naturally, if you’re like most people, the obvious interpretation of that task is to immediately grab a taco and start shoving it into your face. If, however, you were to then challenge me to replicate that task, what exactly do you imagine happening next? Do I begin shoving a taco into my own face? Or must I literally shove a second taco into your face and force you to eat it?

Obviously, the former interpretation is the correct viewpoint, because that's how every English-speaking human on the planet understands it. The whole point of issuing the challenge in the first place is to see if you have the power within yourself to replicate a power that I had within myself. Yet, for some strange reason, the moment we try to apply this same line of reason within a religious-philosophical context, then all of a sudden people start acting like a bunch of pedantic morons. By invoking the type/token distinction in this way, it is literally meaningless for me to challenge you to "eat a taco." I have to instead say something horribly obtuse, like "I challenge you to bring about the event of you eating this taco."

Well I'm sorry guys, but events are not the same thing as actions, and I should not have to specify a particular actor in order to coherently define some particular act. When you challenge me to jump five feet in the air, you obviously mean that I have to propel myself with my own legs off the ground beneath me. If, however, I then challenge you to jump five feet in the air, then obviously you must now propel yourself off the ground with your legs. All logically possible actions are, in some way or another, inherently self-referential. Deal with it.

With that taken care of, the next most common objection I tend to hear is that omnipotence doesn’t really mean the ability to do all that is logically possible. Rather, it means something more like the ability to do all that is consistent with one’s nature. That is to say, if the proposition “Y is doing X” is logically self-consistent, then for an omnipotent being, it will always be true that “Y can do X” [5]. 

Okay, fair enough. If you want to just summarily change the definition of omnipotence again, then that’s great. It was a bad definition from the get-go, and we can only grow as philosophers by trying to find something better. But can we please all be grown-up enough to admit that this is nothing more than an indirect admission of defeat? The previous definition was inherently flawed, and so now we’re changing it into something else. Yet whenever I talk to Christian apologists about this, they almost always pretend as if the new definition is really what it was supposed to be all along, and how dare I straw-man such brilliant thinkers by ever suggesting otherwise!

Fine. Whatever. Let’s just roll with it and see what we find this time, shall we? Can an omnipotent being tell a lie or what?

Typically, the answer to this question is that it depends on the being. For example, the God of Christianity cannot tell a lie because doing so would contradict His perfectly honest nature. Thus, to ask God to lie is the logical equivalent to asking a perfectly honest being to not be perfectly honest---apparently, a logical contradiction. But don’t worry, God still gets to be omnipotent anyway because He can still do all the things that are consistent with his divine, unchanging nature. Likewise, God cannot stand before a podium and shout “I am not omnipotent” because that would produce a contradiction as well. Omnipotence is an inherent part of God's nature, so therefore it doesn't have to go on the list of things God can do. Bam. Problem solved!

This is usually the part where I begin to lose all patience with religious philosophers, because responses like this are clearly not well thought out. It really gets under my skin, too, because it represents a profound laziness that makes no effort whatsoever to consider the practical implications of what is actually being said. To illustrate, simply imagine God Himself standing on my doorstep in all His glory, when I issue the following challenge:

Dear God,

I challenge you, right now, to tell me a lie. Tell me that you’re a potato. Go.

Pray tell, what exactly do Christians imagine happening next? Because as far as I can tell, they seem to imagine something like that scene from Liar Liar where Jim Carry tries to say that the pen is red, but just can’t bring himself to do it [6]---as if some invisible, metaphysical force of honesty is somehow preventing the words from coming out of his mouth! Call me crazy, but I hardly find that to be consistent with the idea of unlimited potentiality. Or maybe Christians just imagine God standing there with a dumb look on His face, as if He didn’t even understand the question? Or what if he just says “I’m sorry, but that would violate my essential nature. No thanks.” What in the hell am I supposed to do with that?

But let’s take it one step further. Suppose you challenge me to lift a 1000-lbs car over my head---except that ooh, I’m sorry, but that would violate my essential nature! You see, I’m a being comprised of physical muscle mass that can only lift 200 lbs. When you ask me to lift 1000 lbs, then you’re asking me to perform a contradiction---A being that cannot lift more than 200 lbs is lifting more than 200 lbs. Not only that, but any challenge you give me can be counteracted in the exact same way. No being can logically be expected to do the things it cannot do.

So congratulations, my dear Christians! You’ve solved the omnipotence paradox. All you had to do was replace it with the omnipotence tautology. Literally anything and everything in the universe is now omnipotent because nothing can ever logically do the things it cannot do! 

“Aha!” I hear you saying. “It is only incidental that you cannot lift 1000 lbs. I can still imagine a possible world wherein you are lifting 1000 lbs over your head. Therefore, it may be logically possible, but not physically possible!"

Actually, no. What you're imagining right now isn't me. It may be an entity very similar to me, but that's not really me. Because as we just established, I am not a being who can lift 1000 lbs over my head.

Or better yet, let's play that game in reverse. I can imagine a possible world wherein God is telling a lie. Now what? What’s the difference? Why is lying a violation of God’s essential nature, but lifting 1000 lbs is totally consistent with mine? Because as far as I can tell, this entire line of reasoning appears to be nothing more than blatant special pleading. When God can’t do a thing, then it must be because it violates His essential nature. Yet when I can’t do a thing, then apparently it’s little more than a conditional happenstance of my feeble, limited existence.

So once again, we have another example of responding to an argument without any effort to actually address the argument. But the thing I find absolutely hilarious about this new definition is how (of all people) the famous apologist Alvin Plantinga himself personally debunked it as far back as the 1960s [7]. All you have to do is imagine a man called Mr. McEar, who just so happens to have one essential property---he has only the power to scratch his ear, and nothing else. Thus, by definition, any other task you challenge him to complete is a logical violation of his essential nature. Hardly an “all-powerful” being, wouldn’t you say? Yet, according to our new definition, Mr. McEar is still just as omnipotent as almighty God Himself!

All tangents aside, the real problem with this whole “essential nature” nonsense is just that: essentialism---the idea that there exists some kind of intrinsic “essence” to things that makes them what they are. It’s a perfectly natural bias through which human beings tend to look at the world, but it’s still completely bogus. Ever since the Greek philosopher Plutarch introduced the Theseus paradox back in the first century [8], philosophers have had very good reasons to reject essentialism as a worthless, incoherent concept. A chair does not have some magically objective “essence of chairness” that makes it a chair. It’s just some arrangement of physical material stuff that human beings have arbitrarily decided to sit on and call a “chair.” Likewise, there is no such thing as “essence of Godliness” that would make God “God.” Rather, there is only a distinct collection of empirically verifiable properties which, if demonstrated, would earn some lucky entity the official title of “God."

So not only do we have Christians pushing yet another idea of omnipotence that just doesn’t work, but it’s grounded on philosophical presumptions that have been categorically debunked for almost two thousand years. However, it really needs to be emphasized that all of these crazy problems would vanish in a heartbeat if only the theists would just stop insisting on such bungled definitions. It’s sad, too, because it’s really not that hard to come up with something relatively functional. So let’s do the theists’ job for them and just define omnipotence in a way that isn’t stupid, shall we?

Omnipotence: the capacity to create, destroy, and rearrange matter/energy in accordance with arbitrary whims. 

There. Done! If we ever encounter any being with this kind of power, I will be more than happy to refer to such a being as “omnipotent.” Can he create rocks? Sure. Can he lift rocks? Absolutely. But can he create a rock so heavy that even its own maker cannot lift it? Nope. Not a chance. But guess what? That’s perfectly okay, because it's still logically consistent with the stated definition.

Notice how a definition like this also solves all kinds of goofy philosophical issues. For example, one lesser-known problem with omnipotence is the problem of creating two omnipotent beings at once. So let’s imagine a possible world wherein two beings are both competing for the official title of “omnipotent deity.” All we have to do is make a game out of it. Challenge one guy to turn my car into a pile of squirrels while challenging the other guy to turn it into a sack of potatoes. Whichever outcome occurs will then determine which guy is the loser and which guy earns the title. Done.

Or better yet, let’s consider another lesser-known problem. I challenge you to truthfully tell me what I ate for dinner last year. You’ll notice that this is not really so much a test of power, but rather a test of knowledge. Yet according to most classical definitions for omnipotence, there is no distinction. The omnipotent being must be able to do it because I formulated the challenge as a logically coherent action. If, however, we adopt the new definition, then it is now possible for a being to be omnipotent, but not necessarily omniscient. All-powerful and all-knowing are now philosophically distinct concepts, as we should reasonably expect.

Notice also that there are still many possible ways to potentially break the definition. For example, could an omnipotent being create another omnipotent being? Or what if I challenge the being to kill itself? Would that violate the definition? Maybe, maybe not. But you’ll notice that I’m not racking my brain with obtuse rationalizations just to protect a stupid definition. If it works, then great. It not, then oh well. We'll just think of something better.

The ultimate irony in this entire discussion is that, when all is said and done here, I’m basically just fixing the theists’ philosophical problems for them. Yet if past experience is any guide, the overwhelming majority of them will never see it that way. Instead, they’ll probably view this entire discussion as a literal attack on God Himself, as if the words used to describe some possible entity might have real power over whether or not it actually exists. That’s what happens when you live your life defending dogma rather than honestly searching for a better understanding of the world. But the thing I find really embarrassing about this entire debate is that by clinging to their philosophically warped definitions, it is the Christians themselves who are logically forcing their God squarely into the realm of nonexistence. Even if there were a God-like thing somewhere out there in the cosmos for us to meet, the rules of language would prevent us from ever rationally calling it such.

Thank you for reading.

Notes/References:

1. Earl Conee, "The possibility of power beyond possibility," Philosophical Perspectives, Vol. 5, pp 447--473 (1991)
2. See, for example, the Catholic Encyclopedia or the Internet Encyclopedia of Philosophy "S is omnipotent if S can perform any action A such that A is possible"
3. If X is true in the actual world, then X is necessarily possible. 
4. See, for example, this video here
5. See also Type-token distinction
6. (PlaceForTruth.org) "When used of God, it refers to fact that He is all-powerful, that He is unconstrained by any outside force; He can do anything consistent with His character."
7. (GraceBibleChurch) "God is infinitely able to do all things that He desires to do, but must at all times be consistent with His perfect attributes or essence."
8. Plantinga, Alvin. 1967. "God and other minds: a study of the rational justification of belief in God." Ithaca, NY: Cornell University Press. 
9. Ship of Theseus

The Problem of Free Will (and How to Solve It)

Watch the Full Video Here.

 

Imagine yourself sitting in the jury box for a courtroom trial of the infamous Neckbeard the Pirate. Looking over the list of charges, you see what appears to be quite the nefarious career: Looting, pillaging, extortion, raping, kidnapping, murdering… the list goes on and on. Not only that, but the defendant doesn’t even deny his actions. He confesses outright to every last crime, plus a few extra that didn’t even make the list. It seems to be a textbook open-and-shut case, except for an unusual plea made by the defense.

"Please don’t send me to prison!” says Captain Neckbeard. “I had no choice. You see, years ago, the Canadian government installed a microchip in my brain that forced me to do their evil bidding. It wasn’t really me who committed those horrible crimes. It was the agency controlling me through the implant. I was just an unwilling puppet in the whole ordeal.”

“Golly,” you think. “That’s a pretty far-fetched claim. He can’t possibly expect us to believe this, can he?"

Sure enough, however, the story checks out. The defense submits a series of CT scans that clearly show the presence a device implanted in his prefrontal cortex. The very chip itself is then submitted as evidence, followed by a series of testimonies from neurologists, cognitive scientists, and electrical engineers all explaining exactly how it works. Representatives from the Canadian government even take the stand and admit openly to having abducted their own citizens and implanting them with mind-control devices. It was all just part of a top-secret spy project gone terribly awry.

Ask yourself. Given such evidence, how exactly would you place your verdict? Would you vote guilty and throw the defendant in prison for the rest of his life?  Or would you acquit the defendant of all charges?

If you’re anything like most people, the evidence in this scenario would probably convince you to acquit. After all, it wasn’t really the defendant who was doing all those horrible things. It was the operator of the mind-control chip. It therefore seems perfectly reasonable to conclude that the defendant was not acting in accordance with his own free will and thus does not bear any moral responsibility for his crimes.

Now to be fair, a full-on mind control chip is a pretty fantastic idea, but there really are actual courtroom cases that closely resemble this exact scenario. At least one classic example was the case of a Virginia man who developed severe pedophilic tendencies after sprouting a tumor in his right orbitofrontal cortex [1,2]. Rather than directly force his actions, however, the tumor released a frenzy of antisocial desires while simultaneously blocking the part of his brain responsible for impulse control. Fortunately, once the tumor was surgically removed, the defendant was eventually restored to normal social behavior. So ask yourself now: How would you cast your vote if you were on his jury? Would you vote to acquit? Or would you vote to convict?

Again, if you’re anything like most people, you would probably vote to acquit, and that's exactly what happened in this particular case. But how far can this kind of thinking reasonably extend? For example, what if for every act of piracy, a full one-million dollars was donated to the Red Cross and then used to save 100 lives? Thus, being the perfectly moral agent that he is, Captain Neckbeard had no choice but to engage in a few acts of lesser evil for the sake of a much greater good. Or better yet, what if Captain Neckbeard just really enjoys being a pirate so much, that absolutely nothing else in his life could possibly bring him happiness? Or what if Neckbeard just got into piracy one day because he felt bored on a Sunday afternoon? At what point do we transition from complete, merciful forgiveness to the usual imposition of criminal justice?

These simple thought experiments represent the foundation for an age-old principle known as free will. It’s a classic problem that philosophers have passionately discussed for thousands of years, and it still continues to spark debate to this very day. Yet despite the gallons of ink that have been spilled over this topic, it’s surprisingly rare to find anyone with a comprehensive solution that actually works. That’s a real shame, too, because it’s not exactly difficult to provide functional answers to these kinds of questions. All it takes is a little willingness to explore the problem honestly, plus the intellectual discipline to apply rigorous standards of logical consistency. That’s why I personally find the issue so fascinating, and why I think you’ll all enjoy following me along as we finally settle the problems of free will once and for all.

The Twins Problem

Now before we begin, it’s important to understand that the fundamental problem with an idea like free will has very little to do with whether or not it really exists. Rather, the far more compelling problem is how best to define that term in the first place. It’s as if we all have this deep, intuitive sense over what free will ought to mean, but just can’t seem to pin it down into any hard, quantifiable terms. It’s a giant gap that undermines nearly every dedicated treatment on the subject. After all, what’s the point of engaging in a public debate when no one has yet to even agree on what the debate is supposed to be about? So before we even touch on the practical problems of free will, it really helps to step back and ask ourselves what exactly those two little words really mean.

To help answer that question, simply imagine yourself sitting in a room behind a table. Across from you are what appear to be two identical twins. They look the same, they act the same, and in all physical respects, they seem to be as alike as two people can possibly be. There is, however, one key difference that sets them apart. One of these entities has free will, and the other does not. Your job is to figure out which one is which, and do so with repeatable, reliable, consistency.

Ask yourself: How exactly would you go about telling the difference? What observations do you make? What experiments do you perform? What empirically verifiable distinction must we look for in order to differentiate between a being that has free will and a being that does not?

Bear in mind now that whatever answer you give to this question is, effectively, your definition for free will. It’s a textbook application of a well-known principle called verificationism, and it represents the ultimate foundation on which all human language operates. It’s an amazing philosophical tool that works wonders at cutting through the pseudo-intellectual background noise and getting right to the heart of such difficult ideas.

To illustrate, suppose someone tries to tell you that free will is an “immaterial construct” and thus cannot be detected or measured using the empirical methods of science. Okay, that’s fine if you want to think that, but it immediately runs into a pretty glaring problem. When Captain Neckbeard says, “I was not acting out of my own free will,” and the prosecution says, “Yes, you totally were,” pray tell, how exactly are we supposed to figure out who’s right? Do we just randomly guess? Should we assume one side is always telling the truth, no matter what? Because the moment we reject the application of any objectively verifiable criteria, then the only way to settle such disputes it by pure, unfettered say-so. Microchip in your brain? Sorry, that’s an empirically verifiable distinction. How about a brain tumor? Nope. Still verifiable and thus material---nothing whatsoever to do with free will!

Clearly, any attempt to side-step verificationism is little more than a philosophical dead end. Yet despite this obvious limitation, it can still be like pulling teeth just to get a clear definition out of people. It's infuriating, too, because it means that any attempt to pin free will down with a hard definition will inevitably be met with angry accusations of “straw man” from every corner of the blog-o-sphere. Nevertheless, we have to start somewhere, and there are at least some popular definitions that do provide a workable framework for verification and analysis.

One statement in particular that tends to occur over and over again is the famous expression that free will inherently represents “a capacity to have done otherwise.” What exactly that means is open to some interpretation, but it nearly always involves an explicit rejection of predetermination. It’s a classic philosophical viewpoint known as libertarian free will, or metaphysical libertarianism, and it holds that free agents are not necessarily bound by the initial conditions of their circumstances when making decisions.

To demonstrate how this works from a verificationist perspective, simply imagine our twins being given a choice between chocolate and vanilla milkshakes. After long and careful deliberation, they both eventually conclude that chocolate is the preferred flavor and so naturally pick that milkshake accordingly. But suppose for a moment that there existed a magic rewind button capable of reversing time itself. Every last subatomic particle in the universe, including those making up our very own brains, will be reset back to exactly where they were at some point in the past. If we were to then press this button and replicate our experiment between chocolate and vanilla, what outcomes should we expect to observe? According to most schools of thought, the twin without free will should consistently pick the chocolate milkshake every time. However, for the twin that does possess free will, there is the distinct possibility that, on occasion, he just might decide to take the vanilla.

That description may sound a little goofy, but it really is the basic train of thought provided by the overwhelming majority of thinkers on this subject. They make no effort whatsoever to tell you what free will actually is, but only to tell you what free will isn’t---namely, that free will is not a thing that can logically coexist with a deterministic universe. The two ideas are thus incompatible.

Clearly, there are some pretty serious problems with this viewpoint that need to be addressed. For starters, there are no magic rewind buttons with which to reset the entire universe. Consequently, the distinction between a being with free will and a being without is completely immeasurable. Again, when Captain Neckbeard claims that he was not acting in accordance with his own free will, how exactly are we supposed to verify such a claim? Do we really need an honest-to-goodness time machine with which to observe his actions? And exactly how many times must we watch him repeat his crimes before we are convinced that his actions were predetermined?

Obviously, that’s not ever going to be an option, nor does it even make sense to try. The past is the past, and no being can ever possibly “do otherwise” on anything that has already been done. Free will in this specific sense is therefore completely dead in the water before the boat has even sailed. Nevertheless, we cannot simply acquit every criminal in existence because of some nuanced philosophical quirk, can we? Just because the popular conception of free will tends to make no sense, does that automatically mean everything about it is completely worthless and inapplicable?

Of course not! For instance, rather than reset time itself, what if we merely replicate the initial conditions of some past experiment and then observe a replication of outcomes in the future? This turns out to be a much more workable idea because it represents something we can actually utilize in the real world. It also just so happens to be the textbook definition of determinism according to every modern theory of probability [3]. The implication is that I don’t have to necessarily rewind the entire universe per se, but I can, in principle, replicate all of the relevant conditions that gave rise to a particular event. If our universe is indeed deterministic, then for any physical experiment you may ever hope to contrive, I can predict and replicate the outcome of that experiment with perfect consistency. It also means that, for all practical purposes, your future might as well be set in stone because every outcome that occurs will always be causally predetermined by the conditions that came before it.

So given this slightly tweaked definition, is it safe to conclude that people have free will or what? In short: probably not. After all, if our decisions are merely the product of the neural connections within our brains, then in principle I could reset those conditions and watch you repeat the exact same decision under a given scenario. Or, equivalently, if I knew the exact arrangement of every last neural connection in your brain, then I could, in principle, predict exactly how you will behave when presented with a choice.

One of the most dramatic demonstrations of this principle was recently published by neuroscientists at the Max Plank Institute in Germany [4]. Using functional magnetic resonance imaging (fMRI), human subjects had their brains scanned while randomly pushing buttons with either their left or right index fingers. Upon post-analysis of the data, it was found that decisions could actually be predicted, with greater than 50% accuracy, a full 10 seconds in advance of the subjects’ own awareness. The uncomfortable implication is that, given enough computational power and scan resolution, even human behavior itself could be predicted with the exact same accuracy as any other natural phenomenon.

For many, this tends to have pretty devastating implications for the idea of free will and particularly for our entire concept of criminal justice. After all, if every decision we make is merely the result of physical interactions between atomic states in our brains, then how exactly is that any different from the microchip scenario? Captain Neckbeard didn’t “choose” to commit his crimes any more than a laptop “chooses” to follow its programming. And since we don’t go around tossing laptops into prison for misbehaving, then what’s the point of doing the same thing to criminals? If, however, we could hypothetically reset the initial conditions and observe Neckbeard “doing otherwise,” then most people would generally conclude that he ought to be held morally responsible for making the wrong decisions.

Fortunately for the libertarians, there does seem to be at least one ray of hope lurking deep within the bowels of modern physics. To see how it works, simply imagine what would happen if a single neutron were freely tossed out into empty space. At first, all we would observe is a lone subatomic particle floating along at a constant velocity. If, however, we waited around long enough, then we would eventually observe a phenomenon called free neutron decay, wherein the neutron spontaneously bursts into a proton, an electron, and a neutrino. If we then repeat this experiment many times over, we will eventually observe that exactly half of the decays seem to occur in about 10.3 minutes or less, while the other half take longer.

None of this is particularly compelling so far, except for one major detail. No matter how perfectly we replicate the initial conditions, we will never be able to consistently replicate the exact moment of individual neutron decay. Try as we might, it will always be a matter of pure, unfettered probability. Nothing specifically causes this event to occur, and it is a fundamental property of nature herself that subatomic particles should behave this way. It’s a famous principle called the Copenhagen interpretation of quantum mechanics, and it is a very well-established interpretation among physicists today. The implication is that if our brains are fundamentally made of atoms, and atomic behavior is not predetermined, then it stands to reason that human behavior itself should likewise contain some trace elements of indeterminism for free will to hide in.

This may sound a little crazy at first, but it really is a popular argument getting promoted by scientists and philosophers today [5, 6]. It’s weird, too, because the Copenhagen interpretation isn’t exactly well-liked among modern physicists. While it may be common practice to teach this interpretation in most schools, there is also an open admission among everyone involved that it's both a logical and philosophical mess. There are plenty of alternative interpretations that arguably do better [7,8], and it's only a matter of time before someone finally demonstrates a clear, empirical distinction. If anything, we really just begrudgingly accept Copenhagen out of respect for tradition rather than any strict adherence to philosophical parsimony.

Ignoring that, however, the real problem with this view is that it seems to grant free will to completely pre-programmed machines. To see how, imagine a simple robot that picks out milkshakes in accordance with the decay of free neutrons. If the neutron decays in 10 minutes or less, then pick the chocolate milkshake. If it takes longer, then pick the vanilla. For all practical purposes, this robot will appear to behave exactly as the supposedly “free” twin, in that no replication of initial conditions will ever result in a perfect replication of outcomes. Yet we can also clearly see that there is nothing “free” about this configuration because the robot is still just following its programming. And since your own brain states are fundamentally governed by similar atomic events, then even your own mind is arguably just a glorified realization of exactly such a machine.

If that wasn't convincing enough, however, then just think of it like this: Imagine being offered a choice between your favorite flavor of milkshake and a giant pile of dog feces. In principle, you’d think that one should always want to go for the milkshake every time because milkshakes are delicious and satisfying while dog feces are grotesque and poisonous. Yet if libertarian free will really were a thing, then we necessarily must expect that, on at least some rare occasions, you would arbitrarily feel yourself overcome with the inexplicable urge to literally eat shit. Then when asked why you on Earth you did that, the only explanation you could possibly give is that some mysterious compulsion overpowered your sensibility and made you to do anyway it against all reason. That’s hardly the action of a “free” agent, don’t you think? And in what logical sense do we accomplish anything by punishing someone for that kind of behavior?

So no matter how we look at it, the idea of libertarian free will simply doesn’t work. By definition, libertarianism cannot coexist with determinism, and by definition, the opposite of determinism is pure, freaking randomness. This whole stupid debate between determinism and free will is nothing but a gigantic red herring. Neither situation provides us with a satisfying description for how a morally responsible agent ought to be behave, and neither situation provides a compelling framework for the administration of criminal justice. It should therefore come as no surprise that libertarian free will is probably one of the most widely rejected ideas in the history of academic philosophy [9]. Yet for some strange reason, the overwhelming majority of debate on this subject is still fixated on a distinction that doesn’t matter either way. It’s as if everyone is so hell-bent on answering the question of determinism that they never stop to wonder what makes the alternative scenario any better.

Remember now that all we’re really trying to do here is define a word. Libertarianism is just one possible definition for free will, and there are still plenty of untapped definitions we have yet explore. But it’s important to always keep in mind that there is no such thing as an objectively “correct” definition. There are only good definitions and bad definitions. Good definitions are clear, consistent, concise, and generally capture the intuitive understanding we typically associate with such terms. Bad definitions are either unclear, unverifiable, convoluted, or logically absurd in their implications. Metaphysical libertarianism is nothing more than a "bad" definition because it fails to cohere into anything meaningful or practical. If that means free will is absolutely dead in your eyes from today until eternity, then fine. We'll all say it together right now: Free will does not exist! Does that make you happy? But guess what? We still have to deal with the fact that crime exists in this world, and we can't expect to manage it properly without a viable concept of moral accountability.

To that end, philosophers have developed all kinds of alternatives to libertarianism collectively known as compatibilism---the idea that, whatever we decide free will happens to be, it is still logically “compatible” with a deterministic and/or random universe.  It’s a huge variety of competing theories unto itself, and we could easily spend hours picking apart the more noteworthy contenders. But rather than get bogged down in an endless spiral of even more bad definitions, let’s just step back for a moment and ask ourselves why on Earth we care so much about free will in the first place. That is to say, when we sentence people like Captain Neckbeard to a life in prison, what exactly are we trying to accomplish? What’s the goal, here? What consequences are we trying to actualize through the act of punishment that cannot be achieved by simply letting him go?

You would be amazed at how hard it is to find any notable philosophers in history that come close to addressing these kinds of questions. It’s as if we’re all are so hyper-focused on the minute details of free will itself, that hardly anyone ever stops to ask themselves what the point of all this is supposed to be. It’s amazing, too, because it's not like this is some kind of deep, philosophical mystery for the ages. According to every official legal doctrine in the entire Western World, there are exactly five reasons for the punishment of criminal behavior.

Starting with Number 1, we have the doctrine of restitution---the idea that punishment exists to fix, or set right, any harm that was caused by a particular act. For example, when you’re backing out of your driveway and you happen to run over your neighbor’s mailbox, then at least one form of punishment would be to simply compensate them for any damages and inconvenience suffered.

At Number 2, we have the doctrine of deterrence---the tendency for people to refrain from certain behaviors if they believe that doing so will prevent any undesirable consequences. For example, everyone knows that speeding is generally dangerous, yet the temptation to do so can also be very intense. Thus, to reduce the likelihood of everyone driving too fast for their own good, we set limits on our top vehicle speeds and then impose a modest fine for anyone caught breaking the rules.

Moving on to Number 3, we have the doctrine of rehabilitation---the tendency for individuals to modify future behavior after personally suffering the effects of a punishment. For example, maybe you didn’t believe that a certain stretch of highway was really being patrolled, and so you figured you could get away with speeding. If, however, you are caught and fined, then the credibility of the punishment gets reestablished, and you become much more likely to follow the rules in the future.

Proceeding to Number 4, we are given the doctrine of incapacitation---the need to deny certain individuals the means and opportunity of committing certain crimes altogether. For example, imagine your eyesight is going bad and you just can’t help but drive like a maniac every time you hit the road. Since no amount of fines are ever going to prevent you violating the rules, it eventually becomes prudent to simply take away your license and completely revoke all driving privileges.

Finally, at Number 5, we have the doctrine of retribution---the visceral satisfaction granted to society by watching bad people suffer. When you go out and break the speed limit, then there must be something inherently evil about you that just deserves to be punished. We therefore impose speeding tickets on you for the pure sake of hurting you.

You might have noticed that the doctrine of retribution is conspicuously out of place on this list. While the other doctrines exist to serve clear, pragmatic goals, the last one is essentially just institutionalized revenge. Even the very word itself literally means "payback" in Latin! When you inflict harm onto society, then society tends to get very angry. And the only way to quell that anger is, apparently, to inflict some sort of proportionate harm back onto you. It should therefore come as no surprise, then, that retribution and libertarian free will nearly always go hand in hand. They treat good and evil as ethereal forces interwoven in the fabric of space and time, and that only the actions of metaphysically “free” agents are somehow capable of offsetting this delicate cosmic balance. That’s why retribution is incidentally the most controversial doctrine of criminal punishment by far. Philosophers and legal experts around the world have written heavily about the absurdity of this doctrine [10-12], and it is only by sheer, institutional inertia that it still remains an official part of our criminal justice system today.

Notice also that if we simply disregard retribution altogether, then the other four doctrines are all perfectly compatible with deterministic presuppositions. They embrace the idea that actions taken today will necessarily result in predictable human outcomes tomorrow. It's a perfectly pragmatic system with tangible social benefits, which means we're going to continue punishing people anyway whether or not libertarian free will is a real thing. So why not just bite the bullet already and use this as our foundation for defining free will, since apparently it's already the foundation for our entire system of criminal justice today. For example...

Free Will Finally Settled

Imagine our two identical twins again and offer them a choice between chocolate and vanilla milkshakes. All other things being equal, we should naturally expect both twins to pick the chocolate over the vanilla and do so continuously upon repeated iterations of this experiment. But now imagine what would happen if we tried to convince the twins to choose vanilla. For example, we could try bribing them, begging, pleading, threatening; anything we like. Just make it known that actions taken in the present will have positive or negative consequences in the future. For the twin that does not possess free will, no amount of reward or punishment will ever alter his behavior. You could offer him a million dollars or you could physically beat him senseless, but he will always go for the chocolate, no matter what. For the twin that does possess free will, there will exist some distinct threshold of reward and/or punishment that will alter his behavior---he can be convinced to choose the vanilla rather than the chocolate.

Now in all fairness, we don’t have to explicitly define free will in exactly these terms, and there are probably dozens of other formulations that could do it more rigorously. That’s not the point. The point is that free will is already so heavily intertwined with the ideas of punishment and moral culpability, that we might as well use those as the foundation for a functional definition. There's no need to invoke any magic rewind buttons for the entire stinking universe when we can easily achieve a perfectly satisfying result by just observing the natural consequences of reward and punishment.

For instance, take the classic courtroom scenario of Captain Neckbeard the Pirate. Should we convict, or should we acquit? To answer that, we simply ask ourselves whether or not the institution of punishment will deter future misbehavior under similar circumstances. That is to say, if I punish Captain Neckbeard for his crimes, can I expect that punishment to deter both himself, and other agents, from engaging in piracy in the future?

For the special case of mind-control devices, the answer is obviously no. No amount of reward or punishment will ever deter anyone from committing a crime when there’s a full-on microchip in their brain that's forcing them to do it anyway. If, however, Captain Neckbeard simply got into piracy one day because he was bored, then there is every reason in the world to suspect that the institution of severe punishments will greatly deter other bored individuals from following a similar path. We would therefore say that brain chips most definitely rob people of their free will, while casual boredom on a Sunday afternoon does not. It's a perfectly clear distinction that's both meaningful and practical, and it doesn't require the invocation of any obtuse metaphysical nonsense.

Notice that we can immediately answer all kinds of wacky philosophical questions through the adoption of this kind of framework. For instance, have you ever wondered why we don't hold our animals to the same degree of moral accountability as humans? Like, if my cat goes potty in the wrong place, how come we don’t punish him like we would for a person who commits the same crime? Under compatibilism, the answer is quite simple. While I might be able can train my cat to use the litter box through careful application of reward and punishment, I cannot deter a cat by making an example out of his peers. That’s because a key ingredient for free will is a general capacity for complex rational thought within a broader social context. It makes no sense to deter misbehavior against those who are mentally incapable of projecting the example of others onto themselves. It is therefore perfectly consistent to speak of our animals as possessing perhaps some semblance of free will to varying degrees, but not nearly to the same magnitude as us humans.

What about robots? What would it take to finally declare that some artificially-constructed robot has officially “passed the singularity” and developed a free will of its own? Again, it’s not a hard question to answer, so long as we consistently apply the definition. At what point will the institution of reward and punishment either deter or encourage certain behaviors?

To illustrate, imagine a possible world wherein every home comes preinstalled with its own robot butler. Now imagine that, for whatever reason, our butlers tend to act out in strange ways. For instance, maybe they smash up our dishes and then rearrange our furniture while we sleep. Under most circumstances, we would simply correct the malfunction by tracking down the faulty lines of code and then updating them accordingly. In the future, however, there might not be any code to fix. Most machine learning algorithms today are not based pure, iterative logic, but on neural networks derived from fitness functions acting on the raw experience of the environment itself. Thus, if we ever want to correct our robots’ misbehavior, we may actually have to train them through the institution of reward and punishment. And if, by some happenstance, our robots reach a point wherein they can learn from the experiences of each other, then we wouldn’t have to train them all individually to achieve the desired result. Instead, we could single out an individual robot and then make a very public spectacle out its punishment. If doing so results in a marked deterrence of future misbehaviors, then we will have officially satisfied the definition of free will. And why not? For all practical purposes, that’s basically how we govern human social behaviors already, so it makes perfect sense to describe a hypothetical robot population in exactly the same terms.

But hey. Maybe that’s not good enough for you. Maybe you think it’s either libertarian free will, or nothing at all. That’s fine if you want to think that, but it’s not going to change our presently accepted doctrines of criminal justice. Whether the universe is deterministic or not, we are still going to use reward and punishment as our philosophical basis for moral culpability. And since the notion of free will is already inextricably linked to that principle, then we might as well just call it by the same, established name. Thus, when libertarians speak of “a capacity to do have done otherwise,” they literally have it backwards. It’s not about changing events that already took place in the past, but about steering events that might take place in the future. We don't have to replicate initial conditions down to the very last atom when we can easily achieve everything we want by merely altering the initial conditions of similar situations that have yet to pass.

So the next time you find yourself in a courtroom wondering whether or not to throw someone in jail, there now exists at least one philosophical foundation on which to guide that decision. It doesn’t even have to be perfect, either, but just "good enough" so as to provide functional justification to the pragmatic satisfaction of society. I freely admit that there are probably dozens of gaps in my presently-described compatibilism, and everyone is more than welcome to chip in and help refine it over time. But you can’t replace something that works with nothing that doesn’t. Metaphysical libertarianism cannot help you in this situation or any other. Compatibilism does.

Thank you for listening.

Notes/References

1. Burns, J. M. and Swerdlow, R. H., "Right orbitofrontal tumor with pedophilia symptom and constructional apraxia sign," Archives of Neurology, Vol. 60, pp. 437-440 (2003) [link]
2. Darby, R. R, Horn, A., Cushman, F., and Fox. M. D., "Lesion network localization of criminal behavior, PNAS, Vol. 115, No. 3 (2017) [link]
3. See, for example, [link]
4. Soon, C. S., Brass, M., Heinze, H., and Haynes, J., "Unconscious determinants of free decisions in the human brain," Nature Neuroscience, Vol 11, No 5 (2008) [link].
5. Hartsfield, T. "Quantum mechanics supports free will," Real Clear Science (2013) [link]
6. [link]
7. [link]
8. [link]
9. Bourget, D. and Chalmers, D. J., "What do philosophers believe?" Philosophical Studies, Vol. 170, No. 3 (2014) [link]---Less than 14% of philosophers accept or lean towards libertarianism.
10. Barnett, R. E, "Restitution: A new paradigm of criminal justice," Ethics, Vol 87, No 4 (1977)

The Language of Logic

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There's a classic episode of the original Star Trek series wherein Spock takes command over a stranded away team after crash landing on a distant planet [1]. As the team desperately works to repair its crippled shuttle, hostile aliens repeatedly hamper their efforts with violent attacks. Frustrated by the danger, some of the crew members demand permission to vaporize the monsters with their phasers, thereby eliminating the threat. Spock, however, refuses, and insists that a nonlethal show of force will be sufficient to scare them away without bloodshed. He immediately orders the crew to implement his plan, but it unfortunately backfires terribly. Rather than run away in terror, the aliens respond with more ferocious attacks than ever, and they even manage to kill another member of the crew. It’s a thrilling bit of drama that culminates in a heated argument between Spock and McCoy:

Spock: “Most illogical reaction. We demonstrated our superior weapons. They should have fled.”

McCoy: “You mean they should have respected us?"

Spock: “Of course."

McCoy: “Mister Spock, respect is a rational process. Did it ever occur to you they might react emotionally? With anger?”

Spock: "Doctor, I am not responsible for their unpredictability."

McCoy: "They were perfectly predictable to anyone with feeling. You might as well admit it, Mister Spock. Your precious logic brought them down on us."

Spock [some time later]: "Strange. Step by step, I have made the correct and logical decisions. And yet two men have died."

Skeptical writer Julia Galef once analyzed this episode for her presentation at Skepticon in 2011 [2], and I think she makes some very profound points about the Hollywood portrayal of logic. Remember that Spock is supposed to serve as a living embodiment of pure, logical reasoning, yet his behavior is clearly nothing of the sort. After all, how logical could your decisions really be when they consistently fail to produce an expected outcome? But rather than take responsibility for the obvious flaws in his own reasoning, the guy practically blames the world itself for not doing what he wanted.

Now in all fairness, Hollywood fiction writers are not exactly experts in logic, nor do they have much incentive to fill that role. Still, that does not excuse such a dismal portrayal of logical reasoning. Very few people have the luxury of studying this stuff in any formal capacity, which means the rest of us have little choice but to fill that void with whatever scattered fragments we can find in our popular culture. The natural result is thus a widespread confusion over what exactly logic is, how logic works, and how competent we really are at applying logic to our daily lives.

To illustrate, if we take the Vulcan philosophy of logic at face value, then a logical agent is apparently someone who just suppresses their feelings. Thus, to be logical is to simply be dispassionate, unimpulsive, and unintuitive. Any decisions based on such a mindset are good and correct, by definition, no matter the consequences. But if that’s all that logic is, then why would anyone want to adopt it? The central message seems to be that too much logic does nothing but turn us into unfeeling robots that get people killed!

It’s important to understand that logic is an essential building block to our modern lifestyle, and we only hurt ourselves by misrepresenting its inner workings to the public. Logic is not just a mere suppression of emotion, but a collection of mental tools designed to help us understand the world. Life is filled with serious problems that affect all of us on a global scale, and we cannot expect to solve them through brute intuition alone. It takes hard work to analyze this stuff and formulate solutions, yet the very tools we need for that process are being needlessly muddled and demonized by our media.

But what is logic, really? This is not an easy question to answer, and even respectable authorities are sometimes hesitant to give a truly definitive statement [3]. Some authors describe logic as the study of correct reasoning [4,5], or the study of valid inference [6]. Others describe logic as thinking about thinking [7], or maybe the science of reasoning and arguments [8,9]. These are all perfectly valid descriptions, but they also tend to lack a certain philosophical clarity. It’s a lot like trying to define what a sport is, in that plenty of vague definitions exist, but any hard answer you give will inevitably make certain groups of people very angry. Nevertheless, just because a definition can never be absolutely 100% perfect, that does not mean we should completely refrain from trying. There’s a whole world of needless confusion out there, and it only takes a few simple thought experiments to provide real insight.

To begin, suppose I were to pick up a baseball and place it in your hands. What exactly would you experience? Naturally, you can see it, touch it, taste it, and smell it. It has mass, volume, texture, and a definite position in space and time. Clearly, it’s the most tangible manifestation of a material object that there ever was.

But suppose I were to ask you to hold a game of baseball in your hands. Now what do you experience? What exactly does that even mean? Does the game occupy a particular position in space? Can you touch it? Weigh it? Measure its volume?

Of course not. But why? What’s the difference?

Obviously, the difference is that a game of baseball is not a tangible object. It’s something people do. When you observe a game of baseball, you’re not exactly watching a “game,” per se. Rather, a far more accurate description is that you are watching people as they play baseball. That is to say, they are engaging in a process defined by rules. As long as they are collectively choosing to follow the rules of baseball, then we can say they are playing baseball. And when they choose not to follow the rules, they are simply not playing baseball; they are doing something else.

By analogy, logic operates under a very similar principle. It is not a singular entity unto itself, nor does it occupy any particular location in the universe. It is, however, a process that people engage in. It’s something you do. When people choose to follow the rules of logic, then we simply say that they are being logical. And when people fail to follow the rules of logic, then they are not being logical. Unlike baseball, however, which defines the rules for an athletic activity, logic is like a set of rules built into human language. It’s a way of expressing ourselves rigorously so that ideas can be clearly communicated and then formally analyzed.

This is an important point to emphasize, because there is a huge community of hack philosophers out there who habitually fail to understand such distinctions. It’s especially common among religious apologists wherein a lack of spatial extension is immediately equated with literal transcendence beyond the limits of our material universe [10, 11]. One classic manifestation of this confusion is the famous Transcendental Argument for the Existence of God [12], which actually tries to derive God’s existence from the very laws of logic themselves. It’s all loosely based on a naïve viewpoint called Logical Realism, wherein logic is treated as a singular force unto itself, existing objectively and independently of any human influence---almost like an ethereal energy field that surrounds us, penetrates us, and binds the very fabric of space and time.

The reality, of course, is that logic is fundamentally a human invention. Just as English, Spanish, and Japanese are all linguistic conventions created by humans, so too is logic just another similar kind of convention. Many systems of logic are even literally described as formal languages, which is in direct contrast with informal, or natural languages.

To see why this distinction might be important, suppose you were to hear someone utter the following natural-language sentence:

I saw the man on the hill with the telescope.

This is a perfectly well-constructed English sentence, but you may have noticed that it also exhibits a peculiar quality. Namely, the meaning of this sentence is unclear. Do I have the telescope? Does the man have it? Or does no one have it, and the telescope is just sitting on the hill? There is no objectively correct answer to this question without some sort of external context to back it up.

This is a well-known property of natural language called ambiguity---the quality of allowing multiple interpretations for a given sentence. It isn’t necessarily a bad thing, mind you, and there are plenty of situations where it might even exist intentionally. For example, a pun is a specific style of joke that deliberately utilizes ambiguity for comic effect. Poets and songwriters will often deliberately exploit ambiguity to add multiple layers of meaning to their writing [13]. Hucksters and snake-oil salesmen may even use ambiguity to make extravagant claims without necessarily promising anything concrete.

That’s all fine and dandy for some, but what happens when ambiguity leads to costly misunderstandings? For example, maybe I want to borrow money from a bank, or perhaps launch rockets into space. These are situations that demand as little ambiguity as possible and so require the use of much stricter language. A formal language can therefore be thought of as any structured set of rules that attempt to mitigate ambiguity. Scientists, engineers, computer programmers, lawyers, and mathematicians are all particularly fond of formal languages because the very nature of these professions are all built on precise communication.

To demonstrate, let’s use formal language to clarify the meaning of our natural-language sentence:

I saw the man, and the man was on the hill, and the hill had a telescope.

Notice how this sentence is much clearer than its predecessor, thanks in no small part to our use of the word AND. It’s a textbook example of a little tool called the logical connective, in that it literally connects propositions together to form more complex expressions. There’s a whole bunch of them you’re probably familiar with, such as NOT, OR, XOR, IF-THEN, etc, and they all fall under the scope of classical propositional logic.

This is by no means a unique system, either, and there are all kinds of interesting sentences we could construct though alternative logical frameworks. For example, suppose I were to tell you that

For every car on the highway, there exists a driver.

This charming little sentence was brought to you by First-Order Logic, which tells us how to use tools like the universal quantifier (for every) and the existential quantifier (there exists).

Another fun system you may have heard of is called Modal Logic, and it basically gives meaning to words like possible, necessary, and actual. These words are called modal operators, and they allow us to construct such happy sentences as

It is possible to paint a car red, but it is necessary to put wheels on it.

That’s all well and good so far, but there’s much more to logic than a bunch of wordy tools for constructing fancy sentences. Often times, we need to analyze the interplay between ideas, which makes it awfully nice to define some formal way of expressing those relationships. That’s why no system of logic is ever truly complete without some corresponding deductive system to go with it. In its simplest form, a deductive system is very similar to the idea of grammar that we typically associate with natural languages. Only rather than govern the flow of words in a single sentence, a deductive system governs the flow of sentences within an argument.

To see how this works in practice, let’s borrow a page from the classic Mel Brooks' film, Robin Hood: Men in Tights, by considering the following English sentences [14]:

1. The king’s illegal forest to pig wild kill in it a is.
2. It is illegal to kill a wild pig in the king’s forest.

Notice that both of these sentences contain the exact same collection of words, but in different arrangements. The first arrangement is generally considered “bad” in the sense that the words failed to follow the proper rules of English grammar. As a result, your brain was most likely unable to derive any coherent meaning from it. In contrast, the second arrangement is generally considered “good” because it correctly followed the rules of grammar. That’s why your brain was able to make sense out of it in accordance with established conventions.

By analogy, an argument behaves very much the same way. Simply begin with a collection of sentences, called premises, and then apply some rule of inference to see whether or not a conclusion supposedly follows. To demonstrate, consider the basic structure of a classic syllogism:

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

Now compare that against the following:

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

Once again, we have the exact same scenario as before in that both arguments contain identical words, but with different arrangements. Just as grammar dictated the proper flow of words in a sentence, we can clearly see that logic dictates the proper flow of sentences in an argument. The first argument is thus said to be invalid for the simple reason that it failed to follow the rules of a formal syllogism. Likewise, the second argument is said to be valid because it does follow the rules.

Bear in mind now that there is no universally correct way to stick words together in a natural language sentence. Languages around the world happily mix and match the flow of nouns, verbs, adjectives, conjugations, and the like, and no one complains about which arrangements are objectively “real.” The only thing that matters is for us to agree on a given convention so that meaningful communication can take place. Anyone who refuses to follow the agreed-upon rules for English grammar will thus find themselves unable to talk effectively with other English-speaking humans.

By extension, the exact same principle applies to logic. There is no universally correct way to stick sentences together in an argument, but there are rules we have agreed upon for the sake of communication. The very sentence, "All men are mortal," is really just a declaration of a simple rule: You show me an example of a thing that is a man, and I shall henceforth agree to label that thing as a mortal. Why exactly should anyone feel compelled to do that? Because that’s just what it means to say that "all" men are mortal! So when you finally do come to me with the proposition that Socrates is a man, then all we have to do is follow the rule by declaring Socrates to be a mortal as well. It has nothing to do with some objective state of external affairs, but a convention of language and understanding. In principle, I could even violate that convention outright by refusing to accept the mortality of Socrates, but all that would result is a bunch of needless confusion and frustration. It would like saying “hey guys, let’s play some hockey” before throwing a football at the goalie and then shouting “checkmate” at the referee. It’s not playing by the rules.

This idea is important, because it directly conflicts with a classical philosophical principle known as rationalism---the idea that pure, deductive logic is the ultimate source of all human knowledge. According to many popular schools of thought, such a doctrine would actually have you believe that the deepest mysteries of life, the universe, and everything, can all be perfectly well-understood by sitting in an armchair and thinking really hard about them. Descartes, Spinoza, and Leibniz were all particularly famous for holding this sort of view, and we can easily spot their influence in more modern philosophy as well. For example, the Ontological Argument for the Existence of God is a classic manifestation wherein the very idea of God Himself can supposedly be used to deduce His own existence. It's a textbook case of blatant philosophical question begging because pure logic, in and of itself, will never tell you anything about objective reality. At best, it can only tell you whether or not your attempts to describe reality have been formulated correctly.

To demonstrate, suppose I were to fill an entire argument with complete, nonsensical gibberish like so:

1. All flurbles are snuffins.
2. Zarky is a flurble.
3. Therefore, Zarky is a snuffin.

Notice that we again have a perfectly valid argument in the simple sense that it merely follows the correct rules of logic. Never mind the fact that flurble, snuffin, and Zarky have no accepted meaning within the English language. The conclusion follows logically from the premises in accordance with the syllogistic convention. You show me an example of a thing that is a flurble, and I will agree to categorize such a thing as a snuffin.

Clearly, something very important still seems to be missing from our logical framework. After all, why should I, or anyone else for that matter, accept the proposition that all flurbles are snuffins? By who’s authority should anyone feel bound by this declaration? Does the dictionary contain some entry that categorizes them accordingly? Is there a children’s show where the characters follow this rule? Maybe there’s an obscure corner of Madagascar where scientists have experimentally uncovered this phenomenon? Or what if some old lady next door to me just happened to utter that little fact the other day, and she’s never been wrong before?

This is why you generally can’t do logic without some formal system of semantics to go with it. After all, we can agree all day on the basic structure of a given deductive system, but it won’t do much good without some authority by which to establish premises in the first place. To that end, it generally helps to associate our propositions with some kind of indicator that officially denotes their authoritative “correctness.” In logic, this is known as a truth-value, and is typically expressed through a binary set containing the elements True and False {T,F}. Thus, to say that a proposition is “true” is to basically say that you accept it as a premise, and so you agree to abide by the formal conventions of some deductive system. Propositions that are “false” would then naturally fail in that regard.

That’s pretty intuitive so far, but it’s important to always keep in mind that we don't have to adopt a binary set of truth values. For example, some systems of logic actually use three truth values instead of two, and are thus referred to as tri-state logics {T,F,U}. Another well-known system is called fuzzy logic, and it utilizes an entire spectrum of truth-values by mapping them across all real numbers between 0 and 1. In principle, you could even walk to a chalkboard right now and invent your own completely original logic that uses 17 truth values on alternate Thursdays. Again, there is no objectively correct system to use, other than whatever collection of rules we happen to agree upon for the sake of communication. And since the binary system just so happens to be simple, familiar, and functional, it almost always ends up being the de facto presumption under most situations.

Once we’ve finally agreed on an official system of truth values, the next step is to formally establish which propositions are true and which ones are false. In logic, this is known as a truth assignment function, though many references will also call this an interpretation. Thus, to interpret a logical proposition is to assign it a truth value accordingly.

To demonstrate, consider again the simple proposition that all men are mortal. Is that true or is that false? One interpretation could be that every human being we’ve ever encountered has been mortal so far, and so we might as well just take it for granted that all future humans will be mortal as well. Alternatively, you could say that the English dictionary specifically defines “mortality” as an inherent property of human beings, thus making it true by definition. For that matter, maybe you think the old lady next door is the ultimate authority on all things mortal, and so if she says it, then it must be true.

These are all perfectly valid interpretations in the simple sense that they tell us how to assign truth values to a given proposition. So if you happen to abide by one of these interpretations, then great. We can finally build arguments on premises that are officially true. If, however, you reject these interpretations entirely, then that’s great too. All it means is that you have arbitrarily chosen to assign truth to propositions in accordance with some other set of rules.

Remember that in the formal context of propositional logic, truth is just a label that we assign to propositions. That means propositions can either be true or they can be false, but there is no such thing as raw “essence of truth” unto itself. So whenever you come to me with a simple proposition like all men are mortal, then sooner or later that proposition must be interpreted if we ever expect to do any logic on it.

At least one common method of interpretation is to simply assert a small handful of propositions outright and then see what happens. Propositions like this are called axioms, and they serve as very powerful building blocks for many formal languages. For example, according to the language of natural numbers, it is simply a rote fact of life that:

 

For any natural number n, n=n. 

 

Why exactly should that be the case? Because we say so, that’s why! It’s just one of the things we demand to be true whenever we talk about natural numbers. It's no different from demanding that all bachelors be unmarried men. All languages are built on rules, and there is nothing wrong with declaring those rules as a foundational property of the language itself.

Once the axioms of a language have been officially established, the next step is to begin deriving new propositions in accordance with some deductive system. Any new true propositions generated in this fashion are called theorems, and they represent the heart and soul of virtually all mathematical inquiry. That's why we say mathematics is an invention and not a discovery. Everything you were ever taught about the nature numbers, sets, functions, etc, all began as little more than a collection of arbitrary axioms being operated upon by logical rules of inference.

If that all sounds a bit circular to you, then just remember that axioms technically have nothing to say about objective reality. Rather, they simply define the foundational rules for a particular language. If that language happens to work well at describing practical scenarios with functional precision, then all the better. But it’s important to always keep in mind that there is nothing physically forcing us to adopt a particular axiomatic system. In principle, we could easily mix and match the rules all day, and there are plenty of situations where it might even be beneficial to do so.

For example, take the classic Peano axiom that:

 

There is no natural number n such that n+1=0. 

 

Where exactly is it etched in stone that we must absolutely adhere to this axiom from now until eternity? Why not just discard this rule entirely and then replace it with something wacky like 12+1=1? Now we suddenly have a perfectly self-consistent system where all sorts of funny things can happen, like 7+8 = 3, and 10+11 = 9. It’s nothing mysterious or unfathomable. It’s just modular arithmetic, and people around the world use it every day as a practical system for telling time.

This has all been a tiny, oversimplified sampling of the rich tapestry that exists within the world of modern logic, but hopefully we can begin to recognize the essential properties that make logic distinct. When all is said and done, a "logic" is little more than a formal language coupled with a deductive system and semantic interpretations. Granted, this is not necessarily a perfect definition, and there are probably plenty of experts who would take issue with the finer details. That’s fine, but we can clearly see that logic is far more than a mere absence of emotional impulsivity. It’s not an ethereal force that governs the universe, either, but a linguistic convention built on rules---rules that are designed help express ideas rigorously and then analyze the interplay between them.

So the next time you find yourself stranded on a distant planet surrounded by hostile alien monsters, just remember that it’s okay to feel a little bit emotional. But no matter what feelings may be aroused in any given moment, you’re eventually going to have to start making decisions, and presumably you’d like those decisions to improve the situation. Often times, we may not even have the luxury of careful deliberation, but must instead act upon brute, intuitive impulse. However, on the rare occasions when we do have time to think about a problem in detail, then it usually helps to have some official system in place for evaluating information, formulating a plan of action, and then coordinating that plan among your peers. So step back, take a breath, and use your logic! 

Notes/References:

1. "The Galileo Seven," Star Trek, Season 1, Episode 16
2. J. Galef, "The Straw Vulcan," Oral Presentation at Skepticon 4 (2011) [link] 
3. C. DeLancey, A Concise Introduction to Logic, Open SUNY Textbooks (2017)
4. I. M. Copi, C. Cohen, and K. McMahon, Introduction to Logic, 14th ed, Pearson Education Limited (2014)
5. P. Suppes, Introduction to Logic, Van Nostrand Reinhold (1957)
6. Columbia University, The Columbia Encyclopedia,  8th ed, Columbia University Press (2018)
7. S. Guttenplan, The Languages of Logic: An Introduction to Formal Logic, 2 ed, Wiley-Blackwell (1997)
8. P. Hurley and L. Watson, A Concise Introduction to Logic, 13th ed, Cengage Learning (2017) 
9. L. T. F. Gamut, Logic, Language, and Meaning, Volume 1: Introduction to Logic, University of Chicago Press (1991) 
10. W. L. Craig, "Do the laws of logic provide evidence for God?" ReasonableFaith.org (2016) [link] 
11. J. Warner, "Is God real? Evidence from the laws of logic," ColdCaseChristianity.com (2019) [link]
12. M. Slick, "The Transcendental Argument for the Existence of God" (2008) [link] 
13. "The machinations of ambiguity are among the very roots of poetry." - William Empson
14. Robin Hood, Men in Tights [link]