This post is based on a talk I gave at my local Church. I have slightly expanded the text (adding material I either cut out or supplementary), and edited it for this medium.

Introduction and Purpose

Today, I’m discussing the topic of miracles. It’s a big topic. There’s a lot I could discuss. I could have a closer look at the Biblical miracles. Or look at miracles through Church history. Or whether miracles happen today. But I’m discussing something else. The philosophical question.

Atheists and agnostics reject the possibility of miracles. It’s often a big reason why they reject Christianity. Here are a few quotes from prominent atheists. I’ll discuss their arguments later. Some say science has removed any need for miraculous explanation. Others say historians should adopt a neutral approach which considers miracles unlikely. Others claim miracle accounts can never be well established enough to be believed. Our society is suspicious of miracles.

It’s also a motivation to drifting away from Christianity into liberalism. Liberalism’s what you get when you try to squeeze Christianity into the atheist’s secular philosophical framework. It certainly used to be true that a first stumbling block for liberals was Christ’s virgin birth. Why doubt this? They’ve already absorbed the belief that miracles are implausible.

Does Christianity without miracles make sense? Clearly not. We’ve just read from 1 Corinthians 15. “And if Christ has not been raised, your faith is futile and you are still in your sins.” If we abandon miracles we have to abandon the resurrection, and, consequently, Christianity. So we need to be able to understand and answer the arguments which claim to show that we shouldn’t believe that God performs miracles.

Biblical Description of Miracles

What is a miracle? A standard philosophical definition is “A miracle is a violation of the laws of nature by a supernatural agent.” I don’t like this definition. I’ll explain why later. Although its clearly not a definition early Christians would have used. The notion of the laws of nature as we understand it today is a relatively modern concept: only about 800 years old.

The New Testament predominately uses three words to describe what we call miracles.

Sēmeion (σημεῖον) is usually translated as sign. It’s a distinguishing mark, or characteristic. A sign points to something else. In logic, it provides evidence without being a deductive proof. I’ve listed a few New Testament examples.

This, the first of his signs, Jesus did at Cana in Galilee, and manifested his glory. And his disciples believed in him. (John 2:11)

The Pharisees came and began to argue with him, seeking from him a sign from heaven to test him. (Mark 8:11)

Now the betrayer had given them a sign, saying, “The one I will kiss is the man; seize him.” (Matthew 26:48)

The first refers to Jesus turning water into wine. But the sign isn’t about new wine. It points to Christ’s divine glory. In the verse from Mark, the Pharisees sought direct evidence for Jesus’ claims about Himself. The third verse isn’t a miracle. But it’s a sign. Judas’ action conveys a meaning beyond the simple kiss.

So a sign is more than just an unusual event. It also points to a deeper meaning.

Teras (τέρας) is often translated as wonders. In classical literature it’s portent of doom, an omen, a frightening phenomenon sent as a warning. New Testament examples include these passages.

"For false Christs and false prophets will arise and perform signs and wonders, to lead astray, if possible, the elect." (Mark 13:22)

So Jesus said to him, “Unless you see signs and wonders you will not believe.” (John 4:48)

And awe came upon every soul, and many wonders and signs were being done through the apostles. (Acts 2:43)

Wonders are spectacular events creating an emotional reaction. They aren’t all from God. Wonders from false prophets lead people astray. God uses wonders to bring people to Him or His apostles. The word emphases our emotional reaction.

Dynameis (δυνάμεις), is often translated “mighty work,” or power, or similar. The translators aren’t always consistent. It means a capability, force or inherent power to bring about an effect. It could refer to powerful natural forces, such as fire or wind. Or the military power of a King. Some New Testament examples include these passages:

“Woe to you, Chorazin! Woe to you, Bethsaida! For if the mighty works done in you had been done in Tyre and Sidon, they would have repented long ago in sackcloth and ashes." (Matthew 11:21)

"And the stars will be falling from heaven, and the powers in the heavens will be shaken." (Mark 13:25)

Even Simon himself believed, and after being baptised he continued with Philip. And seeing signs and great miracles performed, he was amazed. (Acts 8:13)

Dynameis focuses on the power of the one performing the action.

These words don’t rely on the modern distinction between natural and supernatural. They apply to both natural and supernatural events. The lines between natural and supernatural are, in this respect, somewhat fuzzy. What we regard today as natural events were often regarded as having a supernatural origin. This is one reason I dislike the philosophical definition of miracle. It assumes a distinction between natural and supernatural which isn’t always appropriate.

Greek has a fourth phrase which also means miracle. It doesn’t appear in the New Testament. The Jewish historian Josephus’ description of Jesus uses paradoxōn ergōn (παραδόξων ἔργων):

About this time there lived Jesus, a wise man, if indeed one ought to call him a man. For he was one who performed surprising deeds and was a teacher of such people as accept the truth gladly. He won over many Jews and many of the Greeks. He was the Christ. And when, upon the accusation of the principal men among us, Pilate had condemned him to a cross, those who had first come to love him did not cease. He appeared to them spending a third day restored to life, for the prophets of God had foretold these things and a thousand other marvels about him. And the tribe of the Christians, so called after him, has still to this day not disappeared. (Josephus, Antiquities of the Jews, Book 18)

This carries a negative and sceptical connotation. It literally means paradoxical works. Events which contravene the usual patterns of cause and effect. This is closer to the philosophical definition of miracle. But it’s absent from the New Testament. It’s not how the apostles thought about miracles.

So a miracle

• Comes from someone with inherent power,
• points to that person’s nature,
• and produces an intense and perhaps slightly fearful emotional reaction.

Laws of nature?

The philosophical definition mentions laws of nature. What are laws of nature? Deists and atheists have a different answer compared to a theist’s understanding about God’s relationship with the natural world. Unfortunately, we are taught the atheist understanding in school. Many people, even many Christians, don’t realise there’s an alternative.

I define Deism as the belief that the universe is a self-sustaining system but not closed, as it was created and its rules set up by God.

I define Atheism as the belief that there are no supernatural beings, the universe is a closed self-sustaining system. Matter moves by itself.

I define Theism as the belief that the universe is neither closed nor self-sustaining, but God is constantly active directing matter’s motion alongside matters’ natural powers and causation.

I define Occasionalism as the belief that there are only divine causes, and no material causes.

Deists and atheists believe that the physical universe operates by itself. The laws of physics stand on their own. Some say the laws are just observed regularities. Others that they describe the powers of natural objects. Others think of them as something guiding matter’s motion, using a mechanical clock as an analogy. In each case a scientific explanation means God isn’t directly involved. Deists believe God set up the laws of nature, and maybe gives the universe a little push now and again. Atheists regard invoking God as unnecessary and redundant. The laws explain everything. Perhaps even themselves. Other philosophies, such as Pantheism, Panentheism, ultimately take a similar position.

This philosophy clearly distinguishes between natural causes and God sitting outside the natural world. God’s interventions violate the laws of nature.

What does the Bible say?

He [Jesus] is the radiance of the glory of God and the exact imprint of his nature, and he upholds the universe by the word of his power. (Hebrews 1:3)

He is the image of the invisible God, the firstborn of all creation. For by him all things were created, in heaven and on earth, visible and invisible, whether thrones or dominions or rulers or authorities—all things were created through him and for him. And he is before all things, and in him all things hold together. (Colossians 1:15)

Christ upholds the universe. In him all things hold together. Christ isn’t just a passive bystander. God is actively involved to keeping the universe going moment to moment. Psalm 104 expresses this idea in another way.

From your lofty abode you water the mountains; the earth is satisfied with the fruit of your work. You cause the grass to grow for the livestock and plants for man to cultivate, that he may bring forth food from the earth. (Psalm 104:13)

God waters the mountains. God causes the grass and plants to grow.

But wait a minute? Don’t physics and biology explain why grass grows? How can both God cause it and physics cause it? We only have to make this choice if we accept the atheistic division between natural law and supernatural intervention. What if the laws of physics describe how God sustains the universe in the absence of any special purpose? Then saying science did it is just another way of saying God did it.

Theism is the belief that God created the universe, not as something self-sufficient, but needing God’s constant activity to sustain and move. Every event in the universe is due to God’s action. Christianity’s underlying world-view is one type of theism.

If everything’s God’s work, how do we distinguish miracles from ordinary events? That’s why we needed to turn to the Biblical words. A miracle is a work of God’s power. So is everything else. But a miracle is also a direct sign teaching us about aspects of God’s nature not obvious from non-miraculous events. It creates a reaction of fear or awe in a way non-miraculous events don’t.

Theologians discuss God’s general and special providence. General providence is what God provides for all mankind, for example by providing rain, regardless of how they stand with Him.

"But I say to you, Love your enemies and pray for those who persecute you, so that you may be sons of your Father who is in heaven. For he makes his sun rise on the evil and on the good, and sends rain on the just and on the unjust." (Matthew 5:44)

Special providence is when God acts with purpose for His people, for example by sending His Son.

For God so loved the world, that he gave his only Son, that whoever believes in him should not perish but have eternal life. For God did not send his Son into the world to condemn the world, but in order that the world might be saved through him. (John 3:16)

In general providence God acts neutrally. He doesn’t show favouritism. In special providence, God acts to benefit His people. These acts reveal something about God’s nature. We ought to react to them with wonder. Perhaps familiarity has dulled us of this, but its amazing that God, who is so pure that evil can’t dwell with him, would give Himself for people like us. So acts of special providence are miracles.

Why does God mostly govern the world by general providence? I think the answer’s in Genesis 3.

And to Adam he said, “Because you have listened to the voice of your wife and have eaten of the tree of which I commanded you, ‘You shall not eat of it,’ cursed is the ground because of you; in pain you shall eat of it all the days of your life; thorns and thistles it shall bring forth for you; and you shall eat the plants of the field. By the sweat of your face you shall eat bread, till you return to the ground, for out of it you were taken; for you are dust, and to dust you shall return.” (Genesis 3:17)

Before the fall, our ancestors lived under special providence, under God’s special favour. God actively protected them from thorns and sweat. Then they rejected God. They wanted to be like God, and know good and evil, and live by their own strength. So God gives us what we want. A world where we can pretend we rule. Of course, the main curse of the fall was our spiritual separation from God. But that also means separating from God’s constant protection in the physical world.

If God causes all the events in the universe, where does that leave science’s study of material causes? Why think an event only has one cause? Material causes and God’s action together explain the event. Denying material causes is a heresy known as occasionalism.

How I think about physical law and miracles

So far, that’s standard Christian theology. But how does it work in practice? Let’s speculate a bit. How can both God and material beings cause an event?

Well, there are different types of causes. Cause just means an explanation, and there are different types of explanation. We can ask

1. What thing did this thing come from?
2. What things could emerge from this thing?
3. Why this particular event rather than another?

The efficient cause answers the first question. The final causes answer the second question. The final causes discuss would could happen, which is different from actually will happen. You can have several possibilities, only one of which is realised. In classical mechanics, the physics you learnt at school, there’s only a single possible effect. What’s meant by possible? Logical possibility implies there would be a contradiction; but that’s not involved here. Possible means what’s allowed by Newton’s laws. But then we must ask why Newton’s laws are usually followed.

In contemporary physics, Newton’s laws aren’t followed. The image shows a classic two slit experiment.

You fire particles one at a time through a barrier with two slits. You can’t predict where each individual particle will hit the detector. You send one particle through, and it will hit one of those dots on the detector. We can’t predict which one. Then you fire another identical particle through; exactly the same circumstances and it will land on a different one of those dots. But as you keep sending particles through, you will get a pattern which matches the calculated probability distribution on the right. The same circumstance can have different outcomes. One happens in practice. Why that one, and not another? Physics can’t tell you. We can only predict frequency distributions after repeating the experiment many times. But if the universe is rational, something must explain why that outcome happened, and not one of the other possibilities. This is the event cause. The final cause lists possible outcomes assuming that the physical laws are followed. The event cause chooses between them.

Efficient and final causes both refer to material particles. These are what physics studies. We can use the previous state of the universe to predict the frequencies of possible future outcomes. The event cause doesn’t have any physical explanation. That leaves supernatural explanations. The event cause is God’s free choice and power to bring it about.

If God doesn’t have any special preference, he’s just as likely to choose one option as another. We can’t say what will happen in any given occasion. But in the long run, it will even out. That implies various symmetries and regularities, and we can use those to predict the frequency distributions.

But suppose God does seek a particular outcome. He wouldn’t then pick each individual microscopic event seemingly at random, but as steps toward that goal. The symmetries are broken. The old probability calculation is useless. God uses the same means to interact with the universe. But God’s intentions are different, it’s a different context, so a different outcome.

How do we identify whether something is a miracle? We can’t always. But certain events have a very low probability, maybe zero, assuming God is indifferent to the outcome. They can still happen, but only when that assumption’s false. God did desire a particular outcome. These are definitely miracles. But sometimes, God’s desire would be for an event which physics doesn’t predict a low probability. Those are still miracles. God’s still providing a sign. It’s just not useful when debating atheists.

Are miracles God’s violations in the material universe, while non-miracles aren’t? No. Both miraculous and non-miraculous events arise from God’s actions and free choices. The difference is whether or not God wants to favour some people with a wondrous sign.

Are such events demonstrations of God’s power? Yes. Are they signs pointing to aspects of God’s character? Yes. Would they invoke a sense of wonder? They are beyond our ordinary expectations so yes.

Or, to put it in a simpler way, God actively sustains every event in the universe. He has a free will. It’s rather bold to claim that He can’t occasionally do things differently when He has a good reason to.

So lets discuss the main arguments raised against miracles.

A miracle is because we don’t understand physics better

1. A miracle is a violation of the laws of physics.
2. Our knowledge of the laws of physics doesn’t correspond to the real laws of physics.
3. If we see a violation of the laws of physics, we modify our knowledge so the known laws also predict that event.
4. The true laws of physics would explain every event that happened.
5. Therefore there are no miracles.

As discussed, this argument depends on an incorrect definition of miracles. If we define the laws of physics as what happens when God acts indifferently, they can’t be expanded to also include miracles. Premise 3 breaks down. Or we could define them to describe all God’s actions. Then a miracle doesn’t violate those laws, and premise 1 fails.

Naive argument against miracles

A naive argument against miracles is “Hasn’t science shown that the universe operates according to regularities without needing to invoke God?” Saying Without needing to invoke God depends on your philosophy of physics. It begs the question against theism. But doesn’t the universe appear regular? Would science be possible if it wasn’t? So we get this argument.

1. The universe is often observed to produce outcomes consistent with physical predictions.
2. Therefore the universe always produces outcomes consistent with physical predictions.
3. Therefore miracles are impossible.

One clear objection for me presenting this argument (and the one just below this) is that it's a straw man. And I agree. Nobody advocates for this precise argument, or at least nobody who has given the matter any decent amount of thought. You can’t jump from point 1 to point 2. Atheists use more sophisticated arguments. I’ll come to. So why do I start with these straw men arguments? To highlight the errors which the more sophisticated arguments have to avoid. My contention is that while those arguments are more subtle, and its far less obvious, they often make the same underlying mistake as either this argument, or the one below, or both. It's just harder to pick through the arguments and realise this is the problem.

Here’s another really bad argument (from Voltaire):

1. A miracle is the violation of mathematical, divine, immutable, eternal laws.
2. This definition is self-contradictory. A law cannot be immutable and violated.

This uses a bad definition of miracle, and a bad definition of laws. It assumes what it sets out to prove: that the laws are universal. The theist will (as I did above) adopt a definition of laws which denies that they are universal. To my mind, there is also an issue with the language here (I took this statement of the argument from the Stanford Encyclopedia, just breaking it up into point form; so this isn't just me taking issue with the language of my own paraphrase of the argument, but someone else's paraphrase of Voltaire's argument). I would usually define immutable as unchanging, while the contrary to being violated is inviolable or universal. One can have a law which is unchanging but still violated from time to time. But clearly, the problem with this argument is that it has defined the laws of physics in such as way that the advocate of miracles would not accept. For example, I defined the laws as describing God's actions when He is indifferent to the outcome. This leaves open the possibility that God might act differently when He is not indifferent to the outcome. This definition isn't consistent with defining the laws as inviolable. In fact, whether or not the laws are inviolable, and miracles violations of those laws, is the very matter under dispute. This sort of argument from definition is just begging the question. If you are going to argue against miracles, you have to either use definitions that theists would accept, or show that the premises behind the theist understanding are either self-inconsistent or inconsistent with observed science (again without begging the question by making scientific law inviolable or jumping from often to always. Again, most serious atheist scholars are well aware of this and try to avoid this mistake. But, nonetheless, I think their arguments often just hide it and merely make it less obvious than eliminate it.

Hume’s argument against miracles

Hume’s argument is among the most influential. The following is my own paraphrase, but I believe it to be a faithful reconstruction of the thrust of his argument (while omitting many of the details and examples he used in support of the second part of it). (Obviously in a short talk I have to paraphrase and summarise.)

1. A miracle is a violation of the laws of nature by a supernatural agent.
2. We should always prefer more probable explanations over less probable explanations.
3. The laws of nature are observed regularities supported by vast experience.
4. Violations of these laws are by definition very unusual.
5. Miracles are thus the most improbable explanation.
6. Miracles reports are ultimately based on human testimony.
7. People can lie, misunderstand, be mislead, and so on.
8. It might be very unlikely the testimony is false, but it can’t be as improbable as a miracle.
9. Therefore we should never believe a miracle account, even if we witness it ourselves.

This argument has convinced many people. Is it sound?

Premise 3 is based on Hume’s wider philosophy of physics. He’s an empiricist, meaning he only trusts observation, and is distrustful of theoretical arguments. You make observations. You draw a line connecting those observations. You make more measurements and confirm the line. This is then called a law of nature. Many of the laws in Hume’s day when modern science was in its infancy were formulated in this way. You can never be certain the law is correct, but the more data points supporting it the more likely it is to be correct.

Can you replace premise 3 with another philosophy of physics? Such as the one I proposed earlier, where a miracle violates the underlying symmetries constraining physics? Or the mechanistic philosophy accepted by many deists. And certainly you can do this, and many people have, but it introduces another problem into the argument. This sort of definition doesn’t help calculate the probability that the laws are violated. We can express the laws in terms of some underlying principle, whether that's some mechanistic rule, or symmetry, or whatever. I ignore for simplicity the issue that we don't yet have a perfect understanding of those laws, or that we often have to make approximations to calculate the effects of those laws. Worrying too much about such concerns would just lead us back to the "can't we change physics" argument discussed above. Such an understanding of laws would allow us to clearly distinguish when these laws are violated and when they are followed (one of my concerns below). But such a definition of laws is limited in scope. Such laws correctly predict what happens when the laws are followed, but they don’t address how often they are not followed. We need to address how often they are not followed to say those exceptions are low probability, for point 4 of the argument. Saying they are always followed is a philosophical, not scientific, prediction. Essentially, it's just collapsing back into Voltaire's argument discussed above. And clearly this philosophy would be unproven (or if you can prove it, that itself would disprove theism, making arguments concerning miracles redundant), and theists would reject it in favour of an alternative philosophy of science. So if you adopt an additional assumptions to get from the adaptation of point 3 using the alternative definition of law, to point 4. What could these assumptions be? I think there are two options. Firstly, you could make the dubious philosophical assertion that the laws are inviolable. Or secondly, you can fall back on observation, and effectively count how many times the laws are violated compared to how many times they are observed (which is the approach I follow below). I take this to effectively reduce to Hume's original version of the argument based on his understanding of the laws.

But am I missing Hume's point? He defines the laws as regularities supported by an overwhelming number of observations. Doesn't this definition in itself show that violations of those laws are low probability? This is why I discussed those three other arguments first. Making this sort of argument collapses into one of those errors. Either you define the laws so broadly that they will include both those events which are signs from God and those which aren't, meaning Hume's definition of a miracle has to be rejected, or you end up jumping from often observed to always observed, which would beg the question, or you beg the question by assuming that miracles don't happen by implying this in a definition of natural law which theists would reject. And this is why in this talk I keep coming back to simply counting how many miracles there are compared to non-miracles in a sample of events. I cannot see any other way that isn't immediately invalid that you can get from premise 3 of the argument to premise 4.

I’ve discussed probability quite a bit. What is a probability? What’s it used for?

A probability assumes a set of possible outcomes. Those outcomes should be

• Complete, in that they cover all possibilities.
• Orthogonal, in that they don’t overlap.
• Irreducible, in that they can’t be further subdivided.
• Consistent, in that there is either only one way you can represent those outcomes, or you never compare using results derived from two different representations. I'm particularly thinking of the different bases used to represent the amplitudes in quantum physics as a violation of this rule. Amplitudes aren't probabilities. This need underlies the single framework rule in the consistent histories interpretation of quantum physics.

A number is assigned to each of those outcomes. If those numbers obey certain rules, they are probabilities. A probability distribution is all those numbers together. Those rules can be expressed in several ways, but I usually fall back on Kolmogorov's axioms, expressed in the following equations:

Frequency distributions obey similar rules. A frequency distribution is when an experiment is repeated many times, and you count how many times you get each outcome. Divide the frequencies by the total number of observations, and the distribution obeys the same rules as probabilities. What’s the difference? A frequency distribution is measured. A probability is calculated. Calculated from what? Numerous assumptions and premises. Perhaps the system has various symmetries. Perhaps from some scientific model. Perhaps you estimate it from a small representative sample of events.

What are probabilities used for? Firstly, to predict frequency distributions. You assume some theory is true, and accurately describes what happens in the world. You use that assumption to calculate a probability distribution to predict the expected frequency of each outcome. You then test the theory by comparing the probability distribution with a measured frequency distribution. If they don’t match, you re-examine the assumptions behind the scientific theory, and come up with a better theory. Which you then re-test with another set of data. This is how modern science proceeds. But frequency distributions don’t predict individual events. Miracles are individual events. Treating a probability as a predictor for a frequency distribution isn't consistent with how probability is used in Hume's argument. Because Hume isn't trying to predict frequency distributions, but instead is evaluating whether we should believe an event happened, clearly he can't use probability in this way.

Then there’s decision theory. I don’t want to encourage anyone to gamble, but if you do gamble, decision theory teaches you how to win. It’s all about balancing rewards and risk with the chances each will be achieved Suppose you play a game with a fair six-sided dice. Rolling a 6 wins you £120. Anything else loses you £30. Should you play? The probability of rolling a 6 is 1/6. Your expected winnings (i.e the amount you win when you roll a 6 times the frequency you roll a 6) are £20. The probability of rolling something else is 5/6. Your expected loses are £25. You might get lucky and win an individual game. But in the long term, you’ll lose. You shouldn’t play this game.

Hume’s argument suggests you should always favour the biggest probability. That’s incorrect. It depends on the risk and reward. Let’s change the rules of the game. This time you only lose £18 if you roll something other than a 6. Your expected winnings are still £20. Your expected losses are now only £15. Even though you lose 5 games out of 6, in the long run your winnings exceed your losses, and you can expect to get money from playing this game. This is just very basic game theory. The same mathematics underlies Pascal's Wager, a well discussed argument suggesting its better to believe in God. I don't want to discuss Pascal's wager here; it makes various assumptions beyond this basic mathematics, and people question whether those assumptions are sound (I personally think they aren't as originally presented, but can easily be adapted to resolve the frequently-raised problems). But nobody questions Pascal's mathematics.

To be fair to Hume, this mathematical theory was developed after his time. He didn't know it. But obviously today, when evaluating Hume's argument, we should lay aside his primitive understanding of probability, and utilise the theory as understood today. Either Hume's argument needs to be adapted to use modern Bayesian probability theory, or, if it can't be adapted, then Hume's ignorance and misuse of probability is a good reason to reject it.

So Hume’s premise 2 is dubious. You shouldn’t go for the option that seems most likely, but the one that best balances rewards and costs. For example, if you want to reject the evidence for Jesus’ resurrection, you should also consider the cost to you if it happened and you disbelieve it.

I’ve already discussed why the definition in premise 1 is incorrect. Hume’s argument depends on divine interventions in the universe being uncommon. In theism, every event that happens involves divine action. A rather strange definition of “uncommon.”

Are miracle claims uncommon? Craig Keener reported in his book (volume 1, P.238 in the edition I have) that 73% of Pentecostals and 52% of charismatics claim to have witnessed miracles. That’s 200 million miracle reports within our lifetime, not counting Roman Catholics and other Christian traditions.

How can we calculate a miracle’s intrinsic probability? We could take a group of observed events, and say the probability of a miracle is the number of miracles in that set divided by the total number of events. But how do we know how many miracles there are unless we have a way of identifying what is and isn’t a miracle? We can’t use Hume’s conclusion that miracles are always the lowest probability option to guide us. That assumes that miracles are low probability, which we can’t use to demonstrate that miracles are low probability without circular reasoning. So this requires an independent way of identifying what is and isn’t a miracle. Which makes Hume’s argument redundant. We could use an alternative understanding of natural law, such as a mechanistic law, or derived from symmetry to determine whether or not an event is a miracle. But I still don't think this would help us. Such an description would allow us to conclude that if the event occurred as described then it would be a miracle. But that leaves the question of whether we should believe that it occurred as described. This is obviously the question that Hume's argument attempts to answer. But to answer the question (at least if we proceed as Hume would want us to) you need to know the probability that miracles occur, which you can't derive from mere knowledge of the laws, as discussed above. We are still left with the dilemma, either Hume's argument is redundant, or it begs the question.

Could you construct the sample from events you know aren’t miracles. This tells you that the probability of a non-miraculous event being a miracle is very small. That isn’t helpful. The sample needs to be representative to draw conclusions about the wider population. The same circumstances must apply. But a miracle doesn’t have the same circumstances. In a miracle, God desires to reveal a sign. In a non miracle, he doesn’t; he’s indifferent to the outcome. The probability can’t just rely on a count of non-miraculous events. We must also ask how likely it would be that God would produce a sign in those circumstances.

Let’s leave that concern aside, and count the number of miracles that happen in a given set of events and use that to estimate the intrinsic probability that an event is a miracle, before we take into account any testimony in its support. But this approach relies on various assumptions. Probabilities are always calculated from various premises and assumptions. For example, I claimed the probability of rolling a six from a fair six-sided dice is one in six. Why is this? Both the dice and the means by which it’s thrown respect a symmetry. The mechanics isn’t biased by the final outcome. We assume this symmetry will be reflected in the final probability distribution. The six possible outcomes all have the same probability. So there are three assumptions:

1. That the dice respect these symmetries.
2. That the means of selecting the result (throwing the dice) respects the symmetry.
3. Such symmetries should be reflected in the final outcome.

I mentioned earlier that contemporary physics uses symmetries to frame the laws which calculate the probability distribution which predict the frequency distribution. The methods to get from symmetry to probability are far more complex and the calculations much harder, but it’s the same underlying principle. Symmetry is used to predict frequencies.

What’s the probability that I would pick out a Chinese person in this room? There isn’t one. It depends on the assumptions. We can divide the number of Chinese people by the total number of people. That gives us a number. Is it a useful number? Only if I choose the person at random with everyone equally likely. If instead I deliberately pick out someone I know is Chinese, the probability’s going to be 1. Different assumptions lead to different probabilities.

Going back to miracles. Reconstructing a useful probability from a sample of events requires several assumptions. Hume’s argument involves comparing the number of miracles and non-miracles in a set of events to estimate the probability. But, as with my example involving picking out Chinese people, that estimate is only useful if miracles occur or are selected at random, with each event equally intrinsically likely to be a miracle. So this assumes:

1. There is a symmetry in the causes between miracles and non-miracles. Which there isn’t.
2. Miracles happen at random according to a uniform distribution. Which they don’t, because they depend on God’s choice.
3. We select events to investigate at random. Which we don’t. We don’t ask did Jesus rise from the dead because we put all the billions of people who have lived into a hat and happened to draw Him out. We look to Jesus because the apostles witnessed something, recorded it, and many believe their testimony changed their lives.

Remember, a miracle occurs when God purposely decides to reveal a sign because the circumstances are different to those cases where God only directs through general providence. Hume’s argument is only valid if the circumstances are the same and God picks when to perform a miracle at random. In theism, this would only be true if God only governed by general providence; alone and there are no miracles. So Hume adopts a definition of the laws of nature which denies miracles to try to prove miracles don’t happen. It’s ultimately the same mistake as in the naive arguments. Hume’s argument is circular and invalid.

I should at this point address an objection? Can't we avoid this problem using Bayesian probability? Indeed isn't this precisely what Hume does? He starts with a very low intrinsic probability for the miracle, and then states that we use the evidence to adjust that, but that evidence can never be good enough to overturn the original low intrinsic probability.

Let's express this mathematically.

This equation is the starting point. It's Bayes' theorem, a standard result of probability theory. In this use, the symbols have the following meaning

• M = we should believe the report of the miracle.
• E = The evidence for the miracle.
• P(M|E) = we should believe the report of the miracle given the evidence.
• P(E|M) = How likely would we get this evidence if the miracle happened.

The argument would go that P(M) is so low that it cannot be adjusted to make P(M|E) sufficiently high that we should believe it. I think I've seen William lane Craig highlight one obvious issue with this naive argument: that the denominator P(E) would also be exceptionally small in an atheistic universe where miracles cannot happen, and this would cancel out the extremely small P(M). And there is some merit in this objection. But this isn't the point I want to make.

My point is that this equation is incorrect as it stands. It forgets that all probabilities are conditional, and dependent on the precise assumptions used to calculate the probability. So, instead, we have to express the equation as below.

So here R represents the assumption that miracles occur at random according to a uniform distribution, or this particular event is just as likely to be a miracle as any other event, or however you want to phrase the assumption needed to calculate the probability. I agree that P(M|R) is a very small number. But the issue is that theists reject the premise R. Theists don't believe that miracles occur at random, but according to God's sovereign choice based on the circumstances surrounding the miracle which will differ from one event to another in ways beyond those which physicists tend to consider. Indeed, however you phrase premise R in order to get a small enough P(M|R), it will implicitly assume that theism is false. To get a truly neutral evaluation of whether miracles occur, we need to calculate P(M|E) without any reference to the assumption R. But that's not what this equation gives us. It states that miracles are a very low probability if we assume R is true which implicitly assumes theism is false. It's saying we shouldn't believe miracle accounts if theism is false. But we don't need Hume's argument to tell us that. If miracles are presented as evidence for particular types of theism, we can't evaluate those miracles by assuming theism is false without begging the question.

Can we use Bayes' theorem to convert that P(M|ER) into P(M|E)? Almost. We need to first introduce another set of assumptions X. These are the truly neutral assumptions, which both atheists and theists accept, and which can be used to assess the probability that R is true. The equation then becomes.

So this gets the result we want. The probability that miracles occur given the evidence and the underlying universally accepted assumptions. We see the numerator has P(M|RX), Hume's very low probability that miracles occur. But then we also have the fraction P(R|X)/P(R|EXM). If R is low probability given the assumption X then both the numerator and denominator of this expression will be equally small, and such effects will cancel out. But that denominator also considers the probability that R is true assuming that the miracle happened. But, as long as there is a viable theistic alternative to R, this must be just as small as P(M|RX). If one of the more dramatic miracles occurred, then theism is true. If theism is true, then R is false. And this probability is exceptionally small, and certainly small enough to cancel out P(M|RX). It's basically asking us how well the miracle can be explained in terms of "natural processes" (as the atheist would understand them). Some claimed miracles can be attributed to the normal workings of nature under general providence. But others, such as resurrections or resuscitations, can't be. Remember, this sidesteps any questions concerning whether the evidence is good enough. That's addressed elsewhere in this equation. It asks if R could be true, in effect whether atheism or deism could be true, if the miracle happened.

So this equation summarises the objection. Hume's argument relies on an additional premise, which I have expressed as that each event is equally likely to be a miracle. That premise contradicts theism. Miracles can only happen if theism is true. So the assumed premise entails that miracles don't happen, so consequently Hume's argument assumes what it sets out to prove and begs the question.

Spinoza’s argument against miracles

Spinoza was a pantheist. He believed that the universe is in some way God. That’s the background behind his first premise.

1. The will of God is identical with the laws of nature.
2. A miracle is a violation of the laws of nature.
3. Necessarily, God’s will cannot be broken.
4. Therefore, miracles cannot happen.

Premise 1 contradicts the theistic definition of miracle. The laws of nature describe God’s actions if there’s no special desire to benefit or harm someone. There’s only identity if God never has that desire. So the argument concludes miracles can’t happen by assuming miracles can’t happen. That’s not going to work. And we have the usual flawed definition of the miracle.

Couldn’t God design the laws of nature so He wouldn’t need miracles? Why would He? Both miracles and non-miracles arise from God’s actions. There’s no extra effort for God to produce a miracle.

Historian’s argument against miracles

Historians need to construct the most probable representation of the past. They have to assume regularity in the basic rules of society. The philosopher Flew presented the argument as shown:

The basic propositions are:

• first, that the present relics of the past cannot be interpreted as historical evidence at all, unless we presume that the same fundamental regularities obtained then as still obtain today;
• second, that in trying as best he may to determine what actually happened the historian must employ as criteria all his present knowledge, or presumed knowledge, of what is probable or improbable, possible or impossible; and,
• third, that, since miracle has to be defined in terms of practical impossibility the application of these criteria inevitably precludes proof of a miracle.

This assumes what it sets out to prove. It defines miracles as impossible events. Historians can assume this if they like, but every conclusion would be contingent on that assumptions being true. If historians don’t explicitly state that, they mislead. If they do, they are irrelevant.

Assuming miracles don’t happen isn’t an unbiased position any more than assuming miracles do happen. A historian ought to be truly neutral, and remain open and let the evidence speak for itself.

What about miracles from other religions?

What about miracle claims from other religions? Don’t they contradict Christianity? And can’t the same arguments Christians use to dismiss them also be used to dismiss Christian miracles?

• Any miracle claim is evidence against atheism. It might not be very good evidence, but its still evidence.
• Not every religion allows miracles, or contemporary miracles. For example, Sikhism, Buddhism, Islam, and the various Chinese religions don't promote contempoary miracles in the same way that Christianity or Hinduism do.
• Not all these claims will be true. We must use the same standards to judge them as we do for Christian miracle claims. We shouldn’t accept every Christian miracle claim outside the Bible. We do accept some. Are the claims in other religions comparable to those Christian claims we reject, or those we accept? If its those we reject, we can’t be charged with hypocrisy by dismissing them.
• These could be the works of demonic powers.

I’m most familiar with pagan religions and Islam. Pagan claims are never recorded by eyewitness. There’s always many people between the event and the record. And that gives us reasons to doubt the text describing the miracle. But we can trace reports of Christ’s resurrection to the apostles in Jerusalem at most a few years after the event, based on Paul’s testimony in 1 Corinthians. The gospels were written while eyewitnesses lived. The resurrection is central to Christian theology. It had to come first, with Christianity built around it. So we dismiss the pagan claims because they are far removed from eyewitness testimony, but accept Christian claims which can be traced to the eyewitnesses.

Islam’s miracle claims are about trivial matters and were first recorded a century and a half after Islam's false prophet Muhammad. So a similar lack of quality as the pagan or Buddhist miracle claims. Here’s one example, where bushes move around to protect Muhammad's dignity.

We travelled with the Messenger of Allah until we halted in a spacious valley. The Messenger of Allah went to relieve himself, and I followed him, bringing a bucket of water.

The Messenger of Allah looked, but he did not see anything with which to conceal himself, then he saw two trees at the end of the valley. The Messenger of Allah went to one of them and took hold of one of its branches, and said: "Follow me, by Allah's Leave," and it came with him like a camel with a nose ring that follows its driver. Then he went to the second tree and took hold of one of its branches and said: "Follow me, by Allah's Leave," and it came with him in a similar manner.

Then when he reached the middle of the space between them, he joined them together and said: "Come together and (conceal) me, by Allah's Leave," and they joined together.

I went away, lest the Messenger of Allah realise that I was nearby, and go even further away. I sat down, thinking to myself. Then I saw the Messenger of Allah coming, and the two trees had parted and each one was standing in its own place. (Sahih Muslim 7518)

This is first recorded in the Hadith, long after Muhammad's time. It was carried down by a supposed single chain of witnesses, any of whom could have invented or embellished it. Nothing in Islam depends on this story. It's a trivial matter, with no underlying meaning or purpose. Unlike the Biblical miracles, it isn't a sign pointing to God's nature, but merely a matter of convenience. The sort of thing that appears in other religious fan-fiction, such as the gnostic texts. It could easily have been invented in the centuries between Muhammad and the story first being recorded. Again, we should compare with the miracle stories in the New Testament, which can be traced back to the eyewitnesses, are for specific purposes revealing God or Jesus' nature, and are central to Christianity: it would be a very different religion if they didn't happen.

The Qu’ran is our only contemporary source. It states that Muhammad didn’t perform miracles, but was only sent as a warner. This is stated in several verses; I'll give just one example.

The disbelievers say, “If only a sign could be sent down to him from his Lord.” You, O Prophet, are only a warner. And every people had a guide. (Qu’ran 13:7).

Clearly the disbelievers comments shows that they hadn't seen a clear sign validating Muhammad's supposed prophet-hood. But all Allah had in response is the statement which is both irrelevant and false that every people had a guide. You might possibly compare this to Matthew 12:38

Then some of the scribes and Pharisees answered him, saying, "Teacher, we wish to see a sign from you." But he answered them, "An evil and adulterous generation seeks for a sign, but no sign will be given to it except the sign of the prophet Jonah. For just as Jonah was three days and three nights in the belly of the great fish, so will the Son of Man be three days and three nights in the heart of the earth."

But there are important differences here. Firstly, the gospels clearly describe many signs performed by Jesus. There is no such parallel in the Qu'ran. Indeed, the context of this passage, a little earlier in the passage, is with the same scribes and Pharisees postulating that Jesus drove out demons by the power of Beelzebub. They had already witnessed at least one type of sign, but came up with an excuse to dismiss it. Secondly, Jesus didn't respond by saying "I am only a warner," but instead alluded to perhaps his greatest sign, the resurrection. Thirdly, in Jesus' teaching, "no sign will be given" is limited in context, to the "evil and adulterous generation." This doesn't preclude signs being given to those who aren't evil and adulterous. Yet Muhammad's claim is universal. His is only a warner and guide to his people.

The Qu’ran only attributes three signs to Muhammad:

1. The “giving” of the Qu’ran. Muhammad composed a book. Clearly there’s a natural explanation. It is possible for a human to recite the Qu'ran, to put it's words into the correct order. Therefore there is no logical, biological or neurological impossibility in a human doing so for the first time and composing it. Muslims point to the Qu'ran's great literary beauty. But this clearly is an argument. It's a wholly subjective measure. How do we draw the line about what level of quality is impossible for men, and impossible for demons, and only within God's power? Is being the best work of literature in a particular language enough to qualify? If so, you would have to grant divine status to The Iliad, or the works of Shakespeare or Milton, or Dante, or of Du Fu, and so on. These tower above literary traditions far greater than those of the Arabs. It's not at all obvious that the Qu'ran is superior in quality to these works. It's characterisation is one dimensional. It's disorganised. It's repetitive. It contains numerous factual errors and contradictions.
2. Muhammad's night journey. He had a vivid dream about going to Jerusalem and then into heaven. Again, there’s an obvious natural explanation. People often have strange dreams.
3. "The splitting of the moon," but the Qu’ran doesn’t describe what this was, so we can't judge whether it involves anything supernatural. The reference is embellished in the Hadith, where its taken literally as the moon dividing and then rejoining. But that's too late to be a useful source, and its strange this wasn't recorded by other peoples.

We aren’t hypocrites for dismissing these while accepting Christianity’s miracles.

Can Miracles prove God’s existence?

Can miracles prove God’s existence? Proof in the strict mathematical or philosophical sense isn’t easy. My answer’s going to be “Yes,” but before I get to that I need to raise a few words of caution.

Can we be sure the miracle was performed by God, not some demonic power? Demons can produce mighty works. The Egyptian priests who opposed Moses could replicate some of the Exodus miracles.

Then Pharaoh summoned the wise men and the sorcerers, and they, the magicians of Egypt, also did the same by their secret arts. (Exodus 7:10)

The second beast in Revelation performs great signs to deceive people.

Then I saw another beast rising out of the earth. ... It performs great signs, even making fire come down from heaven to earth in front of people, and by the signs that it is allowed to work in the presence of the beast it deceives those who dwell on earth (Revelation 13:11)

Matthew’s got a similar warning about false prophets deceiving with signs.

For false Christs and false prophets will arise and perform great signs and wonders, so as to lead astray, if possible, even the elect. (Matthew 24:24)

How should we distinguish these signs from God’s? Well, what do the signs point to? Do they encourage devotion to God, or distract us from it? Are they beneficial or harmful? Demons and magicians have limited power. There’s no reliable record of them raising people from the dead.

Many miracles aren’t evidence for God. Claims outside the Bible are sometimes fabricated. Some signs from God are also explicable through non-miraculous processes. Those are good for the person experiencing them, but won’t convince others. We must also be wary of selection bias, where we remember the prayers that were answered, but forget about those which weren’t. Particularly for low probability rather than events which would be zero probability if they weren’t miracles. Does this remission only happen spontaneously one time in a hundred? Sounds impressive, until you also count 99 times people prayed and it didn’t happen.

Just because some miracle claims are fiction doesn’t mean they are all fiction. Just because some are genuine doesn’t mean they’re all genuine. We need to be cautious with miracle reports. Cautious doesn’t mean dismiss; it just means be careful. If you claim something as a great sign from God, and then it turns out to be fictional or a misunderstanding, you’ll just look like an idiot. And they will still think you’re an idiot when you discuss miracles with conclusive evidence, such as Jesus’ resurrection.

I firmly believe that miracles happen today. There are very well documented cases which defy physics and biology. But that doesn’t mean we should jump on every bandwagon. We should always be diligent.

It’s clear that many people have used signs as evidence for their belief, both in Jesus’ time and onwards to today. Equally, the apostles referred to Jesus’ signs as God’s attestation of Jesus, and Jesus himself stated that people should believe on account of his works, which would include his signs.

Evaluating evidence for a miracle depends on philosophical commitments. A theist is open to it being a sign from God. An atheist will latch onto any outlandish explanation before admitting that. So can we use miracles to argue against atheism?

Yes, despite these difficulties. Because we don’t need to determine whether the miracle happened, not at first, to use the evidence for that miracle to judge between the different philosophies. Everyone agrees there are reports of miraculous events. Which philosophy better explains why those reports exist? In theism, the explanation is easy. The best documented reports exist because there’s a good chance they accurately record genuine miracles. That fits all the facts without any difficulty. But if you accept an atheistic worldview, you need an alternative explanation. Explanations which fit all the facts are sometimes highly convoluted and improbable. Then we have to ask if the facts are the problem, or the anti-miraculous philosophy.

We have two different families of philosophies:

• Atheism or Deism, where miracles are impossible (or so improbable we always dismiss them).
• Theism, where miracles are possible and expected.

We must judge each philosophy by the evidence. There are claims of miracles. Some are supported by very strong evidence. We don’t need to evaluate whether the miracle occurred to judge between theism and atheism; we merely need to ask which philosophy better explains why the evidence for the miracle exists. Atheists need an outlandish and highly improbable story to explain this. Theists don’t. The theist explanation of the evidence for the miracle is only improbable if you have already decided theism is false. Should we dismiss this evidence because it disagrees with our philosophy, or judge the philosophy because it disagrees with the evidence? When there’s an alternative which makes far better sense of the data, clearly we should choose the philosophy which doesn’t need convoluted excuses or conspiracy theories to explain the data. Since miracles can’t happen if atheism is true, but can happen if theism is true, then if there are miracle claims which can’t be easily explained in atheism but can be easily explained by theists, then this is clear evidence against atheism.

Using the mathematics of Bayes' theorem, this argument can be expressed as

• T is the proposition that Theism is true, and the miracle occurred by God’s choice not at random.
• P(E|RX) is the probability that we would find the evidence for this miracle if miracles happened at random very infrequently (very small).
• P(E|TX) The probability that we would find the evidence for this miracle if miracles happen by God’s sovereign choice (could be very high).
• The probability of model R being true is very small given the evidence E.
• We don’t need to judge how likely it was the miracle occurred to use the evidence for it to judge between the two philosophies.

Conclusion

• Atheists dismiss Christianity using arguments that miracles don’t happen.
• Those arguments aren’t very good.
• They assume a world-view inconsistent with theism (and with science). They presuppose that a theistic God doesn’t exist. Such arguments therefore can’t be used to argue against theism, because they just beg the question.
• In theism, miracles make good sense and are expected.
• Using well attested miracles as evidence for God is thus valid and a powerful argument against atheism and deism.

Sources

Craig Keener, Miracles: The Credibility of the New Testament Accounts (2 Volume Set)", Baker Academic (2011), is an important reference outlining many contempoary miracle accounts and responding to Hume's argument.

The stanford encyclopedia article on miracles is a useful general resource.

Most apologetics works, such as William Lane Craig's Reasonable Faith: Christian Truth and Apologetics, Crossway (2008), will have a section on miracles.

I briefly mention my own ideas concerning the philosophy of physics, published in greatest depth in What is Physics (2017).

Hume's argument is found in An Enquiry Concerning Human Understanding, (1748).

Spinoza, Tractatus Theologico-Politicus. (1670)

Voltaire, Philosophical Dictionary (1764)

Flew, Antony, God and philosophy (1966)

At a more popular level, there's always C.S. Lewis, Miracles Geoffrey Bles (1960).

The Two-slit experiment image was taken from inductiveload "Two-Slit Experiment Electrons." Wikimedia Commons, 2 Nov. 2007