Updated: Sep 27, 2022
The views expressed in this article are those of Apologetics Central only and not those of any other entity associated with the author.
Insurance is a way to manage your risk. When you buy insurance, you purchase protection against unexpected financial losses. The insurance company, in exchange for your premiums, promises to indemnify you against unexpected losses you suffer in the future (dependent on the contract). If you have no insurance and an accident happens, you may be responsible for all the related costs .
The insurer can indemnify people who take out policies with them because it pools the funds (or premiums) collected from different policyholders and relies on the law of large numbers and statistical models to predict the number and amount of future claims that will arise in the period of cover to be provided.
The purpose of this article is to tangibly explain the sense in which the concept of insurance implicitly presupposes the Christian worldview in principle and in practice. We are now going to embark on a philosophical investigation with regards to the principles that undergird the actuarial and statistical principles used in insurance. Hopefully, when we reach the end, the article will instil in the reader (if the reader works in the industry) a new or renewed realisation of their place in God's creation.
A coin toss
The best way to illustrate the principle of the pooling of risks is by using the example of coin flips. It is common knowledge that a coin flip has a theoretical 50/50 chance to land on either heads or tails.
Now, the law of large numbers is a theorem that describes the result of performing the same experiment a large number of times . The law of large numbers states that an observed sample average (which is the average of the observed results as the experiment is repeated, e.g. the average value observed when throwing a dice an n number of times) from a large sample n (where n is a sufficiently large number of experiment repetitions) will be close to the true (population) average.
Let's say, for example, that we flip a coin once and observe the result. Let's say the first result was heads. The observed sample average for the number of heads is 1, and the observed sample average for the number of tails is 0. This, however, is a far cry from our known theoretical distribution of 50/50. Let's say we flip the coin again, and we observe tails. On the second throw, the observed sample average for the number of heads is 50% (1/2), and the number of tails is 50% (1/2) as well. Hence, our sample distribution now suddenly reflects the theoretical (population) distribution.
If we flip the coin a few more times, we'll observe that our sample average tends toward the population average, such that we can confidently predict that about 50% of the coins will land on heads, and 50% will land on tails.
This application by the Wolfram demonstrations project illustrates the law of large numbers at work. As mentioned before, the probability of heads is set to 0.5 (50%). You can set the number of times you want the experiment to complete by editing the repetitions. The experiment will simulate 1000 coin tosses for each repetition. Note that although the observed probability of landing on heads might start very low/high (as you will always start with 1 heads and 0 tails or vice versa), it always converges to 50% (or the theoretical value) as we observe more and more tosses.
The law of large numbers and insurance
The above observation is extremely useful and foundational to the concept of insurance. Imagine if you will that a coin toss determines whether you lose $100 or not. You know that the result of the coin toss is either heads or tails, each with a 50% probability. This means that your expected loss for a coin toss event is 50% x $100 + 50% x 0, which is $50.
What should an insurer charge you to insure you against the event of losing $100? Let's say the insurer charges you the expected loss amount determined to be $50. When you pay the insurer $50, you are indemnified from the risk of losing $100. No matter what happens when the coin is tossed, you get to keep your remaining $50, and the insurer will pay $100 when it lands on heads, or $0 when it lands on tails on your behalf.
Thus, the risk of loss has been effectively transferred to the insurer.
From the insurer's perspective, they have collected $50 in premiums, and now they are exposed to the risk of losing $50 ($100 - $50) if the coin lands on heads, or gaining $50 apples ($0 - $50) if the coin lands on tails.
Would you take this deal if you were the insurer? The insurer won't. They stand nothing to gain. This is just a fancy way of gambling
So what can the insurer do? This is where the law of large numbers comes into play. What if it's not just you that want to take out insurance on the coin toss event, but many thousands of other people as well?
If this is the case, the insurer can actually apply the law of large numbers, and with confidence say that they know about 50% of their clients will observe the coin landing on heads, and 50% will observe the coin landing on tails (it does not matter who the individuals are that observed these separate events). Hence, the insurer can confidently say the following: If they charge each person $50 to indemnify them (and let's say there are 1,000 people taking out the insurance), the insurer will be able to collect $50,000 in premiums.
The expected loss (according to the law of large numbers) is 50% x 1,000 x $100, which is $50,000! Since the insurer has collected $50,000, they can confidently say that they will break even.
Now imagine that they no longer charge $50 for the premium, but $52. In this case, they collect $52,000 in premiums, and still only expect to pay out $50,000 in claims. Hence, they can confidently expect $2,000 for themselves as a profit!
Whether you'd be willing to sacrifice $52 apples to remove the risk of the loss of the $48 depends on each person's risk profile. However, this is beyond the scope of this article
This is insurance in a nutshell.
As the probability of the risks decreases, the premiums to indemnify against the particular risk become more minor to the point where you can confidently charge less than $100 per month to compensate someone for the loss of their car being stolen (that has a value that might exceed $20,000).
Now that we've got some basic statistics out of the way, let's get philosophical. We are going to follow a brief history of philosophy in order to show how the above (general workings of insurance) presuppose the Christian worldview. We will be following Van Til in his Christian Theistic Evidences.
A priori and a posteriori reasoning
A priori reasoning is notably connected with rationalism, and a posteriori reasoning is connected with empiricism.
A priori reasoning is a "stop and think" type of reasoning, and a posteriori is a "wait and see" type of reasoning. A priori reasoning attempts to get to the actual states of affairs apart from the taints of experience, whereas a posteriori reasoning believes that the actual state of affairs must be sought through experience and not in a priori (or innate) ideas.
This particular distinction becomes important as we turn to offer a brief exposition of Butler and Hume's philosophies.
Bishop Joseph Butler's analogy
Bishop Joseph Butler was an Anglican Bishop (1692 - 1752) that wrote the Analogy of Religion, Natural and Revealed. In his book, Butler undertook the task of refuting unbelief (specifically that of deism) by way of analogy and probability. Butler's work remained the standard for Christian apologetics up and till the influence of David Hume (1711 - 1776) and Immanuel Kant (1724 - 1804) took hold.
For Butler, the degree of probability that a certain event will take place may increase in proportion to the number of times that we have seen a similar event take place in the past . He explains:
Thus a man’s having observed the ebb and flow of the tide today, affords some presumption, though the lowest imaginable, that it may happen again tomorrow: but the observation of this event for so many days and months, and ages together, as it has been observed by mankind, gives a full assurance that it will.
The Works of Bishop Butler, edited by R. Hon. W. E. Gladstone, Vol. 1, Analogy, p. 3.
According to Butler, after having spent some time observing the world and its inner workings, we must always act in accordance with the highest probability. For example, it would make little sense that after having observed the sun rising every day for over 25 years of my life, to assume that it won't do so the following morning and act upon that assumption by removing anything that is solar-powered and replacing it.
In the same way, having tossed a coin an N number of times (where N is a sufficiently large number) and observed that the ratio of heads to tails is about 50/50, it would make little sense to postulate that it's actually 70/30 or that it won't continue to be 50/50.
Butler then to argues that Christianity (as a worldview) has a practical presumption in its favour. If there is a chance that Christianity is true, we must act upon it, and this acting upon it will be no different than our everyday acting on presumption and probability (like having great confidence that the sun will rise tomorrow and acting upon it) . However, Butler does not think that there's a mere chance that Christianity is true, rather he affords it a large probability of being true. And this probability rests on analogy.
Analogical reasoning, for Butler, is reasoning about the unknown possibilities from the known constitution and course of nature. The constitution and course of nature are our starting point regarding the facts from which we reason are concerned . For Butler, we can legitimately make conclusions about the unknown, assuming that it will be like the known. And so Butler argues by way of "analogy" toward what he believes to be the probable existence of a future life, and other things building up a highly probable and cumulative case for the Christian worldview. The exact nature of his arguments doesn't concern us. We are merely interested in his use of "analogy" and probability, as well as his justification for it as described earlier.
To be fair to Butler, he does also note that the constitution and course of nature are created and controlled by God's eternal decree and plan for history - but insofar he attempts to make his argument appeal to the principles of unbelievers, this is an inconsistency.
David Hume refutes Butler
David Hume was a Scottish empiricist philosopher who published his monumental work the Treatise of Human Nature in 1739-1740. Hume had high regard for Butler, and apparently tried to get Butler to read his work before publication as he indicated in a letter to Lord Kames (another Scottish philosopher).
Basic to all of Hume’s opposition to Christianity and to theism is his conception of knowledge as derived from the senses. His objections to miracles as well as his objections to natural religion are based upon his theory of knowledge. He marched right up to the very citadel of his opponents in order to attack them there .
For Hume, as a consistent empiricist, all knowledge starts with the senses. We have no innate knowledge of the sort the rationalists postulated (e.g. Plato's forms). There are no ideas that are not faint copies of previous sensations. So, if you have an idea of a horse in your mind, this is because you've had a previous sensation of a horse (or sensations of horses). So for Hume, ideas are formed by sensations (or impressions).
(Note: For Hume, we may still speak of apriori knowledge, say in the field of algebra, but once we start talking about factual knowledge (the external world), a priori knowledge becomes taboo).
Since a priori reasoning has been discarded and with it, the certainty that it was supposed to bring when it comes to factual matters (reality), the question before us is whether we are justified in the sort of a posteriori reasoning that Butler employed in his analogy. Can we at least depend on probability? May we not reasonably expect that the “constitution and course of nature” will continue in the future as it has in the past?
To answer this question, Hume depends on the nature of the connection between the various ideas formed in our minds by the different impressions. Firstly, Hume notes that one idea might simply recall another idea. There is no systematic relation between our particular ideas, and this is so because there is no systematic relation between our particular sensations. Ideas as copies of sensations are therefore discrete and independent.
‘Tis therefore by experience only, that we can infer the existence of one object from that of another. The nature of experience is this:
We remember to have had frequent instances of the existence of one species of objects; and also remember, that the individuals of another species of objects have always attended them, and have existed in a regular order of contiguity and succession with regard to them.
Thus we remember, to have seen that species of object we call flame, and to have felt that species of sensation we call heat. We likewise call to mind their constant conjunction in all past instances.
Without any farther ceremony, we call the one cause and the other effect, and infer the existence of the one from that of the other.
From the mere repetition of any past impression, even to infinity, there never will arise any new original idea, such as that of a necessary connexion; and the number of impressions has in this case no more effect than if we confin’d ourselves to one only.
Hume, A Treatise of Human Nature
The above is significant for our purposes here. Hume has just removed the foundation of causation, or cause and effect. There are no sensations of a principle such as "cause and effect". There is no necessary connection produced by the sensation of fire, followed by the sensation of heat. They are two separate sensations and two separate ideas. They might merely recall the other.
In this sense, whether one has the impression of fire followed by heat only once, or a million times, no amount of impressions will ever form the idea of cause and effect in our minds.
Cause and effect, therefore, have been reduced by Hume to something that is dependent on custom. There is no logical relation between the impression we label "cause" and the impression we label "effect" when the ideas are formed. There is thus no logical relation between the past and the future.
What about probability?
Since, according to Hume, there is no logical relation, can we still postulate a probable relation?
Hume now expands on the above quote and tries to determine where the notion of cause and effect comes from. How can we assume that the future will be like the past when we observe certain causes?
Whether experience produces the idea by means of the understanding or imagination; [that is] whether we are determin’d by reason to make the transition, or by a certain association and relation of perceptions.
Hume, A Treatise of Human Nature [Brackets my own]
If reason determined us to make the transition from ideas to the idea of cause and effect [that is, that instances of which we had no experience will resemble instances in which we had experience], then it remains to be shown what such an argument would look like. The argument for such a transition must either be founded upon knowledge (that is it follows necessarily from our impressions and existing ideas) or probability.
For an argument founded upon knowledge, Hume argues that we can at least form a clear idea of a change in the constitution of nature (at least in the future) that would render any notion of cause and effect bust. Hence, it cannot be founded upon knowledge. Hume writes, "To form a clear idea of anything, is an undeniable argument for its possibility, and is alone a refutation of any pretended demonstration against it."
For an argument founded upon probability (that is that the future will only probably resemble the past), Hume writes, "Tis... necessary that in all probable reasonings there be something present to the mind, either seen or remember’d, and that from this we infer something connected with it, which is not seen nor remember’d".
The basic principle is that all probability reasoning goes from what has been seen, to that which has not been seen in order to attach some probability to it. However, the only principle that can lead us beyond our immediate impressions and ideas is the principle of cause and effect.
Now the problem appears: This idea of cause and effect which sits at the back of all probabilities, is itself then derived from experience in which past impressions have generally been conjoined with each other. Hence, if one sensation is observed, we can presume the existence of one that is similar to its usual effect.
Therefore, Hume writes, "according to this account of things, which is, I think, in every point unquestionable, probability is founded on the presumption of a resemblance betwixt those objects, of which we have had experience, and those, of which we have had none; and therefore ‘tis impossible this presumption can arise from probability. The same principle cannot be both the cause and effect of another; and this is, perhaps, the only proposition concerning that relation, which is either intuitively or demonstratively certain." . Hence, if cause and effect rest on probability, we notice that probability itself is dependent on cause and effect. So probability cannot offer a justification for cause and effect (or the assumption that the future will resemble the past).
Chance and the law of chances
Before we move on from Hume, it would be useful to peruse what Hume wrote on chance as well.
For Hume, chance is the negation of cause. Chance is pure and complete indifference. Because chance is pure indifference, one chance cannot be superior to another chance. If one chance ends up being superior to another, then again we must have a cause at the back of it. He indicates that "this truth is not peculiar to my system, but is acknowledg’d by everyone, that forms calculations concerning chances."
Where nothing limits chance, every notion, even the most extravagant, is upon equal footing and there can be no circumstances that give one notion an advantage above another. Hume writes, "Thus unless we allow that there are some causes to make the dice fall, and preserve their form in their fall, and lie upon some one of their sides, we can form no calculation concerning the laws of hazard."
In essence, unless we presume certain causes at work when tossing our coin that preserves it as it is thrown, as it twists in the air, as it bounces, and as it comes to rest on the table, there is no way for us to calculate probabilities for the landing on each side of the coin.
Thus far we have the following:
Chance is the negation of cause.
Total negation of cause produces total indifference in the mind.
There must be a mixture of causes among the chances in order for there to be a foundation in any reasoning (as is the case in the dice example).
But now, Hume asks, what if we've already tossed a coin an N number of times where N is a sufficiently large number? Can we at least say that the coin will fall either on heads or on tails with a 50/50 probability based on past experiences? Here Hume indicates that we can use the same arguments employed in the earlier section to demonstrate that this belief cannot be held either by demonstration or by probability.
To re-iterate Hume's argument once more for the sake of clarity: If we attempt to base the above on knowledge, that is, that past experience of coin tosses indicated a 50/50 split between heads and tails, it remains to be demonstrated how these discrete impressions of a coin toss and the final result are related. There is no logical relation.
If we attempt to base the 50/50 split on probability, we find ourselves in an infinite regress, as probability is the very thing we're trying to establish.
And so we reach the end of our section on Hume. Grant an infinite number of possibilities, to begin with, as absolutely pure empiricism must presuppose, then there is an infinite number of improbabilities to cancel every infinite number of probabilities. That is, there is no probability at all. Such is Hume’s argument. Hume is right when he says again and again that “an entire indifference is essential to chance.” 
This leaves us with a gruelling problem. Hume seems to have successfully refuted Butler's arguments, in doing so, he has also completely pulled the rug out from under the entire insurance industry and those working in risk management.
The problem of brute facts
Van Til writes,
The whole point of Hume’s argument is that there is no rational presumption of any sort about future events happening in one way rather than in another. We may expect that they will, but if we do, we do so on non-rational grounds.
Our reasoning is based upon past experience. Past experience is nothing but an accumulation of brute facts which have been observed as happening in a certain order. Why should not the events of the future be entirely different in nature from the events of the past?
Cornelius Van Til, Christian-Theistic Evidences, 21.
For Van Til, a brute fact is a fact with no pre-determined meaning. It is a fact divorced from a system. Brute facts are "discrete facts". So, if past experience is nothing but the accumulation of these brute facts, there are no rational grounds for believing the brute facts (which by their very nature exclude the idea of the system) will continue to act in the same way in the future.
It makes little sense, therefore, for an insurer to build a business that tries to indemnify customers against future risks if all the insurer has to goon is a past accumulation of brute facts! Something drastic is missing from our picture...
Timothy McGrew responds to Hume
Timothy McGrew is a professor of philosophy at Western Michigan University and the chair of the department of philosophy. He is considered a specialist in the philosophical applications of probability theory. McGrew, like Joseph Butler, is a Christian and has concerned himself with the rational defensibility of the Christian religion . We include McGrew in our discussion not because he managed to successfully refute Hume but to indicate that McGrew, although he believes to have answered Hume, still relies on brute facts to make his argument. His attempted answer will serve to further our purposes as we critique it.
Notable for our purposes then, is that McGrew wrote a paper in 2001 titled, Direct Inference and the Problem of Induction in which he sought to refute Hume's contention outlined above. If Hume's contention proves to be correct, then there would be no rational grounds for any belief let alone Christianity. So, if there is no answer forthcoming it would be concerning, to say the least, for the insurance industry (and the world in general). So, can McGrew save Butler's arguments (and insurers) by refuting Hume ?
McGrew starts off his paper by noting that it would be difficult to overestimate the influence of Hume's problem of induction (making inferences with regards to the future based on past experience). He mentions that there exists the conviction in a considerable amount of modern philosophers that Hume's problem is insoluble. Despite the above, he aims to show that this pessimism is unfounded and to refute Humean scepticism on a theoretical, practical and modern level with regard to induction .
McGrew intended to accomplish this by using the law of large numbers (as introduced earlier) but in reverse.
Basically, McGrew is seeking the probability that the frequency with which a feature X occurs in a population lies within a small interval, e, of the value p, that is (p-e, p+e), given that an n-fold sample exhibits X with frequency m/n (where m is the number of members of the sample exhibiting X).
Or, more simply, you want to know what the split in proportion is between heads and tails on a coin toss. Imagine you sample 100 coin tosses (that is n = 100), and you observe that 50 of them are heads (that is m = 50). From this we can determine that p = 50/100 = 50%. Now, McGrew is asking, what is the probability the actual proportion of heads lies in an interval (p - e, and p + e), where e is a sufficiently small number and p = 50% (which is what we observed in our sample).
The only problem, according to McGrew, is to ensure that we have a large enough sample to make the inference that the actual proportion lies between p + e, and p - e. He presents a well-known statistical formula that lies beyond the scope of this article to determine a number.
Being satisfied that his sample size is big enough to afford confidence that his sample is representative of the population, McGrew presents his argument:
For any property p, at least a of n-fold samples exhibit a proportion that matches the population. [This step merely means that given the above formula we glossed over, he can be a% confident that his sample represents the population].
S is an n-fold sample of this population. [Image we toss a coin n times].
S matches the population. [Assume the coin tosses we made are representative of a common coin toss with no outside factors influencing us].
S has a proportion of 0.5 heads.
The proportion of 0.5 heads lies in the interval [0.5-e, 0.5+e].
x is a sample of the population. [I.e. a coin toss].
With probability [0.5-e, 0.5+e], x is heads.
As McGrew indicated, he simply used the law of large numbers and a few direct inferences to make the above work. Hence, he believes to have solved the problem of induction. He indicates: "this solution to the problem of induction is of more than academic interest. Prima facie, it is a cogent response to Hume’s challenge. Hume himself grants that we have experience of bread nourishing us and of the sun’s rising. If we may take our experience to be a sample, then it appears that we possess all the tools necessary to make a rational defence of everyday extrapolations against Humean scepticism." 
To be fair, he goes on to mention that philosophical battles are not so easily won and offers a few refutations to possible objections. However, I don't believe McGrew successfully answered Hume at all for the reason we indicated above: He does not escape the problem of brute facts.
Were Hume alive today, I believe that his response to McGrew would have been short and cogent.
"Your final paragraph, Dr McGrew, exposes the flaw in your reasoning. It is indeed the case that we experienced the nourishment of bread and the sun's rising day after day, but it remains to be shown why you would expect this to continue in the future. Brute facts don't form a population from which you can sample. A string of brute facts cannot produce a nicely contained population from which to extrapolate, to begin with. Chance must reign supreme.
One way out is to postulate causes that keep chance in check (so that we can say with confidence that bread will probably nourish us or that the sun will probably rise), but in doing so you'll simply beg the question. A universal principle of cause and effect that undergirds this sort of induction is the very thing you're supposed to prove. It seems you've tacitly presupposed it when offering your argument. You can't calculate probability against a backdrop of pure chance, Dr McGrew.
This much also becomes clear when I read the conclusion of your paper where you yourself admit that 'the universe can play some trick on us'. Your response to this admission is to quote Herodotus, the ancient Greek historian:
'There is nothing more profitable for a man than to take counsel with himself; for even if the event turns out contrary to one’s hope, still one’s decision was right, even though fortune has made it of no effect: whereas if a man acts contrary to good counsel, although by luck he gets what he had no right to expect, his decision was not any the less foolish'.
I see this as an admission of defeat. With this quote, you admit that you cannot solve my problem of induction. There is no, and can never be any, necessary or logical connection between brute facts. It's all in the hands of fortune (or chance). There are no rational grounds to expect the future to resemble the past."
The author of nature
Now we've reached the climax of our journey. Throughout the previous sections, I fully expect the reader to be truly perplexed by what is said. How can Hume not be refuted? How can the vast majority of philosophers believe Hume's problem to be insoluble? Our entire existence depends on induction. When we boil a kettle or enjoy a sunrise, it seems so trivial to us? Surely Hume missed something obvious.
As a Christian, I do believe that Butler and McGrew are a lot closer to the truth than Hume. When you boil a kettle and expect the water to become hot, and when you drive out earlier in one of the national parks to enjoy a sunset, I fully agree with the common-sense principle that we are justified in expecting the future to resemble the past with reasonable confidence. I use the law of large numbers in my everyday job as an actuarial analyst at the company I work for. I don't believe Hume was correct at all. Nor do I believe that Hume lived in a way that is consistent with the logical conclusions he reached.
However, Hume was more consistent than Butler, McGrew, and everyone that doesn't buy his arguments and yet proclaims to live by the principles of brute facts and chance. Given Hume's non-Christian starting point, he was correct.
So, what is the correct answer to Hume, then? Butler himself provides the answer but fails to realise the consequences of his admission.
Butler speaks of "the author of nature", but fails to realise that if there is an author of nature, this fact cannot be compatible with the idea of brute facts and chance.
The matter may be put as follows: If an “Author of nature” is really presupposed it will and must in principle control the nature of reasoning that we employ. If we presuppose an “Author of nature,” then the facts are created by him. That means we cannot be empiricists, in the sense in which Butler takes empiricism and in the sense in which Hume takes empiricism. If an “Author of nature” is presupposed, all the facts of the “course and constitution of nature” are bound together by the mind of God . There are no brute facts. All facts are God-created and God-interpreted facts.
The same can be said for knowledge of the a priori sort. Our minds are also created by the "Author of nature". So we can never be a priorists of the Cartesian sense (that of Descartes), but this is an article for another time.
Future possibilities lie solely in the hands of God. If we start with brute facts, we've effectively negated the author of nature (begged the question) and his revelation from the start of our reasoning process. For the Christian, there is an entirely reasonable expectation that the constitution and course of nature will be the same in the future as it has been in the past because of the rationality of God that is back of it. There is no principle of chance that can subvert the will of God . The point is that only that will happen in the future which will be in accord with the plan of God for history.
Now, we can contrast this position with that of Hume by saying that for Hume the basic concept of thought is a bare possibility, while for one who holds to an “Author of nature” the basic concept of thought should be God’s complete rationality . And this is what Butler and McGrew missed in their answers. If you start with bare possibility and brute facts, you fall into Hume's problem of induction. However, if you start with the God who reveals Himself and who is the Sovereign King over the entire creation, it denies the existence of brute facts in its entirety. Although Butler and McGrew are Christians, they've adopted principles that are antithetical to the faith that they proclaim. In not starting with the God who made them and governs the world as ultimate, they have effectively sabotaged their own defence of Christianity and conceded the debate to the unbeliever (Hume) before the argument began. Butler and McGrew should not take out insurance if they are consistent with brute fact.
For the Christian (Butler and McGrew in practice but not principle), history (past present and future) has genuine significance as history itself is a revelation from God. All things being made by Him and dependent on Him are necessarily revelational of Him. It is also for this reason that the Christian can expect that the future will be like the past because of God's covenantal promises to creation, but yet expect that God may at any time send His Son to change the constitution and course of nature (i.e. by dying on the cross and raising Him from the dead). There are no facts and laws that are not put in place by God - and He has the full right to change the constitution and course of nature, but because of His faithfulness, He maintains the world in a way that is conducive to us.
God's promise to Noah
Perhaps most strikingly this can be seen in God's promise to Noah which we are still witnessing today whenever we see a rainbow.
And God said, “This is the sign of the covenant that I make between me and you and every living creature that is with you, for all future generations: I have set my bow in the cloud, and it shall be a sign of the covenant between me and the earth.
When I bring clouds over the earth and the bow is seen in the clouds, I will remember my covenant that is between me and you and every living creature of all flesh. And the waters shall never again become a flood to destroy all flesh. When the bow is in the clouds, I will see it and remember the everlasting covenant between God and every living creature of all flesh that is on the earth.”
God said to Noah, “This is the sign of the covenant that I have established between me and all flesh that is on the earth.”
Genesis 9:12-17, ESV
If the course and constitution of nature were that of brute facts, there was no way that God could make such a promise to Noah as even God would be subject to bare possibility with regards to the future. But, the possibility is not at the back of God, God is at the back of possibility. Hence, God, by way of covenant, relates Himself to Creation and governs it according to His good will.
Insurance and the Christian worldview
The sum total of what has been said boils down to this: There are no brute facts. History (past present and future) is solely in the hands of our God. This is His world, and no one else's. Whenever we set out to use the law of large numbers, or fit statistical models, were are in effect calling on the providence of God. The insurance industry, perhaps now more clearly than others, should return to its foundations and honour the God who governs His world in such a wonderful and consistent way that we can generalise it with statistical methods.
The Christian is called to live a life of analogical thinking: That is thinking about God, oneself and the world in a way that is God-honouring and not self-exalting. It is a way that is said to "think God's thoughts after Him". All insurance models are, therefore, analogical. They are generalisations of the way that our God governs His world in terms of cause and effect and laws of nature. Notice how Van Til's use of the word "analogy" differs completely from Butler's use of the word "analogy". For Butler, analogy involves the concepts of brute fact. For Van Til, it removes the concept of brute fact altogether.
It is a sad thing that we've become so accustomed to thinking about our world as self-existing and as something that contains its meaning within itself. This is ultimately an act of rebellion. Van Til puts it as follows in his famous pamphlet Why I believe in God:
You went to a “neutral” school. As your parents had done at home, so your teachers now did at school. They taught you to be “open-minded.” God was not brought into connection with your study of nature or of history. You were trained without bias all along the line. Of course, you know better now. You realize that all that was purely imaginary. To be “without bias” is only to have a particular kind of bias. The idea of “neutrality” is simply a colorless suit that covers a negative attitude toward God. At least it ought to be plain that he who is not for the God of Christianity is against Him. You see, the God of Christianity makes such prodigious claims:
That the world belongs to [the God of the Bible], and that you are His creature, and as such are to own up to that fact by honoring Him whether you eat or drink or do anything else. God says that you live, as it were, on His estate. And His estate has large ownership signs placed everywhere, so that he who goes by even at seventy miles an hour cannot but read them. Every fact in this world, the God of the Bible claims, has His stamp indelibly engraved upon it.
How then could you be neutral with respect to such a God? Do you walk about leisurely on a Fourth of July in Washington wondering whether the Lincoln Memorial belongs to anyone? Do you look at “Old Glory” waving from a high flagpole and wonder whether she stands for anything? Does she require anything of you, born an American citizen as you are? You would deserve to suffer the fate of the “man without a country” if as an American you were neutral to America.
Well, in a much deeper sense you deserve to live forever without God if you do not own and glorify Him as your Creator. You dare not manipulate God’s world and least of all yourself as His image-bearer, for your own final purposes.
Cornelius Van Til and Eric H. Sigward, The Pamphlets, Tracts, and Offprints of Cornelius Van Til, Electronic ed. (Labels Army Company: New York, 1997).
The reader should know that despite our rebellion, God has made a way for us to be reconciled, and this is through the atoning work of Jesus Christ on our behalf. The estate owner has made criminals his friends and redeemed them so they have free access to His home. Do you know the God who made you, and who is offering you peace with Him right now?
 Naked Insurance. 2022. Insurance - Encyclopaedia | Naked Insurance. [ONLINE] Available at: https://www.naked.insure/encyclopaedia/insurance. [Accessed 29 March 2022].
 Investopedia. 2022. Law Of Large Numbers Definition. [ONLINE] Available at: https://www.investopedia.com/terms/l/lawoflargenumbers.asp. [Accessed 29 March 2022].
 Cornelius Van Til, Christian-Theistic Evidences (The Presbyterian and Reformed Publishing Company: Phillipsburg, NJ, 1978), 1.
 Cornelius Van Til, Christian-Theistic Evidences (The Presbyterian and Reformed Publishing Company: Phillipsburg, NJ, 1978), 17.
 Cornelius Van Til, Christian-Theistic Evidences (The Presbyterian and Reformed Publishing Company: Phillipsburg, NJ, 1978), 20.
 David Hume, A Treatise of Human Nature.
 Cornelius Van Til, Christian-Theistic Evidences (The Presbyterian and Reformed Publishing Company: Phillipsburg, NJ, 1978), 25.
 YouTube. 2022. Timothy McGrew - The Historical Reliability of the Gospels - YouTube. [ONLINE] Available at: https://www.youtube.com/watch?v=UjjiW2DrbGw. [Accessed 23 May 2022].
[11[ No doubt there are more philosophers who attempted an answer to Hume's problem of induction. McGrew is chosen here because of his popularity in the online Christian apologetics circles, and because I have heard the claim from two independent friends that McGrew has solved Hume's problem of induction.
 McGrew, Timothy. “Direct Inference and the Problem of Induction.” The Monist, vol. 84, no. 2, 2001, pp. 153–78. JSTOR, http://www.jstor.org/stable/27903722. Accessed 23 May 2022.
 Cornelius Van Til, Christian-Theistic Evidences (The Presbyterian and Reformed Publishing Company: Phillipsburg, NJ, 1978), 21.
 Ibid. pg. 21-22