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Media bias

Proverbs 18:17: the antidote to Fake News

In the era of, not so much fake, but exaggerated, partisan, and selectively reported news, how can we discern the truth of a matter? God shows us the way in Proverbs 18:17, where we are told the first to present his case seems right until a second comes and questions him. What does it look like, to put this verse into action? Let’s take a classic example from the US gun debate. In the early 1990s Emory University medical professor Arthur Kellermann told Americans that owning a gun was associated with a 2.7 times greater risk of being murdered. Kellermann shared that in his study of three metropolitan areas they had found three-quarters of the victims were murdered by someone they knew, and nearly half by gunshot wounds. That raised the question of whether having a gun in the house might increase rather than decrease a person’s chance of being murdered. The New York Times, and other media outlets, spread these findings far and wide. But was the anti-gun case as compelling as it seemed? To find out, we have to continue on and hear from the critics – the first has presented his case and now we need a second to come and question him. Critics noted that Kellermann’s study showed an equal risk increase associated with owning a burglar alarm. National Review’s Dave Kopel pointed out, this study overlooks “the obvious fact that one reason people choose to own guns, or to install burglar alarms, is that they are already at a higher risk of being victimized by crime…. Kellermann’s method would also prove that possession of insulin increases the risk of diabetes.” The National Rifle Association wanted people to understand that a study of homicides couldn’t give a good measure of how effective guns could be for personal protection. "99.8 percent of the protective uses of guns do not involve homicides," explained NRA spokesman Paul H. Blackman, but instead would involve brandishing the weapon to hold off an assault, or perhaps firing the weapon to scare or wound the assailant. The first presenter might have had us thinking guns clearly needed to be banned. But that was only half the story. Even after hearing from the critics we don’t have the full picture – veteran newsman Ted Byfield once noted that to provide every side of a story we’d need more ink than exists in the whole of the world – but by hearing the two sides argue it out we have a much better picture. God tells us in Prov. 18:17 that if we hear only one side – even if it’s our side – then it’s likely we’re going to miss something. So if the truth matters to us we want to give even our opponents a hearing. At least the thoughtful ones (Prov. 14:7).

Adult biographies, Assorted, Book excerpts

When gray hair meets green

Age has its privileges and the freedom to dish out sympathetic sarcasm is one of them

****

Half his head is shaven. The middle part is green and the right side bright orange. He is clean, very clean. His red jeans are ripped, to show his boxer shorts. His torn T-shirt is white and clean. Lots of piercings; huge earlobe holes, like some African tribesman. Have not seen that since 1954. He is talking to an old crying Native man. I see him going to the coffee counter and returning with a coffee and a bun and giving it to the Native man. That was the last I saw of him that day. Two weeks later he wandered into the kitchen while Sue and I were trying to figure out how to feed about 80 people on 30 eggs and 72 buns. First we decided the staff would not eat that day. No worries there as this allowed me to stick to my diet plan. Someone brought in a hot apple strudel, six inches by twelve. We looked at it and just laughed. He stood in the doorway as we boiled the eggs - very small eggs, not meant for sale and therefore donated to the shelter. He got in my way as I was peeling the eggs. Suddenly he found himself with a spoon and knife in his hand. "Cut the eggs right through the middle and scoop out the egg, dump it in the green bowl." The old lady, me, had spoken. He looked at me funny and went to work. One of the guys ran out and got a jar of Mayo. In no time at all, we had egg salad on the buns and got the kid to bring out the trays to the hungry. When all the buns were gone and the apple strudel still on the counter, the kid got busy. He ran to the back freezer and came back with ice cream – two half full pails, chocolate and strawberry. It was just the two of us in the kitchen. He found the styrofoam soup bowls and plastic spoons. We divided the strudel into some 60 pieces and added two kinds of ice cream. When he carried the first tray out, he was greeted with a shout of "Dessert!" Sue came back and took the second tray. He came back into the kitchen and again it was just the two of us working together. When everything was gone, he suddenly said: "The way I live I have about 10 to 15 years to live." "So do I,” I informed him dryly. He glanced up at me with a stunned look on his face. Then he started talking again. "I’ve had fun. Got drunk every day, that's why I’m here. Community service. Can't wait to get back to drinking." "First time?" I asked him. "No, the second and the last time," he said. I agreed and told him that the third time would probably be jail and even more fun. He asked, "Well did you have a fun life?" "Sure did and no splitting headache in the morning. Besides that, I can even remember the fun I had." I asked him if he’d ever played in a band, toured Europe by motorbike, or traveled all over the world. I told him that I completely understood that going to a bar and spending the evening drinking and then staggering around with a splitting headache was, of course, much more fun. But at least I had fun for more years than he had had. We cleaned the kitchen, no longer talking. Before he left, he told me he had six more hours to serve and probably would not see me again. I agreed with him and told him I realized that it would be jail for him. He left but came back a little while later. "Look,” he said, “if I ever want to be told off, can I look you up?” "Sure, be glad to,” I replied. We grinned and shook hands! So now there is another kid in my prayers and I do not even know his name. 

This is a chapter from Gerda Vandenhaak’s book “Geertje: War Seen though the Eyes of a Child as an Adult” which is available at www.gerdavandenhaak.com or Alder and Elm Christian books (1 587-988-1619)

Science - Environmental Stewardship, Theology

Global warming crisis? A brief biblical case for skepticism

The media tells us that the question is settled, there is a 97% consensus, and that anyone who has questions is a “denier,” likened to those who are either so foolish, or malicious, as to deny the reality of the Holocaust. But there are reasons to question. And while climate science might be beyond most of us, God has given us another means – a far more reliable means – of discerning truth, via His Word. Gender: the Bible shows the way Sometimes it doesn’t take much Bible study to be able to discern truth from error, and that’s certainly true in today’s gender debate. Young children are being surgically mutilated and hormonally sterilized and yet the government, doctors, psychologists, and media are applauding. While it might not be at 97% yet, the consensus is growing such that fines are being issued, teachers fired, students expelled, and Twitter mobs set loose on any who disagree. Despite the pressure, few Christians are being fooled, though that might be due as much to the newness of the debate as it is that Evangelicals are turning to their Bibles for guidance. But if they do open His Word it won’t take a believer long to figure out God’s position. In Genesis 1:27 we learn it is God, not Man, who determines our gender:

“So God created Man in His own image; in the image of God He created him; male and female He created them.”

Population: following the Bible would have saved tens of millions The overpopulation crisis has a longer history to it and, consequently, many more Christians have bought into it. Since the 1950s we’ve been hearing that sometime soon the world’s population will outstrip the planet’s resources. In his 1969 book The Population Bomb Paul Ehrlich warned:

“The battle to feed all of humanity is over. In the 1970s hundreds of millions of people will starve to death in spite of any crash programs embarked upon now. At this late date nothing can prevent a substantial increase in the world death rate.”

You would think that by now it would be easy to see that these overpopulation fears were mistaken. As economist Arthur Brooks has noted, what’s happened is the very opposite of Ehrlich’s dire prediction:

“From the 1970s until today the percentage of people living at starvation’s door has decreased by 80%. Two billion people have been pulled out of starvation-level poverty.”

Yet the overpopulation hysteria has never gone away. And the damage it has done has been on par with that of a Hitler or Stalin – tens of millions have been killed. Under threat of this crisis China implemented their infamous one-child policy, with its fines and forced abortions for couples who tried for two. And the deaths weren’t limited to China; overpopulation fears were used to justify the push for legalized abortion in countries around the world. Murdering your own children wasn’t cold and selfish anymore; now it was a woman doing her part to save the planet. Christians opposed abortion, of course, but some believers started questioning whether overpopulation concerns might be correct. Maybe God’s call to “be fruitful and multiply” and fill the earth (Gen. 1:28) was just a temporary directive that we’ve fulfilled and should now treat as being over and done with. But it takes only a little more digging to find out that’s not what God thinks. Overpopulation proponents saw children as more mouths to find – they saw them as a problem – but God speaks repeatedly of children as a blessing (Ps. 113:9, 127:3-5, Prov. 17:6, Matt. 18:10, John 16:21). And opportunities present themselves when we see children as God sees them. When we understand they are a blessing, then we realize that not only do children come with a mouth that needs filling, but they also have hands that can produce even more than their mouth consumes. And they have a brain to invent and problem solve. When we see children this way – as a blessing and not a curse – then we'll realize there’s a real practical benefit in having lots of them: as we’ve been told, many hands make light work, and two heads are also better than one! That’s why it shouldn’t have surprised Christians when in the 1950s and 60s a group of inventive sorts, led by American Norman Borlaug, helped develop much higher-yielding strains of cereal crops. This “Green Revolution” turned wheat-importing countries into wheat exporting countries by more than doubling yields. And while there are no prophecies in the Bible specifically mentioning Norman Borlaug, Christians could have seen him coming, and in a sense some did. Those who continued having large families, despite the dire predictions, could do so confident that any problems caused by the innumerable nature of their progeny would be solved by something like the Green Revolution happening. Today, decades later, we can look back and see that a country like China, that ignored what God says about children, is facing a different sort of demographic crisis. A young Chinese couple will have two sets of parents and four sets of grandparents to look after and support, but have no siblings or cousins to help them. As soon as 2030 China will see their population start to decline, with not nearly enough working age citizens to provide for their aging population. It’s not all that different in the Western world where, even without government coercion, our families have been shrinking and women are averaging far less than two children each. We aren’t as near the crisis point as China, but by aborting a quarter of the next generation, we’ve created our own coming demographic crisis. Global warming: a biblical case for skepticism The population and gender debates remind us that the Bible is more reliable than any-sized consensus no matter how big. They also teach us that the world can get things not just completely wrong, but monstrously so, leading to the deaths of tens of millions. That’s why when it comes to global warming, where we’re being told once again that the fate of the planet is at stake, we want any and all guidance we can get from God’s Word. Cornelius Van Til once noted:

“The Bible is thought of as authoritative on everything of which it speaks. Moreover, it speaks of everything. We do not mean that it speaks of football games, of atoms, etc., directly, but we do mean that it speaks of everything either directly or by implication.”

The Bible does speak to global warming, but not directly. This isn’t like the gender debate, which runs smack up against Genesis 1:27 (“male and female He created them”) or the overpopulation crisis, which directly opposes the very next verse (“be fruitful and multiply”). When it comes to global warming the Bible isn’t as direct. But there are lots of implications. Time and space only allow me to present a half dozen texts. I’m not pretending that any one of them makes the definitive case for skepticism. But I do think that together they start pointing us decidedly in that direction. "You will know them by their fruits" – Matt. 7:15-20 In Matthew 7 Jesus tells us that we can tell a good tree from a bad one by the fruit on it. His concern wasn’t with trees though, but with telling false prophets from good ones. When it comes to global warming the science is beyond most of us, but we can evaluate the people. So let’s return to this 97% consensus we’ve heard so much about. This statistic is used to argue that there is no question but that the planet is headed to catastrophic climate change. But is this a reliable number, or is it like the greatly exaggerated 10% figure commonly given for the homosexual population? The figure has a few different origins, but one of the more commonly cited is a paper by John Cook and his colleagues reviewing 11,944 published peer-reviewed papers from climate scientists. Did 97% of those papers’ authors agree with the statement “humans are causing global warming”? That’s what we would expect. But instead of 10,000+ papers with that position, there were 3,894, or approximately 33%. So how did the 97% figure come out of that then? Well, it turns out only approximately 34% of the papers took a position one way or the other, with just 1% disagreeing or uncertain, and 33% agreeing. Thus, of the 34% who took a position, 97% agreed that humans are causing global warming. Is it honest to ignore the two thirds who didn’t state a position, and say there is a 97% consensus and no room for a debate? How this statistic has been used reminds me of a trick from another debate – equivocation about the definition of “evolution.” In his book, The Greatest Show on Earth, Richard Dawkins notes that when poachers shoot elephants with long tusks, the next generation is liable to have shorter tusks. Okay, but creationists also believe species can undergo changes over time. We’re the folks arguing that the array of cats we see today are all modified versions of a single cat kind brought on the ark. Dawkins has presented “minor changes over time” – a definition of evolution so broad that it enfolds even creationists into the evolution camp – as if it were proof of the from-goo-to-you sort of evolution that is actually under dispute. Similarly, the 97% consensus is being presented as if all those counted hold that the warming is catastrophic, humans are the primary cause, and there is a need for immediate, drastic, global action. But the agreement was only that “humans are causing global warming.” And that’s a statement so broad as to enfold even many of the so-called “deniers.” So on a statement we can verify – whether there really is a 97% consensus on catastrophic global warming – we find “bad fruit.” There are many other facts and claims we can’t evaluate, but doesn’t this tell us something about the “tree”? “The one who states his case first seems right, until the other comes and examines him.” – Proverbs 18:17 God says that to find the truth good questions are helpful. That’s not going on here, where questioners are likened to Holocaust deniers. But here’s a few questions worth considering: Aren’t there bigger priorities than global warming, like the millions who will starve to death this year, or the billions who lack basic access to clean water and sanitation? If fossil fuels are harmful, and solar and wind problematic, why aren’t we turning to nuclear? How will the world’s poor be impacted by a move away from fossil fuels toward more expensive alternatives? Are we again (as we did in response to overpopulation fears) seeking to save the planet by harming those who live on it? Samuel’s warning against kings – 1 Samuel 8:10-22 President Obama’s chief of staff famously said, “You never want a serious crisis to go to waste” and if you want to understand what he meant, looking no further than Justin Trudeau’s proposed ban on single-use plastics. This past year a video of a sea turtle with a plastic straw stuck up deep inside his nose went viral, alerting the tens of millions of viewers to the growing problem of plastics in our oceans. The movement to ban plastic straws has taken off since then. But will Trudeau’s single-use plastics ban save turtles? No, because our straws don’t end up in the ocean. Of the mass of plastic in the ocean it’s been estimated the US is responsible for one percent, and it’d be reasonable to conclude that Canada is responsible for far less. So how, then, does all the plastic end up in the ocean? It turns out that the vast majority of it comes from poorer countries that don’t have proper trash disposal. They simply dump their waste into the ocean and into their rivers. Trudeau’s ban will do nothing to help the turtles…but it will expand the government’s reach. The proposed solutions for climate change all involve expanding the government too, giving it a larger role in directing all things energy-related. So, how is 1 Samuel 8 relevant? Here we find Samuel warning against an expansion of government – get a king and he’ll start intruding into all areas of your lives. If there is a biblical case to be made for limited, small government (and there is) then Christians have a reason to question crises that seem to necessitate an ever-expanding role for the State. “…and it was very good.” – Gen. 1:31 While we no longer live in the perfect world Adam and Eve started with, we have only to wriggle our toes, or watch a ladybug crawl across the back of our hand to recognize that God’s brilliant design is still evident and at work all around us. We are on a blue and white marble, spinning at just the right angle, and orbiting at just the right distance from the sun, for it to rain and snow in season. We have a moon just the right size, and circling at just the right distance for us to study our own sun, and to bring the tides that sweep our beaches each day. And our planet is graced with a molten iron core that generates the very magnetic field we need to protect us from the solar winds, which would otherwise strip away the ozone layer that protects us from ultraviolet radiation. It is wheels within wheels within wheels, and while we can do damage to it, when we appreciate how brilliantly our world is designed we aren’t surprised there is a robustness to it. Meanwhile, the unbeliever thinks our world is the result of one lucky circumstance after another – a tower of teacups, all balanced perfectly, but accidentally. If the world did come about by mere happenstance, then what an unbelievable run of happenstance we’ve had, and isn’t there every reason to fear change? Sure, the teacup tower is balanced now, but if we mess with it, how long can we count on our luck to hold? “He who oppresses the poor taunts his Maker” – Prov. 14:31 At first glance, this text might not seem to provide much direction in this debate. After all, couldn’t a Christian who holds to catastrophic man-caused global warming cite it in support of their position too? Yes they could. If climate change is real, then the oppression it would bring on the poor would be a reason to fight it. Yet this text does provide a very specific sort of direction. It lays out limits on what sort of global warming plans Christians should view as acceptable: any plan to save the planet that does so by hurting the poor is not biblical. That means increasing energy costs has to be out. Millions are starving already and raising energy prices will only increase those numbers. “Be fruitful and multiply” – Gen. 1:28 Children come with an inevitable “carbon footprint” which is why some global warming proponents echo the same sentiments as the overpopulationists before them. “Save the earth; don’t give birth” is catchy, but if that was the only possible way we could lower carbon emissions then Christians could, on that basis, conclude there was no need to worry about CO2. Because God tells us children are a blessing, not a curse. Of course there may be other ways to lower carbon emissions. But the more we hear people portraying children as a problem, the more we should recognize there is an element in the global warming movement intent on attacking God’s Truth, rather than taking on any real problem. Conclusion Other passages could be mentioned like Genesis 8:22, Romans 1:25 and Psalm 102:25-26 but this is good for a start. And that’s what this is: a start. My hope here is to encourage an exploration of what Scripture says that’s relevant to the issue of global warming.  The Bible isn’t silent on this topic; we need to look at global warming biblically.

Christian education

A Christian perspective on 2+2

What does math have to do with God? Many people see no connection. Aren't logic, numbers and geometry the same for Christians and atheists? Math is thought to be the hardest subject to integrate with Christianity. Yet, there are very close links between math and God. Mathematical realism The key question concerns truth. Most mathematicians believe that mathematical truths such as "6+1=7" are universally and eternally true, independent of human minds. They believed that they are discovering properties of, say, numbers, rather than merely inventing them. This view of math dates back to Pythagoras (582-507 BC) and Plato (427-347 BC). They held that mathematical concepts apply best to ideal objects. For example, geometry deals with exact circles, but no physical object is exactly circular – perfect circles don’t actually exist. Furthermore, such things as the number "7" seem to exist at all times or, even, beyond time. This led to the notion that math exists in an ideal world of eternal truth. This is called mathematical realism. Where do such eternal mathematical truths exist? Augustine (354-430) placed the ideal world of eternal truths in the mind of God. He argued that eternal truths could not arise from material things or finite human minds. Rather, mathematical truths must depend on a universal and unchanging Mind that embraces all truth. Only God can have such a mind. Thus math was held to be true because of its supposed divine origin. It was held, moreover, that God created the universe according to a rational plan that used math. Since man's was created in the image of God, it was thought that man should be able to discern the mathematical structure of creation. Indeed, since man was God's steward over creation, man had the duty to study nature and to apply the results towards the glory of God and the benefit of man. Such theological considerations were key factors motivating the scientific revolution. Most founders of modern science, such Kepler, Galileo and Newton, were all driven by their Biblical worldview. Naturalist math Ironically, the very success of mathematical science led to the demise of the Christian view. The universe seemed to be so well controlled by mathematically formulated laws that God was no longer deemed necessary. Such over-confidence in scientific laws led to a denial of biblical miracles. This undermined biblical authority. Consequently, many scientists banished God and embraced naturalism, the notion that nothing exists beyond nature. THE LOSS OF CERTAINTY With the rejection of a divine Mind, there was no longer any place for eternal truth. This, in turn, led to the collapse of mathematical realism. Naturalists came to consider math as just a human invention. But if math is just a human invention, why should it be true? Mathematicians tried to prove the truth of math using the axiomatic method. Math was to be grounded on a set of undoubtedly true, self-evident principles, called axioms, from which everything else could be derived. The axiomatic method had been used with great success by the Greek mathematician Euclid (circa 300 BC). He derived all the truths about normal (or Euclidean) geometry from only 10 axioms. This became the model for the rest of math. Towards the end of the 19th century the search was on for a set of self-evident axioms upon which all of math could be based. Any system that yields a contradiction is, of course, false. A system of axioms that will never yield a contradiction is said to be consistent. A system is said to be complete if all true theorems (and no false ones) can be derived from the axioms. The goal, then, was to find a set of axioms that could be proven to be consistent and complete for all of math. Initially, there was some success. Simple logic and Euclidean geometry were proven to be both consistent and complete. Unfortunately, in 1931 the Austrian logician Kurt Gödel proved that the program was doomed. He proved that any large system of axioms (i.e., large enough for arithmetic with addition and multiplication) will always be incomplete.  There will always be theorems that can be neither proven nor disproven by the system. Thus all of math can never be based on a finite set of axioms. Math will always be larger than our human attempts to capture it within a system of axioms. Moreover, Gödel proved also that we can never mathematically prove the consistency of any system large enough for arithmetic. Hence we cannot be sure of the validity of arithmetic, even though we use it all the time! The soundness of math now had to be accepted largely on faith. THE LIMITS OF INVENTION Rejecting theism affected not only the soundness of math but also its content. Classical math was based on the concept of an all-knowing, all-powerful, and infinite Ideal Mathematician. The operations and proofs allowed in classical math were those that could in principle be done by God. It was thought that, if math is just a human invention, its methods should be adjusted accordingly. Only those mathematical concepts and proofs were to be considered valid that could be mentally constructed in a finite number of explicit steps. The "there exists" of classical math was to be replaced by "we can construct." This came to be known as constructive math. It entailed a new approach to both logic and proofs. Classical math is based on what is called two-valued logic. Any mathematical proposition is either true or false. Take, for example, Goldbach's Conjecture concerning primes. A prime is a number that is divisible only by itself and 1 (e.g., 2,3,5,7 & 11 are the first five primes). Goldbach's Conjecture asserts that any even number can be written as the sum of two primes (e.g., 10=3+7; 20=13+7). No one has ever found a number for which it did not hold. But no one has as yet been able to prove it. Classically, this conjecture is either true or false, even though we do not yet know which it is. Constructionists, however insist that there is a third possibility: a proposition is neither true nor false until we can construct an actual, finite proof. The rejection of two-valued logic restricts one's ability to prove theorems. Classical math often uses an indirect method of proof called Proof by Contradiction. To proof a theorem, one first assumes the theorem to be false and shows that this leads to a contradiction; hence the initial assumption is false, which means that the theorem is true. Since such proofs rely on two-valued logic, constructionists reject them. They accept only those theorems that can be directly derived from the axioms. Unhappily, this means rejecting so many results of classical math that one lacks the sophisticated math needed in modern physics. EVOLUTIONARY CONJECTURES If math is just a human invention how did it ever get started? Naturalists propose that evolution has hard-wired our brains to contain small numbers (e.g., 1,2,3…) as well as a basic ability to add and subtract. They conjecture that all our mathematical thoughts come from purely physical connections between neurons. Even if an evolutionary struggle for survival could account for an innate ability for simple arithmetic, it is hard to see where more advanced math comes from. Our ability for advanced math is well in advance of mere survival skills. The evolutionary approach fails to explain also the amazing mathematical intuition of leading mathematicians. Further, if our mathematical ideas are just the result of the physics of neural connections, why should they be true? Such accounts of math cannot distinguish true results from false ones. Indeed, if all knowledge is based on neural connections, so is the idea that all knowledge is based on neural connections. Hence, if true, we have no basis for believing it to be true. In spite of naturalist objections, most mathematicians remain realists. They view new theorems as discoveries rather than inventions. The excitement of exploring an objective mathematical universe is a powerful incentive for research. Realism explains why mathematicians widely separated in space, time, and culture end up with the same mathematical results. Moreover, if math is just a human invention, why is it so applicable to the physical world? Math is indispensable for science. Further, if math is a human invention, one might ask: how did math exist before Adam? Are we to believe that "2+2=4" did not hold, so that two pairs of apples did not add up to four? Christianity and math How does math fits within a Christian worldview? The Bible tells us that man was created in the image of God (Gen. 1:26-30). The divine image included not only righteousness but also rationality and creativity. This involves the capacity for abstract thought, as well as the ability to reason, to discern and to symbolize. Man was created with the innate potential to do math, to help fulfill his role as God's steward (Gen. 1:28). Adam could have confidence in his mental abilities because God created these to function properly. He was the result of God's purposeful plan rather than an evolutionary accident. With Adam's fall into sin, man lost much of his original image. Yet, man's mathematical ability is still largely functional. It seems that we are born with various basic, innate mathematical abilities such as those of logic, counting and distinguishing shapes. JUSTIFYING MATH How can we justify human math from this basis? One could try to ground the soundness of math on the Bible. After all, the Bible frequently uses logical arguments (e.g., I Cor. 15:12-50 or Matt. 12:25-29) and arithmetic operations (e.g., Luke 12:52). Gordon Clark claimed that all the laws of logic could be deduced from the Bible. Similarly, J.C. Keister asserted that all the axioms of arithmetic are illustrated in Scripture. Although such biblical examples may confirm our rules of arithmetic and logic, they fall short of rigorous proof. One must be careful in drawing general conclusions from a limited number of specific cases. Moreover, this method gives no basis for the vast bulk of math that extends beyond basic arithmetic and logic. A better approach might be to ground the truth of math on the attributes of the biblical God. For example, God's character has a logical aspect. God's word is truth (John 17:17); God never lies (Titus 1:2) and is always faithful (Ps. 117:2). God means what he says, not the opposite; hence the law of non-contradiction holds. God's identity is eternally the same; hence the logical law of identity must be eternally valid. Thus the very nature of God implies the eternal and universal validity of the laws of logic. Logic is not above God, but derives from God's constant and non-contradictory nature. God's character also has a numerical aspect: the Biblical God is tri-une, consisting of three distinct persons. Since the three persons of the Godhead – Father, Son, and Holy Spirit – are eternal, so are numbers. Consider further God's infinite power and knowledge. God knows all things. This includes not just all facts about the physical world but also all necessary truths and even all possibilities. As such, God's knowledge surely embraces all possible mathematical truths. Thus math exists independent of human minds. God surely knows whether any proposition is true or false. Hence the usage of two-valued logic in math is justified. God is the source of all being, upholding everything. He even establishes necessary truths and contingent possibilities. God upholds all truths, including truths about math. God surely knows whether any mathematical proposition is true or false. God's knowledge includes that of the actual infinite. The concept of infinity is crucial to the philosophy of math. We can distinguish between potential infinity and actual infinity. Potential infinity is the notion of endlessness that arises from counting. Given any large number, we can always obtain a yet larger one by adding 1 to it. There seems to be no largest number. Potentially we could go on forever. Actual infinity, on the other hand, is the notion that the set of numbers exists as a completed set. Augustine, however, considered actual infinity to be one of the mathematical entities that existed in God's mind. He wrote, "Every number is known to him 'whose understanding cannot be numbered' (Ps. 147:5)." Since God knows all things possible, this must surely encompass also the totality of all possible numbers. A BASIS FOR MATH Modern math is based on set theory. A set is a collection of objects. We can consider the set of all dogs, or the set of all even numbers, and so on. We use brackets {} to denote a set. Thus, for example, the set of even numbers is written {2,4,6...}. Treating each set as an entity in its own right, we can then do various operations on these sets, such as adding sets, comparing their sizes, etc. Remarkably, almost all advanced math can be derived from the nine axioms of modern set theory. Not all math, since Gödel proved that all of math can never be derived from a limited number of axioms. Yet, it does cover all of the math that most mathematicians ever use in practice. So far no contradictions have been found. Can we be sure, however, that no contradictions will ever be found in this system? Gödel, you will recall, proved that it cannot be proven mathematically that the system is consistent. The best we can do is to appeal to the plausibility of the individual axioms. Everyone agrees that the axioms all seem to be self-evidently true when applied to finite sets. Several of these axioms, however, deal with infinite sets. They postulate that certain operations on finite sets apply also to infinite sets. Infinite sets are needed to get beyond number theory (which just concerns whole numbers) to real numbers (such as √2 = 1.414213..., which requires an infinite number of decimals to write out fully). Real numbers are needed for calculus, upon which physics heavily relies. The axioms concerning infinite sets are rejected by constructionists since infinite sets cannot be humanly constructed in a finite number of steps. However, these axioms are very plausible given an infinite, omniscient and omnipotent being. Georg Cantor (1845-1918), the founder of modern set theory, justified his belief in infinite sets by his belief in an infinite God. He thought of sets in terms of what God could do with them. Cantor believed that God's infinite knowledge implies an actual infinity of thoughts. It included, at the very least, the infinite set of natural numbers {1,2,3...}. Actual infinity could thus be considered to exist objectively as an actual, complete set in God's mind. Cantor believed that even larger infinite numbers existed in God's mind. Even today, almost every attempt to justify the principles of set theory relies on some notion of idealized abilities of the Omnipotent Mathematician. The existence of sets depends upon a certain sort of intellectual activity - a collecting or "thinking together." According to Alvin Plantinga,

"If the collecting or thinking together had to be done by human thinkers there wouldn't be nearly enough sets - not nearly as many as we think in fact there are. From a theistic point of view, sets owe their existence to God's thinking things together."

Plantinga grounds set theory on God's infinite power and knowledge. He concludes that theists thus have a distinct advantage in justifying set theory. A detailed theistic justification of modern set theory has been developed by Christopher Menzel (2001). Ultimately, the consistency and certainty of math can be grounded upon the multi-faceted nature of God Himself. Trust in God generates confidence in math. Bibliography John Byl’s The Divine Challenge: On Matter, Mind, Math & Meaning (2004) Christopher Menzel’s "God and Mathematical Objects" in Mathematics in a Postmodern Age: A Christian Perspective (2001) edited by Russell W. Howell & W. James Bradley Nickel, James Nickel’s Mathematics: Is God Silent? (2001) Alvin Plantinga’s "Prologue: Advice to Christian Philosophers" in Christian Theism and the Problems of Philosophy (1990) edited by Michael D. Beaty Vern Poythress’ "A Biblical View of Mathematics" in Foundations of Christian Scholarship (1976) edited by Gary North

This article first appeared in the February 2008 issue of Reformed Perspective under the title, "A Christian perspective on math." Dr. John Byl is the author of "God and Cosmos: A Christian View of Time, Space, and the Universe" and "The Divine Challenge: On Matter, Mind, Math & Meaning." He blogs at Bylogos.blogspot.com

Some guidelines in teaching math  The goal of Reformed education is to prepare students to serve the Lord (I Cor. 10:3). This entails teaching them to think and function within a Christian worldview. In any discipline one must teach not only the subject matter but how this coheres with other disciplines and finds meaning within the Christian worldview. God's truth functions as a comprehensive unity. Math should thus be taught in terms of various contexts. 1. Mathematical Context In addition to mathematical knowledge we should instill insight into why math works, an appreciation of its beauty and a love for math. 2. Theological Context Math must be connected to the Christian worldview. We should show how Christianity explains mathematical truth, the rational structure of the universe, and our ability to do math. Studying math should be motivated by the love of God and directed to His glory. Studying math tells us something about God (e.g., His wisdom, coherence, boundlessness, consistency, dependability, righteousness). 3. Applied Context We should illustrate how math is an important tool for other disciplines, such as science. Math helps us to fulfill the cultural mandate and to more deeply appreciate God’s wonderful world. We should stress both the strengths and limits of mathematical models: these have to be applied and interpreted in ways that are consistent with Scripture. More generally, math helps to develop logical thinking and analytical problem-solving abilities, skills that are useful in all facets of life. 4. Social context Math teaching can be enriched by linking topics to their historical-cultural context. One could tell interesting anecdotes about pertinent mathematicians, touching also upon their religious motivation. This will bolster also the theological context since Christianity played a large role in the scientific revolution and since most leading mathematicians  (e.g., Descartes, Pascal, Newton, Euler, Cantor, Gödel) were theists.

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Tagged: featured, Saturday selections

Saturday Selections – February 15, 2020

Newsies learn to clickbait (4 minutes)

Who knew that fake news could be so toe-tapping?

Canadians waiting longer to receive healthcare

Free healthcare comes with a cost, and it isn’t just the taxes we pay – when the government is the only provider, then there is no competition to push innovation or efficiencies. It shouldn’t surprise us, then, that by the Fraser Institute’s estimates, Canadian wait times to receive healthcare have more than doubled since 1993. You can see the infographic at the link above, or the longer Fraser Institute report here.

Yes, you can trust the gospels…even when they seem to conflict (10-minute read)

Some scholars argue that the gospel writers didn’t care about the facts, but were just trying to send a message. Christian philosopher Lydia McGrew explains the message only has meaning if it is factual, and shows a way how alleged discrepancies can be resolved.

5 ways you are probably not a Calvinist

Dr. Wes Bredenhof lays out 5 views that John Calvin held that most Reformed folk probably don’t…

Follow your passion? The Christian vision of work

We’ve been telling young people to “follow your passion,” but is that a biblical view of calling?

Separating Church and State? (3 minutes)

The Devil is all about twisting truth right around so that what is good and right is then used for evil. So it is with the separation of Church and State. As Dr. Michael Wagner explains here, Church and State should be separate. But it is a very different thing to say that the government should be separated from Christian beliefs. Of course, the Devil would like God’s truth silenced. And our godless government doesn’t want Christians shining their reflected light in the halls of Parliament. That’s what they’re after when they speak about the separation of Church and State.

However, by their own standards, they have no basis on which to shut us up. We don’t ask anyone else to abandon their beliefs when they pursue political office, so why should Christians be expected to? Everyone hates double standards (Matt. 7:2).


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