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Religion - Roman Catholic, Theology

What must Ben Shapiro do to be saved?

Does a person need to put their faith in Jesus to be saved? That was the underlying question conservative political commentator Ben Shapiro put to Roman Catholic Bishop Robert Barron in episode 31 of his Sunday Special. Ben Shapiro pulls no punches when he asks,

What’s the Catholic view on who gets into Heaven and who doesn’t? I feel like I lead a pretty good life—a very religiously based life—in which I try to keep, not just the Ten Commandments, but a solid 603 other commandments, as well. And I spend an awful lot of my time promulgating what I would consider to be Judeo-Christian virtues, particularly in Western societies. So, what’s the Catholic view of me? Am I basically screwed here?

Same question, different responses In asking this, Shapiro is asking the same question as the rich young ruler—albeit in a less elegant way. It’s the most important question a person can ask: What must I do to inherit eternal life? Like the rich young Jewish ruler from the first century, Shapiro qualifies his question with a list of good deeds. Both young Jewish men boast of their religiosity and their sincerity to keep the Law. Although their questions are similar, the answers they each receive are different. In Jesus’ response, He shows the rich ruler that he—like all of us—falls short of God’s perfect standard (Mark 10:21). In fact, he has not even kept the greatest commandment to love God above everything else, including his wealth. Jesus’ point is clear: You can’t enter God’s kingdom by working. Paul makes the same point in his letter to the Romans. He says, “For by works of the law no human being will be justified in his sight, since through the law comes knowledge of sin” (Rom. 3:20). Paul adds, “For all have sinned and fall short of the glory of God, and are justified by his grace as a gift, through the redemption that is in Christ Jesus, whom God put forward as a propitiation by his blood, to be received by faith” (Rom. 3:23–25a). In His short encounter with the rich ruler, Jesus illustrates how not to inherit eternal life. But, in an encounter with another Jewish ruler, He explains how to inherit eternal life. Speaking to Nicodemus, Jesus says, “For God so loved the world, that he gave his only Son, that whoever believes in him should not perish but have eternal life” (John 3:16). Here’s what we learn from Jesus’ interactions with these two Jewish leaders. First, good works won’t work. Second, eternal life is received by faith—believing in Jesus. Contrast Jesus’ response to Bishop Barron’s:

No. The Catholic view—go back to the Second Vatican Council [which] says it very clearly.

Christ is the privileged route to salvation. God so loved the world He gave His only Son that we might find eternal life, so that’s the privileged route. However, Vatican II clearly teaches that someone outside the explicit Christian faith can be saved. Now, they’re saved through the grace of Christ indirectly received, so the grace is coming from Christ. But it might be received according to your conscience.

So if you’re following your conscience sincerely—or, in your case, you’re following the commandments of the Law sincerely—yeah, you can be saved.

Now, that doesn’t conduce to a complete relativism. We still would say the privileged route—the route that God has offered to humanity—is the route of His Son. But, no, you can be saved. Even, Vatican II says, an atheist of good will can be saved.

The belief that someone can by saved today without explicit faith in Christ is called inclusivism. Barron does a good job laying out the inclusivist position—a position taught by the Roman Catholic Church. Unfortunately, Bishop Barron doesn’t give any biblical support for the view. Why I am not an inclusivist There are a number of reasons why I am not an inclusivist. One of the most compelling arguments against inclusivism is found in the account of Cornelius. In Acts 10 and 11, Luke records what Cornelius is like.

At Caesarea there was a man named Cornelius, a centurion of what was known as the Italian Cohort, a devout man who feared God with all his household, gave alms generously to the people, and prayed continually to God. (Acts 10:1–2)

Cornelius seems to have a lot going for him. But he’s got a problem: He’s never heard the gospel. Knowing how Cornelius has responded to the light he’s been given, God gives him more light. He sends him a vision. In the vision, an angel tells Cornelius to send for a man named Peter.

And he [Cornelius] told us how he had seen the angel stand in his house and say, “Send to Joppa and bring Simon who is called Peter; he will declare to you a message by which you will be saved, you and all your household.” (Acts 11:13–14)

Notice the text says that Cornelius isn’t saved at this point. He has to hear “the message” by which he can be saved. God-fearing? Yes. Devout and sincere? True. Generous and religious? Absolutely. Even Peter is impressed by Cornelius’s spiritual accolades. Now notice what Peter doesn’t do. He doesn’t reassure Cornelius that he has been saved “by grace indirectly received”—as Barron put it. He isn’t saved by “sincerely following his conscience.” He doesn’t speak of two routes to God: a “privileged route” received by faith in Christ and another route where faith in Christ isn’t required. No, the text says Cornelius needed to hear a message “by which he will be saved.” What was that message? We are not left guessing. Peter tells us,

And he [Jesus] commanded us to preach to the people and to testify that he is the one appointed by God to be judge of the living and the dead. To him all the prophets bear witness that everyone who believes in him receives forgiveness of sins through his name. (Acts 10:42–43)

Even with all of his spiritual nobility and religious sincerity, Cornelius was still lost and in need of salvation. If inclusivism were true, Peter would not have needed to make a trip to Cornelius. But Peter had to make the trip because—as Paul says—“How will they call on him in whom they have not believed? And how are they to believe in him of whom they have never heard? And how are they to hear without someone preaching?” (Romans 10:14–15). How can people call on Jesus if they have not believed in Jesus? The answer is, they can’t. How are people going to believe in Jesus if they have never heard of Jesus? The answer is, they can’t. How are they going to hear the good news if no one tells them the good news? The answer is, they won’t. Paul’s line of thinking is clear and straightforward. If no one is sent to these people, then there will be no one to preach the good news. If no one preaches to these people, then they will not hear the good news. If these people do not hear the good news, then they cannot believe. And if they do not believe, then they cannot be saved. One way to be saved In sum, Paul tells us that the people need to hear and believe the gospel in order to be saved. There is no other means of salvation. By the way, this is consistent with Peter’s testimony. He says, “And there is salvation in no one else, for there is no other name under heaven given among men by which we must be saved” (Acts 4:12). Notice he doesn’t merely say that there is no other savior. He says there is no other name. His name—Jesus’ identity—seems necessary. That’s why Peter tells Cornelius, “Everyone who believes in him receives forgiveness of sins through his name” (Acts 10:43). The story of Cornelius should be an encouragement to us because it shows the lengths to which God will go to make sure people seeking after God will hear the gospel so that they can be saved. God had given Cornelius some light—through creation and conscience—but this was not enough light to save him. Since Cornelius responded positively to the light he was given, God gave him more light—specifically, the gospel. Inclusivism is a bad idea Ideas have consequences. And bad ideas have victims. Inclusivism is a bad idea because it gives people—like Shapiro—false hope that they can have eternal life without coming to Jesus on His terms. Those who refuse to come to Jesus will not receive life (John 5:40). Jesus explicitly states, “I told you that you would die in your sins, for unless you believe that I am he you will die in your sins” (John 8:24). Bishop Barron is wrong. Shapiro cannot be saved by “following the commandments of the Law sincerely.” Paul addresses this very thing in his letter to the Galatians. He says,

Yet we know that a person is not justified by works of the law but through faith in Jesus Christ, so we also have believed in Christ Jesus, in order to be justified by faith in Christ and not by works of the law, because by works of the law no one will be justified” (Gal. 2:16).

Shapiro’s good works will never be enough. Only those who put their trust in Christ will receive eternal life. The answer to Shapiro’s question isn’t hard. In fact, the apostle Paul answers the question “What must I do to be saved?” in a single sentence. “Believe in the Lord Jesus, and you will be saved” (Acts 16:31).

This article is reprinted with permission from Tim Barnett and Stand to Reason (str.org) where it first appeared here. The Ben Shapiro picture has been adapted from one copyright © by Gage Skidmore and is used here under a Attribution-ShareAlike 2.0 Generic license.

Adult non-fiction, Theology

Heaven: what can we know?

A summary review of Randy Alcorn's Heaven

****

Christians don't seem to speak about Heaven as much as in the past. There is more interest in establishing the Kingdom of God on earth than in preparing for the afterlife. SLOPPY THINKING When Christians do think about Heaven, they seem disconnected from the Scriptures. According to popular thought, where Christians go when they die is the same place they will spend eternity. Even contemporary believers base their thinking on Heaven more on sloppy, syrupy, sentimental television programs than on any clear teaching of Scripture. There is a hint in our attitude toward Heaven that it will be "angelic," that we will end up playing harps on a misty cloud in the "heavens." We will be wearing long white robes, and talking pious talk forever and ever. Some even picture Heaven as a boring place. But these conventional caricatures of Heaven do a terrible disservice to God and adversely affect our relationship with Him. Heaven is not a sing-along in the sky, one great hymn after another, forever and ever. Hell will be deadly boring. Heaven is exciting! Everything good, enjoyable, refreshing, fascinating, and interesting is derived from God. When we have an infinity of newness to explore, we can never be bored. THINKING ABOUT HEAVEN [caption id="attachment_5954" align="alignright" width="197"] 560 pages / 2004[/caption] So why think about Heaven? Because the Scriptures remind us to think on things above. Doing so gives us insight into the brevity of our time on Earth and the value of life eternal. The doctrine of Heaven then, should not be marginalized by the church. Rather, it should be preached, taught, studied and loved. In calling us to this end, theologian/novelist Randy Alcorn, prolific author, founder and director of Eternal Perspective Ministries, has made a beautifully written contribution with his book Heaven. Is Heaven a real place? It's as real as a morning cup of coffee. Ah, but will we drink coffee in Heaven? Alcorn asks, "Can you think of any persuasive reason why coffee trees and coffee drinking wouldn't be part of the resurrected Earth?" His answer? "No." Despite biblical references that this Heaven and Earth will pass away, Alcorn strongly argues – from Scripture, word studies, and historical theology – that the "destruction" of the current Heaven and Earth will be temporary and partial. He firmly believes in the literal fulfillment of Isaiah's prophecies about the Messiah's second coming and the New Earth because Isaiah's detailed prophecies regarding the Messiah's first coming were literally fulfilled. The ultimate fulfillment of hosts of Old Testament prophecies will be on the New Earth, where the people of God will "possess the land forever" (Isaiah 60:21). Alcorn states, therefore, that God never gave up on his original plan for human beings to dwell on Earth. In fact, the climax of history will be the creation of a New Heaven and a New Earth, a resurrected universe inhabited by resurrected people living with the resurrected Jesus. THE RESURRECTION The key to understanding the New Earth is the physical resurrection of Jesus Christ. We are told that Jesus' resurrected body on Earth was physical, and that this same, physical Jesus ascended to Heaven, from which he will one day return to Earth (Acts 1:11). Alcorn states that the physical resurrection of Jesus Christ is the cornerstone of redemption – both for mankind and for the earth. Indeed, without Christ's resurrection and what it means – an eternal future for fully restored human beings dwelling on a fully restored Earth – there is no Christianity. Because we know that Christ's resurrected body is physical and that our resurrected bodies will be like his, there isn't a compelling reason to assume that other physical depictions of the New Earth must be figurative. Consequently, the predominant belief that the ultimate Heaven that God prepares for us will be unearthly could not be more unbiblical. Earth was made for people to live on, and people were made to live on Earth. Alcorn also believes that Christ's redemptive work extends resurrection to the far reaches of the universe.

"The power of Christ's resurrection is enough not only to remake us, but also to remake every inch of the universe – mountains, rivers, plants, animals, stars, nebulae, quasars, and galaxies."

THE INTERMEDIATE STATE Christians often think about Heaven as their final destination. However, this belief is not based on Scripture. Alcorn explains the difference between the present (or intermediate) Heaven, where Christians go when they die, and the ultimate, eternal Heaven, where God will dwell with his people on the New Earth. When we die in Christ we will not go to Heaven where we'll live forever. Instead, we'll go to an intermediate Heaven. In the intermediate Heaven, we'll wait for the time of Christ's return to Earth, our bodily resurrection, the final judgment, and the creation of the New Heaven and New Earth. The intermediate Heaven then is a temporary dwelling place, a stop along the way to our final destination: the New Earth. In the intermediate Heaven, being with God and seeing His face is its central joy and the source of all other joys. We will be fully conscious, rational, and aware of each other. We will know what is happening on Earth. We will be distinct individuals, live in anticipation of the future fulfillment of God's promises. We will be reunited with believing friends and family. We will be one big family. We will be aware of passing of time. But we will never be all that God has intended for us to be until body and spirit are again joined in the resurrection. CHRISTOPLATONISM Why do we find it so difficult to grasp that the intermediate Heaven is not our final destination? Alcorn rightly blames the influence of the ancient Greek philosopher Plato. Plato believed that material things, including the human body and the Earth, are evil, while immaterial things such as the soul and Heaven are good. He asserted that the spirit's highest destiny is to be forever free from the body. This view is called Platonism. The Christian church, highly influenced by Platonism, came to embrace the "spiritual" view that human spirits are better off without bodies and that Heaven is, therefore  a disembodied state. From a christoplatonic perspective, therefore, our souls merely occupy our bodies, like a hermit crab inhabits a seashell, and our souls could naturally – or even ideally – live in a disembodied state. Christoplatonism has had a devastating effect on our ability to understand what Scripture says about Heaven, particularly about the eternal Heaven, the New Earth. The Bible, however, contradicts Christoplatonism from the beginning of Genesis to the end of Revelation. It says that God is the Creator of body and spirit; both were marred by sin, and both were redeemed by Christ. THE NEW HEAVEN AND EARTH  The New Heaven and Earth is a real, tangible place. The New Earth has dirt, water, rocks, trees, flowers, animals, people, rain, snow, wind and a variety of natural wonders. An Earth without these would not be Earth. Alcorn believes there will be animals from various nations. He believes these animals have souls, though not the same type as humans. Alcorn firmly believes that we will be eating and drinking in the New Earth. However, there won't be marriages. Alcorn notes that the institution of marriage will have fulfilled its purpose. The only marriage will be between Christ and His bride – and we'll be part of it. The city at the centre of the New Earth is called the New Jerusalem. The ground level of the city will be nearly two million miles. Alcorn suggest that we will walk on streets of real gold. The New Jerusalem will be a place of extravagant beauty and natural wonders. It will be a vast Eden, integrated with the best of human culture, under the reign of Christ. More wealth than has been accumulated in all human history will be spread freely across this immense city. We will also have our own homes. In this New Earth we will also enjoy periods of rest. Alcorn says that God prescribed rest for sinless Adam and Eve, and He prescribed it for those under the curse of sin. Hence, regular rest will be part of the life to come in the new universe. Alcorn argues that there will be a government on the New Earth. The need of government didn't come about as a result of sin. God governed the universe before Satan fell. Likewise, He created mankind as his image-bearers, with the capacity for ruling, and before Adam and Eve sinned, God specifically commanded them to rule the Earth. On the New Earth there will be no sin. Therefore, all ruling will be just and benevolent, devoid of abuse, corruption, or lust for power. As co-rulers with Christ, we'll share in the glory of the sovereign ruler himself. We will become the stewards, the managers of the world's wealth and accomplishments. Alcorn believes in the transformation of the entire universe. If the new creation is indeed a resurrected version of the old, then there will be a New Venus, after all. In the same way that the New Earth will be refashioned and still be a true Earth, with continuity to the old, the new cosmic heavens will likewise be the old renewed. It will provide unimaginable territories for us to explore and establish dominion over them to God's glory. And if Christ expands His rule by creating new worlds, whom will He send to govern them on his behalf? His redeemed people. Some may rule over towns, some cities, some planets, some solar systems or galaxies. Alcorn comments, "Sound far-fetched? Not if we understand Scripture and science." CULTURE Alcorn notes that Scripture is clear that in some form, at least, what's done on Earth to Christ's glory will survive. But he also argues that cultural products of once pagan nations will be brought in by its people "proclaiming the praise of the Lord" (Isaiah 60:6). Treasures that were once linked to idolatry and rebellion will be gathered into the city and put to God-glorifying use. Alcorn believes that Isaiah and Revelation indicate that these products of human culture will play an important role on the New Earth. But the idea of bringing into the New Heaven and Earth cultural products is also a much disputed idea. Will we still want these treasures when our whole environment will be different? He says that there will be technology, machinery, business and commerce. There will be music, dancing, storytelling, art, entertainment, drama, and books. We will design crafts, technology, and new modes of travel. We will not only work in the New Earth, we will keep on learning. Alcorn looks forward to reading nonfiction books that depict the character of God and the wonders of his universe. "I'm eager to read new biographies and fiction that tell powerful redemptive stories, moving our hearts to worship God." Interestingly, he also believes that the Bible will be in Heaven. "Presumably, we will read, study, contemplate, and discuss God's Word." But why would there be a Bible in Heaven? The Bible serves God's people in this world as a guide for their lives and to strengthen their faith. In Heaven there is no need for the Bible. We see then God face to face. We witness then the fulfillment of His promises. ETERNAL REWARDS  Alcorn argues that God will hand out different rewards and positions. He says that our works do not affect our salvation, but they do affect our rewards. The rewards hinge on specific acts of faithfulness on Earth that survive the believer's judgment and are brought into Heaven with us. Alcorn believes that the position of authority and the treasures we're granted in Heaven will perpetually remind us of our life on Earth, because what we do on Earth will earn us those rewards. IMAGINATION AND SPECULATION Alcorn asserts that God expects us to use our imagination in describing Heaven, even as we recognize its limitations and flaws. He states that because the Bible gives a clear picture of the resurrection and of earthly civilization in the eternal state, he is walking through a door of imagination that Scripture itself opens. He writes: "If God didn't want us to imagine what Heaven will be like, he wouldn't have told us as much about it as he has." But at times his imagination gets the best of him. He repeatedly uses the words "perhaps" and "speculation." For example, he claims that perhaps intermediate bodies in the intermediate Heaven – or at least a physical form of some sort – serve as bridges between our present bodies and our resurrected bodies. He suggests that our guardian angels or loved ones already in Heaven will be assigned to tutor us. We could also discuss ministry ideas with Luis Palau, Billy Graham, or Chuck Colson. He also argues that we will explore space. He suggests that to view the new heavens, we might travel to the far side of the moon and other places where stargazing is unhindered by light and atmospheric distortions. HEAVENLY MINDED. EARTHLY GOOD.  Thinking about Heaven should impact the way we live on Earth. Alcorn comments that understanding Heaven doesn't just tell us what to do, but why. It is incentive for righteous living to the glory of God. Anticipating our homecoming will motivate us to live spotless lives here and now. In other words, what God tells us about our future lives enables us to interpret our past and serve Him in our present life. EVALUATION Alcorn quotes frequently from the writings of many Reformed authors, including Francis Schaeffer, Al Wolters, Anthony Hoekema, Herman Ridderbos, Jonathan Edwards, John Calvin, Cornelis Venema, Paul Marshall and Richard Mouw. He is also greatly indebted to writings of C.S. Lewis and A.W. Tozer. His work clearly shows the impact these scholars made on him. But Alcorn also adds his own perspectives on the life to come. He writes: "I will try to make the case carefully and biblically. There is plenty in this book for everyone to disagree with." I have already stated a few of my disagreements, so let me now state a few more. Alcorn overly quotes from his own writings. His "works equal rewards" theology is questionable. I can't find any Biblical support for his suggestion that God might create new beings for us to rule over in the afterlife. The rich concept of Sabbath rest gets short thrift – rest is not something physical; it is spiritual. It is not negative, what we do or not do, but positive, something we have. This rest is a gift from God, something we enjoy in close association with Him. I suggest that Alcorn thinks about Heaven too much from an egocentric viewpoint – focusing in on what interests us the most. With all the discussions of what we may do in Heaven, we easily forget that Heaven is the place of habitation of the Triune God. I also have questions about the purpose of Alcorn's speculations. We must not say more than Scripture. God has not revealed to us what the new cosmos will be like. We don't know anything about extra territorial space travel. We easily forget that the apostle Paul says: "No eye has seen no ear has heard, no mind has conceived what God has prepared for those who love him – but God has revealed it to us by his Spirit" (1 Cor. 2:9,10). But my critical observations don't take away the appreciation I have for Alcorn's work. He gives new insights, and makes you think about the best that is yet to come for God's people.

Rev. Johan Tangelder (1936-2009) wrote for Reformed Perspective for 13 years. Many of his articles have been collected at Reformed Reflections. This article first appeared in the 2005 July/August issue.

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.

Documentary, Movie Reviews, Pro-life - Abortion, Watch for free

Harder Truth

Documentary 9 min / 2003 This film changed me. It is a video, taken in the womb, of an abortion. It is evil uncovered and brought into the light. Just as it took pictures of dead Jews, stacked like cordwood, to drive home the horror of the Holocaust, and it took the newspapers carrying pictures of the lynched teen Emmett Till to reveal the wickedness of what was happening in the American South, so too, visuals are important in the abortion debate. Ours is a visual culture and graphic pictures of bloody, broken, tiny bodies communicate what abortion really is (Eph 5:11). These images cut through words like “choice,” “rights” and “freedom” and make plain the fact that abortion is murder. While this short video, Harder Truth, is one I believe should be widely shared and seen, it contains pictures that are deeply disturbing so it should be shown with care. When you share this, the audience should be warned about what they are about to see. And what are they going to see? While there is no verbal narration, the film begins with two minutes of text detailing what is going to be shown and why it is being shown. Then there is two minutes of a baby in the womb, developing from zygote to fetus. Then, just after the 4-minute mark, we see what an abortion actually is and what it does to the baby. The final four minutes of the film show remains of aborted babies: bloody broken bodies, tiny detached arms and legs, and crushed skulls. I've shown this at dozens of presentations and, as the video itself suggests, when I show it I tell the audience that anyone who wants to look away should feel very free to do so. I also find that, while the film is very short, its nine minutes of content can be overwhelming and I often show only a middle selection of two or three minutes. The toughest consideration in showing this film is, how young is too young? As pro-life apologist Scott Klusendorf notes, girls as young as 12 can, in many jurisdictions, get an abortion without their parents’ knowledge or permission. Twelve is very young. But if they are old enough to get an abortion isn’t it important they know the real truth of it? I've been asked why I bother showing this to pro-life audiences. After all, we don't need to be convinced abortion is wicked, do we? Well, yes, we do. Abortion happens in even 100% pro-life churches too, and the reason it does is because sometimes those pro-life convictions are only an inch deep. That shouldn't surprise us. Abortions are all done behind closed doors. The victims are invisible. We might hear that 100,000 babies are murdered each year in Canada, and ten times that amount in the US, but those are just numbers, and too big for us to really fathom. So when a young teen finds herself pregnant and, mistakenly or correctly, thinks her parents will disown her if they ever find out, will inch-deep convictions stop her from taking the "solution" the world is readily offering? So there is a need then, to show even our Christian, pro-life, young people, the grim reality of what abortion is. Every bit as important, we need to tell our daughters that we will love them and will help them if they ever have an unplanned pregnancy. WARNING: THIS VIDEO CONTAINS GRAPHIC IMAGES OF AN ABORTION.

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Tagged: featured, Greg Koukl, Jonathon Van Maren, Saturday selections

Saturday Selections – Oct. 20, 2018

How our sun and atmosphere show evidence of being Intelligently-designed (3 minutes)

A different take on pro-abortion bully Jordan Hunter

When Jordan Hunter kicked pro-life protester Marie-Claire Bissonnette on a street in Toronto, video of his attack went viral. That viral video led to Hunter losing his job, and to the police pressing charges. Both results were unusual – though violence and destruction of property are regularly committed against pro-lifers, it’s probably more common that pro-lifers are arrested by the police than the police arrest someone for attacking pro-lifers. It felt good to be on the winning side for once. But one commentator questioned whether the pro-life camp came out looking good.

On a related note, even as this was all about the unborn – Hunter kicked Bissonnette for speaking up for the unborn and the unborn were the reason Bissonnette was out there protesting – what got lost in the news coverage was the unborn themselves. The press presented this as being about the principles of freedom of speech, and peaceful protest. Jordan Hunter was certainly attacking those principles, but those principles don’t need defending like the unborn do. So, when attention comes our way, how can pro-lifers direct the media spotlight towards the unborn? Most importantly, we have to stick to our own talking points, about the humanity of the unborn, no matter where a reporter might want to take us. The media wants to do something on freedom of speech? We talk about how important it is that we be free to tell the country about the humanity of the unborn. They want to talk about peaceful protest? We talk about how it isn’t our own peace we most want to ensure, but peace for the unborn. Of course, sticking to our message is no guarantee that the unborn’s humanity will make it to the nightly news – we can’t control reporters – but by ensuring all our answers are about the unborn (even as the media tries to take us in other directions) we can make it more likely the media will pass along at least some Truth about the unborn.

A warning for parents: Instagram is full of porn

Reformed commentator Jonathan Van Maren shares a secular magazine’s warning about Instagram, and then shares a helpful resource – Social Media and Teens: The Ultimate Guide to Keeping Kids Safe Online – that parents may appreciate.

The deadly Canadian M.A.I.D

Three Canadians doctors are promoting the idea of euthanasia for children without their parents’ permission. That’s where you end up when life is no longer understood as intrinsically valuable.

Man wins women’s cycling race

A man who says he is a woman just won a women’s cycling race. How is that fair? The transgender winner argued that because he’s lost to the women he was competing against more times than he’s beat them, that makes it fair. That might make it competitive in much the same way that if a 40-something-year-old on foot raced his 8-year-old daughter on her bike, it might be close for the first 50 meters or so. But that doesn’t make it any less a matter of apples competing against oranges.

What was the sin of Sodom and Gomorrah?

Some are arguing it wasn’t homosexuality but was really about inhospitality or rape. Koukl shows how an honest look at the text says otherwise. (5 minutes)


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