{"id":6793,"date":"2022-11-01T02:25:24","date_gmt":"2022-11-01T02:25:24","guid":{"rendered":"http:\/\/farefwd.com\/?p=6793"},"modified":"2022-12-01T05:09:20","modified_gmt":"2022-12-01T05:09:20","slug":"constructive-doubt","status":"publish","type":"post","link":"https:\/\/farefwd.com\/index.php\/2022\/11\/01\/constructive-doubt\/","title":{"rendered":"Constructive Doubt"},"content":{"rendered":"\t\t
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Constructive Doubt<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t
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What do mathematics and faith have in common? A lot, it turns out\u2014including a potentially generative role for doubt within a community of practice.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t

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By Hayden Kvamme<\/em><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t

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As a pastor with a bachelor\u2019s degree in mathematics, I always love receiving the question, \u201cWhat did you study in undergrad?\u201d My response, \u201cMath,\u201d rarely fails to surprise my conversation partner. I usually go on to explain that, in addition to math, I took a serious interest in philosophy in college, through both the philosophy department and the classics department. My most cherished memories studying philosophy bring me back to a ten-week stint in Scotland, where I took three philosophy courses and one divinity course at the University of Edinburgh. My favorite of the three philosophy courses was Philosophy of Math (or, as they called it, \u201cMaths\u201d).<\/p>

From a young age, long before I perused the Edinburgh syllabus, the question of the truth of mathematics fascinated me. If anything was true, I figured, it was math. Admittedly, I may have believed this because math had come easy to me through high school and thus made intuitive sense. As I raise my three- and five-year-olds, I continue to notice how something as simple as a basket of fruit on the kitchen counter can tell you nearly everything you need to know about the fundamentals of arithmetic. Say you have two bunches of three bananas in the basket. Take the bunches first: 1+1 = 2. Now consider the bananas, two bunches of three: 2*3 = (1+1)*3 = 3+3 = 1+1+1+1+1+1 = 6. This exercise can exhaustively explain the operations of addition and multiplication. With enough patience, you could evaluate any whole number addition or multiplication problem with this strategy (though it\u2019s not a very efficient one). Remarkably, you could evaluate any whole number exponent problem with this strategy as well. That\u2019s a lot of math from a basket of fruit. Move from the kitchen out to the deck, and you can watch calculus happen with the drop of a ball to the grass below. And so on. From this simplicity, I thought, you can get the rest of math for free, like an elaborate, impossible-looking skyscraper built on the surest of foundations. And of course, any uncertainty along the way could be met by that crusher of doubt, the mathematical proof.<\/p>

This is how I experienced the beginning of my undergraduate studies in math. But as a student of pure (rather than applied) mathematics, I soon left the realm of concrete numbers and moved deeper into the worlds of linear and abstract algebra, topology, real analysis, and eventually algebraic topology. At the beginning of each class, I increasingly felt less like I was ascending to the next level of the skyscraper and more like I was wandering into an entirely unfamiliar part of the building. These new rooms were not in sequence with the old rooms; they were elaborate, mysterious additions reached only with intricate access codes. My continued travels also convinced me that what I had thought was the foundation of the building (numbers), was in reality something more like one half of an unfinished basement, serving as storage for the moment, in need of some tidying up, and certainly not to be confused with the true foundation.<\/p>

All of this set me up beautifully for maximum curiosity and joy as I began my Philosophy of Math course in Edinburgh. A first-year writing class at my liberal arts school, also on the subject of math, had whet my appetite for the subject, but this course was the real deal. Digging into the history of math, I began to see that I hadn\u2019t been alone in imagining numbers as the foundation of math, but that over time mathematicians and philosophers alike had come to notice problems with this view. This made me even more curious about the question of whether \u201cnumbers\u201d exist, and what it would even mean if they did.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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My continued search for the foundation of the math superstructure didn\u2019t yield straightforward answers, but it did make the building a lot more intriguing.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t

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Augustine was one of the first to suggest that numbers exist eternally in the mind of God, an idea that proved more Platonic than Christian. Nevertheless, at first glance, it\u2019s hard even to make sense of what an alternative description of the ontology of numbers could be. One can\u2019t trek across the world to discover the number one, hiding in a cave like some long-buried fossil. The most common alternative suggests that numbers are creations of our own minds, perhaps ideally expressed as primeval sets (or so one theory goes). This seems to imply that numbers exist only<\/em> in the human mind. Yet this suggestion seems just as absurd as discovering the number one in a cave. If numbers exist only in the human mind, then why is it that we can all agree on their meaning? If this<\/em> is the foundation of numbers, then perhaps it\u2019s no alternative to Augustine\u2019s theory after all. Perhaps in this case thinkers in the Augustinian vein, like Descartes and Berkeley, would be right: if numbers do exist in our minds, it\u2019s because God put them there, copies of the eternal numbers in God\u2019s own mind.<\/p>

My continued search for the foundation of the math superstructure didn\u2019t yield straightforward answers, but it did make the building a lot more intriguing. As I reflect on my studies and compare them to my journey of faith over the years, I\u2019ve noticed that I spent my childhood and early adulthood in a similar search for foundations of faith. For a long time I thought I\u2019d found the answer in the resurrection of Jesus. Like the numbers one and two, Jesus\u2019 death and resurrection seemed as sure a foundation as any for the construction of the Christian faith. Scripture seems to imply as much: the stone that the builders rejected has become the cornerstone.<\/p>

I was about seven when I asked my parents, \u201cDid Jesus really live on this earth?\u201d When they replied in the affirmative, I was awe-struck. Jesus was a real person in history. Having read the stories about him in the New Testament, this baffled me. Later, I was quickly persuaded by something like C.S. Lewis\u2019 \u201cLiar, Lunatic, or Lord\u201d argument, and frankly I didn\u2019t understand how anyone could think otherwise. It seemed as easy as one, two, three. And from there, as with mathematics, it seemed everything else would come for free. If Jesus died and rose from the dead, then he was Lord; he was right. And if he was right, then one had no real choice but to trust his Scriptures, the Old Testament, however bizarre they might be. And since history had more or less proven that the New Testament was the best witness to Jesus we have, why not include it in the canon, too? From here one can explore historical and systematic theology; just as importantly, one can become acquainted with a church, begin to practice faith, and in general live as a Christian. In this way the resurrection of Jesus was like the foundation of a house. We may quibble about how to furnish this or that room, but that\u2019s not going to stop us from building. Working from the single fact of Jesus\u2019 resurrection seemed as elegant and sure as any mathematical foundation could be.<\/p>

Not even my philosophy of math course at the University of Edinburgh changed this basic outlook for me. Instead, the intellectual earthquake came in a one-off conversation with my topology professor back on the other side of the Atlantic.<\/p>

\u201cHow do you make sense of whether math is true?\u201d I asked him. He responded, \u201cI think of math less in terms of truth and falsehood than in terms of art.\u201d The rest of his response made his perspective clear: the search for absolute truth in math was a fool\u2019s errand; one would be better off to work as a mathematical artist in pursuit of elegance and beauty.<\/p>

I didn\u2019t know what to make of his response. But it stuck with me. As I look back at the conversation, I realized it was one moment in a process that slowly changed my epistemology of math and faith alike. Looking back at my studies, what I notice is that, despite its apparent objectivity and sure-footedness, in practice math works a lot like other fields, including theology. Mathematics doesn\u2019t happen in an armchair or in an empty and desolate room, but in a community of practice. After all, the mathematical imperative, prove it<\/em>, is never meant to imply that anyone could prove it outright or in a vacuum. Instead, this is the task: given the axioms we\u2019ve agreed upon, demonstrate logically that the conclusion follows.<\/em> In other words, prove it to us, your fellow mathematicians. And at that point, of course, aesthetics assumes paramount importance. The best proofs do turn out like works of art. They are called simple, elegant, beautiful. The resulting picture can indeed take your breath away. In nearly every branch of mathematics, only a handful of axioms has generated a breathtaking amount of math. While to my knowledge consolidations of the field (like the \u201cTheory of Everything\u201d in physics) remain elusive, the elaborate skyscraper of mathematics leaves me in as much awe today as it did when I began college.<\/p>

While this communal framework may disappoint those in search of absolute truth, it illuminates the function of doubt. On the dull end of the spectrum, a mathematician could doubt a particular proof, identifying an error in its reasoning or ambiguity in its form. More broadly she could wonder whether a more elegant construction of the proof exists that more beautifully illustrates the result. But mathematical doubt can function even more creatively. Some brilliant mathematicians over the years have served as something more like meticulous building inspectors, using accepted axioms to generate outlandish results with the goal of making the mathematical community wonder whether and where the whole construction took a wrong turn. (One need only consider the Banach-Tarski paradox to get the idea.) Such exercises aren\u2019t merely cynical or deconstructive; they can invite the collective to go back to the drawing board, and wonder whether such a strange result implies that we\u2019ve been using the wrong set of axioms, and what the alternatives might be.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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I welcome questions and doubts, because they lead to parts of the building too long neglected. The foundation remains sure.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t

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I\u2019ve come to appreciate that doubt can serve a similar role within the community of faith. When we think of doubt, we may imagine a drifter whose doubts have led him to a lonely island, sad and discouraged. This is one possible consequence of doubt, but it isn\u2019t the only one. This picture comes from an individualistic, and therefore limited, imagination of a walk of faith. It also ignores the reality of the church as a genuine community. Granted, some communities or individuals may attempt to shun doubters. But this is neither the only nor the main approach the church has taken with doubters through the years. Like the insightful mathematician, one can doubt from within the community, offering an invitation for the collective to re-evaluate its axioms without any intention to cut ties. This can result not only from joyful curiosity, but from jarring tragedy as well, both of which have a way of bringing new questions and doubts to light. A fruitful Christian community stands ready to learn and grow in such a moment, eager to explore uncharted or under-explored territory.<\/p>

In fact, this is often precisely how the Spirit moves. Take what Old Testament scholars call the Babylonian Exile. One can scarcely imagine a more jarring experience of faith than that of the Israelites of the 6th<\/sup> Century B.C., when the Babylonians came and destroyed the Holy City of Jerusalem, desecrated its temple, and dragged many of the people of God away to a foreign land as slaves. Any sane person in such a situation would have to wonder at this point what the love of God really meant, and doubt whether their conventional understanding could withstand such an extreme disaster. For some, the traumatic experience likely did lead to a loss of faith. But for others, the experience invited them to reevaluate the premises, story, and practices of faith. This in turn led these latter individuals to generate some of the most stunning works of faith ever recorded. Out of this rubble came the prophetic corpus of Isaiah, Jeremiah, and Ezekiel. Moreover, our best evidence tells us that the whole of the Old Testament was collected and edited as the Israelite community\u2019s most faithful God-breathed response to the horror of the Babylonian Exile. Doubt led, in the end, not to despair, but to a creative, collective reimagining of faith.<\/p>

This has been my own experience of doubt as well, both personally and as a pastor. I consistently find it essential and healing to situate questions and doubts within<\/em> the community of practice. Engaging with doubt playfully and creatively has proven incredibly fruitful over time, in large part because, at its best, it causes the community to come together and tell the story of faith with attention to new angles. The resilient truth of faith tends in such moments to reveal itself not in this or that proof, but in the surprising beauty and inter-connection of the whole. A deep dive into the historicity of the resurrection may still be one of the best apologetic arguments for the truth of the Christian faith. But it\u2019s still misleading if \u201cChristian faith\u201d is treated as a known entity beforehand, rather than, at least in part, a process of discovery. Even in first-century Israel, the resurrection of Jesus did not serve to prove Christianity so much as to enliven a significant contingent of God\u2019s people to reevaluate everything they knew about God\u2019s faithfulness, creation, exile, the Kingdom of God, life, and death. The result was the New Testament, the early church, and Christianity itself.<\/p>

The upshot of this is that, though the resurrection may be foundational, the foundation <\/em>of our faith is found within the Godhead itself. \u201cIn God we live and move and have our being,\u201d Paul writes, or quotes. One could just as easily say that in God is where math lives and moves and has its being, too. One need not posit any particular theory on the existence of numbers to hold this position; but the ambiguity doesn\u2019t discount math\u2019s truth. To pursue truth, whether through math, theology, spiritual practices, or some other means, is not necessarily a quest toward the foundation. After all, one comes to trust the foundation of a building not by seeing it (that\u2019s usually a bad sign), but by living in it and discovering over time that the structure is sound.<\/p>

For the average twenty-first century seeker of truth, a serious reckoning with the resurrection proves even more jarring than it would have to a first-century Israelite. To take Jesus seriously is to take ancient Israel and its experience of God seriously, to come to the Old Testament, and with it the New, not as a cynical archeologist in search of truth and falsehood, but as a humble guest to an intricate, creative, and surprising maze of a building. Increasingly, I\u2019m just grateful to walk through the door and take a slow tour with other people of faith. I welcome the questions and doubts, because they lead to parts of the building too long neglected. The foundation remains sure.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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Image<\/strong> by Hydrogen Iodide<\/a> courtesy of Creative Commons<\/a>.\u00a0<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t

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Hayden Kvamme<\/strong>\u00a0is an associate pastor at Gloria Dei Lutheran Church in Rochester, Minnesota, where he shares in all aspects of pastoral ministry. A math major at Dartmouth, Hayden received his Masters of Divinity degree from Wartburg Seminary in Dubuque, Iowa. He now lives with his wife and their two children in Rochester.<\/em><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"

What do mathematics and faith have in common? A lot, it turns out – including a potentially generative role for doubt within a community of practice. 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