Why You Should Care about Math

“Mathematics,” wrote the agnostic philosopher Bertrand Russell, “is, I believe, the chief source of belief in eternal and exact truth.” Of course, there are lots of other reasons to believe in eternal, exact truth, but Russell’s getting at something really interesting: math has consequences for how we think.

Here’s the story.

Pythagoras introduces abstract numbers

PythagorasFor the ancient Greeks, math was one with metaphysics. It all started in the sixth century BC, with Pythagoras—the first of the Greeks to treat numbers as abstract entities existing in their own right. (Before him, numbering was all about the things being numbered, not the numbers themselves—as David Foster Wallace puts it, “the Babylonians and Egyptians were . . . interested in the five oranges rather than the 5.”) In fact, as Russell explains, Pythagorean numbers and math were more real than sensory reality:

“Geometry [derived from Pythagorean math] deals with exact circles, but no sensible [perceptible] object is exactly circular . . . . This suggests the view that all exact reasoning applies to ideal as opposed to sensible objects; it is natural to go further, and to argue that thought is nobler than sense, and the objects of thought more real than those of sense-perception. . . . numbers, if real at all, are eternal and not in time. Such eternal objects can be conceived as God’s thoughts.”

And here’s the important part—for pretty much the first time ever, all this reasoning started spilling over into the observed world. Russell explains:

“Geometry . . . starts with axioms which are (or are deemed to be) self-evident, and proceeds, by deductive reasoning, to arrive at theorems that are very far from self-evident. The axioms and theorems are held to be true of actual space, which is something given in experience. It thus appeared to be possible to discover things about the actual world by first noticing what is self-evident and then using deduction.” (Emphasis added)

It’s largely thanks to Greek math that we have deductive philosophy, the rigor of logic, and the scientific method. Were it not for Pythagoras, Russell writes, “theologians would not have sought logical proofs of God and immortality.” Russell’s conclusion is simple: “I do not know of any other man who has been as influential as he was in the sphere of thought.”

Plato reimagines abstraction as the theory of forms

plato-greek-mathematicsThe Pythagoreans exerted tremendous influence on Plato, whose most important innovation was the theory of forms. Plato held that what’s real in the world is not matter, not individuals, but classes, genres, species. Over two thousand years later, Schopenhauer put it like this: “Whoever hears me assert that the grey cat playing just now in the yard is the same one that did jumps and tricks there five hundred years ago will think what he likes of me, but it is a stranger form of madness to imagine that the present-day cat is fundamentally an entirely different one.”

So here’s the cool part: Plato’s forms are abstract in the same way as Pythagoras’ numbers. As Wallace puts it, “The conceptual move from ‘five oranges’ and ‘five pennies’ to the quantity five and the integer 5 is precisely Plato’s move from ‘man’ and ‘men’ to Man.” (Mathematicians who believe that numbers and mathematical relations exist on their own, outside of human conception, are even called Platonists.) Russell made the same connection: “what appears as Platonism is, when analysed, found to be in essence Pythagoreanism. [Plato’s] whole conception of an eternal world, revealed to the intellect but not to the senses, is derived from him.”

And Plato’s forms, of course, influenced pretty much the whole of Western thought. It’s partially thanks to Greek math, then, that we so readily categorize the world.

Zeno and Aristotle argue about infinity

aristotle-greek-mathematics“There is a concept,” wrote Jorge Luis Borges, “that corrupts and upsets all others. I refer not to Evil, whose limited realm is that of ethics; I refer to the infinite.” The story gets even more interesting with Zeno, who, working in Pythagoras’ footsteps, was the first to tease out infinity’s corrupting, upsetting properties. He was the one who argued that fleet Achilles could never catch the tortoise—that, first, Achilles would have to cover half the remaining distance, then three-quarters, then seven-eighths, forever approaching but never passing his competitor. The thrust of the problem: Achilles must occupy every point previously occupied by the tortoise, but as soon as he does, the tortoise has moved on and Achilles has—forever—another vanishingly small point left to occupy.

Aristotle, a former star pupil of Plato’s, countered by proposing two senses of the infinite: actual and potential, corresponding to extension and subdivision. No real-life distance, he said, is actually infinite; every distance is potentially so. (An irony: Aristotle also countered Plato’s forms, arguing that if two men are joined by the form Man, the men and Man have something in common—and isn’t there, then, a third form comprising men and Man? And a fourth form comprising men, Man, and the third form that joins them? Aristotle rejected Zeno’s infinite regress as merely potential; he rejected Plato’s forms using an infinite regress that is itself potential.)

Satisfied? Me neither. But, though Aristotle’s answer to Zeno isn’t that compelling, it was enormously influential—by relegating infinity’s tricky parts to the merely potential, it basically let math keep functioning in the presence of the infinite.

Calculus and set theory finish what the Greeks started

Not until Leibniz and Newton invented calculus would Western math develop the tools to start really answering Zeno. And when they did, it was Aristotle’s potential infinities that allowed for infinitesimals—quantities so small they can’t be added, yet somehow big enough to serve as divisors. (Berkeley, the famous empiricist and apologist, argued that calculus, no less than religion, comes down to faith—that “he who can digest a second or third [infinitesimal ratio] . . . need not, methinks, be squeamish about [anything] in divinity.”) Calculus’ notion of limits lets us look at a Zenoan infinite sequence—one-half, one-quarter, one-eighth, one-sixteenth—and prove that the segments add up not to infinity but to one; this answers the paradox, though not in a way that’s philosophically interesting. After all, by relying on infinitesimals, it relies on Aristotle’s old loophole-esque potential infinities.

More interesting is the work of Georg Cantor, who defined an infinite set as that which can be divided into subsets that are also infinite. (Cantor felt that his insights into the infinite had been directly communicated to him by God.) Because no member of the infinite set {10, 20, 30, 40 . . .} lacks a corresponding number in the infinite set {1, 2, 3, 4 . . .}, there are precisely as many multiples of ten as there are of one. The part, infinitely subdivided, is just as large as the whole; there are as many points on Zeno’s racetrack as there are in the whole universe. So check it out: after Cantor, we can conclude that Achilles, despite the longer distance ahead of him, doesn’t need to cover more points. Since both distances’ points are infinite—actually infinite, not just potentially so—the sets are 1:1 matches, and Achilles’ greater speed can win the day. For Russell, this was the first response worthy of being called a true solution.

Thanks to Pythagoras, we can think about numbers as abstract entities existing in their own right. Thanks to Plato, we can apply the same kind of abstraction to forms in general. Thanks to Zeno and Aristotle, we can complete the process of abstraction by thinking about infinity. And thanks to modern calculus (with its Aristotelian infinitesimals) and set theory (with its deeply Zenoan behavior), we can do more than just function in the presence of infinity—we can use it to solve problems.

* * *

5 reasons you should study Greek math

pythagoras-greek-mathematicsIf you’ve found this interesting, it’s worth your time to keep learning about Greek math. Here’s why:

  1. Everyone involved was enormously influential. Pythagoras was, for Russell, the single most influential person in the sphere of thought. Plato and Aristotle are widely considered the fathers of Western philosophy. Zeno’s infinite regress has become something of a philosophical testing ground—it reappears not only in Aristotle but also in Agrippa, Plotinus, Aquinas, Leibniz, Mill, Bradley, Carroll, James, Cantor, and Russell himself.
  2. Greek math contributed to Platonism, and Platonism—through Clement, Origen, Augustine, and others—influenced early Christianity.
  3. Greek math is the context for some of modernity’s most interesting thought. Modern notions of infinity make more sense when you know Zeno’s and Aristotle’s arguments.
  4. These texts represent a remarkable value. You can get the Greek Mathematical Works Collection—which sets you up to study Pythagoras, Zeno, Greek geometry, and more—on Community Pricing for just $14; that’s 58% off. Then add the Works of Plato ($30 | 83% off), and deepen your study with the Select Works of Aristotle ($100 | 62% off). For such rich material, that’s a smart investment.
  5. The Logos editions are the most useful—ever. Math, with its refutations, its shared ideas, and its centuries-long lines of influence, is part of history’s Great Conversation. To study it, you need to be able to make connections. In the past, that would have required flipping through paper books and poring over indexes; not so with Noet, Logos’ philosophy and classics division. You’ll study primary texts alongside commentaries, follow lines of thought from author to author, and record your insights with notes and highlights that show up across all your devices.

Math matters. Understand its origins with the best texts and tools.

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Then keep reading—you know why math’s important; what about philosophy?

What Did Ancient Heresy Mean for the Early Church?

Last week, we looked at the Epicureans, who sought to maximize individual pleasure. Two weeks ago, we looked at the Stoics, who sought freedom from the world. Now let’s look at another competitor with early Christianity, this one much closer to home—the Gnostics.

Everyone knows that Gnosticism, popular in the first few centuries AD, was rejected as heresy. What’s really interesting is what it meant for the early church.

Evil world, secret knowledge, layered heavens

irenaeus-gnosticismGnosticism was “a system of religious thought that blended elements of Christianity with Greek philosophy and Zoroastrianism. The basic tenet is that the created world [is] evil and salvation [comes] through secret knowledge (gnosis)” (FSB). But the diversity of Gnostic schools makes the system hard to pin down. Indeed, wrote a sarcastic Irenaeus, “since their teachings and traditions are different, and the newer ones among them claim to be constantly finding something new, and working out what no one ever thought of before, it is hard to describe their views.”

So let’s look at the strangest, most interesting cosmology: that of one of the later Gnostics, Basilides.

Basilides’ heaven was not one but many, concentric. At the distant center was a single god, ruling over seven lesser gods; these seven created a heaven. They also created seven more gods and another, lower heaven, the symmetrical image of the first; the gods of this lower heaven created yet another heaven, with its sevenfold pantheon; these, another, and so on—365 heavens total. (Thus was the problem of evil resolved: by sheer distance between the world and the divine.) At the very bottom was the god of the Hebrew Bible, who, reduced 365 times over, was nothing but a demiurge—a creator god, working not with essences (like the inner gods) but with mere matter.

From there, Gnosticism was characterized by:

  • Dualism between essence and matter, light and darkness, spirit and body. (Most Gnostics, judging all things fleshly as sinful, were ascetics; others, judging all things fleshly as equally sinful, were hedonists.)
  • A focus on enlightenment. The Gnostics thought that they, through divine revelation, possessed secret knowledge that would allow them to pass from earth up through the ringed heavens—enlightenment unavailable in Scripture alone. (Enlightened souls were the only thing on Earth worth redeeming.)
  • A vastly different notion of Christ. God took mercy on darkened, matter-bound humanity, sending a redeemer—a redeemer whose body was, since flesh and pure spirit are incompatible, merely an illusion. Therefore, Jesus’ physical crucifixion was illusory, too.

History tends to record Gnosticism as a subset of Christianity, but, given these radical departures, it’s more accurate (and interesting) to regard it as a standalone worldview. That’s especially true when you consider its diverse heritage.

Where did Gnosticism come from?

plato-gnosticismGnosticism’s three great influences were Platonism, Zoroastrianism, and elements of Christianity.

  1. From Plato, the Gnostics inherited the distinction between spirit and flesh, key to the Gnostic conception of personal enlightenment. Likewise, the Platonic distinction between form and matter influenced the Gnostic distinction between an essential heaven and a material earth. And the demiurge, too, comes to Gnosticism from Plato, who imagined a creator god in his Timaeus.
  2. From Zoroastrianism, the Gnostics inherited the dualism between light and darkness. More generally, Gnostic dualism owes something to Zoroaster’s consolidation of the Iranian pantheon into opposing forces of “illuminating wisdom” and “destructive spirit.”
  3. From Christianity, Gnosticism inherited pieces but by no means the whole: Jesus, but not his physical resurrection; the Bible, but only as an untrustworthy text to be modified by aggressive misreading and supplemented by such forged additions as the Gospel of Judas. (The Gnostic tendency to modify Scripture is unsurprising—they thought of it, after all, as the work of an inferior deity, given to errors, omissions, and deceit.)

Irenaeus’ counterarguments

Alarmed by the Gnostic worldview, Irenaeus set out to disprove it in Against Heresies. He argued that:

  • The church was authoritative because of apostolic succession. According to the Gnostics, only their oral tradition, derived from the apostles, granted divine knowledge; Irenaeus countered that “The Church . . . received from the apostles and their disciples its faith.” Because the church leaders learned from people who’d learned from people who (a few steps earlier) had learned directly from Christ and his apostles, the church was to be trusted.
  • The gospel was reliable because it was written after the apostles came to divine knowledge. The Gnostics thought the gospel was written before the apostles came to full enlightenment; Irenaeus responded that, right after the Resurrection, “the Holy Spirit came upon [the apostles], and they were filled with all things and had perfect knowledge.”
  • The sheer diversity of competing Gnostic viewpoints undermined the Gnostic claim to truth. With so many Gnostics “constantly finding something new, and working out what no one ever thought of before,” how could any one be correct?

Gnosticism’s defeat was decisive—so much so that we know the school primarily through the writings of Irenaeus and other critics.

Gnosticism’s consequences

The debates over Gnosticism helped shape the early church in three ways. They contributed to:

  1. An increased focus on apostolic succession, so important to Irenaeus’ arguments.
  2. A standardized scriptural canon. In AD 150, Marcion proposed his own canon, which omitted the OT and was edited by Marcion himself. Irenaeus responded with a list of 21 canonical books, including the four Gospels.
  3. An emphasis on creeds to separate false from proper belief. The Apostles’ Creed, specifically, not only predates but also answers Gnostic heresy: “I believe in God the Father almighty, creator of heaven and earth” rejects the Gnostics’ subaltern demiurge and flawed physical world; “Jesus Christ . . . born of the virgin Mary” rejects the Gnostic conception of Jesus’ body as illusory; “I believe in the holy catholic [universal] church” rejects the Gnostic claim that enlightenment is for a select few.

Gnosticism was remarkable not only for its strangeness, its startling diversity of cosmologies, but for its historical consequences. It’s in large part thanks to Gnosticism that the third- and fourth-century Christians solidified the doctrines we now regard as orthodox; that alone makes the Gnostics worth studying.

* * *

prudentius-gnosticismIf you’re interested in church and intellectual history, you should know the rise and fall of Gnosticism. Noet sets you up with many of the school’s most important texts, as well as smart tools for better scholarship.

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Then keep reading about early-church context:


 

What if Life Were All about Pleasure?

Paul, in Acts 17:18, addresses adherents to two philosophical schools: Stoicism and the Epicureanism. We already know that the Stoics had much in common with the early Christians; not so the Epicureans, for whom life’s highest goal was individual pleasure.

But Epicureanism is worth studying as more than just early-church context. Though it fell out of favor in the third century AD, it nevertheless anticipated today’s intellectual climate in startling ways.

So, who were the Epicureans?

diogenes-laertius-lives-of-eminent-philosophers

  1. Moderates, not hedonists. “The philosophy,” notes the Faithlife Study Bible, “emphasized physical and intellectual pleasure and emotional calm (the most pleasure with the least pain).” But, though epicurean’s modern sense connotes excess, the ancients were moderates: Epicurus, quoted in Diogenes Laertius’ Lives of Eminent Philosophers, writes that “Nature’s wealth . . . is easy to procure; but the wealth of vain fancies recedes to an infinite distance.” Therefore,

    “When we say . . . that pleasure is the end and aim, we do not mean the pleasures of the prodigal or the pleasures of sensuality. . . . By pleasure we mean the absence of pain in the body and of trouble in the soul. It is not an unbroken succession of drinking-bouts and of revelry . . . it is sober reasoning . . . and banishing those beliefs through which the greatest tumults take possession of the soul.”

  2. Utilitarians. The Epicurean approach to pleasure was practical. They tolerated pain when it brought about greater pleasure; they obeyed social contracts to avoid crime’s anxiety, shame, and punishment; they did good deeds so that others might respond in kind.
  3. Empiricists. “[A]ll our notions are derived from perceptions,” wrote Epicurus, “either by actual contact or by analogy, or resemblance, or composition, with some slight aid from reasoning.” That is, the senses are the best criteria for knowledge.
  4. Atomists. They argued, notes the FSB, that “the world was made of atoms and that such material was all that the world contained.” Even the gods were made of atoms; so were souls.
  5. Believers in distant, nonintervening gods. Their gods were immortal, blissful, and almost infinitely distant—”limited beings” made from the same atomic stuff as humans, who, in their divine equanimity, didn’t care about evil and had “no real effect on the world” (FSB).
  6. Disbelievers in the afterlife. Since souls, made of atoms, disintegrate at death, and since the gods don’t care about evil, there’s no afterlife of divine punishment to fear. Instead, we should:

    “Accustom [ourselves] to believe that death is nothing to us, for good and evil imply sentience, and death is the privation of all sentience; therefore a right understanding that death is nothing to us makes the mortality of life enjoyable . . . by taking away the yearning after immortality. . . . Death, therefore, the most awful of evils, is nothing to us, seeing that, when we are, death is not come, and, when death is come, we are not.”

    For Epicurus, the fear of death was the “greatest anxiety of the human mind”—the pain most worth eliminating.

How did the Epicureans anticipate modernity?

classics-in-empiricist-philosophy-collectionAs you can see, Epicureanism disagreed with Christianity on an awful lot: cosmology, theodicy, the meaning of life.

No, its conclusions are familiar for another reason—they sound like those of modern secular culture.

  • Epicurean empiricism prefigured that of Locke, Berkeley, and Hume. In fact, it even came close to anticipating the idealism of the last two, according to which only perceptions exist, not objects. Epicurus writes, “the objects presented to madmen and to people in dreams are true, for they produce effects—i.e., movements in the mind—which that which is unreal never does” (emphasis added).
  • Epicurean atomism was remarkably similar to nineteenth-century atomic chemistry: atoms as indivisible, eternal building blocks, things as mere accumulations of atoms colliding with each other. More, the Epicureans came up with a “many worlds” cosmology long before twentieth-century quantum physics did, if for different reasons. Writes Epicurus:

    “there is an infinite number of worlds, some like this world, others unlike it. . . . For the [infinite] atoms out of which a world might arise, or by which a world might be formed, have not all been expended on one world or a finite number of worlds, whether like or unlike this one.”

  • Epicureanism’s matter-of-fact approach to social living shares much with Locke’s utilitarianism, and even modern libertarianism. Since individuals are their own best judges of how to live, society means essentially “Leave me free to maximize my pleasure; in turn, since I don’t want the negative repercussions, I won’t infringe on the freedom of others.” Libertarians, sound familiar?
  • The Epicureans thought the fear of death animated the rest of life’s anxieties; in the twentieth century, Heidegger and the existentialists agreed. (Of course, from there, their conclusions differed: For the Epicureans, the fear of death was illusory, to be transcended; for the existentialists, it was key to living bravely and authentically.)

Empiricism, atomism, extreme individuality, fear of death as the root of all anxiety—what makes these parallels really interesting is that they aren’t straighforward lines of influence. From the third century AD to the sixteenth, Epicureanism was almost entirely forgotten.

* * *

lucretius-on-the-nature-of-thingsThere are two reasons you should know Epicureanism:

  1. It, with Stoicism, was a big part of the context against which early Christianity established itself. Studying it helps you understand the early church—you’ll get more out of passages like Acts 17:18 and Phil. 3:18.
  2. As we’ve seen, it’s an indirect precursor to secular modernity—one that’s even more interesting for its indirectness. Even though Epicurean philosophy is largely forgotten, modernity tends toward the Epicurean; if you’re interested in engaging the culture, you’ll want to understand this fascinating echo.

Epicurus left us very little—Diogenes Laertius lays out his thought (and quotes him at length) in Lives of Eminent Philosophers, and Lucretius, in On the Nature of Things, builds on Epicurus’ destroyed magnum opus, On Nature. Luckily for scholars, we’re building Logos editions of both through Logos’ philosophy/classics division, Noet—and, right now, you can get these foundational texts on Community Pricing for $5 each. For such rich context, that’s a tiny investment.

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How Ancient Thought Agreed (and Disagreed) with the Early Church

Stoicism, a school of Hellenistic thought founded in the third century BC and popular through AD 529, was more than a philosophy—it was a way of life. In this scope as a worldview, it was, writes Paul Tillich, “the only real alternative to Christianity in the Western world.”

But, fascinatingly, Stoicism shared more than scope with Christianity. It came to many of the same conclusions about how to think and live.

Who were the Stoics?

stoics-of-the-roman-era-collectionBeginning with Zeno of Citium, the Stoics located happiness not in goods or success but in virtue alone; they emphasized self-control as the path beyond destructive emotions. This self-control took the form of:

  • Meditation. The Stoics would, visualizing their personal futures, imagine the worst possible outcomes—not as distant, unlikely events, but as present sufferings. They sought to realize that even the worst misfortunes can be survived and are not worth fearing.
  • Training. They practiced rigorous physical discipline, from sexual abstinence to hard exercise to the avoidance of tempting foods.
  • Self-vigilance. They monitored their thoughts and emotions, seeking to avoid lust, greed, and ambition in favor of reason.

Seneca and Epictetus argued that a properly practicing Stoic was, in a sense, beyond misfortune. The Faithlife Study Bible’s article on Paul and the Stoics notes, “Stoics believed that the ideal sage was one who could face calamity and misfortune with casual indifference, feeling neither sorrow nor regret. Stoics were proud of their ability to endure hardships and often paraded their fortitude and strength through ‘hardship catalogs,’ which listed the adversities they had endured.” (It’s that serene indifference to misfortune that colors our modern sense of stoic.)

Similar notions of the self

If contemplation, discipline, and vigilance sound familiar, it’s because the early church and Stoicism were in so many ways alike. Both were characterized by:

  • An emphasis on hardship. As the FSB points out, Paul’s letters also feature “hardship catalogs”—for example, 2 Cor. 4:8–9 and 6:9–10. And, like the Stoics, Paul believed that enduring hardships leads to growth in character: he writes, “we rejoice in our sufferings, knowing that suffering produces endurance, and endurance produces character” (Rom. 5:3–5; cf. 1 Cor. 9:24–27).
  • A sense of man’s depravity, and a constant self-examination. Like the early Christians, the Stoics regarded humanity’s natural state, with its lust, ambition, and other impulses, as deeply flawed. Both worldviews focused on the observation of self and the suppression of wrong thought.
  • An inner freedom from the world. Adherents to both worldviews lived apart from the world’s shortcomings and hardships. The early Christians looked with hope to the world that is to come; the Stoics reminded themselves that all is predetermined and that misfortune is illusory.
  • An aversion to excess. Since the Stoics and the Christians both regarded greed as wrong thinking, they shared a distaste for material excess. For the Stoics, mere wealth wasn’t bad—it simply wasn’t good. “Wealth consists not in having great possessions,” said Epictetus, “but in having few wants.”

Differing notions of the divine

But, though Stoicism shared much with Christianity, it differed profoundly in its account of the divine. For the Stoics, the universe was “a vast quasi-rational being with intelligence and will” (FSB), whose animating force they called (what else?) logos. They didn’t believe in the afterlife; they did believe that the universe would end and then repeat itself.

(You’ll notice that the Stoic outlook far anticipated cosmologies we regard as modern. The notion of God as the universe’s totality reappeared with Spinoza and, famously, Einstein; eternal recurrence was taken up by Nietzsche and Schopenhauer.)
reading-mark

Of course, Christianity’s and Stoicism’s distinct understandings of divinity entailed differing ways of life. Sharyn Dowd, in Reading Mark, notes that:

The Stoics . . . were also determinists; they believed that everything that happened was caused by the universal divine logos that pervaded and controlled all nature and human life. Therefore, the Stoics did not believe in petitionary prayer. People should accept the life circumstances decreed for them by the divine and not seek to change those circumstances in any way. (Emphasis added)

Even the Christian ascetics, so like the Stoics in their emphasis on discipline and their distaste for worldly excess, operated within different spheres and worked toward different goals:

  • For the Stoics, the work of self-examination was largely private. For the early Christian ascetics, penance and self-examination were deeply public, instantiated in professions of faith and confessions.
  • The Stoics sought self-control in order to master the self. The ascetics sought self-control in order to renounce the self.
  • For the Stoics, dependence on the world was to be replaced by dependence on oneself—”The wise person,” taught Seneca, “is self-sufficient.” Paul, in contrast, taught that Christians are profoundly dependent on God (FSB).
  • For the Stoics, love was at best suspect, toxic to self-sufficiency. For Paul and the early Christians, love was everything (FSB).

But despite these key differences, the parallels between Stoicism and Christianity—an emphasis on hardship, an understanding of humanity as innately flawed, a vigilant self-examination, an inner freedom, an aversion to excess—are remarkable.

* * *

diogenes-laertius-lives-of-eminent-philosophersStoicism was the immediate context within which early Christianity flourished—the great alternative in terms of scope as a worldview, the status quo that the church rejected in radical ways. To know the one is to better know the other.

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lewis-and-shorts-latin-dictionaryYou have the Latin skills. You have the primary sources. Now you’re ready to take advantage of the best Latin dictionary. Lewis and Short’s Latin Dictionary, better known as “Lewis and Short,” covers the classical through late-medieval periods. You’ll get 2,000-plus pages of lexical data, contextual examples, and Logos’ smart tagging—when you come across unfamiliar Latin words in tagged texts, you can jump to definitions quickly and easily.

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Or keep reading—how well do you know the sophists?

Why Philosophy Matters

People talk about philosophy in terms of “or.” Philosophy or faith. Philosophy or literature. Philosophy or science, as if the mind were incapable of doing both and reaching its own conclusions.

But that position is ahistorical—great thinkers have long worked across disciplines—and counterproductive: you can glean profound insights from philosophy without emptying it of artistic value, without betraying scientific principles, without sacrificing your faith.

Whatever your worldview, philosophy matters.

Here’s why:

1. Philosophy helps you engage your culture

ancient-philosophy-bundleTo understand your culture, you need to understand its prevailing ideas. When you know philosophy, you can see where modern perspectives come from.

If you’re a pastor, understanding the culture helps you identify and address your congregation’s weaknesses, doubts, and blind spots. If you’re a student, it helps you think clearly about who we are, how we got here, and where we’re going. If you’re a parent, it helps you answer your child’s questions about the world.

2. Philosophy sharpens your critical thinking

“The test of a first-rate intelligence,” wrote F. Scott Fitzgerald, “is the ability to hold two opposed ideas in the mind at the same time, and still retain the ability to function.” In that case, the study of opposing ideas is the training of intelligence. And philosophy is nothing if not the study of opposing ideas—universal classes of things vs. heterogeneous individual things, nonexistent selves vs. essential selves, rationalism vs. empiricism. As you follow the Great Conversation through the ages, you’ll consider more and more opposing accounts of the world. You’ll learn to recognize sophistry and language games, as opposed to attempts at truth.

(If you disagree with my arguments here, why? Have you found an unquestioned assumption, a circular argument, an inadequate proof? If so, you’re doing philosophy’s rhetorical work—and isn’t that a critical skill worth strengthening?)

3. You can cherry-pick the good

Some of the West’s most creative thinkers combined insights from disparate disciplines. Their genius wasn’t raw innovation; it was the creativity to pick out elements of disparate worldviews and combine them into something new. You can do the same—you can pick out philosophy’s useful elements without accepting the whole thing.

  • Not a postmodernist? You can still find insights into language in the twentieth-century “linguistic turn,” which studied how words’ forms (signifiers) and senses (signifieds) interact to create meaning.
  • Disagree with Kant’s conclusion that things in themselves are unknowable? You can still incorporate his categorization of knowledge as either sensible (five red balloons) or conceptual (fiveness, redness).
  • Not an existentialist? You can still appreciate Kierkegaard’s nuanced readings of Abraham, Job, and infinite faith.

4. When you know the old claims, you know the counterarguments

modern-philosophy-bundleSince most of today’s ideas aren’t new, neither are most of the interesting counterarguments. When you know intellectual history, you know time-tested answers—in advance.

  • Are you arguing with someone who doesn’t trust our sensory perceptions of the world—who thinks we might all be dreaming, or brains in a vat? Berkeley and Hume advanced similar arguments; Thomas Reid has already responded that common-sense belief in the world is the basis for any meaningful philosophy.
  • Defending moral absolutes against a relativist? Turn to the arguments of Socrates and Plato, who’ve already developed arguments for morality built on the notion of absolute truth.
  • Debating a vehement atheist who claims that the universe nowhere testifies to a creator? Aristotle, St. Anselm, Descartes, and Leibniz are ready with rational counterarguments.

5. Philosophy helps you understand your faith

Christian theology didn’t develop in a vacuum—Paul found philosophy worth engaging, after all. From then on, philosophy and theology developed side by side, but deeply intertwined. Augustine, Aquinas, Descartes, Kierkegaard—many of philosophy’s greatest thinkers were Christian, and many of philosophy’s greatest works address issues relevant to Christians (God, morality, origins). And philosophy is just as useful when it’s not Christian: it’s the context against which theological thought defined itself, so when you know the one, you better understand the other.

Even within deist thought, orthodox positions developed against a backdrop of unorthodox alternatives. As you study Western intellectual history, you’ll come across some nonbiblical but fascinating notions of the divine:

  • There’s Eriugena’s God, who “does not know . . . what He is because He is not a ‘what,’ being . . . incomprehensible both to Himself and to every intellect.”
  • There’s Alain de Lille’s God, “an intelligible [intellectually knowable] sphere, whose centre is everywhere, and whose circumference is nowhere.”
  • There’s Spinoza’s infinite God, roughly synonymous with the whole universe, of which thought, matter, and even human souls are all attributes.

Such alternative accounts are the negative space: the context against which, over time, modern theology established itself. To understand them is, in turn, to more fully understand the orthodox.

6. Philosophy matters because its questions matter

The value of philosophy isn’t just in its answers—it’s in the questions it asks. Though religion and philosophy disagree on much, they’re concerned with similar questions.

  • How should we live?
  • What are good deeds?
  • What can we know, and how?

If you’re thinking about these questions, you’re doing the work of philosophy. You may reach conclusions vastly different from those of Plato or Kant, but you’re still interested in the same things. That alone makes philosophy worth studying.

* * *

noet-classical-foundations-bundleFor centuries, thinkers have turned to the West’s philosophical canon for time-tested wisdom, fascinating questions, and sheer intellectual pleasure. Now, with Noet, you’ll be able to study these works in the most useful format they’ve ever appeared in.

Noet’s Classical Foundations Bundle (124 volumes, plus the Perseus Classics) sets you up with the core texts of the Western tradition: Plato, Aristotle, Descartes, Spinoza, Leibniz, Locke, Berkeley, Hume, and Kant, as well as Homer, Dante, Milton, Dostoyevsky, and far, far more. With Logos’ original-language tagging and smart searches, you’ll be ready to grasp Greek and Latin nuance and find just what you’re looking for.

Philosophy matters. Study it with the very best tools.

Pre-order your Classical Foundations Bundle before the price goes up, or customize your library with Noet’s Ancient and Modern Philosophy bundles.

Or keep reading—how well do you know the sophists?

Good and Bad Arguments: What’s the Difference?

“You can never reach another physical location: to get there, you have to cross half the intervening distance; next, you have to cross half the distance that remains; next, half again—no matter how far you go, half the remaining distance remains.”

That’s Zeno’s dichotomy paradox, and it’s easy to disagree with. It’s much harder to refute.1

It’s what’s called sophistry: “the use of reasoning or arguments that sound correct but are actually false,”2 or at least misleadingly strong.

But sophistry hasn’t always meant something bad, and the sophists—teacher-scholars who flourished first in Greece and later in Rome—are absolutely worth knowing.

  1. They made some key contributions to early Western thought.
  2. They provided the counterarguments against which Plato and Aristotle, pushing for objective truth and virtue, defined philosophy itself.
  3. They can help you learn to recognize misleading arguments, which, unfortunately, aren’t just an ancient phenomenon.
  4. [Read more...]

  1. Aristotle countered Zeno’s paradox by arguing that as distance decreases, the time needed to cover it decreases correspondingly. Archimedes, and modern calculus, found a way to calculate the sum of infinitely many terms as they get progressively smaller. Diogenes the Cynic simply stood up and walked. []
  2. From Merriam-Webster. []

Why Postmodernism Isn’t New

ancient-philosophy-bundle“Every age has its own outlook,” wrote C. S. Lewis; “We, therefore, need the books that will correct the characteristic mistakes of our own period.” But we need more than that—we need books that reach our conclusions long before we do, books that remind us that our new outlook isn’t so new after all.

We call our times postmodern, often with something like fear. But postmodernism is in large part a renovation of ancient ideas—ideas you should know.

Postmodernists say:

“Right and wrong are human interpretations”

Though moral relativism has a postmodern flavor, it dates back to the ancient Greeks. Plato ascribed it to Protagoras; later, Herodotus assessed other cultures’ customs without questioning their rightness and wrongness. Later yet, Sextus Empiricus determined not that morality is relative to culture, but that moral knowledge is itself impossible.

Is moral relativism postmodern? Yes, in the sense that it exists today; no, in the sense that it’s uniquely characteristic of postmodernism. Before your next debate on moral relativism, you should read Plato, who, fearing moral chaos, argued that morality must be not only in the actor’s self-interest but also based on objective truth.

“But objective truth doesn’t exist!”

We usually trace this postmodern claim back to Nietzsche’s assertion that there are no facts, only interpretations. But it, too, has ancient roots: in the fifth century BC, Protagoras argued that “Man is the measure of all things.” Later, Plato and Socrates clashed with the Sophists over the nature of absolute truth: while the Sophists venerated persuasion and rhetoric, Plato and Socrates responded that the measure of an argument isn’t its persuasiveness, but its truthfulness.

Much later, Kant argued that truth is merely nominal (“true” means something within language), not real—not a statement about a thing’s essence. “Kant drew out the limits of our mind,” said Hegel, “and because of this we can not have a knowledge of the absolute truth.” But Hegel still found a way to truth: his “dialectic,” which, like science, moves from increasingly accurate oppositions—thesis, antithesis—to synthesis, the resolution that best corresponds to what is real.

“What we experience isn’t the world—it’s just our perceptions of the world”

modern-philosophy-bundleAgain we turn to Plato. In The Republic, his Socrates explains that without philosophy, we are like bound prisoners in a cave who, having seen nothing else all our lives, see shadows on the wall and interpret them as real things. Without philosophy, Plato claims, we mistake erroneous perceptions for reality; with philosophy, we see the world as it really is. Around two thousand years later, though, Descartes argued that wax’s physical characteristics reveal nothing about the wax itself: after all, its color, scent, shape, size, hardness, and coldness are all subject to change. George Berkeley took doubt even further, arguing that the world doesn’t even exist: only our perceptions of it do. (Sound postmodern?)

But Thomas Reid rejected that notion in compelling terms, arguing that common-sense belief in the world is the basis for all philosophy—that if you don’t believe in the world as perceived, the conversation is useless.

“We don’t have individual identities or souls”

Postmodernists from Foucault to Lacan to Riceour have argued that personal identity is unstable—that, without any essential “I,” we identify with images or stories to define ourselves. This thesis of shifting (or nonexistent) identity smacks of postmodernity, but it, too, is ancient. Plutarch wrote, in the first century AD, “Dead is the man of yesterday, for he is passed into the man of today . . . Nobody remains one person.” Heraclitus wrote that we cannot step into the same river twice: not only has the river changed; we have, too. Much later, Hume took Berkeley’s claim (“the physical world doesn’t exist”) even further, arguing that not even individuals really exist—we’re nothing but perceivers of perceptions.

But if the claims are old, so are the counterarguments. Spinoza argued that all things do have an essence, and that the nature of that essence is to persist in its being. Descartes argued, famously, that because we think, we exist.

* * *

To engage with our time’s prevailing ideas, you need to know where they come from—you need to know philosophy, both ancient and modern. Noet’s Ancient and Modern Philosophy bundles equip you with the core texts of the Western philosophical tradition: Socrates, Plato, Aristotle, Descartes, Spinoza, Leibniz, Locke, Berkeley, Hume, and Kant.

Pre-order the Ancient and Modern Philosophy bundles today, or build your library with the comprehensive Classical Foundations Bundle—everything you need to understand the origins of Western thought.

Then keep reading—where did history come from?

Where Did History Come From?

Herodotus-The-Persian-WarsIn the fifth century BC, the Greek historian Herodotus changed how we think about ourselves. He wrote The Persian Wars, and our modern understanding of history—that of a unified narrative characterized by cause and effect—was born.

Herodotus: father of history

The Persian Wars examines not only the Greco-Persian Wars, but also the rise and rule of the Persian Empire and the history and cultural background of Scythia and Egypt. These volumes, Herodotus’ only works, have had such a vast influence that Cicero called Herodotus the “father of history.” For George H. Chase, writing in vol. 51 of the Harvard Classics, “what distinguishes [Herodotus] from his predecessors and gives him a unique place in the history of literature is the fact that he was the first writer to undertake the narration of a series of events of world-wide importance upon a comprehensive plan and to trace in those events the relations of cause and effect” (emphasis added). Herodotus was also among the first writers to assess historical stories for truthfulness, though not without certain oversights.1 He wrote in a clear, simple style—“a wonderful achievement,” notes Chase, “when one considers that this is the first literary prose that was written in Europe.” [Read more...]

  1. His fact checking, though a major step forward, overlooks some delightful fables: Herodotus famously describes “ants, not as big as dogs but bigger than foxes,” and notes that “the sand which they carry from [their] holes is full of gold.” These gold-digging ants chase down and kill camels. []

How to Land a Marketing Job at Logos

Hire MeAs of today, Logos’ marketing department has 21 openings. We’re looking for writers, editors, coders, strategists, managers, and more, and we want to hear from you.

So how do you land a job at Logos?

1. Be distinct

“Objective: self-starter / team player seeks a dynamic web 2.0 position that advances my career and leverages my talents.”

Nope—the last thing you want to do is blend in with generic language. Rather than adapting an online template or a cover letter from a different job, start by studying the job listing. Think about how you would filter out candidates, and write to beat that filter—be specific about how you meet each qualification.

One good way to stand out: get your portfolio online. That lets us quickly get a feel for your work and personality; plus, it shows some tech know-how. Even if you’re no web designer, WordPress makes it simple to get started.

2. Be polished

We want to hire the best people, the people with the highest standards. We also work with extremely tight deadlines. It says a lot if your cover letter and résumé, written without any deadline, are full of spelling and grammatical errors. Check everything you’re not sure about against Merriam-Webster—“Is ‘phenomenon’ plural?” “Does ‘sign-up’ need that hyphen?” Then proofread until everything’s perfect, and then a few times more. [Read more...]