Seventy-Three, Yes. Higally-Piggle, No. What Is Math Anyway?

What does it mean that seventy-three is a genuine number, but higally-piggle isn’t? Smithsonian Magazine delves into the old question: What is math? The answer is provided below. (See the original article for all the links.)

It all started with an innocuous TikTok video posted by a high school student named Gracie Cunningham. Applying make-up while speaking into the camera, the teenager questioned whether math is “real.” She added: “I know it’s real, because we all learn it in school… but who came up with this concept?” Pythagoras, she muses, “didn’t even have plumbing—and he was like, ‘Let me worry about y = mx + b’”—referring to the equation describing a straight line on a two-dimensional plane. She wondered where it all came from. “I get addition,” she said, “but how would you come up with the concept of algebra? What would you need it for?”

Someone re-posted the video to Twitter, where it soon went viral. Many of the comments were unkind: One person said it was the “dumbest video” they had ever seen; others suggested it was indicative of a failed education system. Others, meanwhile, came to Cunningham’s defense, saying that her questions were actually rather profound.

Mathematicians from Cornell and from the University of Wisconsin weighed in, as did philosopher Philip Goff of Durham University in the U.K. Mathematician Eugenia Cheng . . . wrote a two-page reply and said Cunningham had raised profound questions about the nature of mathematics “in a very deeply probing way.”

Cunningham had unwittingly re-ignited a very ancient and unresolved debate in the philosophy of science. What, exactly, is math? Is it invented, or discovered? And are the things that mathematicians work with—numbers, algebraic equations, geometry, theorems and so on—real?

Some scholars feel very strongly that mathematical truths are “out there,” waiting to be discovered—a position known as Platonism. It takes its name from the ancient Greek thinker Plato, who imagined that mathematical truths inhabit a world of their own—not a physical world, but rather a non-physical realm of unchanging perfection; a realm that exists outside of space and time. Roger Penrose, the renowned British mathematical physicist, is a staunch Platonist. In The Emperor’s New Mind, he wrote that there appears “to be some profound reality about these mathematical concepts, going quite beyond the mental deliberations of any particular mathematician. It is as though human thought is, instead, being guided towards some external truth—a truth which has a reality of its own…”

Many mathematicians seem to support this view. The things they’ve discovered over the centuries—that there is no highest prime number; that the square root of two is an irrational number; that the number pi, when expressed as a decimal, goes on forever—seem to be eternal truths, independent of the minds that found them. If we were to one day encounter intelligent aliens from another galaxy, they would not share our language or culture, but, the Platonist would argue, they might very well have made these same mathematical discoveries.

“I believe that the only way to make sense of mathematics is to believe that there are objective mathematical facts, and that they are discovered by mathematicians,” says James Robert Brown, a philosopher of science . . . . “Working mathematicians overwhelmingly are Platonists. They don’t always call themselves Platonists, but if you ask them relevant questions, it’s always the Platonistic answer that they give you.”

Other scholars—especially those working in other branches of science—view Platonism with skepticism. Scientists tend to be empiricists; they imagine the universe to be made up of things we can touch and taste and so on; things we can learn about through observation and experiment. The idea of something existing “outside of space and time” makes empiricists nervous: It sounds embarrassingly like the way religious believers talk about God, and God was banished from respectable scientific discourse a long time ago. . . .

Massimo Pigliucci, a philosopher at the City University of New York, was initially attracted to Platonism—but has since come to see it as problematic. If something doesn’t have a physical existence, he asks, then what kind of existence could it possibly have?

. . . The Platonist must confront further challenges: If mathematical objects exist outside of space and time, how is it that we can know anything about them? Brown doesn’t have the answer, but he suggests that we grasp the truth of mathematical statements “with the mind’s eye”—in a similar fashion, perhaps, to the way that scientists like Galileo and Einstein intuited physical truths via “thought experiments,” before actual experiments could settle the matter.

Consider a famous thought experiment dreamed up by Galileo, to determine whether a heavy object falls faster than a lighter one. Just by thinking about it, Galileo was able to deduce that heavy and light objects must fall at the same rate. The trick was to imagine the two objects tethered together: Does the heavy one tug on the lighter one, to make the lighter one fall faster? Or does the lighter one act as a “brake” to slow the heavier one? The only solution that makes sense, Galileo reasoned, is that objects fall at the same rate regardless of their weight. In a similar fashion, mathematicians can prove that the angles of a triangle add up to 180 degrees, or that there is no largest prime number—and they don’t need physical triangles or pebbles for counting to make the case, just a nimble brain.

Meanwhile, notes Brown, we shouldn’t be too shocked by the idea of abstractions, because we’re used to using them in other areas of inquiry. “I’m quite convinced there are abstract entities, and they are just not physical,” says Brown. “And I think you need abstract entities in order to make sense of a ton of stuff—not only mathematics, but linguistics, ethics . . .”.

Platonism has various alternatives. One popular view is that mathematics is merely a set of rules, built up from a set of initial assumptions—what mathematicians call axioms. Once the axioms are in place, a vast array of logical deductions follow, though many of these can be fiendishly difficult to find. In this view, mathematics seems much more like an invention than a discovery; at the very least, it seems like a much more human-centric endeavor. . . .

But this view has its own problems. If mathematics is just something we dream up from within our own heads, why should it “fit” so well with what we observe in nature? Why should a chain reaction in nuclear physics, or population growth in biology, follow an exponential curve? Why are the orbits of the planets shaped like ellipses? Why does the Fibonacci sequence turn up in the patterns seen in sunflowers, snails, hurricanes, and spiral galaxies? Why, in a nutshell, has mathematics proven so staggeringly useful in describing the physical world? Theoretical physicist Eugene Wigner highlighted this issue in a famous 1960 essay titled, “The Unreasonable Effectiveness of Mathematics in the Natural Sciences.” Wigner concluded that the usefulness of mathematics in tackling problems in physics “is a wonderful gift which we neither understand nor deserve.”

However, a number of modern thinkers believe they have an answer to Wigner’s dilemma. Although mathematics can be seen as a series of deductions that stem from a small set of axioms, those axioms were not chosen on a whim, they argue. Rather, they were chosen for the very reason that they do seem to have something to do with the physical world. As Pigliucci puts it: “The best answer that I can provide [to Wigner’s question] is that this ‘unreasonable effectiveness’ is actually very reasonable, because mathematics is in fact tethered to the real world, and has been, from the beginning.”

Carlo Rovelli, a theoretical physicist at Aix-Marseille University in France, points to the example of Euclidean geometry—the geometry of flat space that many of us learned in high school. . . . A Platonist might argue that the findings of Euclidean geometry “feel” universal—but they are no such thing, Rovelli says. “It’s only because we happen to live in a place that happens to be strangely flat that we came up with this idea of Euclidean geometry as a ‘natural thing’ that everyone should do,” he says. “. . . Remember ‘geometry’ means ‘measurement of the earth’, and the earth is round. We would have developed spherical geometry instead.”

Rovelli goes further, calling into question the universality of the natural numbers: 1, 2, 3, 4… To most of us, and certainly to a Platonist, the natural numbers seem, well, natural. Were we to meet those intelligent aliens, they would know exactly what we meant when we said that 2 + 2 = 4 (once the statement was translated into their language). Not so fast, says Rovelli. Counting “only exists where you have stones, trees, people—individual, countable things,” he says. “Why should that be any more fundamental than, say, the mathematics of fluids?” If intelligent creatures were found living within, say, the clouds of Jupiter’s atmosphere, they might have no intuition at all for counting, or for the natural numbers, Rovelli says. Presumably we could teach them about natural numbers—just like we could teach them the rules of chess—but if Rovelli is right, it suggests this branch of mathematics is not as universal as the Platonists imagine.

Like Pigliucci, Rovelli believes that math “works” because we crafted it for its usefulness. “It’s like asking why a hammer works so well for hitting nails,” he says. “It’s because we made it for that purpose.”

In fact, says Rovelli, Wigner’s claim that mathematics is spectacularly useful for doing science doesn’t hold up to scrutiny. He argues that many discoveries made by mathematicians are of hardly any relevance to scientists. “There is a huge amount of mathematics which is extremely beautiful to mathematicians, but completely useless for science,” he says. “And there are a lot of scientific problems—like turbulence, for example—that everyone would like to find some useful mathematics for, but we haven’t found it.”

Mary Leng, a philosopher at the University of York, in the U.K., holds a related view. She describes herself as a “fictionalist” – she sees mathematical objects as useful fictions, akin to the characters in a story or a novel. “In a sense, they’re creatures of our creation, like Sherlock Holmes is.”

But [Leng says] there’s a key difference between the work of a mathematician and the work of a novelist: Mathematics has its roots in notions like geometry and measurement, which are very much tied to the physical world. True, some of the things that today’s mathematicians discover are esoteric in the extreme, but in the end, math and science are closely allied pursuits . . . “Because [math] is invented as a tool to help with the sciences, it’s less of a surprise that it is, in fact, useful in the sciences.”

Given that these questions about the nature of mathematics have been the subject of often heated debate for some 2,300 years, it’s unlikely they’ll go away anytime soon.

Unquote.

Nope, anybody who reads this post (or the whole underlying article) has to accept that math depends on axioms or rules. They are invented, not out of the blue, but because they’re plausible and useful. Once you settle on the axioms or rules, discoveries can follow. Therefore, Platonism is wrong. Its competition, which is usually called “nominalism”, is right. I’m glad that’s finally settled.

On a related note, the National Public Radio site has a short article on time travel. The article cites research in physics that purports to show that paradox-free time travel is possible:

Researchers ran the numbers and determined that even if you made a change in the past, the timeline would essentially self-correct, ensuring that whatever happened to send you back in time would still happen. . . . In other words, a time traveler could make changes, but the original outcome would still find a way to happen — maybe not the same way it happened in the first timeline but close enough so that the time traveler would still exist and would still be motivated to go back in time. [According to one of the authors], “No matter what you did, the salient events would just recalibrate around you.”

I’m not qualified to judge the technical merits of this research, but I doubt it shows that paradox-free time travel is guaranteed in every case. If you went back in time and murdered your grandfather before he met your grandmother, and your grandfather didn’t have an identical twin, I’m pretty damn you’re grandmother would have an insurmountable problem generating your precise DNA, whether or not “the numbers” say otherwise.

On yet another mathematical topic, America’s Electoral College is authorized to determine that 63 million counts more than 66 million. That’s why we all need to vote this year.

A Starting Point for the Rationalists

I hear the president is on tape from months ago saying how dangerous the virus is, but that he didn’t want the public to know the facts (and protect themselves?). An impeachable offense, you say, if only his time wasn’t running out? He is also reported to have said that joining the military and possibly being killed or wounded is dumb. It’s the kind of thing losers do. And California has its worst wildfire in history as the globe keeps on warming. But I’m on a news vacation until November, so enough of that.

In May, I wrote about a philosopher, Michael Della Rocca, who argued in an interview that we should adopt monism, which I described as:

. . . the view that reality is somehow one thing; the universe doesn’t consist of many things (such as electrons and gluons, or apples and oranges). Neither does it consist of only a couple of things (like mind and matter).

I didn’t like his argument, which is why the post was called “Punished by a Philosopher”.

One of the things Prof. Della Rocca said was that the Principle of Sufficient Reason is crucial to understanding “rationalist” philosophers like Spinoza and Leibniz, and presumably Descartes, their predecessor:

Rationalism can mean lots of different things to different people, but for me the Principle of Sufficient Reason (the PSR) is central to rationalism. The PSR is the principle according to which there are no brute facts that obtain or no things that exist without an explanation. That is, each thing or each fact has an explanation. The PSR is the guiding force of Leibniz’s and Spinoza’s work. . . 

I was reminded of Prof. Della Rocca’s interview when I read an interview with another philosopher at the same site. John Carriero is also an expert on the rationalist philosophers. He doesn’t think the Principle of Sufficient Reason is as fundamental as Della Rocca does:

You ask about the secondary literature. I think scholars have become increasingly sensitive to the role that the First Principle Theory is playing in early modern rationalism. I think there sometimes remains a tendency, perhaps out of a principle of charity, to try to work around the First Principle Theory and extract something that feels less alien.

For example, sometimes scholars are more comfortable working with a (what seems to me ungrounded) “principle of sufficient reason”—or some other disembodied form of “rationality”—than thinking in terms of a really existing First Principle that is ultimate the universe’s intelligibility. Descartes, Spinoza, and Leibniz do hold that reality is deeply intelligible, but that’s because reality originates in a First Principle with certain features, and, for them, the intelligibility of the universe bottoms out in the First Principle’s essence. 

I don’t think Prof. Carriero denies that the rationalist philosophers endorsed the Principle of Sufficient Reason. Unlike Della Rocca, however, he just thinks philosophers like Descartes, Spinoza and Leibniz believed there was something more fundamental. He calls it their (or a) “First Principle”.

I’m not 100% certain that I understand what this First Principle is supposed to be. But somebody named Uma who posts on the internet may have part of the explanation:

Aristotle defined a first principle as “the first basis from which a thing is known”.

A First Principle is a basic, essential, foundational truth that is “known by nature.” It is not an assumption or deduction based on another theory or supposition. A key element of First Principle thinking is that just because something is “known by nature” or true in the universe does not mean it has ever been articulated and described by humans.

Here’s what Corriera says about the rationalists’ First Principle in response to the interviewer (Richard Marshall aka 3:16):

3:16:  I think you position Descartes’ radical thinking in terms of a philosophical theology. So what’s the place of philosophical theology in Descartes’ work? You say something surprising (to me at least) when you say that it was probably more important to Descartes than it was to Aquinas! How come?

JC: Let’s think of philosophical theology as the theory of the universe’s First Principle: whether the universe has a First Principle, and, if so, the nature and character of that First Principle.

For Aquinas, First Principle Theory is the culmination of philosophy, what philosophy leads to. Each of the arguments for the existence of God in the Summa Theologiae —the so-called Five Ways—is based on each of the Aristotelian four causes . . .  Before you embark on philosophical theology you need to have studied the natural world, and learned what change or motion is, learned about . . . what form and matter are, and learned about the four causes and how they are related. So, for Aquinas, not only it is possible to do a lot of philosophy before you get to First Principle Theory, it is necessary to do so.

Descartes reverses this. A large part of the Meditations project is to position us as knowers within the universe, and for him that project is inextricable from philosophical theology. This means more than ticking off the “God exists” and “God is not a deceiver” boxes. It means understanding our position: this involves understanding what the First Principle is . . . , the nature of our dependence on God, how error enters a universe authored by a supremely perfect being, and, finally, seeing how all Scientia [knowledge] depends on the recognition of God. Descartes views the need to orient ourselves in this way as a sort of propaedeutic [preparatory study] that has to come before other disciplines; and so, for him, First Principle Theory does not come after natural philosophy, as it does for Aquinas.

But what is this First Principle? This is a long interview but I couldn’t find a precise definition. This comes closest:

[Descartes] thinks that Scientia requires a systematic understanding of our position as intellectual beings within the universe . . .  Achieving such an understanding involves knowing something about the First Principle of the universe (God), as the source of the universe’s intelligibility, the origin (or author) of our natures, and the Being that ultimately accounts for our minds’ being plugged into the universe’s order.

So, for the rationalist philosophers, the First Principle, apparently more fundamental than the Principle of Sufficient Reason, is God — or rather what the existence of God as a perfect being and creator of the universe means, as far as we human beings are concerned.

I think this makes a lot of sense. I don’t mean it makes sense for our intellectual starting point to be a perfect creator of the universe. I mean it makes sense that certain 17th century philosophers had that starting point. The rationalists began with their understanding of God and went on from there. Their writings are more understandable if they had God as their intellectual bedrock. It explains why God shows up in their arguments, sometimes seemingly out of the blue (like the most wonderful deus ex machina there could possibly be). Having this kind of philosophical/theological perspective explains why they rely on their understanding of God to justify so many other beliefs. 

Prof. Corriera’s view does explain a passage from Spinoza that he cites. Spinoza argues that empirically-minded philosophers or theologians who begin with the natural world and then draw conclusions about God have it backwards:

For the divine nature, which [philosophers like Aristotle and his followers, as well as, presumably, later philosophers as well] should have considered before all else—it being prior both in cognition and in Nature—they have taken to be last in the order of cognition, and the things that are called objects of sense they have taken as prior to everything. Hence it has come about that in considering natural phenomena, they have completely disregarded the divine nature. And when thereafter they turned to the contemplation of the divine nature, they could find no place in their thinking for those fictions on which they had built their natural science, since these fictions were of no avail in attaining knowledge of the divine nature. So it is little wonder that they have contradicted themselves on all sides. (Ethics, 2p10s)

The professors can argue whether God or the Principle of Sufficient Reason was more fundamental for the rationalist philosophers. Did God make things so that everything happens for a reason? Or does that fact that everything happens for a reason explain God’s presence and proclivities?

Or is there no God and stuff happens for no reason at all? That may be too cynical a view, but it’s definitely in the running.

By the way, I’m 100% certain the professors would agree that Descartes, Spinoza and Leibniz would all recommend making every effort to vote for Democrats this year. God or no God, it’s the only rational thing to do.

Happiness, Schmappiness

What follows is 42% of an article about Schopenhauer written by a philosophy professor for Aeon:

On 13 December 1807, in fashionable Weimar, Johanna Schopenhauer picked up her pen and wrote to her 19-year-old son Arthur: ‘It is necessary for my happiness to know that you are happy, but not to be a witness to it.’

Two years earlier, in Hamburg, Johanna’s husband Heinrich Floris had been discovered dead in the canal behind their family compound. It is possible that he slipped and fell, but Arthur suspected that his father jumped out of the warehouse loft into the icy waters below. Johanna did not disagree. Four months after the suicide, she had sold the house, soon to leave for Weimar where a successful career as a writer and saloniste awaited her. Arthur stayed behind with the intention of completing the merchant apprenticeship his father had arranged shortly before his death. It wasn’t long, however, before Arthur wanted out too.

In an exchange of letters throughout 1807, mother and son entered tense negotiations over the terms of Arthur’s release. Johanna would be supportive of Arthur’s decision to leave Hamburg in search of an intellectually fulfilling life – how could she not? – including using her connections to help pave the way for his university education. But on one condition: he must leave her alone. Certainly, he must not move to be near her in Weimar, and under no circumstances would she let him stay with her.

What her line of 13 December doesn’t reveal is that Johanna simply couldn’t tolerate Arthur: ‘All your good qualities,’ she wrote on 6 November, ‘become obscured by your super-cleverness and are made useless to the world merely because of your rage at wanting to know everything better than others … If you were less like you, you would only be ridiculous, but thus as you are, you are highly annoying.’ He was, in short, a boorish and tiresome know-it-all.

If people found Arthur Schopenhauer’s company intolerable, the feeling was mutual. He spent long depressive periods in self-imposed isolation, including the first two months of 1832 in his new rooms in Frankfurt, the city that became his adoptive home after a stint in Berlin. He defended himself against loneliness with the belief that solitude is the only fitting condition for a philosopher: ‘Were I a King,’ he said, ‘my prime command would be – Leave me alone.’ The subject of happiness, then, is not normally associated with Schopenhauer, neither as a person nor as a philosopher. Quite the opposite: he is normally associated with the deepest pessimism in the history of European philosophy.

Schopenhauer’s pessimism is based on two kinds of observation. The first is an inward-looking observation that we aren’t simply rational beings who seek to know and understand the world, but also desiring beings who strive to obtain things from the world. Behind every striving is a painful lack of something, Schopenhauer claims, yet obtaining this thing rarely makes us happy. For, even if we do manage to satisfy one desire, there are always several more unsatisfied ones ready to take its place. Or else we become bored, aware that a life with nothing to desire is dull and empty. If we are lucky enough to satisfy our basic needs, such as hunger and thirst, then in order to escape boredom we develop new needs for luxury items, such as alcohol, tobacco or fashionable clothing. At no point, Schopenhauer says, do we arrive at final and lasting satisfaction. Hence one of his well-known lines: ‘life swings back and forth like a pendulum between pain and boredom’.

Schopenhauer knew from his extensive studies of classical Indian philosophy that he wasn’t the first to observe that suffering is essential to life. The Buddhists have a word for this suffering, dukkha, which is acknowledged in the first of its Four Noble Truths. The fourth and final of these truths, magga, or the Noble Eightfold Path that leads to the cessation of dukkha, would also inspire large parts of his moral philosophy.

The second kind of observation is outward-looking. According to Schopenhauer, a glance at the world around us disproves the defining thesis of Gottfried Leibniz’s optimism that ours is the best of all possible worlds. On the contrary, Schopenhauer claims, if our world is ordered in any way, it is ordered to maximise pain and suffering. He gives the example of predatory animals that cannot but devour other animals in order to survive and so become ‘the living grave of thousands of others’. Nature as a whole is ‘red in tooth and claw’, as Alfred, Lord Tennyson later put it, pitting one creature against another, either as the devourer or the devoured, in a deadly fight for survival.

Civilisation doesn’t help much either. It adds so many sites of human suffering. In The World as Will and Representation (1818), Schopenhauer wrote:

if you led the most unrepentant optimist through the hospitals, military wards, and surgical theatres, through the prisons, torture chambers and slave stalls, through battlefields and places of judgment, and then open for him all the dark dwellings of misery that hide from cold curiosity, then he too would surely come to see the nature of this best of all possible worlds.

If you had to guess the world’s purpose just by looking at the results it achieves, you could only think it was a place of punishment.

These observations, the first on human nature and the second on nature itself, support Schopenhauer’s pessimistic claims that life is not worth living and the world should not exist. We are never given in advance the choice whether to exist or not but, if we were, it would be irrational to choose to exist in a world where we can’t profit from life but only lose. Or as Schopenhauer puts it in another key line: ‘life is a business that does not cover its costs’. . . .

Schopenhauer doesn’t deny that happiness exists. He does, however, think that we are generally mistaken about what happiness is. According to him, happiness is no more than the absence of pain and suffering; the moment of relief occasionally felt between the fulfilment of one desire and the pursuit of the next. For example, imagine the satisfaction of buying your first home. What makes us happy here, Schopenhauer would say, is not the positive state of being a homeowner, but the negative state of relief from the worries that come with not owning your own home (as well as relief from the notoriously stressful process of buying property itself). This happiness, Schopenhauer would be quick to point out, is likely to be short-lived, as a host of new worries and stresses emerge, such as paying down the mortgage, or doing up the bathroom. . . .

Instead, Schopenhauer gives us a different picture of a happy life, one that is not total happiness. While suffering can’t be excluded from life altogether, it can be reduced by making sure no kind of suffering goes on for too long. Going back to Schopenhauer’s image of the pendulum, a happy life would include enough success in fulfilling our desires that we are never in too much pain, but also enough failure to ensure that we are never too bored. It would be a ‘game of constantly passing from desire to satisfaction and from this to a new desire, a game whose rapid course is called happiness and slow course is called suffering.’ A well-paced oscillation between wish and fulfillment, which is at most a semi-satisfied life, is the best we can hope for as far as happiness is concerned.

If a good life, conceived as a happy life, is a futile aim for ethics, this raises the question of what the real aim of ethics should be. The background of Schopenhauer’s pessimism is never far away from this question. It’s not obvious to Schopenhauer that the semi-satisfied life presented above is better than nonexistence. Such a life would still contain a preponderance of suffering, even if no kind of suffering would go on for too long.

Rather than trying to make the world into a happy home, then, Schopenhauer opts for an ethics that might save us from the world altogether. He endorses asceticism, the practice of severe self-denial exemplified in the saints and mystics of many world religions . . .

Note that Schopenhauer’s otherworldly ascetics are not happy. They have entirely given up the game of a semi-satisfied life. Instead, they accept, and come to symbolise, the universality and inevitability of suffering, in order to transcend it. In relation to the ascetic, Schopenhauer is more likely to use words such as composure and peace than happiness and pleasure.

To say that Schopenhauer endorsed asceticism might appear to suggest that he practised it himself. Far from it. The most ascetic part of his daily routine in Frankfurt was the cold sponge bath he took between seven and eight every morning. After that, he made his own coffee and settled down to write for a few hours before receiving selected visitors, until his housekeeper appeared at noon, cuing them to leave. He played flute for half an hour each day – an activity that, according to Friedrich Nietzsche, belied the sincerity of his pessimism – and then made his way to his favourite spot to eat, the Hôtel d’Angleterre, for a hearty afternoon meal. After this he might make himself another coffee, take an hour’s nap, then read a little light literature before walking his dog, a white poodle called Atma, while smoking a cigar, all before settling in for his typical nine-hour sleep. The life of the Buddha it was not.

Unquote. 

Happy or not, we can still vote for every Democrat in November and damage that other party for years, possibly decades, to come. Arthur and Atma would agree.

Understanding Perspectivism: Scientific Challenges and Methodological Prospects, edited by Michaela Massimi, et al.

I’ve been building up to writing a book about perspective and perspectivism for about ten years now. I’ve read articles and books and written thousands of words in emails (mostly to myself) and other places. (It doesn’t pay to rush these things.) 

This isn’t about perspective in the artistic sense — how painters make a two-dimensional surface look three-dimensional — although that’s a related idea or practice. This is about perspective in the sense of a point of view or frame of reference or standpoint. It’s what we mean when we say “that’s your perspective” or “this is where I’m coming from”. Similarly, it’s what we mean by statements like “she’s speaking from a scientific perspective” or “it’s a bad decision from an ethical perspective”.

Perspectivism is a philosophical view about the importance of perspective when it comes to subjects like science or ethics, but also the way perspective functions in everyday life. This view is associated with Friedrich Nietzsche, but other philosophers have had similar ideas, including some academic philosophers working today. There is even a website devoted to “perspectival realism” funded by a European Union research program.

Understanding Perspectivism features essays by twelve academics. It’s not going to make the New York Times bestseller list. Putting aside the subject matter and the fairly technical language, that’s guaranteed by the price of a hardcover copy: $140. Rather oddly, however, anyone interested can download it free (which is how, no surprise, I got mine).

If you want to know more, there’s a positive account of the book at Notre Dame Philosophical Reviews. I’ll quote a bit that gives a feel for the collection’s subject matter and style:

Another standout [chapter] is David Danks’ “Safe-and-Substantive Perspectivism” which presents a view refreshingly unique from all other chapters. . . . Danks does what philosophers do best and takes a step back, thinking about perspectivism from a broader perspective. He works to dig in to just where and how perspectives enter into science and draws a useful distinction between two extremes: ‘unsafe’ hyperlocal perspectivism and ‘insubstantial’ high-level perspectivism. The former refers to the notion that perspectives set the basis for science at the level of individual scientists, which may be “dependent on local, contingent properties of specific people”. The latter refers to an opposite notion that scientific perspectives are highly abstract and general human activities — a notion that Danks deems uninformative regarding the nature of scientific perspectives.

To that end, Danks offers an alternative that construes science as necessarily and unproblematically perspectival. Here the big picture is that perspectives aren’t unique to science, and consequently aren’t any more of a problem for science than they are for any other domain where there are multiple, often incompatible perspectives, such as general human perception:

“More precisely, these sources of perspectivism are not unique to scientific theories, knowledge, and beliefs but rather apply to their everyday counterparts. That is, there is nothing special (with respect to these arguments) about science, and so the resulting perspectivism about science does not threaten a collapse into complete relativism (or at least, poses no more threat than we face about all of our beliefs and knowledge).”

Spinoza, Nietzsche and Living in a Material World

Charlie Huenemann, a philosophy professor at Utah State, was interviewed in April by Richard Marshall for Marshall’s “End Times” series. It’s a good interview, and I especially liked the way Huenemann compared the philosophies of Spinoza and Nietzsche.

images

    Baruch and Friedrich

[CH] I think of Spinoza as a radical religious reformer. I think he was trying to say this: “There is a single entity whose nature determines the structure and existence of the universe, and that entity is the thing that people have been calling “God” for many centuries. But they got the metaphysics (or theology) very wrong, and now we’re in a position to figure out what this divine thing really is, and to see how the writers of scriptures managed to get the basic moral of the story right, while getting all the metaphysical stuff wrong. And by the way, if you understand what I’m saying, you’ll see that there’s no harm in allowing philosophers to write about such things.”

It’s surprising how explicit Spinoza is about all this in his Theological-Political Treatise. He basically says just what I said, though with greater care, and elegant Latin. And saying that was hugely radical for his day. The hypothesis that it was somehow a cloak meant to disguise a view that was even more unthinkable seems to me very unlikely. If that’s what he was up to, then he was an idiot, or at least completely out of touch with his audience. The book he wrote was seen immediately as about the most heretical thing a person could write. So it’s implausible to suspect that he was pulling any punches.

[RM] You say you pit a Spinoza naturalism against a Nietzsche naturalism. Can you sketch for us the salient elements that form this contrast and what it tells us about contemporary attitudes towards naturalism . . . ?

[CH] I should say at the outset that I myself don’t feel like I have a dog in this fight. I suspect the naturalism I would describe as Nietzschean is probably true, and that it’s sort of disappointing, and Spinoza’s naturalism is far groovier, but implausible. . . I can’t blame someone for going in with Spinoza: it’s profoundly moving to see the whole of nature as divine. On the other hand, if someone throws in with Nietzsche, they should be fully aware of all they are repudiating. In distinguishing the two kinds of naturalism, I mainly want to direct readers’ attention to the “meaning of life” consequences of these ways of being a naturalist.

Anyway, on to the distinction. Spinoza sees the universe as divine in some important sense. There is an essence to it that lives and breathes in all of its parts. We can come to know that essence through rational demonstration, but he also leaves room for a more immediate and somewhat mystical access to that essence. In his naturalism, humans are part of nature in a way that might best be called “belonging”: we share an essence with all natural things, and in virtue of sharing that essence we can come to know our universal union with all things and attain a special kind of joy in contemplating it. It’s in that sense that I’d call Spinoza’s nature a sanctuary. It’s a sanctuary from despair, alienation, and disconnection – which, incidentally, must have been significant forces in Spinoza’s own life. To be a Spinozist is to see all things, including oneself, as an expression of divinity.

But Nietzsche’s naturalism is quite different. Here I need to be careful, because I think Nietzsche isn’t perfectly consistent over his writings, and sometimes (especially when Zarathustra is speaking) nature is every bit as holy and mystical as anything found in Spinoza. But in other moods, Nietzsche seeks to establish a naturalism that is more like our modern-day naturalism, which is fundamentally a denial of any special features of the universe that might make us feel more at home. The universe itself is a product of chance; that life evolves in some parts of it is entirely accidental; humans are pushed and pulled by all sorts of blind, non-teleological [i.e. non-purposeful] forces. Nothing is inherently significant, and that certainly includes us. Clearly Spinoza agrees with some elements of this (such as denying teleology and any special human significance), but somehow Spinoza manages, at least by the end of the Ethics, to restore a sense of natural divinity and belonging.

In the parts of Nietzsche’s philosophy that might be called “nay-sayings”, any sense of belonging is obliterated as merely wishful thinking. We stand at the edge of an uncaring abyss, which is oblivion, death, and meaninglessness. This is followed by Nietzsche’s “yea-saying” part, in which we take it upon ourselves to create meaning, etc. But that challenging, never-ending project of “becoming who you are” makes sense only against a backdrop of an utterly uncaring natural world. To put the distinction into a tidy formula, Spinoza thinks we need to sync ourselves with nature, while Nietzsche thinks we need to weaponize it in the war we wage against meaninglessness. (That strikes me immediately as too tidy, but on the other hand I kind of like how it sounds, so I’ll stick with it!)

Because of their similarities, Nietzsche was enthusiastic about Spinoza early on, but I think he eventually saw Spinoza as illegitimately allowing himself a refuge under the banner of “reason”. If Spinoza had sought true authenticity, he would have torn that banner down and faced down the irrational, chaotic indifference Nietzsche saw in the natural order. (This indifference of the world was an important element in Nietzsche’s own life, too.) It’s the will to power we are dealing with, according to Nietzsche, not the reason for all being.

So, if we want to be naturalists, we might ask ourselves just what it means to be purely natural beings. Is it to be inconsequential by-products of an meaningless process of generation and destruction? Or do we somehow attain an important kind of peace (or even salvation, in some sense) by coming to understand our place in nature? The people who popularize science tend to suggest something uplifting like the second view: human glory consists in coming to understand the vast cosmos, etc. Few people allow the first view any air time, except maybe dystopian sci-fi authors. I realize it’s no fun to mope about in existential despair, and it’s pointless to be pointless. Still, the real character of Nietzschean naturalism . . . needs to be seen clearly for what it is, and we’re guilty of false consciousness when we pretend that anything of alleged intrinsic value survives it.

[LF] With all this in mind, is there any doubt that Spinoza, Nietzsche, Huenemann and Marshall would agree that the current American president is a disaster and we should vote him and every other Republican out of office in November?

No, there isn’t any doubt. If you’re willing and able to support Democratic candidates in addition to voting for them, please consider doing so.