Wittgenstein, Occam, and the Scientific Method

(3.24) If a sign is not necessary then it is meaningless. That is the meaning of Occam’s razor.

and again,

(5.57321) Occam’s razor is, of course, not an arbitrary rule nor one justified by its practical success. It simply says that unnecessary elements in a symbolism mean nothing.

But also,

(5.453) The solution of logical problems must be simple for they set the standard of simplicity.

Thus, the scientific rationalist extrapolation of Occam’s razor (that simpler explanations for natural phenomena are superior to more complex ones) has grounding if the relation between mathematics and the natural world obtains. However, with even a small dose of Humean skepticism, this relation is impossible to know for certain: at best, the relationship between mathematics and nature can be a statistically significant conjunction, but nothing more. For this reason, Wittgenstein says,

(6.363)  The process of induction is the process of assuming the simplest law that can be made to harmonize with our experience.

(6.3631) This process, however, has no logical foundation… It is clear that there are no grounds for believing that the simplest course of events will really happen.

Empiricist approaches to scientific knowledge are built on rationalist foundations. At best, the natural laws we invoke in our mechanical descriptions of the universe are “forms of laws” of causality.


Mathematics and Aesthetics

The following is an unfinished, obtuse, and probably bad post I wrote at the end of last semester. I hope to revise it soon—but the gist of the idea, that mathematics is not an exercise of “pure reason,” but it heavily relies on the mathematician’s “aesthetic” sense. This sense is still rational, but not explicitly logical.

I’ve often thought of mathematics as a mere exercise in necessity. Something about the pure logical foundations of higher math—the way that theorems and propositions of such significance were supported ineluctably on pillars of axioms reasoning that seemed so indubitable as to be tautological—something about that computerized, Spock-like ideal of ironclad reasoning attracted me. But I’ve been somewhat mistaken.

Now that I’ve tried (and more often than not failed) to do mathematics, I’ve begun to think it more proper to say that the material of mathematics is logic: without consistent, logical relations between concepts, mathematics would not exist. But a thing’s material reality is, at best, only half the picture. Logic can limit the number of things you can say that are useful in discovering or describing truth—by guiding the statement of valid claims and restricting the statement of invalid ones—but it does not tell you with necessity what should be said, what should be claimed. If logic were the only guiding principle of mathematics, Euclid had already finished his elements as soon as he formulated his axiomatic definitions of lines and points and planes. Since an ironclad and ineluctable chain of reasoning connects the definitions of Euclidian geometry with the Pythagorean theorem, to state the (reduced) former thing is, in a sense, to state everything. This level of reductionism is akin to thinking that you are a carpenter once you know what wood is, or that to look at a timber forest from 50 years ago is to have seen every boat, home, and kitschy bear statue that would be made from it.

But this is obviously not the case. Just as a kind of formal principle is needed for carpentry to be carpentry, Mathematics itself needs a formal principle, a principle of what should be said, not merely what can be said. And, in my limited experience with mathematics, these formal principles seem to be largely aesthetic. Why should points and lines be constructed so as to join three of each of these elements and make a triangle, and to further compute the relations between the side lengths of the figure? It is either by a principle in the mind of the mathematician to represent the triangles he sees in nature or, else, by an exploring, pioneering, experimenting principle in the geometer to sound the depths of what can be constructed within the possibility space that founded on Euclid’s axioms.

Not only this, but all development in mathematics seems to stem from exploration and attempts to build bridges to these explorations with the necessary building materials of consistent logical statements. It was the futile attempts of ancient geometers to square the circle that clued us into the existence of mathematical concepts inaccessible by geometric construction.

There is also an aesthetic principle of symmetry—in the sense of both true mathematical symmetry and of a parity and evenhandedness and fittingness—that rules mathematical development in addition to those of exploration and a drive for natural representation. The basis of most mathematical conjectures is that a theorem or principle that applies to one type of space or one region of consideration should hold for another space or region deemed similar enough. Even though logic in no way occasions or guarantees the extension of particular truth claims to other spaces, such a belief is the default position of the mathematician when conjecturing, and this jumping off point allows him some formal handhold onto the sheer wall of necessity. [To use another analogy, he can see whether the brick he has picked up actually fits into the wall he is attempting to build.] For example, in topology, the functioning of derived space topologies—in quotient-, product-, and subspaces—is distinct, and there is no necessary reason that these three spaces should function similarly, but what we do know about each of these derived spaces is based off their similarity and correspondence: that connectedness is preserved by projection mappings and identity mappings alike, [there are more examples here which I have not yet listed], etc.   

My concept of aesthetics likely has a definition (or the beginnings of one) that begs the question: aesthetics are concerned with formal principles and relationships between things that are not merely necessary. Such relationships are much easier to see in terms of a superstructure instead of in single propositions itself. The content of 2+2=4 is mostly a matter of necessity. [I hope to develop this idea a bit more with revision]


Rhetorical Nihilism, Tyrrany, and Memes?

In the early days of his campaign, it was conceivable to read Donald Trump like a book with an unreliable narrator. The content was absurd & offensive, but the absurdity was strangely calculated so that the act of being offensive still carried rhetorical value: Trump’s offensiveness wasn’t captained by personal conviction or robust political philosophy, but was reactionary. Trump said precisely the things which would provoke backlash from anyone remotely left-of-center: minorities aren’t an “economic burden,” they’re “rapists.” Hillary doesn’t merely “lack integrity,” she should be “locked up.”

It worked.

The “provoking-qua-provoking” (i.e., forcefully stating beliefs he may not even have held), was the very source of Trump’s electoral power. He perceived that people were annoyed with the monotony of “political correctness,” so he offended and offended—even letting his offenses contradict one another. It was doubly-effective: offensiveness also got him the most airtime of any 2016 candidate, and airtime directly correlates with public support. Target those moves at swing audiences (Pennsylvania, etc.) and you’ve got yourself an election.

The Alt-Right had it First.

The same tactics were already being developed in the growing alt-right movement, a mutated political ideology which incubated in dark corners of the Internet, where casual holocaust jokes and anonymously-shared memes were infused with 1) male bravado and 2) honest disgust at the ineffectiveness of American politics. The internet had cheapened all talk, and unbreakable cultural myths practically made debate meaningless. Joining the alt-right, which claimed to both explain and rise above fruitless politics, yielded a sense of enlightenment. Even freedom from futility, Hope.

Memes—more properly memetics, the ideology behind them—are not incidental to the alt-right (nor American culture at large). They define the alt-right’s conceptions of society’s problem and the rules by which to fix it, as follows:

  1. Standards of “political correctness” (support for minorities, political & religious tolerance, &c.) have been co-opted by virtue signaling.
  2. Thus, standards of “political correctness” don’t exist to be truthful; instead they exist to perpetuate themselves in culture. In other words, “being PC” is a meme.
  3. The reproduction of this meme leaves its host (namely the American public) unable to think outside the “politically correct” box. This causes an inability to absorb any ideas which do not adopt the strictures of political correctness, thwarting discourse.
  4. Since memes operate by the rules of natural selection, the only thing which can kill a meme is another meme which catches and reproduces faster (is more “fit”).
  5. Therefore, to remove the memetic roadblock to public discourse, we must destroy “political correctness” with a rival, fitter meme.

This formulation of the problem is incredibly appealing. Thus, the alt-right co-opted Pepe, uncorked the finely-aged bottles of racially-insensitive jokes and misogynist opinions, and harnessed the power of backlash. Since the very point of the rhetoric was to prod those who hosted the “political correctness” meme, the outrage of those people only stoked the flames. A self-amplyfying, feedback loop began.

Trump Saw an Opportunity for Power, Not for Cultural Renovation.

Trump, seeing the unrest, frustration, and dissatisfaction, spied opportunity. As a businessman, he didn’t care about political philosophies, but merely about value. Power is valuable, and sometimes even lucrative. There was a power vacuum in the presidency following Obama, and the skill set needed to fill the vacuum was precisely Trump’s: marketing.

But now, now that the marketing campaign worked, what does he… do?

The answer is simple: exactly the same thing as before. You market, which for Trump means saying exactly what is desired to the people who want to hear it. (Cf. Evangelicals at Liberty University, and Trump’s use of “Two Corinthians.”)

The point has been accomplished. Trump got power, and he can continue to exert enough control using the same tactics. The only thing which is of concern now is losing power. Sure, he’s relatively safe as president (impeachment proceedings are still rare and inefficient enough that he might weather them), but that all depends on his relations with the public. There’s still some standard of decency which must not be crossed. He nearly hit it with Charlottesville.

That explains why Trump fired Bannon. In the aftermath of last weekend, Trump cut it a little too close to the critical mass of offensiveness which would genuinely tip public opinion. As ardent as white supremacists are in supporting Trump, they have zero—nay, negative—electoral power. He can’t stay in power using fringe groups alone. He must remain painfully tolerated by the establishment until his 4 years are up. So, in an effort to save face after his double-talk on Charlottesville was too agitating, Trump dumped Bannon, the most controversial and alt-right-associated member of his cabinet. That’s scapegoating (another memetic tactic): it creates an illusion that Trump’s administration has been purified, and it creates a independent object (Bannon/Breitbart) which will absorb public hatred.

So Here’s the Extant Danger.

Trump is a jester. In the classic sense. He is not afraid to speak literally meaningless words—emptied of meaning through self-contradiction—because it pleases disparate groups of people and maintains power. However, in front of the backdrop of a perversely democratic* society, Trump is de facto fulfilling the role of the tyrant. “Tyrant” there isn’t just a synonym for “bad president, me no like.” Here’s how Plato describes the genesis of a tyrannical leader and society:

What about when the possessions of his father and mother give out? With that great swarm of pleasures inside him, won’t he first try to break into someone’s house or snatch someone’s coat late at night? … [E]rotic love lives like a tyrant within him, in complete anarchy and lawlessness as his sole ruler, and drives him—as if he were a city—to dare anything that will provide sustenance for itself and the unruly mob around it. … [If the mob] chance to live in a time of peace and quiet, they’ll remain in the city and bring about lots of little evils. … [And] when such people become numerous and conscious of their numbers, it is they—aided by the foolishness of the people—who create a tyrant.

Republic, Book IX

Trump isn’t consciously being tyrannical (if such a thing is possible). But his key tactic in governing is the textbook definition of tyrrany: supplying words, funds, power, “anything that will provide sustenance for [himself] and the unruly mob around [him].”

But notice the last line. It’s on me. (And you. And our neighbors.)

The essential premise of the alt-right’s political engagement—that of memetic thinking, which has spread only with the modern cultural phenomenon that is the Internet—is that rhetoric has value, but no meaning. All opinions are jokes, because all opinions can and will be contradicted as needed. Self-consistency, and with it integrity, is jettisoned. The only virtue is a kind of non-conformity, a kind of brash and brutal honesty that, ironically, simply has nothing to say. This rhetorical nihilism is antithetical to any sort of genuine political discourse, and needs to be refuted. Memetics drives the wedge deeper, and splitting the log won’t solve the problem.

The alt-right adopted offense for a subversive purpose, and in the process have constructed a cultural peninsula for white supremacists and neo-Nazis—the ones who really believe the ideological horrors which alt-righters merely joke about believing. Their nihilism is what allows the bright-eyed and vile idealism of the extremists to flourish. The alt-right, in turn has already surpassed the intended limits of Trump’s opportunist joke by believing it to have cultural value.

So, what will I try to do?

  • Reject the dialectic of memetics. I want to remind myself that there’s more to life and truth than surviving and spreading. I think that looks like having a warm and joyful heart toward my peers and the institutions I’m a part of.
  • Respond with a cool temper. I’m giving up Facebook comment wars, and I’m  putting myself on guard against scapegoating. As a child of the internet, these societal problems have an efficient cause in my heart.
  • Stop virtue signaling. Sharing this on Facebook probably seems like I’m negating myself here. But I’ve been one of those idiots mired in endless shouting matches on the internet. I often select who I talk to and befriend by the cultural (political, religious, etc.) phenomena they identify with. Putting this post here is my attempt to reach outside my echo chamber.
  • Think before I joke. My words are more than mere sounds, and actually mean what I think they mean. I want to add constructive contributions to conversations rather than try to get a quick laugh.

I would love responses and critiques of this perspective from anyone who reads this. If you can’t contact me via Facebook or the comment section, my email is rsquared.reynolds (at) gmail.com. Let’s dialogue about where America, politics, and the Internet are—and how to better them.

* This goes back to Plato again. To him, Democracy wasn’t a positive thing. Instead, it was a far-devolved point of social affairs where the only political and societal value is freedom. In Plato’s estimation, it is “democracy’s insatiable desire for” freedom that is the very mechanism of its destruction.

Code, Theology

Genesis 1

#include <iostream>
#include <exnihilo>
using namespace theTrinity;

void theEarth();

int main() {
    int day = 0;
    while (day < 7) {
        cout << “Let there be ” << create[day]
             << endl;
    // Pretty good!

    if (day == 7){
        return 0;


One Act, One Chance, One Shot


A GUN, black, polished, and revolver-style, lies on an end table made of dark wood at center stage. The end table has one drawer on the front with a knob. The entire stage is dark except for one soft spotlight on the GUN.

GUN: The bullets. It was the bullets. I was so innocent the day I saw their fetid box set down upon the table next to me. They were the ones who raped my virgin chamber; they were the ones who lay in wait in my darkest recesses. I didn’t want to hide them there. I wasn’t the one who let them in. They sat there so parasitically; I could feel them choking me, enervating me, mocking my very dignity. It seemed like weeks. Long, dark, agonizing weeks.

A long pause.

GUN: But the day came. The day came at last when I gave birth to lead and carnage. The heat seared me from the inside out; the sound keeps ringing throughout my whole casing; the residue, the smell. Five times they racked my body. (Another pause.) Why do they silence me!? Does no one hear my shouts? My screams? How many more times must I tell them who I am? I’m not a murderer! I don’t kill people. They do.

A black gloved hand reaches into the light, opens the drawer, puts the gun in, and closes the drawer. Exit GUN.


A gunshot.


Dante Expanded: The Woe of the Cynics

And here my guide and I, with careful steps,
Walked close along the river Styx’s shore,
Avoiding well the mire that entraps.
Quite soon we came upon a sight so sore
My muscles ache to call the scene to mind
And my lungs fill so anxiously with air.
Out from the mud stuck pilings of such kind
That one would see outside the prison’s gate,
Inflicting public death with wood and twine.
Across the posts were beams that bore the weight
Of upstretched arms, suspended by taut ropes,
And from the marsh protrude the filthy pates.
I asked my guide, “What pallid men here grope
To pull themselves above this viscous sludge
Which fallow lies and seems itself to mope?”
And he to me: “These ones, in life, begrudged
Even the truest speaker that they heard,
For these considered self alone best judge.
Just as they dragged their fellows down with word
Quite hurtful as an angry horse’s kick,
So now they are by fellows’ kick interred.
Look, there’s Thersites, churlish man too quick
To spite the Grecian kings for a cheap laugh;
He now, twice beaten, sinks in muck so thick.
But come now, we must gain our fated path.”


Since the effects of a cynic’s crime are not merely personal but corporate, the cynics’ punishment must occur in a communal manner, with each member contributing to the punishment of the others, and each individual’s punishment contributing to the punishment of the group as a whole. Additionally, the punishment must, in some sense, allow the cynics to achieve what they desire, namely self-betterment, and reflect the pessimistic mood in which cynics constantly remain. Finally, the punishment must reflect the oral nature of their sin, since the wound of cynicism is inflicted by speech.

Therefore, their punishment is as follows: the cynics are all suspended over a quicksand-like area of the Stygian marsh by rope tied about their hands. The ropes are tied to a large, wooden gallows overhead which slowly sinks into the mire. At the beginning of the punishment, the ropes are just long enough to keep the cynics’ feet on the surface of the mud, but when one cynic musters the strength to pull himself up by climbing up the rope, all the other cynics try to kick at the one climbing in order to knock him down, their flailing in turn causing the gallows to sink deeper into the marsh. Once the cynics have sunken down to their mouths in the mire, the guardian demons begin to construct a new gallows atop the old ones, and the punishment is repeated for the next round of cynics.


Rose-Gilded Glasses

…we live in a rose-gilded age.

This article by Rebecca Mead of The New Yorker is a deeply insightful piece of social commentary. She sees in the progression of Apple’s iPhone color schemes a relevant metaphor for the state of cultural affairs. Mead observes, “Rose gold is decadent. It is for people who already have enough gold gold.”

And while our overinflated markets, debts, egos, and numbers of presidential candidates can momentarily enthrall us, we’ll want more next week. In an age of escalating absurdity, is it that surprising when we are awakened only by the avant-garde of the absurd—the rose gold of discourse? When the pure truth—the “golden word”—is bandied about with disregard, is hackneyed and clichéd, it fails to catch our eye. The impure truth—the collection of cheap phrases and vulgar assertions which is tied tighter to volition than cognition—then has its day. Because it’s different. It’s extravagant. It’s provocative.

It’s rosy.

Whether it’s blaming all our problems on the Mexicans or the Muslims, poor people or the rich, a world leader or a world of followers, the rose gold word is effectively valued higher than the golden, and precisely for its impurity. Of course nobody, when asked, would deny the inherent cheapness of rose gold. But if you offered someone either a rose gold iPhone or a “gold gold” iPhone, which do you think they would pick? In much the same way, nobody in their right mind would deny that Donald Trump is a narcissistic (albeit brilliant) troglodyte, but…he’s just so darn entertaining! The gold gold has been seen before, but the rose gold is tacky enough to be novel.

The ironic thing about gold is that it inherently has no function, yet it is the symbolic arbiter of all value. Gold can not feed one’s family or shelter one’s body from the elements, and yet gold is prized beyond the objects it was intended to attain. Perhaps we could learn to value less the shocking truth, and rather be content with the (seemingly) mild reality. Or perhaps we like our gold, and like it best when it’s ruddied by blood drawn with our minds and tongues.