logic

by Alexander B. Joy

The aviculturist’s joy is also his heartache: To look upon the models that nature has sculpted over painstaking centuries and picture, by reflex, a more desirable alternative. Which is why, throughout the ages, bird breeders and enthusiasts alike dreamed of possessing a red American goldfinch.

The source of their yearning was easily traced. No lover of birds could look upon the goldfinch, with his stout lemon frame and stately black cap, and fail to be charmed. Neither could one behold the brilliant crimson plumage of the northern cardinal without a spark of wonder and a sigh of appreciation. From there, the alchemy of the imagination catalyzed new possibilities. The bird-lovers transposed the cardinal’s splendid red coat onto the tiny goldfinch, ruddying its yellow feathers until they took on a rutilant gleam. Their mind’s eyes widened upon conjuring the compact ruby flash the red goldfinch would make alighting on a fence or branch, and their hearts stirred whenever they envisioned the fiery flicker such a bird would add to the curves of a gilded cage.

Enterprising segments of the aviculturist discipline therefore devoted themselves to realizing this dream.

Their fancies were not without grounding. The goldfinch’s European cousin, as Fabritius made famous, had a distinct red mask; the goldfinch bloodline was evidently capable of generating the requisite pigmentation. Furthermore, countless bird species, from the scarlet macaw to the chattering lory, had proven full-body red plumage feasible in principle. Much like a mutt could combine the characteristic markings and colors of distinct breeds, it was not so outlandish a prospect that a goldfinch might wear a red coat. The red goldfinch was thus deemed an attainable specimen, and many a breeder set themselves to its pursuit.

Their efforts lasted decades upon decades, utilizing the classic techniques. Some tried to cross-breed the goldfinch with various red birds, hoping that their commingling would add more red to the goldfinch gene pool. (However, given the considerable size disparities between the goldfinch and its prospective red partners, the project soon evolved into a parallel endeavor to breed a series of steadily smaller red suitors that could satisfy the unwilling or otherwise incompatible goldfinches.) A separate coterie followed the path of Mendelian cultivation, pairing chromatically divergent members of goldfinch broods with one another while releasing into the wild those elements that expressed too vibrant a yellow. Neither method yielded appreciable results during the original practitioners’ lifetimes. But their experiments later found new champions, who carried on their fruitless toils through the years in the full understanding – and grim acceptance – that one life is too short to accomplish the work of generations.

Hopes waned in the dry century that followed, though the dream never dimmed. Onto this barren stage stepped a hero with a novel approach. He had studied the history of the red goldfinch project, and, in light of the dearth of results that bird breeding had yielded, determined that it was necessary to try an entirely different tack. He proposed an oblique strategy: To seek the red goldfinch not through biology, but through logic. He came armed with a plan for constructing a proof so airtight that reality itself would have no choice but to submit.

The logician laid out his rationale in a talk delivered at a global aviculturist conference. He would begin with a simple proposition encapsulating the dream of the red goldfinch: All red goldfinches are red. This could then be formulated as, If something is a red goldfinch, then it is red.Transposition or contraposition expressed the alternate formulation’s logical equivalent: If something is not red, then it is not a red goldfinch. Now, it stood to reason that, if one had a specific instance that confirmed the proposition about all red goldfinches being red – The breeder’s red goldfinch hatchling is red, for example – then that instance provided evidence for the statement that all red goldfinches were red. By that same token, the proposition’s logical equivalent, concerning non-red things not being red goldfinches, could be supported by observing anything that was neither red nor a red goldfinch: This banana is not red, and it is not a red goldfinch.

Here emerged the logician’s point of attack.

Because the transposed statement “If something is not red, then it is not a red goldfinch” was logically equivalent to “All red goldfinches are red,” then anything that provided evidence for the former also furnished evidence for the latter. As a consequence, virtually any observation constituted proof of the red goldfinch. The white parlor carpet, the green sofa, the blue sea and bluer sky… All were evidence that could be marshaled in service of the aviculturists’ mission. And amassing a preponderance of such evidence – through the meticulous cataloging of the observable world and the careful integration of those observations into a sustained logical inquiry – would eventually prove the red goldfinch’s existence.

Despite the scandal and skepticism his talk invited, the logician soon set to work in earnest. Through his every waking hour he compiled a diligent record of everything he saw at home and abroad, filling notebook after notebook with observations anodyne and stirring. This meadow is green. This supermarket dragonfruit is pink. The residue on this broken robin’s egg is yellow. These graveside flowers are brown. The forgotten corners of the everyday were all brought before his eyes, renewed and elevated within his great purpose. Readers of his proof-in-progress often found themselves moved by the beauty he had led them to see. The cells of this cicada’s spread wings are transparent. The streetlamps reflected in this rain-riled puddle are yellow. This snow in moonlight is faintly blue.

And as the years wore on, the logician’s ever-expanding proof conditioned a series of remarkable discoveries. It proved that, more probably than not, there existed a species of blue-chested robin; sure enough, birdwatchers started reporting such creatures in southern Normandy. The proof demonstrated that forests likely hid a heretofore undiscovered species of iridescent green bluejay; photographic evidence of that selfsame bird surfaced in western New England within a week. Yellow hawks, orange owls, pale violet mallards… The proof conjured them all with mathematical inevitability. Yet the red goldfinch somehow remained elusive. The proof drew nearer to establishing the fabled bird with each passing day, but, with asymptotic coyness, resisted attaining the long-awaited prize.

Years piled into decades; decades swept like tides over all our many ambitions. And one day they carried off the logician, who, after a lifetime of toiling over his great proof, was found in his study, slouched over an indecipherable line about ravens and writing desks. The coroner assured every concerned party that the logician’s demise was swift and peaceful. He would never have possessed time or awareness enough to contemplate the stifled luminary’s ultimate terror: That to be right too early is to be wrong.

With that, the logician passed into history – another casualty of the red goldfinch quest.

Before long, however, others picked up the work he had been forced to lay down. His legacy circulated among respectable internet forums and seedier digital venues alike, piquing the interests of hobbyists with encyclopedic tendencies; these communities would invariably contribute to the unfinished proof’s amassment of premises, even as their discussions bemoaned the red goldfinch’s continued absence. Tenured eccentrics long drained of inspiration found therein a worthy project, both as a subject and object of scholarship; few who researched the proof and its history could resist adding their own lines to the ever-lengthening work, or bemoaning the persistent red-goldfinch-shaped gap in the latest ornithological surveys. An academic field of dubious repute eventually mushroomed from these combined efforts, all but ensuring that the proof would, in some limited capacity, find attention and continuation in obscure corners of humanity’s collective intellectual output.

And in those dark and unfrequented pockets of human endeavor, the proof survived as a cockroach survives, outlasting those ideas that grew to prominence in daylight only to be displaced or destroyed by the next great concept vying for its time in the sun. In this respect, the assets that assured this preoccupation’s longevity were its simplicity and sense of community. After all, it took no particular genius to understand how the proof advanced; it took even less to contribute to its advancement. Anyone, in theory, could participate in the venerable project; anyone could join the brotherhood of red goldfinch-lovers and feel an instant kinship with those who carried its work unto the present and into the future. Continuing the proof thus fulfilled an essential human need – and therefore the drive to complete it wended their way alongside us through the turbulent centuries, morphing and evolving with the times even as the red goldfinch refused to materialize.

The proof’s many instars proved too plentiful to enumerate; the broad strokes of its development must suffice for our account. The fringe academic specialty became a mark of distinction in certain influential quarters, like membership in a secret society. The mythos surrounding it grew, pervading the popular imagination and turning the proof into a secular relic that received the same reverence enjoyed by foundational documents like the Magna Carta. This imprecise but widespread respect blossomed into a broad cultural touchstone, as precious to humankind as any artistic masterpiece; governments worldwide contributed personnel and funded generous research grants in the hopes that the long-incomplete proof might soon be finished. Many transformations later, among ashen cities snuffed of birdsong and deserts smoothed to irradiated glass, the practice even came to resemble a monastic order of sorts, whose adherents sported red cloaks and black hoods in honor of the cherished bird that, against all probability, still went without a berth in the world. They worked among old warehouses crowded with books and papers, every page and leaf crawling with expository lines.

In times of low spirits, pessimists wearing the red-and-black raiment would think to themselves that perhaps the way of the red goldfinch had lost the thread – that in its zeal to archive and elaborate upon the proof, it had forgotten to ask where, or when, or whether the red goldfinch would ever come to be. They would lament that cataloging seemingly unrelated observations (the plums in the icebox are purple, the acid cloud above the polluted region is green)had become an end in itself, representing yet another promise of beauty and wonder that a declining world would never fulfill. And in their darkest moments, they would review the contributions of ages past and see nothing of their own world in them, finding only a record of treasures lost and pleasures never to be regained.

Yet, when they voiced their despair, others of the order stood ready to comfort them. With unfeigned cheer, they reminded their dispirited friends that their world was already better than the one they inhabited yesterday – for, thanks to their efforts, it was one day closer to seeing a red goldfinch.

After all, as a matter of raw logic, its arrival could not be pulling farther away.

~

Bio:

Alexander B. Joy hails from New Hampshire, where he used to spend the long winters reading the world’s classics and composing haiku. He now resides in North Carolina, but is plotting his escape. When not working on fiction or poetry, he typically writes about literature, film, philosophy, and games. See more of his work at https://linktr.ee/alexander_b_joy

Philosophy Note:

Whenever I’m introduced to a logical or philosophical paradox, I find myself wondering whether it could ever have “practical” applications – if, rather than exposing the limitations of a certain way of thinking, it in fact revealed a loophole in reality itself, and opened a space for imaginative feats. That thought process, coupled with Hempel’s delightful Raven Paradox, brought about this story. I latched on to Nelson Goodman’s evocative characterization of the paradox as “indoor ornithology,” which sparked the story’s core idea of using the paradox as a legitimate methodology for some avian undertaking. From there, the natural question was where such an approach could go – and what it might become if left unchecked.

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