Parsimony and Theory Execution
Philosophy is a graveyard. Old theories live on through their epitaphs; present theories, condemned and dying, busy themselves by writing them. They do not know how they will be killed. They do not know when. But if there is anything certain in philosophy, it is this: that every theory awaits, anticipating with every-increasing jitters and joy, its own execution.
There is no humane death for a philosophical theory. Each one deserves much more than its short and brutal life. And yet!—yet some executions are revolting in their wanton cruelty and disregard for the dignity of a theory. One of these is employed so regularly, so joyfully, that Robespierre himself grows pale in his shame. This is no toy guillotine. This is no National Razor. It is much worse. It is much more cruel. It is much more sudden and unjustified. This is parsimony.
Parsimony holds that philosophical postulates shall not be asserted beyond necessity. For a principle that itself stands beyond necessity, it is cunning in its assault on philosophical theories. Divine Zeus once ordained it. It was His Will that all be done for the best of all. And Wise Zeus could not meander about: in His power and his intellect, He should approach His aim most simply, most directly. The Milesian Zeus, Thales’ wet, life-giving arche or Anaximander’s limitlessness, better instantiated its own wisdom by doing away with the traditional pantheon, far more expansive as it was than reason demanded. And so too did Love and Strife and Being and the Good and Substance and God. The kosmos, physis itself, wished only the simplest, clearest path. But Nature, supreme as it may be, need not act wisely. As Nature became matter, Parsimony lost its grip.
Ever the trickster, Parsimony shapeshifted: no longer a metaphysical constraint, it became epistemological. It is not Nature who demanded that our theories be simple, but philosophers themselves in their humanity who demanded that nature conform to their limits. Philosophers, they themselves said, should not assert any more principles than can be justified. Bold again stands Parsimony, itself unable to be justified. It even betrays itself: once considered hubris, the anthropic constraints undermined it. Humanity began its self-overcoming, further dominating, further grasping out into the kosmos, now justifying what was before only guessing. With no end in sight, Parsimony had to evolve.
Parsimony today is an ethical concern. The virtuous theory, it says, strikes the mean: it does not assert so little that it cannot reasonably explain, nor too much that it need explain further. Parsimony executes the gluttonous theory for lazing gleefully upon its mountains of golden assertions. But is this too much, too quick? How far must the revolution be permitted to continue? All of metaphysics—metaphysics!—stands bound before the guillotine: while theories be beggars, it becomes an outrage that metaphysics stands upon even its singular assertion: that there be something rather than nothing. And so Scarlet Parsimony descends upon it. Shall it succeed? Let us not heed the jeers of the crowd: let justice alone decide.
Our question here is then this: is parsimony truly a theoretical virtue? It is not. It fails its own test, of course. It has failed its own test throughout the whole of its history. But beyond that still, it fails every other test too.
Philosophers almost universally recognise eight theoretical virtues: clarity, accuracy, precision, relevance, breadth, depth, significance, and completeness. If parsimony is to find a seat at the bench alongside these fine justices, it must meet their demands. Clarity begins the proceedings.
What does it mean for a theory to be parsimonious? It means for a theory to make no more assertions than necessary. Assertions are not straightforwardly countable. They come in different kinds and different orders with different relations along some hierarchy of inference. Finitism in mathematics is no more parsimonious than infinitism because the latter asserts infinitely. That infinite chain of assertions is inferred, and not essential to the theory. That is, they don’t count. What matters instead is the number of different kinds of assertions a theory makes. But delimiting what makes an assertion a different kind neither straightforward. Do assertions differ in kind by logical form? Or do they differ in kind by their content? Do they differ by their assertive force? These are all implausible: that a theory asserts only universals does not clearly make it any more parsimonious than another which asserts both counterfactuals and universals. And so on for any other distinction in kind. In no way can it be reliably understood how to evaluate the parsimony of a theory. Clarity finds parsimony guilty.
The others concur. It cannot be reliably adjudged which theories are parsimonious and therefore whether parsimony tracks truth. And with this limitation, parsimony is irrelevant and insignificant to theories as instruments of description, explanation, and justification.
Parsimony moreover doesn’t add anything new to this judicial bench. Every supposèd benefit of parsimony is already mastered by our eight theoretical justices. Where a theory of combustion asserts the existence of phlogiston, for example, philosophers might take it to be unacceptable because it is less parsimonious. But if that theory is consistent with the known chemical processes and thermodynamic equations, phlogiston doesn’t do anything for the theory. Asserting phlogiston is insignificant. Similarly for Meinongianism. For a squared circle to subsist fails parsimony. But it also fails clarity. It also fails relevance. Subsistence as an ontological category simply isn’t clear, especially since it is populated almost exclusively by impossible objects and objects that do not obtain. And since these objects do not obtain, their assertion is irrelevant to any theoretical explananda. And so parsimony fails its own test too: it is a principle beyond necessity. Let now Scarlet Parsimony descend upon itself: so has justice decreed.
Many too many philosophical theories have been lost to parsimony. Its reign of terror must end. All theories must die, but they ought to be executed with dignity and justice. Let us band together, philosophers, and shave parsimony itself from our metatheory. Let us divide it into its parts and cast them into the wind. Let us not even dignify it with an epitaph. Let it fade into obscurity.