Is Truth an Asymptote?
“The truth may be puzzling. It may take some work to grapple with. It may be counterintuitive. It may contradict deeply held prejudices. It may not be consonant with what we desperately want to be true. But our preferences do not determine what’s true. We have a method, and that method helps us to reach not absolute truth, only asymptotic approaches to the truth — never there, just closer and closer, always finding vast new oceans of undiscovered possibilities.”
— Carl Sagan
What does it mean to say that we approach truth asymptotically, and is this a good metaphor for how we gain knowledge? The more traditional view is that we can arrive at a final truth, but this view typically depends either on faith in some kind of divine revelation or a belief in a perfect language in which all knowable truths can be expressed with perfect clarity. As for revelation, take your pick. There are countless creeds on offer, but no way to decide between them. For its part, the perfect language is a chimera, a naïve presumption that ignores a basic fact: to even begin to reason we must focus our attention in some places and not others, on some problems and not others. All rationality is motivated, and motivations are always partial.
The metaphor of truth as asymptote reflects a belief in (a) the inherent fallibility but increasing quality of human knowledge, and (b) a fixed frame of reference against which all knowledge is evaluated. The perfectly straight line represents the immutability of the cosmos, or of those regularities of which our knowledge treats. Our undeniable technological progress constitutes the best evidence that the asymptote of truth is out there, pulling us, as it were, with the attractive force of necessity.
But are the regularities of the cosmos really immutable? Some cosmologists and physicists believe that in the very early universe the strong, weak, and electromagnetic forces were combined, only to crystallize into distinct forces as the universe expanded and cooled. And what will it mean to say the universe is governed by laws after its heat death puts any interaction that might be so governed beyond the realm of possibility, let alone observation?
Assuming these regularities are immutable, are they the unique determinants of the asymptote toward which scientific knowledge strives, or, as many twentieth century philosophers of science held, are scientific beliefs and practices also subject to selection pressures originating in human biology and culture? After all, Nature’s regularities may be unchanging, but those of human nature are not.
And this brings us to other kinds of truth claims. Even if scientists are approaching a fixed asymptote of natural laws, claims of moral or aesthetic truth are predicated upon, and necessarily responsive to, the variable nature of human biology and culture. It may be the case that some moral and aesthetic truths transcend human experience: respecting a norm of reciprocity may be a sine qua non of the evolution of complex social species, and the principle of organic unity that makes symmetrical faces more attractive is likely found in other animals, and for the same reasons. But these truths will not transcend experience per se. We may share some truths with sentient extra-terrestrials, but only because we will share with them the values those truths presuppose.
Which raises further difficulties: if we take moral or aesthetic truth to depend on the proximity of truth claims to a variable human nature, are we not committing the naturalistic fallacy? But aside from this proximity, what other measure do we have? And what happens when the lines diverge? If for a time certain moral truth claims are well-adapted to our human nature, but later become maladapted, is it the case that they were always false? Conversely, is a moral claim, apparently falsified at present, falsified for all time, or must we reserve judgment, given the possibility of an eventual rapprochement between that claim and our evolving nature?