explanations à la David Deutsch

The Beginning of Infinity by David Deutsch contains some intriguing philosophy. One of its central propositions is that good explanations are essential to human knowledge; in fact, Deutsch redefines "knowledge" and many other words accordingly. He musters arguments to tear down competitors with relish: empiricism, positivism, inductivism, instrumentalism, postmodernism, justificationism, anything supernatural. Instead he aligns with general fallibilism and the outlook of Karl Popper.

My interpretation of pragmatism takes a similarly dim view of those competitors but via a more roundabout way. As I see it, a datum is never alone and objective meaning lies in isomorphism. In short, the importance of context shouldn't be underestimated. Information becomes meaningful for a human because the brain is the defining data structure. It verifies, validates, cross-checks, computes, tests, trusts. Information that passes through these filters of diverse physical and/or mental processes can be said to "work"¹. The brain is the singular agent throughout who initiates, performs, and finally evaluates. Of course, in practice humans augment the brain all the time. Total self-reliance is too constricting to seek "truth that works, every truth that works, and nothing except truth that works" ². It's fine that theorists and philosophers and mathematicians can sit in quiet rooms and ponder, but that approach has its limits! Calculating the circumference of Earth doesn't reveal what's on the opposite side...

Deutsch defines the quality of a good explanation: "hard to vary". My version is not as pithy: "good explanatory information permits many isomorphisms to other good information". This appears to be circular because it really is circular. The circularity is largely the point. It implies that there aren't any Ultimate Bits of information with inherent and infallible meanings³. Yet a suitably advanced and knowledgeable information processor can certainly derive meaning from an aggregate of pieces. For information, to be meaningful is to be codependent.

For example, it's a good explanation that matter is composed of elemental atoms. This explanation is good because it's isomorphic to an impressively vast group of experimental results in chemistry and physics. If someone proposes an alternative explanatory material, e.g. mana, then it's fair to ask how isomorphic that explanation is to the same experiments, and if not then why not. Note that my definition of "isomorphic" isn't intended to be mysterious. In some cases it could just mean "closely matching reliable facts". Explanations with many, small, tight isomorphisms are more firmly locked into a greater context of solid information than explanations with few, grandiose, loose isomorphisms. In Deutsch's language, the former are hard to vary and the latter are easy to vary. A single chemical equation is isomorphic to substances and quantities that are measurable and unambiguous. A single mana explanation is not⁴. Additionally, a chemical equation has isomorphisms to atoms and electrons, i.e. complicated orbitals that correspond to the rows and columns of the periodic table. An explanation based on mana doesn't.

Other than preferring different wording of the definition of a good explanation, I sense that I'm not as keen as Deutsch to emphasize a starring role for Reason with a capital R, especially if it's construed as a synonym for mere logic. I'd rather claim that applied reason is one of the important mental tools that humans use to tame reality or at least interpret it. It works alongside nonlogical guidelines like the human delight in mental economy, which is the strong preference for a minimal quantity of concepts with wide if not universal reach, as opposed to a myriad quantity of conflicting concepts with sharply constrained applicability for each. (Deutsch has much to say about explanations with expressive reach, but I may be more eager to acknowledge that reach is also a human craving.)

Fortunately, parts of the book seem to agree with me. It dismantles the famous Zeno paradoxes, and the dismantling amounts to the general principle, "Reality isn't held hostage to entire logical/mathematical conclusions." And that principle is well-known to anyone who applies complicated science because models must be used with care and understanding. Whenever a function is fit to a discovered set of data points, the function might or might not accurately predict every other data point; outside of the data set, there could be "phase changes" in reality that don't fit the function well. That outcome isn't a violation of reason. It's a reminder that good explanations are bounded by a data context. In a battle with good data outside those bounds, obsolete explanations should lose.

But which data is "good", and obtained by which "measurements"? Deutsch's answer is unsurprising: explanations must underpin data-gathering, too. A measuring device is presumed to be reliable because it was built using good explanations. A handful of "outlying" readings can be disregarded as errors because good explanations of statistics show that those readings are truly anomalous.  Data is simply unable to "speak" on its own. Explanations are necessary. Better and better explanations, which are sought iteratively and recursively, are the stepping stones to the titular "infinity" of knowledge.

That proposal is front and center in Deutsch's imagined Socrates dialogue, which holds up explanations as the fundamental units of understanding. And those fundamental units come with a fundamental method, criticism. Criticism is the evolutionary/progressive attempt to continually probe explanations for weaknesses, with the goal of then replacing the failures. Deutsch takes special care to contrast criticism with its opposite method, a catch-all called "justified truth". The latter is the misguided attempt to identify and defend truths that are surely true and cannot be false.  Fallible explanations are confirmed or falsified, but in any case never are off-limits from attacks by critics. Some of the more self-congratulatory sections of the book are detailed praises for the societies/cultures which have more tolerance for the clamor of diverse ideas, especially the iconoclastic ideas that challenge authority or convention.

While I find that line of thought convincing, once again I'd analyze and state it differently with clarifications. Pragmatic philosophizing asks what purpose is served by the intellectual construct called "justified truth". And the pragmatic answer is that its purpose is to distinguish which truths have the greatest certainty. In short, its intent is the same as the intent of criticism: separating the truth from "fooling oneself". The relationship isn't antagonistic at its core. It's playing "good cop/bad cop" in the interrogation of truth. Criticism eliminates the unworthy candidate truths, so justification can select from the possibly infinite number of remaining creative candidates. Far from tossing out "justification" altogether, the (infamous) pragmatic definition of justification/verification is simple reliability of the candidate truth in accomplishing corresponding endeavors. One pertinent endeavor has been previously mentioned: modeling reality in ways which are isomorphic to good information.

Perhaps that answer verges on evasive wordplay. My suggestion is to roll both "relentless criticism" and a shrunken version of the notion of "philosophical justification" into the big ball of conceptual mud called "verification". By doing so, am I questioning the superior value of dynamic evolutionary criticism over static repressive dogma⁵? That's not my desire. Au contraire, to be a conscientious pragmatist is to be an active skeptic. I'll repeat my earlier axiom: individual bits of information cannot be meaningful nor accurate without isomorphic links to other bits. In response to this axiom, a human must probe the links of an assertion to establish its meaning and accuracy. They may judge that the links are dubious or logically incompatible; that is in the category of criticism. They may introduce creative new links, or devise ingenious experiments, to increase the estimation of confidence; that is in the category of justification. Hence, no matter what category applies to the action under discussion, critical thinking and trial-and-error are in effect.

Nevertheless, I doubt that Deutsch would find this alternative scheme to be acceptable. It's much too reminiscent of what the book calls "instrumentalism", i.e. valuing a theory solely or primarily for useful predictions and more or less disregarding its explanatory claims about reality. It differs, though. Unlike instrumentalism it judges the reality of explanations as eagerly as all statements. But explanations must pass the same methodological rules. The grand inquiry is always "How do we know?" If an explanation is real, then by what actions would we detect it? Pragmatic reality consists of the answers to these questions. "Theoretical" explanations with discernible verified effects can certainly be as real as "empirical" observations or measurements or numerical predictions. Arguably, a pragmatist could flip instrumentalism around and claim that specific theoretical explanations are more real than a single empirical item of interest, because the explanation had been verified countless times by countless experts in countless procedures but the single empirical item might come with reasonable doubts (oops, gunk on the lens, or oops, I forgot to carry the 1).

However, to someone who insists on the immutable reality of explanations, such a cure may seem worse than the disease. What's the benefit in calling explanations "real" if the cost is redefining, weakening, or stretching what we mean by "real"? After all, when a human uses an explanation to comprehend a phenomenon, their earnest motivation is to uncover the real stuff responsible for it⁶. They wouldn't frame it as inventing or imagining ideas for some subjective purpose. They see the explanation as having an existence independent of foolish capricious humans, including nonsense-talking pragmatists⁷.

And round and round it goes, for the pragmatist then responds by noting that a real existence independent of all physical or mental human activity is worthless, and even worse unsubstantiated. Moreover, to pair this insistence with a strong emphasis on fallibilism leads to the troubling consequence that explanations are independently real yet changing constantly, because explanations evolve, as Deutsch cogently recommends. So were the past and disproven explanations real? If so, then the human accumulation of the evidence, which disproved the past explanations, must have somehow shifted reality itself. If one starts to admit that the reality of explanations can vary by degree depending on verification, and that humans' current complete picture of reality depends jointly on the explanations that they actively construct and the information that they collect over time, then one may be not far off from a pragmatist.

Given his unmistakable powers of reasoning and debate, I'm sure that Deutsch could trample these thoughts at his leisure. Still, his long and deep book was thought-provoking reading, for which I'm grateful. Although I'm incredulous about whether the human progress of explanations is as all-powerful as hypothesized, his confidence is undeniably touching.


¹ "Work" is intentionally left vague in order to cover the wide scope of all knowledge. Contrary to the common misrepresentation, it isn't synonymous with "profitability" or "convenience". False information could possibly "work" for some selfish purpose but not "work" for understanding reality; for instance, paranoia can be excellent at keeping you safe regardless of how incorrect it is at pinpointing the foremost motives of everyone around you.
² Someone who had that strategy might say, "I reject your reality and substitute my own." Or less humorously, "Reality moves in step with the dictates of my beliefs. I can trust my deductions because my small simple-minded set of fundamental axioms is complete, flawless, and impervious to all criticism."
³ I have enough self-awareness to recognize that I therefore cannot claim that my own philosophical ideas, including the words in this very blog entry, are self-evidently true. All I can attempt is to convince readers of the "reasonableness" of the ideas, where "reasonableness" is a pragmatic judgment of whether the ideas "work", naturally.
⁴ I don't wish to seem biased. I suppose that an imaginary mana explanation could have similar isomorphisms. It could describe kinds of mana, which are capable of recombination, and it could allow proportions of mana to change in formulaic ways. Thus the mana believer could say that normal water is "two-parts ephemeral mana to one part airy mana". If explanation A has many isomorphisms to C and explanation B has many isomorphisms to C, then A is more likely to have many isomorphisms to B. "Different names for the same thing" is a folksy description of an intense isomorphism. In any case, plausibility certainly isn't tied to how "scientific" that words sound, regardless of the custom/preference for Greek/Latin. Despite its laughable sound, "'charm' is a 'flavor' of 'quark'" is a weighty statement because of its isomorphisms to experiments as well as other experimentally-verified statements.
⁵ Dogmas can come in endless forms, varying by the source authority and the severity of imposition. Propositions about the supernatural are some of the purest examples, but other domains aren't immune either. Sometimes the dogmas assume the innocent shape of, "Everyone knows that, so proof isn't necessary."
⁶ I wholeheartedly agree with Deutsch's warning against level-based prejudice of the reality of an explanation. A concise overall explanation, when correctly understood, can be as real and meaningful as hundreds of minuscule details that explain the same occurrence. That means the "real stuff" in the explanation could be relatively abstract or broad. Any time that the orchestration of many parts achieves a total effect greater than every part working independently, higher-level explanations are mandatory. I'm nothing except for a biological group of multitudinous cells, but all those microscopic facts communicate virtually nothing of significance about me.
⁷ Some relevant sections of the book contain excellent critiques of the Copenhagen interpretation of quantum mechanics. Deutsch is good at that.