Grounding the abstract in the concrete.

Operationalizations are attempts to ground phenomena that are meaningful to us into things we can actually measure. The notion of panic might be operationalized through the time it takes a crowd to leave a room. The notion of fitness might be operationalized through average running pace over a set distance. The notion of intelligence might be operationalized through a battery of pattern matching tests. In bridging the abstract with the concrete, operationalizations enable systematic inquiry into higher-level phenomena.

However, there are many different ways of operationalizing the same phenomena. The intensity of neural activity has been operationalized as the level of oxygen present in a brain region relative to a baseline, as seen in an fMRI. It has also been operationalized as the effect on the electric field around the scalp, as seen in an EEG, or on the magnetic field, as seen in a MEG. What about radiation? Ultrasound? Infrared? Which measure is most appropriate?

Digging deeper, we find that these are usually not brief, one-step bridges connecting phenomena to measurements. For instance, neural activity is often linked to increased oxygen saturation, which in turn is then linked to specific spectral signatures. Individual segments are also shared across operationalizations. For example, measures of exoplanet habitability often rely on oxygen levels, whose spectral signature is as idiosyncratic as that picked up by functional neuroimaging.

Ideally, we’d want operationalizations whose every link is rock solid. The two ends of a segment — one more abstract, the other more concrete — should “march in lock-step, always found together and never found apart.” A beautiful example of this is Shannon’s operationalization of information, with strong theoretical arguments supporting this as the “true name” of information. For instance, you provably can’t do better in information-seeking games (e.g., “identify the heavier marble using the minimum number of weighings”) compared to what Shannon’s ideas imply. Alternatively, you provably can’t do better in compression than what Shannon’s source coding theorem implies.

Another operationalization I’ve been fascinated with is one of truthfulness. In brief, the truthfulness of a position is equated with the absence of a coherent challenge to said position. From here, we split into two branches. First, a coherent challenge is equated with consistently winning debates against a party holding said position. Winning a debate is then equated with having the strongest arguments. The strongest arguments are then equated with arguments which are most strongly supported by other strong arguments, PageRank style. Backtracking and going down the second branch, the absence of something is equated with the presence of thorough search efforts that end up fruitless. Such search efforts are then equated with a self-improving system consistently failing at the search task.

This is a complex operationalization. Let’s zoom in on the very first leg, the one linking truthfulness with the absence of a coherent challenge. Every such link is a biconditional, with the first implying the latter, and the latter implying the former. Let’s have an even closer look at the latter direction, the claim that the absence of a coherent challenge to a certain position implies that said position is true. Following a series of syntactic manipulations documented elsewhere, we end up with the claim that the fact that a position is true implies that there is a sufficient reason to accept said position. It turns out that this is essentially the Principle of Sufficient Reason, the crux of many philosophical debates since at least the late 17th century, when Leibniz coined the term. A fascinating property of the principle is that it seems impossible to counter with a counterexample. It’s difficult to identify a case in which the implication is false, i.e., a true position for which there is no sufficient reason. Becoming more certain about the truthfulness of a position would coincide with cataloguing more reasons why it’s true. Conversely, in situations with scarcely any reasons in support of it, a position’s truthfulness is also fragile.

One direction leads to paradox: the impossibility of providing a cogent counterexample to Leibniz’s principle. The other direction is perhaps even more interesting. This involves the claim that the fact that a position is true implies that there is no coherent challenge to it. One might challenge this statement with a view to show its falsehood, as one might challenge other statements to similar ends. However, in this particular case, doing so implicitly involves running a modus tollens argument with the original implication itself as the conditional premise. In other words, by tacitly linking coherent challenges to revealed falsehoods as part of an assumed mechanics of reasoning, one is presupposing the very claim one is attempting to challenge. It is a beautiful instance of what one might call “Cartesian antifragility,” the property of a statement being reinforced by successive attempts to challenge it. Descartes’ Cogito, due to similar antifragile dynamics, marked his most fundamental understanding of the world.

Zooming out again, we’ve explored both directions, one leading to a Leibnizian paradox which is structurally lacking counterexamples, the other to a Cartesian one whose challenges are self-defeating. However, taken together, these two directions form just one of the many links involved in the operationalization of truthfulness described above. The point was to use this “case study” as a means of illustrating the flavors of “demandingness” that we might need to exercise in our search for durable operationalizations. While still embodying a step towards the concrete, coherent challenges remain securely in the abstract realm. That said, different segments of different operationalizations might involve different levels of concreteness, and so rely on different epistemic tools to identify.

However, as one might use their only wish to wish for unlimited wishes, if we were to successfully operationalize one such notion, it ought to be truthfulness. Doing so would allow us to seek ever more appropriate ways of measuring phenomena of interest, and by extension, understand them. Building on the above operationalization, one might claim that the true nature of truth-seeking lies in the conceptual pressures of self-appointed challengers. However, in seeking the true nature of truth-seeking — as just one of many phenomena — beyond this seemingly arbitrary claim, through the very same dialectical mechanics, one is yet again presupposing the original claim. There are a number of such fascinating “Chinese finger traps” imbued with a totalizing coherence that emerge when inquiring about the very mechanics of inquiry. The pristine scout mindset is insufficient for venturing into the metaphysical, where the dark arts of the soldier mindset might be inherently necessary.

Regardless, because of the extreme potential of a robust operationalization of generalized truthfulness, it is this that researchers, augmented or not, should prioritize. Engineering a truth-seeking engine to then direct at various phenomena of interest, especially metaphysical (e.g., morality), is halfway to everywhere of philosophical interest.