Scientific Explanation Revisited
If science is in the business of providing explanations, what are they? Can we build a general model of scientific explanation? Or does science fall short of this explanatory imperative, and instead merely supplies predictive models?
Let’s start by considering some questions:
Why are galaxies receding at an accelerating rate?
Why are there three generations of matter?
Why do charged objects emit waves in oscillating magnetic and electric fields at 299 792 458 m/s?
Why do some humans pursue wealth while others knowledge or prestige?
Why do some believe in supernatural entities while others don’t?
Why is there more matter than antimatter?
Why does time have a direction?
Whether we use the word “why” or “how”, when we raise such questions in our day and age, a presumption prevails that the answer will amount to something other than recourse to revealed truth, established dogma, or personal beliefs. Many of us may hold the notion that something like an answer to these questions ought, rather, to defer to the best “scientific theory”. Understanding of these questions is nested in natural, ordinary language. In our colloquial understanding, raising them amounts to, more or less, asking for an explanation of the identified phenomena. What explains the phenomena mentioned? Or, what accounts for them?
In ordinary language, the noun explanation admits sufficient haziness and ambiguity. The OED offers the following number of definitions for the transitive verb to explain:
1.To make plain or intelligible; to clear of obscurity or difficulty.
2. To describe or give an account of in order to bring about understanding, to explicate; to give details of, enter into details respecting.
3. To assign a meaning to, state the meaning or import of; to interpret.
4. Of a fact, situation, or circumstance: to be the reason or rationale for, to account for; to be the cause of. Also: (of a theory) to account for (a phenomenon)
5. to make clear the cause, origin, or reason of; to account for.
6. To make one’s meaning clear and intelligible, speak plainly. Also: to give an account of one’s intentions or motives.
Looking at these various definitions it appears that the verb to explain applies to a wide scope of objects, ranging from “meanings”, “intentions”, “laws”, “thoughts”, “ideas”, to worldly events and “phenomena”, whether taken to be “natural” or “supernatural”. Scanty inspection of these definitions further suggests that, while they may be interrelated, certain disjunctions persist between the type of objects to which the verb to explain is applied.
For example, to account for one’s actions is not the same as to account for sunsets or eclipses.
To do justice to our current public understanding of the word explanation requires a historical exegesis of the various transformations our culture’s metaphysical assumptions have undergone through the last few centuries.
Foregoing such a laborious task, we will nonetheless occasionally draw examples from the past to make certain differences and distinctions clear.
In our milieu, the hunch prevails that answers to the above questions ought to amount to more than mere linguistic clarification, or haphazard reference to available evidence or scientific theory. Rather, whether a scientific theory or evidence gestures to explain a phenomenon or not, a normative presumption of completeness prevails.
This is to say that, however we circumscribe a phenomenon at whatever level of resolution, our theory and evidence ought to, when formulated in a way that it has probed nature to its fundament, provide a complete explanation, such that no details (data, observation, inferred properties) escape consistency with current theory and evidence.
The expectation of completeness finds robust frustration at quantum scales. For example, whether Schrödinger’s wave function constitutes a complete description of a quantum system rather than the definite state the system takes when the wave function collapses upon measurement has been heavily debated. While, Bell’s inequality test supports the objectivity of the state of superposition, what causes the wave function to collapse (and concomitantly what constitutes measurement) as yet lacks satisfactory explanation — though competing theories exist, chief among them the Copenhagen and many-worlds interpretations. The mutual consistency of the superposition and the collapsed state has also been disputed. Explanatory sufficiency, therefore, will be a topic explored at some length in this digest.
Below I survey in detail the four major models of scientific explanation in the philosophical literature: I) the Deductive-nomological and inductive-statistical, II) statistical relevance, III) causal-mechanical and IV) unification models. In the concluding remarks I hypothesize that alone none of these models suffice, and that successful explanations almost always encode a combination of causal-mechanical and unificationist constraints.
Deductive-Nomological & Inductive-Statistical Models
The most well-known model of scientific explanation, bearing the cumbersome appellation of the Deductive-Nomological Model, was developed during the middle of the 20th century by Karl Hempel & Paul Oppenheim. Both Hempel and Oppenheim hailed from an academic tradition that saw the role of philosophy as consisting chiefly of analysis. Philosophy does not make positive claims about the world, which is the province of science, but can serve instead as its handmaiden by tendering conceptual clarifications and definitions. While today these views are no longer orthodoxy, they exerted an enormous influence in the way philosophy was, and in some ways continues, to be conducted.
The Deductive Nomological Model, heretofore DN, analyzes scientific explanation into two components: that which is to be explained, termed the explanandum, and that which does the explaining, termed the explanans. Respectively, these are analogues to conclusions and premises in logical arguments.
DN models explanation on formal proofs or deductive arguments. In a deductive argument, the conclusion is entailed by the premises if and only if the conclusion is valid. However, Hempel and Oppenheim recognized that deduction alone is a stringent criterion for explanation across all the sciences. As such, they adduced a cousin to the DN model, known as the Inductive-Statistical Model, heretofore IS, which models some explanations on inductive reasoning. Induction consists of inferring general patterns from a sample of observations. Unlike deduction, induction does not guarantee the truth of the conclusion. Instead, it provides degrees of evidentiary strength.
The DN model requires that a proper scientific explanation meet the criteria for a valid deductive inference. Meanwhile, the IS model must meet the criterion of cogency. Cogency applies to strong inductive arguments that provide good evidence for the conclusion.
DN further requires that the premises, namely the explanandum, contain at least one law of nature as a major premise. Even though an agreed-upon definition of law of nature eludes both science and philosophy, the broad consensus is that they must meet two requirements: they must not be accidental generalizations and they must not admit of exceptions. For example, the theory of Special and General Relativity posit that the luminal limit cannot exceed the velocity of ~ 300 000 km/s. If an observation violates this assumption, then the luminal limit would no longer qualify as a law of nature.
The last requirement is that the explanans must contain additional premises that in conjunction with the law(s) of nature entail the explanandum or conclusion. To take an example, if we wanted to explain the boiling point of a liquid, we would take the first and second laws of thermodynamics, namely the laws of the conservation of energy and entropy as the relevant laws of nature. Then we would add as premises the vapour pressure of the liquid, the surrounding atmospheric pressure, and the heat of vaporization for that liquid, which is the amount of energy required to transform a liquid into a gas. These laws and quantities should logically imply the explanandum, namely the boiling temperature. Therefore, given certain average environmental conditions, the intrinsic properties of the substance, and the relevant laws of physics, we can deduce the event in need of explanation.
We can further explain variations of boiling temperatures through either variations of atmospheric conditions or substance types. Despite these variations, we can see that the law that matter expands when heated under constant pressure provides a universal framework for explaining thermodynamic events at certain scales of interaction.
As we just saw, the intuitive force of the DN model is that a particular event requiring explanation can be subsumed under the truth of antecedent conditions and relevant generalized physical formalisms called laws of physics that play the role of exception-less regularities.
Nonetheless, as we hinted earlier, problems concerning the meaning of lawfulness in science beset the DN model. What do we make of generalizations that admit exceptions in the special sciences like biology, chemistry, psychology, and economics? By what criterion do we discriminate accidental generalizations from lawful or structural ones?
Hempel and Oppenheim, in fact, formulated two separate models to accommodate probable events: the Deductive-Statistical & the Inductive-Statistical models.
To see why they formulated two models, notice that the DN model is deterministic or at least strongly implies a deterministic view of nature. Determinism consists of the claim that the conjunction of all events until a particular point in time and the laws of nature entail one and only one possible future. Stated precisely:
D: Given a state description of the universe S0 at time T0 and a state description S1 at time T1 , at a very short time interval after, S0 entails S1.
The idea that certain phenomena can be deduced from available relevant information a la a deductive argument implies that the truth of the premises or the explanans could not have yielded another explanandum. This deterministic presumption that future events are entailed by prior ones, even given a sufficiently short interval, is highly contentious. At the very least, the probabilistic nature of quantum events frustrates the thesis of determinism.
The Deductive-Statistical model (DS) retains the structure of the DN model by adjoining at least one statistical law with relevant premises in order to derive the explanandum. It differs in that DS only permits the deduction of a narrower statistical uniformity from more general statistical laws.
Take, for example, the Central Limit Theorem (CLM) in statistics. The CLM states that as the sample size of the sample means gets larger, these tend toward a normal probability distribution. If we take CLM as the major premise and take as a minor premise a particular distribution of sample means (note: not random variables), we can deduce that the value of a particular sample mean will fall near the centre of the distribution or the mean of the sampling distribution itself. Basically, all this tells us is that assuming the empirical validity of the central limit theorem, values in a sampling distribution are less likely to be dispersed. While we can deduce the likelihood that a particular value will be less dispersed than a value from a population sample, we cannot know for certain that this will be the case.
The Inductive-Statistical model (IS), on the other hand, does not mandate an entailment relation between the explanans and the explanandum. Rather, the explanans only provides inductive support for the conclusion. IS explanations, therefore, do not evaluate in terms of the validity of the deductive inference and the truth-value of the premises, which jointly comprise soundness, but in terms of inductive or evidentiary strength. In Hempel’s model, a statistical generalization and a set of empirical facts justify inference to the explanandum with a high degree of probability. For example, if it is overwhelmingly the case that taking Tylenol relieves headaches, and I have a headache and I take Tylenol, these statements explain the fact that my headache was relieved.
A major problem with the IS model of explanation is that inductive arguments are vulnerable to erosion by additional premises. For example, if it is also a well-supported statistical generalization that Tylenol almost never relieves headaches for people with a certain physiological condition, then this additional statistical law would render the former explanation null. Erosion of inductive strength by additional premises is a structural vulnerability of inductive arguments in general. Conversely, deductive arguments are erosion proof, since additional premises cannot weaken an entailment relation between the premises and the conclusion (formally this is known as the monotonicity of entailment). In the case of a contradiction or inconsistency, the conclusion will still be trivially entailed.
To remedy the conclusion-erosion affordance of IS explanations, Hempel and Oppenheim formulated the requirement of maximal specificity (RMS), which stipulates that all available relevant information must be included in the explanans or premises of an IS explanation.
Despite these caveats, there are problematic examples that provide good reason to believe that DN & IS models fail to meet necessity and sufficiency conditions for scientific explanation. DN & IS fail the sufficiency requirement if we can provide examples that meet the DN & IS criteria but do not in fact suffice to explain the explanandum. Common examples are those that constitute valid deductions but do no explain the conclusion due to explanatory irrelevancies.
Consider the following:
i) All males who take birth control pill regularly fail to get pregnant
ii) John Smith is a male who has been taking birth control pill regularly
iii) Therefore, John Smith fails to get pregnant
Even though the above meets the DS criteria, it doesn’t explain why John Smith fails to get pregnant.
On the other hand, DN & IS fail to meet necessary conditions for scientific explanation if, in lieu of meeting their criteria, the explanandum still qualifies as a bonafide explanation. Here’s a crude example: The glass fell from the kitchen counter and shattered because my roommate’s elbow brushed against it unintentionally.
The DN/IS model proponent can take at least two lines of defense against such ordinary explanations:
a) they can claim that they do not qualify as scientific or
b) they can argue that in fact what explains the purported phenomenon is a hidden DN or IS structure, whereby a presupposition of law-like behaviour within such instances obtains that ought to be made explicit a la a covering law. In this case, something like the following is purportedly assumed: Whenever elbows and other limbs interact with sufficient force with discrete glass objects, given surrounding environmental conditions K, they shatter.
While there’s good reason to deny that this qualifies as the kind of scientific law that Hempel envisioned, what defeats these examples is reliance on vague event scopes or event conceptualizations. Newtonian laws along with the general properties of glass and initial conditions, for example, could be arranged in a DN argument to explain the phenomenon in question if we circumscribe the explanandum in more precise terms.
The upshot of the DN-IS models is that they try to explain or subsume events within nomic (meaning law-like) expectability. However, DN-IS models’ reliance on nomic expectability also belies a glaring exclusion of causality. Recourse to causal sequences, however, lies at the heart of the examples that DN-IS models fail to explanatorily satisfy. Most notably these include explanatory asymmetries and irrelevances. Therefore, even if we grant DN-IS models’ necessity conditions, they remain insufficient as models of scientific explanation because a crucial condition endogenous to the explanatory power of much of science is missing: supplying causal mechanisms as antecedents to effects requiring explanation.
Statistical Relevance Model
The Statistical Relevance Model of explanation, developed by Wesley Salmon in the early 1970s, seeks to remedy some of the problems we have already pointed out with the DN-IS models of scientific explanation. In particular, as the name suggests, this model attempts to capture explanatory relevance constraints in a way that DN-IS, as we saw, cannot.
The general idea is that statistically relevant properties are explanatory, whereas statistically irrelevant properties are not. We can express it this way:
P(B|A.C) ≠ P(B|A)
The probability of B given some class or population A and subclass C is not equal to the probability of B given A. In other words C is statistically relevant to the explanation of B precisely because it changes the probability of the outcome.
To make statistical relevance precise, Salmon employed the notion of a homogenous partition. A homogenous partition is the decomposition of class/population A into mutually exclusive and exhaustive classes A.Cᵢ such that:
P(B|A.Cᵢ) ≠ P(B|A.Cⱼ) for all Cᵢ≠Cⱼ
where no further relevant partitions can be made of A relative to B. For example if B stood for pregnancy, then Cᵢ and Cⱼ are exhaustive and mutually exclusive population subclasses, let’s say male and female (for the sake of simplicity — gender non-binary classes could also be included). If we further supplement another partition — D to account for taking or not taking the birth control pill, then P(B|A.Cᵢ.D) ≠ P(B|A.Cⱼ), given that Cᵢ = female & Cⱼ= male. In other words, D is explanatorily irrelevant to Cⱼ but explanatory relevant to Cᵢ relative to the probability of pregnancy B.
A key difference between the Statistical Relevance and the DN-IS accounts of explanation is that the former does not require explanations to be arguments, whereas the latter does. An upshot of the SR account is that irrelevancies are harmless to arguments, due to the monotonicity of entailment, but fatal to explanations.
Another important difference is that the SR account does not make a high-probability requirement for the explanandum like the IS model, wherein explanatory strength relies on the probabilistic link between the explanans and the explanandum. SR’s eschewal of the high-probability requirement makes it sufficiently flexible to account for quantum mechanical phenomena like radioactive decay and electron positions, which are intrinsically indeterministic. For example, the probability that an electron from my coffee cup is located on the moon is very low but not zero. The SR account can explain this possibility through a homogenous partition of relevant classes.
A weakness of the SR model is its presumption that the notion of statistical relevance adequately captures causal relationships. Further analysis shows that statistical relevance cannot discriminate, for example, between causal relationships where A jointly causes B and C and where A causes B, which causes C.
Causal-Mechanical Model
As we noted earlier, the SR model of scientific explanation fails to capture those relationships paradigmatically associated with satisfactory explanans ( explanation conferring relations), namely causal ones.
Salmon himself abandoned the SR model precisely due to this limitation, and developed an alternative that sought to remedy its shortcomings called the Causal Mechanical (CM) model.
The CM model and subsequent process theories of causation that are more sophisticated versions of the former aim to theorize scientific explanation around the notion of a causal mechanism. In some ways we all have a working understanding of the notion of cause, and plausibly this understanding is rooted in some cognitive modelling of the constraints that everyday objects of experience obey. A glass falls on the floor and shatters. A aircraft jets through the sky sufficiently low and we hear it breaking the sound barrier. When we press the power button, our laptop turns on and we resume our interaction with its graphic interface. Underlying all of these events lies a presumption of causal relationships. The jet has an engine that produces enough energy to propel it at high altitudes against the gravitational pull of the earth. The laptop has a battery and integrated circuitry programmed to convert our mechanical action of pressing into a sequence of steps that propel an electric current through the circuitry. All of these descriptions require theoretical knowledge that transcends mere experience. But in a very important way, they are consistent with a more basic notion of cause rooted in everyday experience absent any theoretical knowledge.
The CM model models scientific explanation precisely on the type of causal relationships we just described. While our ordinary notion of cause may be rooted in experience, the scientific notion of cause fits these observed regularities within a theoretical framework that refines and formalizes rule-based mechanisms that underlie observed events. Even so, it isn’t prima facie clear what a cause consists in at all, whether in the colloquial sense or in the more rigorous scientific sense when we posit forces and conserved properties like gravity, masses, momenta, velocities etc. The CM model then attempts to do just this: formalize the notion of a cause. It does so by distinguishing between causal processes and causal interactions. It defines a causal process as a process that transmits a mark in a spatiotemporally continuous way. A mark consists in a local modification to the structure of that process. For example, a a dent in the surface of a jet flying through the sky will be transmitted spatiotemporally because the movement of a jet constitutes a causal process. A causal interaction, meanwhile, consists of a spatiotemporal intersection of two causal processes that modifies the structure of both. If two jets collide, then each jet will come to have features that it would not in the absence of that interaction. Both the notion of a causal process and interaction, in this early formulation, rely on the notion of a counterfactual: both causal processes and interactions count as such in the absence of marks and interactions just in case that if either occurred, it nonetheless would induce the effects described.
Whether the distinction between causal processes and interactions can be generalized to more complex events at different scales, velocities, and energetic configurations, which are more germane to the processes that the sciences aim to explain, is not altogether clear. Notwithstanding the cogency of this distinction, the intuitive picture of this model of explanation is clear: we explain an effect (i.e. an explanandum) by recourse to the causal processes and interactions that produced it. In other words, we etiologically fit the explanandum into a causal nexus, which constitutes the explanans. Whether we’ve adequately characterized the causal nexus via the above distinctions is a matter for further debate.
A problem that beleaguered Hempel’s DN-S models, however, also crops up in the CM model: that of explanatory relevance. What property of the CM model allow it to discriminate causal features that are explanatorily relevant as opposed to ones that aren’t? In the case of Hume’s famous example of two billiard balls colliding, the CM model does not appear to be able to pick out masses and momenta as the explanatorily relevant features for the effect, namely the outcome of the collision. While mark transmission may be able to discriminate between genuine causal interactions from pseudo-causal ones, it does not appear to succeed in isolating explanatorily relevant properties. However, the problem of explanatory relevance does not seem to me to be fatal precisely because it can be epistemically finessed. Explanation always occurs against a background of assumptions both with respect to explicit theory and an agent’s broader cognitive context. As such, irrelevances are sorted out at the stage of individuating the relevant scale and complexity of events.
The CM model runs into deeper problems, however, when it comes to statistical descriptions and complex systems. At scales where it is impossible to describe the system in terms of individual particles or constituents, statistical descriptions and aggregate measures substitute description at the resolution of causal interaction. The thermodynamic properties of isolated systems are described in just such a way through statistical mechanics, which takes the average distribution of masses and velocities to describe the evolution of the system in time. The crux of the problem is captured by the discrepancy between aggregate effects of molecular motion that statistical mechanics aims to describe and the additive effects of each of the individual molecules. There is no way to arrive at the aggregate description by tracing the individual causal interactions. Aggregate effects can only be achieved by abstracting irrelevant particulars in favour of a macroscopic description.
The problem that statistical mechanics poses can then be generalized to further complex systems like ecologies, populations and economies. Explanation at the scale of biological as well as social phenomena do not appear to be prima facie explainable by recourse to strictly causal-mechanical processes. In what way, for example, is spatio-temporal continuity relevant to explain phenomena like money, inflation, recession, consumer confidence, group and population dynamics etc? In general, statistical descriptions are not causal but predicated on patterns. In the case of the phenomena in question like inflation and group dynamics, these are reliant on a complex hierarchy of patterns with varying degrees of interdependence. Ontologically, the assumption is that statistical descriptions are physically reducible to more fundamental causal interactions. Explanatorily, however, we cannot get the statistical description from the lower-level, say, causal description (though bear in mind that causality as mark transmission is problematic at subatomic scales). Furthermore, the possibility that novel causal powers emerge at different organizational scales ought to be given serious consideration. The invocation of causes qua causes as explanatory occurs at different levels of description. These considerations pose problems for versions of the CM model of explanation.
A more robust version of CM is the conserved process theory of causation, which identifies causation with the conservation of certain quantities like linear momentum and charge. Like its counterpart, this version of CM seeks to codify a cause at the level of physical interaction but without appeal to counterfactuals (hypothetical statements). The problem of explanatory relevance also beleaguers this attempt, since conservation laws are not explanatorily relevant to a great deal of higher-level phenomena. But, as already noted, relevance is an epistemic notion closely related to the economy of description. In a global sense causal-mechanical interactions are relevant to all phenomena, but are held ceteris paribus or constant when it comes to explanation.
Unificationist Model
The unificationist idea posits that explanatory success consists of a body of theory that unifies different ranges phenomena within the same explanatory framework. Unificationism might be more than just an intuitive standard for scientific explanation and the ambitions of science. The history of physics exhibits no dearth of examples where a new theory unifies phenomena previously thought to be distinct or incommensurable with each other.
This was the case with Newtonian mechanics, where two centuries of insights slowly chipping away at the ancient understanding of physics culminated with a new theory of motion that unified the celestial and terrestrial realms. Today, we take this achievement entirely for granted, but it was far from obvious to the ancients and even natural philosophers in Newton’s day. Aristotle, for example, believed that the cleavage of the celestial and terrestrial realms consisted of the interaction of pure, perfect and immutable substance composed of an element called the aether and imperfect and corruptible sublunar substance, composed of the four classical elements: earth, fire, air, and water. In the Aristotelian system, substance comprises the composite of unorganized or undifferentiated matter and its intrinsic organization, also called its form. Therefore, despite predicating substantiality to both the heavens and the earth, Aristotle believed that they obeyed different rules or laws of nature.
If we want to build a model of scientific explanation that takes unification as its core parameter, then we must formalize the notion of unification in order to distinguish genuinely explanatory forms of unification from non-explanation-conferring ones. For example, the notion of unification can be invoked in general classificatory schemas for natural kinds in biology, or mathematical formalisms whose applications range over a diverse set of problems like the Hamiltonian or Lagrangian that have applications in classical as well as quantum mechanics. Neither of these notions of unification fit the adequacy bill for scientific unification. The only explanation-conferring sense of unification appears to be the unification of disparate phenomena under some common mechanism as with Newton’s laws of motion or Maxwell’s laws of electromagnetism. Unlike purely mathematical unifications, mathematical formalisms of the latter type of unification describe some underlying physical mechanism. Just how we can distinguish generally applicable mathematical formalisms from formalisms that genuinely describe physical reality is a problem for the unificationist account.
Philip Kitcher attempted to formalize explanatory unification through the notion of an explanatory store E(K), where K stands for the set of beliefs accepted by science at a particular time and E the set of argument patterns that maximally unify K. Essentially, Kitcher’s account defines unification as the ability to derive as many descriptions of varied phenomena as possible from as few as possible restrictive argument patterns. To give an example, the generalization (A) that the speed of light is constant across all frames of reference is superior to the generalization (B) that the speed of light is constant across all frames of reference on earth. (A) permits more derivations than (B), and the inclusion of (B) complexifies the argument pattern without expanding the space of permissible derivations. An explanatory store along the lines of (A) should comprise as few argument patterns as possible while permitting the largest possible set of derivations to be maximally unified. Thus, unification is a standard that aims to derive as many explanations as possible from as few argument patterns as possible.
Kitcher’s account in many ways resuscitates the D-N model by theorizing unification as essentially deductive while avoiding the covering-law requirement. Furthermore, it collapses causation into unification by positing the latter as more basic than the former. Cause and effect therefore acquire intelligibility within the unification of phenomena under parsimonious generalizations. The question of the priority of explanation over causation and vice versa lies at the heart of the puzzle of scientific explanation. In some deep way, causation appears parasitic on unification because it presupposes the possibility of interaction and thereby some common set of principles that guide that interaction. On the other hand, explanatory unification appears to be parasitic on causation because unification cannot account for the causal asymmetry i.e. causes preceding effects — the essence of causation.
In fact, unification does not seem equipped to distinguish between predictive from retrodictive derivations. When we derive a future state from initial conditions and relevant physical laws we call it predictive, whereas when we derive the present state from future states and relevant laws we call it retrodictive. Retrodictive derivations are especially plausible with time-symmetric theories like Newtonian or quantum mechanics. The unificationist account cannot in principle distinguish between predictive and retrodictive explanations, even though only the latter canonically count as explanatory. We don’t explain the present with respect to the future, but with respect to the past. Staunch unificationists deny the fundamentality of the causal asymmetry since it is not a feature of the laws of physics as presently understood. Failing that, it appears dubious that unificationism can account for the causal asymmetry without axiomatically presupposing causality.
Another issue associated with the unificationist account of explanation concerns whether explanatoriness is fundamentally a matter of degree or all-or-nothing. If explanatory unification is a matter of degree, then it might prove too weak as an account of scientific explanation. On the other hand, if explanatory unification accrues only to the winner, then it is highly exclusionary. In the former account, all kinds of generalizations may be admitted as explanatory, like the gods of Homer. In the latter, theories like Newtonian mechanics will be deemed as lacking any explanatory power. Clearly, neither option on its own is desirable nor adequate to the use-cases that we want our account of explanation to satisfy. A desirable account should accommodate a continuum threshold: namely, rule out non-explanatory generalizations altogether, but admit of degrees of explanatoriness for theories that meet the threshold such that, for example, Newtonian mechanics is less explanatory than General Relativity. The unificationist account appears unable to accommodate both criteria.
Since unification seems to require the systematicity of knowledge, the question arises whether this systematization is carried out at the individual or collective level. Further analysis reveals that neither the community nor individuals possess fully systematized beliefs. Most individuals do not go about consciously ensuring that their beliefs are unified such that they’re deducible from the most parsimonious generalizations. On the other hand, if systematic knowledge is distributed across collectives, it remains unclear just how unified this knowledge is given that individual actors must contribute to the justification of its parts. While the epistemology of unification presents challenges for a robust theory of explanatory unification, such a robust theory presupposes something like ideal explanatory texts. Some form of less than ideal unification seems to be carried out socially, whereby communities of actors contribute rationally to different areas of knowledge and at the very least communicate to ensure their mutual consistency.
Another question worth probing is why unification appears to be a desirable standard at all, assuming that we can formalize it as a robust one. A crucial presupposition of the appeal of unification appears to be the presumption of the unity of nature: namely that for unification to be possible at all at the theoretical level, nature itself must (in some way be already unified) be governed by universal laws. However, framing it this way begs the question about universal laws: how can we know that nature is governed by universal laws rather than the laws being humanly constructed generalizations that encode empirical regularities. This question crystallizes into the debate between necessitarians and Humeans regarding the laws of nature, with the former deeming the laws of nature as necessary rules that govern causal interactions and the latter as mere regularities whose putative necessity is not epistemically accessible. Whichever side of the argument we take, the lawfulness of nature can to some extent be inferred from the success of our models, although their ultimate universality remains underdetermined. For example, exception-less regularities like the luminal speed limit is subject to the test of further evidence and the possibility is left open that it could be falsified. Plausible explanations for our bias for the universality of the natural laws could be cultural or rooted in evolved pattern recognition mechanisms. We should then be able to entertain the possibility that the expectation that the universe is governed by universal laws (or that these laws are formalizable by humans) may be erroneous. However, except for certain anomalous regions like black hole singularities and the big bang, it seems that in large part the universe submits to generalizable constraints. This gives credence to scientific realism, that is to say, to the view that our descriptions correspond to a mind-independent reality that behaves according to regularities and we have evolved tools to represent those regularities.
Our present inability to integrate gravity with the Standard Model, which describes all the known elementary particles and their interactions via the other three fundamental forces in a single mathematical framework may suggest that unification is either a misguided ideal or not possible. Perhaps there are no possible formalisms that can unify subatomic and macroscopic scales in a single descriptive framework simply because they are too disparate (we could also entertain genuine physical emergence, albeit a fringe view). Or it could be that there are missing ingredients in our account of quantum mechanics that prevents us from deriving gravitational interactions from it. At the same time it could also very well be that we will be able to achieve the unification of these two frameworks yet not make progress in our understanding of gravitational singularities or dark matter and energy.
A final question is whether the laws of nature are mutable or immutable. The presumption, again, is that physical science lifts invariances that are exception-less not only across space, but also across time. Multiverse proponents argue that different inflationary evolutions of the early universe would have instantiated different vacuum energy densities. And further that our particular configuration with low vacuum energy is statistically less likely than universes that have higher energy densities. A related question in physical science is what explains the physical constants like the intrinsic weights of elementary particles and whether there are stable configurations with variations thereof.
If we try to imagine laws of physics that mutate over time and under certain conditions, the human intellect cannot conceive that some variables, some substrate is not held constant against this variation. Therefore, it is rationally inconceivable that the laws could vary without anything being conserved or held ceteris paribus. Perhaps this is why the conservation laws are the most universal in physics — they capture the broadest possible invariances necessary for change to take place at all.
Explanatory Variety & Concluding Remarks
Like truth, explanatory sufficiency splinters along several dimensions that together exert mutual constraint on successful models. Truth cannot be exclusively correspondence or coherence, but rather an interplay of correspondence and coherence, much like electromagnetic waves radiate as oscillations in electric and magnetic fields, mutually regenerating each other.
Perhaps the failure of these models suggests that a unified model of scientific explanation may be the wrong approach to begin with, and that perhaps we ought to cede to a multiplicity of valid explanatory models.
Another alternative is that explanatory completeness is elusive precisely because science as a project is incomplete. Further, the possibility that science may in principle always remain incomplete has not been ruled out. If this is the case, the hope of developing a unified model of scientific explanation may also be inherently misguided.
However, even if we give credence to arguments for explanatory indeterminacy, we still ought to explore whether our intuitions about explanatory adequacy are rationally supported.
Both the Causal-Mechanical (CM) and Unificationist (U) models of scientific explanation, despite their individual shortcomings, are rooted in deep intuitions about explanatory adequacy and the motivations of science. Unificationism seeks to uncover universal laws, whereas the causal-mechanical model proceeds from the presumption of the discoverability of the mechanisms or constraints that govern phenomena. The former is top-down, while the latter bottom-up, and together may be thought of as analogues to top-down and bottom-up information processing, whose mutual constraints enable cognitive agents to navigate their environment. In some analogous sense then, scientific explanation perhaps ought to embody both the holistic constraints of unification and local mechanical constraints— which are, for better or worse, built on experiential intuitions.
In spite of all this, there’s a sense that ultimate explanations may forever remain elusive precisely because the explanatory buck can be pushed back indefinitely leading to an infinite regress. While the physical constants appear in some respects brute, the intellect entertains the possibility that their present fixed values may be so in virtue of something else — e.g. because of some symmetry-breaking event in the early universe. Whatever that something else turns out to be, it will serve as the explanans to these constants. If we were to somehow succeed in constructing a plausible account of how the constants came to have the values they have assuming variation is possible, it would not terminate the explanatory buck but push it back further since we would then have to also account for the causes of the constants. It seems to me that this kind of infinite regress could only be avoided with an overarching unified theory that is invariant across multiverses and all the possible variations of the constants, again assuming variation is possible.
Finally, there’s a tendency to mistake mathematical formalisms for reality. Formalisms are mere descriptions of phenomena, and in this respect, even if they affix concrete mind-independent referents, they always abstract a model of some mind-independent or mind-dependent phenomenon. The descriptive status of models is an open question, even though in some respects models must map the territory to yield reliable predictive success. A weakness of mathematical formalisms as models is that they can be made to fit the data in an ad-hoc way as is the case with the cosmological constant problem. As a result, predictive success, given any ad-hoc features, becomes estranged from its designative pretentions. As such, while formalisms track system variables with high accuracy, the ultimate nature of what they track may remain ultimately unknowable or epistemologically inaccessible. The concrete possibility must be entertained then that mathematical formalisms function primarily instrumentally, and cannot, in some cases even in principle, supply ultimate descriptions.
