With this groundwork in place, it is now possible to introduce the shared properties of explanation and argue that, for each such property, there is an analogous, counterpart property of justification. This correspondence will then serve as the basis for an inductive inference presented in Sect. 6. None of the posited properties is essential to the argument (though the “autonomous facts” subsection will be referenced later), so if one posited property is judged to be excessively controversial, it can be discarded without abandoning the conclusion about egalitarianism defended below. Thus, one must merely grant that enough of the posited properties (a) obtain and (b) have justificatory analogs to warrant an inductive inference from additional posited properties of explanation to analogous properties of justification.
Consider, then, the following proposed properties of explanations and justifications:
Acts and objects
Above, explanations have been described as “semantic objects”; however, as Sylvain Bromberger has noted, the term “explanation” is actually ambiguous, referring sometimes to an act of explaining (what he calls the “performance sense” of the word), or, alternatively the propositional content expressed in these speech acts (the “text sense”), with the latter being the semantic objects mentioned above.Footnote 30 Taking the latter as the primary objects of inquiry (though both kinds of explanation will be discussed below), one can then say that explanations have the property of being expressed by a particular variety of act, where both such acts and associated semantic objects share a referring term.Footnote 31
Additionally, it is often said that facts or things (of the non-semantic variety) explain other facts or things.Footnote 32 For example, just as one might say that the theory of gravity explains why objects adhere to the Earth’s surface, one might also say that the fact of the Earth’s massiveness explains the observed phenomenon. This relationship between linguistic practice, explanations qua semantic objects, and the objects referred to by those explanations is another distinctive property of explanation.Footnote 33
Analogously, the term “justification” is ambiguous, referring alternately to a particular kind of act as well as the semantic content expressed by that act. Thus, justifications can also be said to have the property of being expressed by counterpart acts, where both acts and semantic objects share a referring term. Additionally, people often speak as though facts or objects justify other facts or things (e.g., “we are doing things this way because you agreed to it!”). Given this, explanation and justification are analogous in that their referring terms are used in analogous ways.
A second property of explanations is that explanatory acts are things that can be completed (as opposed to merely halted). Indeed, as Bromberger has noted “to explain” is an accomplishment term with distinctive semantic properties indicating the completable nature of the act to which it refers.Footnote 34 Specifically, such terms can naturally be used in sentences of the form “How long did it take for P to ϕ?”—with the relevant contrast being activity terms, which are used in questions of the form “How long did P ϕ?”.Footnote 35
Similarly, justificatory acts are things that can be completed, making the associated verb “to justify” an accomplishment term. Indeed, just as one might ask how long it took someone to explain some state of affairs, one might similarly ask how long it took someone to justify some state of affairs—with the question “How long did P justify X?” seeming malformed in just the same way as does the question “How long did P explain X?”.
In their classic work on scientific explanation, Carl Hempel and Paul Oppenheim argue that the relationship between explanans and explanandum is one of logical deduction where the explanans is a set of premises that, together, logically entail the explanandum (which refers to the fact to be explained).Footnote 36 Additionally, they argue that, for a set of premises to count as the explanation of the conclusion, there must be at least one of the premises that is both a law of nature and essential to the argument such that, if it were removed, the argument would be invalid—with this requirement making their theory a deductive-nomological theory of explanation, as opposed to a merely deductive one. For example, the explanation of why a sample of gas expands is that (1) if something is a gas, then it will expand if its temperature is increased and its pressure remains constant; (2) the temperature of the gas is increased; and (3) the pressure of the gas remains constant. Here, because premise 1 is an essential premise that is also a law of nature—and premises 1–3 jointly entail the conclusion that the gas expands—the set of premises 1–3 is the explanation of why the gas expands.Footnote 37
There is much debate over what, exactly counts as a law of nature, with little agreement in the literature over how the notion should be analyzed.Footnote 38 However, very roughly, Hempel and Oppenheim’s motivating thought seems to be that laws of nature are universal generalizations that are sufficiently syntactically simple—where syntactic simplicity is inversely proportionate to the number of exceptions to the generalization.Footnote 39
Insofar as one is willing to work with this rough-but-intuitive notion, an analogous property of justifications seems to obtain, as justifications also take the form of deductions featuring an essential, law-like premise. For example, a pescatarian attempting to justify the permissibility of eating fish might argue that (1) if a species of animal does not feel pain, then it is permissible to eat members of that species and (2) fish do not feel pain.Footnote 40 Here, premises 1 and 2, together, function as a justification for the deduced conclusion that eating fish is permissible, where premise 1 is also a law-like universal generalization that is essential to the validity of the inference (again, using the rough, intuitive sense of what counts as law-like). Generalizing from this example, a plausible thought is that justifications necessarily take the form of arguments resting on some sort of normative principle—where such principles are the justificatory analog for laws of nature. Thus, both explanations and justifications have the property of being nomological deductions of that which they explain/justify.Footnote 41
Ellipticity and partialness
Given a conception of explanation as deductive argument, two additional properties of explanation noted by Carl Hempel can be posited. First, the explanatory speech acts in which explanations qua semantic objects are expressed rarely present the entire argument that composes the explanation; rather, they are elliptically formulated such that various premises are left unstated.Footnote 42 Putting this more strongly, it might be suggested that such formulations are not just put forward as a matter of empirical fact, but are also acceptable in some normative sense left deliberately undeveloped here.
Analogously, acts of justification are also frequently elliptically formulated, with many premises left unstated. For example, a pescatarian justifying why she is willing to eat fish might simply say, “because fish do not feel pain,” without presenting the entire deduction presented above. And, insofar as one is willing to grant the stronger normative claim posited in the final sentence of the previous paragraph, it seems the same could be said of justifications that are elliptically formulated.
Second, Hempel notes that many explanations for some state of affairs are partial in that they do not actually entail the explanandum, but, rather, that the referent of the explanandum will fall into some particular category.Footnote 43 For example, he cites Freud’s explanation that an erroneous calendar entry occurred because people tend to make mistakes that reflect their subconscious desires. In this case, the argument fails to deduce the specific error Freud made, as it is but one of the many things that reflect his subconscious desires.Footnote 44
Similarly, justifications can be partial in this way. For example, socialists who opt to form a non-capitalist commune might justify this choice by citing various purported harms of capitalism; however, the underlying argument might entail only that they ought to live in some non-capitalist fashion, without demonstrating that they ought to live in the particular fashion that they have chosen. Thus, an additional property of both explanation and justification is that both sorts of objects can and do take partial and elliptical forms in their expression.
Bas Van Fraassen has noted that the fact that a theory explains some phenomenon is generally taken to be a fact that counts in favor of accepting the theory.Footnote 45 However, this entails that a theory can explain a fact even prior to it being accepted as correct (or, perhaps, merely adequate).Footnote 46 Similarly, the fact that some normative theory justifies permitting or restricting a behavior that is pre-theoretically taken to warrant permitting or restricting is generally taken to count in favor of accepting the theory. Thus, both explanations and justifications have the property of (a) counting in favor of theory acceptance and (b) standing in an explanatory/justificatory relation to some proposition even prior to their acceptance.Footnote 47
One popular view is that explanations function as answers to why-questions. If one asks why an event occurred or a thing exists in the way that it does, the appropriate response would be an explanation. Indeed, Hempel and Oppenheim’s paper opens with the observation that “To explain the phenomena in the world of our experience” is “to answer the question of ‘why?’ rather than only the question ‘what?’” (1948).
The exact relation between explanations and why-questions is disputed. Bromberger argues that the answer to the why-question is simply part of the deductive-nomological argument that is an explanation, with there sometimes being multiple correct answers that can be selected from within that argument.Footnote 48 For example, the answer to the question of why a floating piece of ice does not raise the water level might simply be that ice has the same density as water—even though this is but one premise among many in a Hempelian deduction.Footnote 49 Alternatively, Bas Van Fraassen takes the answer to a why-question to be, itself, an explanation as opposed to a mere part of an explanation, (where this identification of answers and explanations is part of his broader pragmatic, question-based approach to theorizing about explanation and its role in science).Footnote 50
Fortunately, this disagreement need not be resolved here, as it is possible to posit a substantive property of explanation vis-à-vis its relation to why-questions while remaining agnostic with respect to the exact nature of that relation. Specifically, it can be maintained that an additional property of explanation is that, for any given explanation, a certain subset (note: not a proper subset) of its premises is the answer to a corresponding why-question.Footnote 51
Here, again, there is a corresponding property of justification that is analogous to this property of explanation. Specifically, note that justifications are also answers to why-questions. The pescatarian provides a justification in response to questions like, “Why don’t you eat steak?” (from a curious stranger); “Why can’t we eat meat?” (from her child); or “Why shouldn’t I eat meat?” (from a challenger). Further, when she replies, “Because it’s wrong to consume creatures that suffer in the process,” that response might be thought to be either a complete justification or a part of a justification; however, on either account it would still be true that, for any given justification, some subset of its premises is the answer to a corresponding why-question.
Another property of explanation is that there is an asymmetry in the direction of explanation such that, while explanans E explains some fact F, the description of F cannot explain any of the facts whose descriptions compose E. In a critical discussion of the issue, Bas Van Fraassen provides a number of examples of this asymmetry: propositions describing the movement of galaxies explain the red shift in the light received from those galaxies, but a description of the red shift cannot explain their movement; a description of changes in the weather can explain the behavior of a barometer, but a description of that behavior cannot explain the weather; and a description of the size and shape of a flagpole can explain the shape of its shadow, but the description of the shadow cannot explain the flagpole’s shape and size.Footnote 52
Similarly, there is a directional asymmetry between justifications and their objects. For example, the fact that a person skips family game night to get dinner with a friend might be justified by the proposition that she promised the friend that she would. However, the choice to make this promise cannot be justified by appealing to the proposition that she skips family game night to get dinner. Thus, the analogy between explanation and justification persists.
An additional property of explanations is that, under the right conditions, their expression brings about a state of understanding for the audience of the explanatory act. This claim is perhaps most explicit in Robert C. Matthews’ pragmatic account of explanation wherein explanations qua semantic objects are defined in terms of their disposition to bring about understanding when conveyed to an audience.Footnote 53
A similar account is provided by Bromberger, who introduces the dual notions of p-predicaments—cognitive states that obtain when people have a question to which they can think of no answer that is not ruled out by their prior beliefs—and b-predicaments, which obtain when people have a why-question but lack the capacity to come up with the correct answer to that question.Footnote 54 To lack understanding, he suggests, is, roughly, to be in one of these predicaments.Footnote 55 Acts of explaining attempt to resolve b- and p-predicaments via the provision of relevant information.Footnote 56 To do this, the explainer might have to furnish the audience with novel concepts with which the latter was not previously familiar and/or correct the audience’s prior false beliefs that conflicted with the correct answer.Footnote 57
Similarly, in his discussion of philosophical explanations, Robert Nozick suggests that explanation is a subset of the kinds of acts that increase understanding.Footnote 58 Specifically, he suggests that philosophical explanations provide such understanding by demonstrating that, contrary to what the audience previously believed, their prior commitments do not imply the negation of some proposition—with this demonstration being an explanation of the possibility of that proposition.Footnote 59 Additionally, an audience can be brought to understand how a proposition could be true by demonstrating how it can be deduced from plausible premises.Footnote 60
Here, again, an analogous relation can be shown to obtain between justification and understanding. Note, first, that justifications bring about a state of understanding, with this achievement revealed by the common locutions that accompany the delivery of such justifications. For example, a person who demands justification and receives a satisfactory one will often say, “I understand,” or “That makes sense,” to indicate that no further information need be conveyed.
Further, the means by which justifications bring about this understanding seem identical to those described immediately above. First, note that those who demand justifications via a why-question appear equally to be in a p- or b-predicament in that they are unable to conceptualize the correct answer to the question and/or posit an answer that does not conflict with prior beliefs. Justifications, then, resolve these predicaments via either the provision of novel concepts (e.g., normative notions) or correction of false beliefs (either empirical or normative) that generate a contradiction with the proposition to be justified. Or, alternatively, one might follow Nozick by showing how already-held beliefs do not, in fact, contradict the justificandum. Thus, not only do successful justifications have the property of bringing about states of understanding, they bring about understanding in the same way that explanations bring about understanding.
Another posited property of explanation is that there are certain limits to what can be explained. Or, to put this point another way, there is a certain set of facts such that, for any given explanation, no member of the set is the object of that explanation.Footnote 61 Specifically, these facts don’t seem apt for explanation, with any demand for an explanation revealing some sort of conceptual confusion on the part of the asker. Shamik Dasgupta, for example, proposes the analogy of a person who demands a mathematical proof of a definition within a particular mathematical system.Footnote 62 As Dasgupta notes, to demand a proof of a mathematical definition betrays a failure to grasp the nature of mathematical definitions and proofs, as a satisfactory understanding of those notions would make it sufficiently clear that such definitions are simply not apt for proof.Footnote 63 His suggestion, then, is that there are also certain facts such that a demand for explanation of those facts would betray a failure to fully understand the relevant concepts involved (e.g., the fact that water is made up of H2O).Footnote 64
Analogously, there are certain actions or states of affairs that seem similarly inapt for justification, with any request for a corresponding justificans betraying some sort of conceptual confusion. For example, a person who demands why one ought to do that which is morally obligatory betrays a failure to grasp the relevant normative notions in the same way that a person who asks why water is made up of H2O betrays a failure to grasp the relevant metaphysical notions.
As Nozick notes, explanation is irreflexive in the sense that the explanans cannot be identical to the explanandum, with “explanations of the form ‘p because p’ [being] inadequate and unsatisfactory.”Footnote 65 Similarly, the property of irreflexivity is shared by justification, where any justificans that is identical to its justificandum is unsatisfactory.
A closely related (potentially identical) property of explanation is that one proposition can only explain another if there is adequate explanatory distance between them.Footnote 66 In a helpful explication of the notion, Elanor Taylor presents two paradigmatic cases of purported explanations that are unacceptable due to a lack of explanatory distance.Footnote 67 First, there is the case of opium’s “dormitive virtue” being posited as an explanation of why the drug tends to make people fall asleep.Footnote 68 And, second, there is the case where a person attempts to explain some medical symptom R by citing syndrome S, where that syndrome is defined strictly in terms of observed symptoms, P, Q, and R.Footnote 69 While Taylor proposes a necessary and sufficient condition of acceptable explanatory distance obtaining, one can remain agnostic on this point and merely hold that a property of all explanations is that they are appropriately distant from their explananda—with distance then construed in accordance with one’s preferred account.
Similarly, all justifications appear to have the property of being sufficiently distant from that which they justify. To mirror the syndrome case, for example, note that one cannot justify why some particular property rights scheme R should obtain by positing that society type S should obtain, where S is defined in terms of imposed rights schemes P, Q, and R. Thus, the property of explanatory distance also has a justificatory analog.
The final property of explanation to be discussed here is that explanations take a contrastive form.Footnote 70 There are a few different accounts of this contrastivity, but the core idea is, again, best conveyed by example: in explaining why geese migrate south as winter sets in, one might explain either (a) why geese migrate south as winter sets in (as opposed to robins); (b) why geese migrate south as winter sets in (as opposed to north); or (c) why geese migrate south as winter sets in (as opposed to summer). The general thought, then, is that there can be different explanations of the same fact, with each explanation corresponding to a distinct contrast case.Footnote 71
Van Fraassen puts this point in question-centric terms, suggesting that any why-question is identical with a triple consisting of (1) a proposition to be explained, (2) a contrast class of rival propositions (which includes the explanandum), and (3) a relation of explanatory relevance which helps to settle what counts as an explanation—where 2 and 3 are both determined by context.Footnote 72 Because he takes explanations to be answers to why-questions, it follows that the same explanandum can have multiple explanantia, with distinct explanantia corresponding to distinct contrast classes.
Alternatively, Peter Lipton puts things in terms of facts and foils, where the same fact might have many different foils and many distinct explanations, with each explanation corresponding to a different foil.Footnote 73 Specifically, he suggests that a fact is explained relative to a foil by citing some event that caused the fact where this event lacks “a corresponding event in the history of” the foil not obtaining.Footnote 74 For example, if both Kate and Frank submit an essay to a contest, Kate’s act of submitting cannot explain why she wins, as there is the same corresponding event in the history of Frank not winning the contest (the foil being Frank winning the contest); by contrast, the fact that Kate wrote the best essay explains why she won, as there is no corresponding event in the history of Frank not winning.Footnote 75
Unfortunately, Lipton states his account in causal terms that make it inapplicable to non-causal varieties of explanation. However, it can, perhaps, be made more general by restating the account in terms of dependence: a fact is explained relative to a foil by citing some sub-fact upon which the fact depends, where there is no corresponding sub-fact upon which the negation of the foil depends. For example, in Lipton’s case of a group of sticks tossed spinning in the air, one would explain why more ended up near the horizontal axis—as opposed to the vertical axis—by appealing to the fact that there are more ways for a stick to be horizontal than to be vertical.Footnote 76 The thought here is that the statistical fact about the position of the sticks depends in some sense on the geometric fact about the possible orientations of a line in three-dimensional space. Additionally, this speculative account would posit that there is no corresponding geometric fact (e.g., that there are more ways for a line to be vertical than horizontal) upon which the negated foil depends. Thus, the original geometric fact would explain why most sticks end up near horizontal, as opposed to near vertical.
Justification, too, is contrastive. Consider, for example, one parent who demands the other justify why their elder child, Anne, should get a car for Christmas. In justifying this (normative) fact, one might justify either (1) why Anne should get a car for Christmas (as opposed to her sibling); (2) why Anne should get a car for Christmas (as opposed to a bicycle); or why Anne should get a car for Christmas (as opposed to her birthday). Given that 1–3 will each call for a distinct justification, justification is contrastive in just the way explanation is.
Further, the apparent details of contrastive justification are analogous to the speculative generalization of Lipton’s account presented immediately above. To justify why Anne—as opposed to her sibling should get the car—one might note that only Anne is old enough to legally drive. Further, note that the truth of the proposition that Anne should get the car depends on this fact, and there is no corresponding fact (e.g., that her sibling is old enough to drive) upon which the negation of the foil (i.e., that the sibling should not receive a car) depends. Thus, in addition to justification being generally contrastive, the specific contrastive property of explanation posited by Lipton seems to have a justificatory analog.
Admittedly this proposal is a bit underdeveloped, as developing a complete theory of non-causal contrastive explanation goes beyond the scope of this paper. However, the hope is the above analysis provides reason for thinking that the analogy will persist even as additional details regarding the contrastive character of explanation are filled in.