The Triptychs of Publius

Introduction: The Philosophical Value of Near Misses

One of Aristotle’s characteristic philosophical practices is to distinguish a genuine phenomenon from things that closely resemble it but fail to possess its defining character. Their resemblance makes them philosophically useful: Aristotle can explain why they fall short, and those explanations tell us something positive about the genuine phenomenon.

In Nicomachean Ethics III.8, Aristotle distinguishes courage from five apparent forms: political courage, experience, spirit, optimism, and ignorance. Each can produce outward steadfastness in danger, but none of these explanations alone establishes the virtue. The failures are diagnostic.

I call the procedure of reconstructing positive explanatory conditions from Aristotle’s diagnoses of apparent instances Aristotelian inversion. This essay develops it through courage, then tests it against expertise in the Metaphysics, plot in the Poetics, constitutional rule and wealth acquisition in the Politics. The claim is not that Aristotle explicitly codified this named method, but that his arguments often permit this constructive reconstruction.

The Method of Aristotelian Inversion

The method has five stages: (1) identify the target phenomenon; (2) identify near misses that reproduce significant features of it; (3) reconstruct Aristotle’s reasons for their insufficiency; (4) invert each diagnosis into a candidate positive explanatory condition; and (5) integrate and validate those conditions against Aristotle’s affirmative account and further arguments.

Near misses come in at least three forms. Counterfeits resemble a genuine phenomenon without possessing it, as when ignorance of danger looks like courage. Partial approximations display something important but lack the governing principle, as when honor motivates steadfastness. Insufficient constituents or explanatory substitutes genuinely belong to a larger phenomenon without explaining its characteristic achievement, as spectacle belongs to tragedy but does not replace plot.

The distinction matters. Inversion does not infer that every feature absent from a failed case is necessary. Its evidence is Aristotle’s reason for the failure. Nor does inversion automatically prove necessity or sufficiency: it discovers candidate explanatory conditions requiring independent validation.

Counterfactual tests can help isolate the relevant explanation. Remove honor, reassurance, spectacle, or private advantage and ask what remains. But the invariant is not necessarily behavior: it may be a governing reason, understanding, organization, or end.

Courage: The Paradigm of Inversion

In Nicomachean Ethics III.6–7, Aristotle characterizes courage as the appropriate confrontation of fearful dangers, especially death in battle, for the sake of the fine (to kalon). In III.8 he distinguishes five approximations (1115a6–1117a29).

Political courage: A soldier may stand firm for honor or to avoid shame. Inversion: genuine courage must be governed by the fine, not merely by recognition.

Experience: Veterans may stand firm because their expertise makes the danger appear manageable. Inversion: courage cannot be reduced to confidence arising from tactical superiority.

Spirit: Anger can propel an agent into danger. Inversion: courage requires appropriately reasoned choice rather than emotional impetus alone.

Optimism: Repeated victories can generate expectations of success. Inversion: courage does not depend upon expecting a favorable outcome.

Ignorance: Someone may appear fearless because the danger is not understood. Inversion: courage involves appropriately knowing what one confronts.

Together these diagnoses suggest a stable disposition to confront appropriate dangers knowingly, through rationally governed choice, for the sake of the fine. Honor, expertise, spirit, and confidence can support courage; they do not independently constitute its governing explanation.

The counterfactual test asks whether the agent would still choose the appropriate courageous action without the contingent supports. It does not require identical behavior when circumstances change. Retreat may be right when a tactical position becomes indefensible. The final stand at Thermopylae illustrates the distinction between knowingly accepting mortal danger for a worthwhile purpose and merely courting death; its historical motives and strategic necessity cannot simply be assumed.

The five approximations do more than mark courage’s boundaries. Their diagnosed insufficiencies disclose positive aspects of its structure (see also NE II.4, 1105a28–b9; II.6, 1106b36–1107a2).

Expertise: Experience and Understanding in the Metaphysics

In Metaphysics A.1 (980b25–981b10), Aristotle distinguishes experience (empeiria) from art or expertise (technē). The experienced practitioner may achieve the same results, even sometimes outperforming a person who has theory but lacks acquaintance with particulars. Successful performance alone therefore does not establish expertise.

The crucial diagnosis is explanatory: experience knows that something works, whereas art grasps why, through a general account of causes. The near miss is successful practice without the understanding characteristic of technē.

Inversion: genuine expertise must involve organized explanatory understanding that guides productive activity. A reconstructed characterization is: Technē is an organized capacity grounded in general explanatory understanding, enabling its possessor to account for and appropriately direct productive activity.

Suppose a familiar treatment ceases to work in changed circumstances. The expert can potentially identify the causally relevant difference and adjust; the merely experienced practitioner may rely on an association. This is diagnostic, not infallible: experts err, and experienced practitioners adapt. The lesson is that the capacity to produce an outcome does not itself establish understanding of its cause.

Tragedy: Spectacle and Plot in the Poetics

In Poetics 6 (1449b24–1450b20), Aristotle distinguishes plot, character, thought, diction, song, and spectacle, while giving priority to plot (mythos), the arrangement of incidents. A production can excite its audience with music, acting, and scenery without possessing an excellent tragic plot.

Here spectacle is not a counterfeit: it is a genuine component of tragedy. The mistake is to treat its effects as an adequate substitute for the organization of action. Aristotle’s diagnosis points to the explanatory priority of plot.

Inversion: a well-formed tragic plot is a unified organization of represented action whose connected incidents produce the characteristic intelligibility and emotional power of tragedy.

Remove the theatrical embellishments: can the sequence of events still sustain a tragic response? Preserve the embellishments but disconnect the incidents: does tragic coherence remain? These variations help isolate plot’s contribution. Plot is not the entirety of tragedy, but it principally explains the work’s characteristic organization.

Constitutional Rule: Authority and the Common Advantage

In Politics III.6–7 (1278b–1279b), Aristotle distinguishes correct from deviant constitutions by their governing end. Rule by one, a few, or many can be correct or deviant; the decisive contrast is between the common advantage and the rulers’ private advantage.

A regime may efficiently administer laws, collect revenues, and maintain order while serving only its rulers. Operational effectiveness is therefore insufficient for constitutional correctness.

Inversion: a correct constitution is an ordering of political authority directed toward the common advantage rather than the private advantage of those exercising power.

The diagnostic counterfactual asks what happens when the interests of rulers conflict with those of the community. Which interests govern the decision? Merely professing the common good is insufficient, since rulers may misunderstand it. This application largely reconstructs Aristotle’s explicit criterion rather than discovering a hidden definition; it shows why effectiveness alone cannot explain correct political rule.

Wealth Acquisition: Instruments Mistaken for Ends

In Politics I.8–10 (1256a–1258b), Aristotle distinguishes acquiring resources for household life from wealth acquisition that treats accumulation as unlimited. Both may involve trade, saving, and increasing possessions. Their governing ends differ.

The near miss becomes visible when increasing wealth undermines the goods that make wealth worth possessing: health, friendship, education, leisure, and household flourishing. An activity can succeed by its immediate metric while failing by the end that justifies it.

Inversion: proper household acquisition is the procurement and management of resources as instruments subordinate to the activities and goods of household life.

If further wealth ceased to support these goods, would the agent continue accumulating without limit? That counterfactual tests whether means have displaced ends. It does not imply that all commerce or additional wealth is bad. The central insight is that an instrument can be maximized in a way that defeats the purpose for which it is valuable. This is also a general problem for theories of rational choice and instrumental optimization.

Discovery, Demonstration, and Aristotelian Method

In Topics I.1–2 (100a18–101b4), Aristotle describes dialectic as reasoning from reputable opinions (endoxa) and discusses its philosophical usefulness, including inquiry into first principles. In Nicomachean Ethics VII.1 (1145b2–7), he describes setting out appearances (phainomena), working through puzzles (aporiai), and preserving the reputable judgments that survive examination. Metaphysics B.1 (995a24–b4) likewise emphasizes the importance of articulating difficulties.

Inversion can be situated within this broader investigative setting without being equated with dialectic or attributed to Aristotle as an explicitly named procedure. It focuses on a specific constructive operation: using Aristotle’s reasons for rejecting near misses to formulate positive explanatory requirements.

Posterior Analytics I.2 (71b9–72a5) emphasizes scientific understanding through causes, while II.3–10 (90a–94a) investigates the relation between definition and explanation. The distinction can be stated interpretively: demonstration proceeds from explanatory principles to what they explain; inversion works from apparent instances and diagnosed insufficiencies toward candidate explanatory principles. This is not Aristotle’s own formal division. Inversion contributes to discovery and refinement, not automatic demonstration of necessity.

Metaphysics Z.4–6 and Z.17 (1029b–1032a; 1041a6–b33) connect questions about what a thing is with explanatory inquiry. But virtue, expertise, tragedy, political correctness, and acquisition need not share one identical metaphysical structure. The unity of inversion is procedural rather than a claim that all five subjects have the same kind of essence.

The scholarly setting includes G. E. L. Owen on appearances, Terence Irwin on dialectic and first principles, Jonathan Barnes on demonstration, and David Charles on definition and essence. These scholars differ, and the relationship between the Topics and ethical methodology is disputed. Inversion is proposed as a narrower interpretive procedure within that larger debate.

Objection: Is Inversion Merely Counterexample Analysis?

Philosophers routinely revise definitions in response to counterexamples. Why name this procedure?

The objection has force. Inversion is not an entirely independent logic, and ordinary conceptual analysis may employ its operations. Yet it identifies a specific, repeatable sequence. A counterexample may establish only that an account fails. Inversion requires a reasoned diagnosis of why a near case fails, and then uses that explanation constructively to propose positive explanatory conditions.

A structured set of near misses is particularly revealing: each can isolate a different deficiency, and their combined diagnoses progressively constrain the positive account. The five apparent forms of courage illustrate this especially clearly. The value of naming inversion lies in making that analytical operation explicit and portable across Aristotelian inquiries, not in claiming that no philosopher has ever reasoned in this way.

Conclusion: From Near Misses to Genuine Understanding

Courageous-looking steadfastness can arise without courage; successful practice without expertise; emotional stimulation without excellent tragic plot; effective administration without correct political rule; and increased wealth without successful household management.

In each case, Aristotle identifies something associated with the genuine phenomenon and explains why that association is insufficient. The explanation becomes philosophically productive. Its inversion suggests a positive condition that an adequate account must accommodate.

The procedure does not replace further argument and does not guarantee that every failed instance reveals a necessary condition. Its power depends on the quality of the diagnosis and validation against Aristotle’s positive account.

When Aristotle explains why something that resembles a phenomenon is not genuinely that phenomenon, he often provides the materials from which we can reconstruct what the genuine phenomenon must be.

The near miss, properly understood, becomes a route to the genuine.

Notes and References

1. Aristotle, Nicomachean Ethics III.6–8, 1115a6–1117a29.
2. NE II.4, 1105a28–b9; II.6, 1106b36–1107a2; III.7, on choice and the fine.
3. Aristotle, Metaphysics A.1, 980b25–981b10.
4. Aristotle, Poetics 6, 1449b24–1450b20.
5. Aristotle, Politics III.6–7, 1278b–1279b.
6. Aristotle, Politics I.8–10, 1256a–1258b.
7. Aristotle, Topics I.1–2, 100a18–101b4; Terence Irwin, Aristotle’s First Principles (Oxford: Clarendon Press, 1988).
8. Aristotle, NE VII.1, 1145b2–7; Metaphysics B.1, 995a24–b4; G. E. L. Owen, “Tithenai ta phainomena,” in Aristote et les problèmes de méthode, ed. Suzanne Mansion (Louvain, 1961), 83–103.
9. Aristotle, Posterior Analytics I.2, 71b9–72a5; II.3–10, 90a–94a; Jonathan Barnes, Aristotle: Posterior Analytics, 2nd ed. (Oxford: Clarendon Press, 1994).
10. Aristotle, Metaphysics Z.4–6 and Z.17; David Charles, Aristotle on Meaning and Essence (Oxford: Clarendon Press, 2000).
11. For debate about Aristotelian ethical method, see Daniel Devereux, “Ethical Method in Aristotle: A Comparison of the Eudemian and Nicomachean Ethics,” Oxford Studies in Ancient Philosophy 3 (1985): 127–152. Secondary references should be checked against full editions before formal journal submission.