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Difference-Making without Making a Difference

The paper argues that Andreas & Günther's latest definition of actual causation collapses their proposed distinctions between factual, counterfactual, and regularity-based accounts, and further demonstrates that all seven of their definitions fail when applied to crucial examples.

Original authors: Sander Beckers

Published 2026-06-24

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Sander Beckers

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine a group of philosophers (Andreas and Günther, or "AG" for short) who have spent years trying to build the ultimate "Causality Detector." Over seven different papers, they built seven different versions of this detector. They claimed each new version was a major upgrade, fixing the flaws of the last one. They also claimed these versions belonged to three completely different "schools of thought" about how causes work:

Factual Difference-Making: Did the event actually change the outcome?
Counterfactual Difference-Making: Would the outcome have been different if the event hadn't happened?
Regularity: Did the event follow a consistent pattern?

In their latest paper, AG introduced their newest detector (AG7), claiming it was a "Factual" detector that was superior to the others and didn't rely on the messy "what-if" thinking of the "Counterfactual" school.

Sander Beckers, the author of this paper, walks in and says: "Hold on a minute. You haven't built anything new, and you haven't fixed anything. In fact, your whole classification system is a house of cards."

Here is the breakdown of Beckers' argument using simple analogies:

1. The "New" Detector is Just an Old One in a New Coat

AG claims their newest definition (AG7) is a unique "Factual" approach. Beckers shows that mathematically, AG7 is identical to one of their older definitions (AG5).

The Analogy: Imagine AG built a red car (AG5) and claimed it was a "Speed Machine." Then, they painted it blue, added a spoiler, and called it a "Factual Speed Machine" (AG7), insisting it was a totally different vehicle. Beckers opens the hood and says, "It's the exact same engine, chassis, and transmission. You just changed the paint job."
The Result: AG's claim that they have a new, distinct type of account is false. They are essentially the same machine.

2. The "Schools of Thought" Are Actually the Same Class

AG argued that their "Factual" and "Regularity" detectors were fundamentally different from the "Counterfactual" (what-if) detectors used by other famous philosophers. They said their new method didn't need to ask "What if?" questions.

Beckers proves that AG's "Factual" detector can be rewritten as a "Counterfactual" detector.

The Analogy: AG claims they invented a "Non-Gravity" elevator that works without cables. Beckers demonstrates that if you look at the math, their elevator is actually just a standard cable elevator that happens to use a different control panel. The "Non-Gravity" label is an illusion; the underlying mechanics are the same as the "Gravity" (Counterfactual) ones everyone else uses.
The Result: The distinction between "Factual," "Regularity," and "Counterfactual" accounts is a "distinction without a difference." They are all the same thing wearing different hats.

3. The "Flip-Flop" Problem: Changing the Rules Mid-Game

The most damaging part of Beckers' critique is that AG's own logic contradicts itself when they look at specific examples. AG uses two famous scenarios to test their detectors:

The "Early Preemption" (The Assassin): A trainee assassin shoots a victim. A supervisor was ready to shoot if the trainee failed. The trainee succeeds. (Intuition: The trainee is the cause).
The "Simple Switch" (The Engineer): An engineer flips a switch to send a train down the right track instead of the left. The tracks merge, and the train arrives on time. (Intuition: The engineer is not the cause; the train would have arrived anyway).

The Contradiction:

In their early papers (AG1–AG4): AG said, "We can tell these two situations apart just by looking at the structure of the story (the wiring diagram). The Assassin story has a 'backup' plan; the Switch story doesn't. Therefore, our rules work perfectly."
In their later papers (AG5–AG7): AG realized their structural rules weren't working for some variations. So, they added a new rule called "Deviancy" (a moral or normality check). They said, "We can't just look at the structure; we have to ask if the backup plan was 'weird' or 'wrong'."

Beckers points out the trap:

If you use the old structural rule, your new detectors give the wrong answer on some switch examples.
If you use the new "Deviancy" rule, your detectors give the wrong answer on some assassin examples (specifically, a scenario where the backup plan is morally "good" rather than "bad").
The Analogy: Imagine a judge who says, "I can tell a murder from an accident just by looking at the crime scene photos." Then, they realize their photo analysis fails, so they add a new rule: "I also need to check the suspect's moral character."
- Beckers says: "You can't have it both ways. If you rely on the moral character rule, you admit your photo analysis was useless. But if you rely on the photo analysis, you get the wrong verdicts. You are changing the goalposts every time you lose a game."

The Bottom Line

Beckers concludes that Andreas and Günther have not made progress.

Their "new" definition is just an old one.
Their "new" category of causation is actually the same as the old categories they claimed to reject.
Their changing explanations for how to solve classic puzzles undermine the reliability of all seven of their definitions.

In short, AG tried to build a new house, but Beckers showed they just rearranged the furniture in the old one, and the foundation is shaky.

Problem
Andreas and Günther (AG) have recently proposed a series of seven definitions of actual causation (AG1–AG7) across multiple papers. In their most recent work (AG7, Andreas & Günther, 2025), they introduce a "factual difference-making" account, claiming it offers superior verdicts on paradigmatic examples compared to previous literature. Furthermore, they classify their definitions into three distinct, competing types: factual difference-making, counterfactual difference-making, and regularity-based accounts. They argue that their novel factual approach avoids the "muddled" appeal to counterfactual dependence found in dominant theories (e.g., Halpern & Pearl, 2005; Halpern, 2016) and that their regularity-based accounts (AG5, AG6) stand in contrast to counterfactual approaches.

The central problem addressed in this paper is twofold:

Internal Consistency: AG fail to compare their current account (AG7) against the six earlier accounts (AG1–AG6) they themselves proposed. It is unclear if the new "factual difference-making" definition actually differs from their previous "regularity-based" definitions.
Theoretical Distinctions: AG claim that factual difference-making, counterfactual difference-making, and regularity-based accounts are distinct categories. This paper investigates whether these distinctions are substantive or merely nominal.
Methodological Coherence: AG evaluate their definitions based on intuitive verdicts for specific examples (e.g., Early Preemption vs. Simple Switch). However, their analysis of these examples has shifted between their earlier and later papers, creating a conflict in their own theoretical motivations.

Methodology
The author employs a formal logical analysis of the definitions provided by AG. The methodology involves:

Formal Equivalence Proofs: The paper rigorously proves the logical equivalence between AG's current definition (AG7) and their previous definition (AG5). It further constructs a counterfactual variant of AG7 (denoted AG7*) and proves its equivalence to the original AG7.
Comparative Analysis: The paper compares the structural conditions and semantic requirements of AG1 through AG7, specifically focusing on the conditions regarding "unsettled" variables, minimal submodels, and deviancy conditions.
Case Study Re-evaluation: The paper re-examines the "Early Preemption" and "Simple Switch" examples (and their variants like "Extended Switch" and "Halpern Switch") under the lens of AG's earlier structural arguments versus their later deviancy-based arguments. It introduces a variation ("Backup 2") to test the consistency of the deviancy condition.

Key Contributions and Results

Equivalence of AG7 and AG5:
The paper proves Theorem 2.2, demonstrating that AG7 is logically equivalent to AG5. Although AG7 uses "factual difference-making" terminology (conditions C1 and C2 regarding unsettled models) and AG5 uses different phrasing (conditions D1 and D2 regarding non-entailment), the definitions yield identical results. Since AG5 is nearly identical to AG6 (differing only in the formulation of the deviancy condition), three of AG's seven definitions are effectively the same.
Collapse of Causal Typologies:
The paper proves Theorem 3.2, showing that AG7 is equivalent to a counterfactual difference-making account (AG7*). AG7* replaces the factual conditions with counterfactual conditions (checking if $\neg C$ prevents $E$ ).
- Result: AG's "factual difference-making" account is revealed to be an instance of a counterfactual difference-making account.
- Result: Consequently, the distinction AG draws between "factual," "counterfactual," and "regularity-based" accounts is shown to be a "distinction without a difference." The presence of a deviancy condition (C5) does not separate these categories, as influential counterfactual accounts (e.g., Halpern, 2016) also utilize deviancy conditions.
Undermining of AG's Motivations via Example Analysis:
The paper highlights a critical inconsistency in AG's treatment of "Early Preemption" and "Simple Switch":
- Earlier View (AG1, AG2, AG4): AG argued that these cases are distinguished solely by their structural properties. They claimed other accounts failed to distinguish them structurally, while their own succeeded.
- Later View (AG5, AG6, AG7): AG shifted to arguing that the distinction relies on a non-structural deviancy condition.
- The Dilemma:
  - If AG stick to the structural view, their later accounts (AG5–AG7) offer the wrong verdicts on variants of the switch example (e.g., Extended Switch, Halpern Switch) that they previously claimed to handle correctly.
  - If AG stick to the deviancy view, their accounts fail to distinguish Early Preemption from Simple Switch in cases where the backup process is not deviant (e.g., "Backup 2," where the supervisor's backup is morally permissible).
- This flip-flopping undermines the claim that AG's definitions offer a stable, superior analysis of these paradigmatic cases.

Significance and Claims
The paper concludes that Andreas and Günther's recent work fails to make a substantive difference in the field of actual causation for three reasons:

Redundancy: Their latest definition (AG7) is equivalent to their previous definition (AG5), meaning the "new" account does not offer a novel theoretical framework.
False Dichotomy: The proposed classification of causation into factual, counterfactual, and regularity types is invalid; AG7 instantiates all three, proving the categories are not mutually exclusive as AG claimed.
Incoherence: The shift in AG's analysis of key examples (from structural to deviancy-based) creates a dilemma that invalidates their core arguments against other accounts. Specifically, it undermines their frequent criticism that other accounts fail to structurally distinguish between Simple Switch and Early Preemption.

The paper asserts that AG's attempt to distinguish between these types of accounts has failed, and their series of seven definitions does not provide a coherent or improved theory of actual causation compared to the existing literature or their own earlier proposals.

1. The "New" Detector is Just an Old One in a New Coat

2. The "Schools of Thought" Are Actually the Same Class

3. The "Flip-Flop" Problem: Changing the Rules Mid-Game

The Bottom Line

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