Allen Gindler, “Refining the Non-Aggression Principle (NAP): A Formal Approach to Bystander Intervention” (draft; 2025).
Abstract:
This paper addresses a critical ambiguity in the Non-Aggression Principle (NAP), a cornerstone of libertarian philosophy that prohibits initiating force against others. While effectively guiding two-party interactions, the NAP lacks clarity regarding third-party bystander intervention. Utilizing formal logic and set theory, this study identifies a logical NULL state inherent in traditional NAP formulations, which leaves bystander actions undefined. To resolve this, the paper introduces a modified NAP (MNAP), explicitly permitting voluntary, consent-based bystander intervention. The proposed refinement enhances the practical applicability of the NAP in complex multi-agent scenarios, offering libertarian societies a coherent framework for ethically and legally addressing immediate situations of aggression through consensual collective action.
This paper has not been published yet but the author sent it to me with some questions. Unfortunately I don’t think in symbolic logic or formal logic notation terms. We ended up having a zoom discussion about this. Some of my interchange with him follows (edited and redacted).
After some initial back forth he sent me a simulation video.
Kinsella:
It looks like cellular automata, e.g. Conways’ Life. I don’t see how this has anything to do with political philosophy.
Gindler:
You’re right, this simulation is based on the Game of Life. Green cells represent NAP members of society, red cells are aggressors, and white cells are empty spaces. The simulation mimics a stateless society and its ability to promote the NAP. The question remains the same: what is the default stance of a bystander according to the NAP?
Kinsella:
… this is kind of interesting but once you start w/ the symbolic logic I can’t follow too closely. I never learned much about this kind of reasoning and have long been skeptical of the use of such notations and reasoning in teleological and normative fields. For the same reason the Austrians have been skeptical of the use of math in economics. It seems to me that the reasoning we employ in law, jurisprudence, political philosophy, and economics has to do with norms and rights and human purposes and essentially can only be understand and argued in words, verbally.
Compressing it down to equations only loses something. I could be wrong, but this has always been my approach. In any case, I simply don’t have the training, patience, or time to learn how to parse through all the symbolic logic expressions you use or to know if they are useful, if they add anything, are necessary, or accurately capture what could be expressed verbally.
One more thing. Your paper turns again to your bystander concern. For example this passage:
“When we attempt to extend the original NAP framework to include the actions of a bystander z who witnesses aggression between x and y, we encounter ambiguity. The original NAP does not explicitly address the permissibility of third-party intervention. The principle focuses solely on the illegitimacy of initiating aggression and the right to proportional self-defense, lacking provisions for whether a bystander has the right—or obligation—to assist a victim of aggression.
Because there is no clear directive within the NAP for bystander actions, we cannot definitively categorize the bystander’s intervention D(z,x) (where z acts against the aggressor x to defend y) as belonging to either the set of permitted actions P or forbidden actions F. More rigorously, it is impossible to infer any action of z (a bystander) from the original premises using mathematical logic. Formally:
∀z,x,y ∈ U, D(z,x) ∈ NULL”
this is interesting, and I think I see where you are heading. It seems to me that we can simply use verbal reasoning to discuss whether and in what situations the bystander is entitled to intervene. first, we know people have the right to use force in self defense and also to consent to other assisting them. So a bystander has a right to help a victim of aggression if we presume consent on part of the victim. ‘the only issue is how does the bystander really know whether A or B is the victim. In acting to help A maybe he is aiding and abetting a crime against B. But if he’s willing to take a risk, and if he’s right, then his acting defending A are rightful. A can’t complain, and B has no right to complain.
Notice that you get this result from merely verbal reasoning. I cannot see how running a crude simulation or boiling down our principles into symbolic logic can do anything more than illustrate verbal reasoning, at best, and at worse, confuse and obfuscate.
You write:
Modified Non-Aggression Principle: Aggression against others is inherently illegitimate. Individuals have the right to defend themselves and are also permitted to defend others who are under aggression. Bystander intervention is optional and requires the victim’s consent. Any defensive action must be proportional to the aggression faced and must cease immediately when the aggression stops.
Since bystanders have no obligation to intervene, neutrality arises from the absence of obligation rather than from explicit non-involvement”
I assume you got this from results of some simulations mentioned in preceding pages.Wouldn’t you need some more nuanced caveats here. For example: “Bystander intervention is optional and requires the victim’s consent.”
Saying it’s optional–I assume you mean in the default case? What if the victim has hired a bodyguard. Is it still optional then?
As for consent, you do not specify whether the consent can be implied. Can’t it, at least depending on context?
BTW, as another point: you might want to read a recent paper that criticizes me and my views on proportionality. Not sure if I agree with the yet but the point is not everyone that is libertarian agrees with the same way of understanding the NAP. [see Dominiak & Wysocki, “Libertarianism, Defense of Property, and Absolute Rights”]
Also in your paper do you only consider aggression against bodies? What about other crimes like trespass, theft etc. of owned resources?
I cannot say if the simulation/symbolic logic approach really achieves anything—I think this is outside my wheelhouse. As I said, I’m skeptical, but who knows. Maybe the results can be interesting.
What I would suggest is you run this by some others who may have something to add. I have in mind Dominiak & Wysocki, authors of the previous mentioned paper, and perhaps Konrad Graf, “Action-Based Jurisprudence: Praxeological Legal Theory in Relation to Economic Theory, Ethics, and Legal Practice,” and see if they have any useful comments.
***
He then assured me he already knew Dominiak & Wysocki and we chatted some more. In any case, food for thought.
