TL;DR. Automation in the information sector is bridging the gap between human cognition and physical reality. It behooves humanity to apply these fruits of scientific advancement to ethics and the institutionalization of law. This essay attempts to show that it is possible to ground ethics on a rigorously logical foundation and derive provable ethical theorems. In combination with the ongoing cognitive automation that allows humans to relate ethical formalisms to real human conflicts, this development paves the way for a world in which all human conflicts are resolved in a provably just way. Realizing the political reforms mandated by an independent and provably correct ethical philosophy, as proposed in this essay, is the only way to completely eradicate systemic injustice.
The Rise of Automation
Of the many scientific advances of the last centuries, not one has more profoundly affected the course of human history — or indeed, human imagination — than the rise of automation. Beginning in the mid Eighteenth Century, automation in agriculture has generated an ever-increasing, ever-urbanizing global population. The automatic production of vaccines, medicines and hygiene products has eradicated infectious diseases such as smallpox and polio, and limited the scope or prevented the outbreak of many others. For good or for ill, the automatic production and deployment of instruments of war has dramatically escalated the destructive potential of power-wielders. However, all these advances pale in comparison to the ubiquity of information and processing power offered by the pinnacle of automation: computers and the internet.
Just as human strength is limited, so is human precision and brain power. While precise and computationally-heavy tasks are often relatively difficult to automate, any such automation will increase product quality, essentially bringing to life products that could not exist before. Especially in sectors where lack of precision or presence of errors can lead to disastrous consequences, such as finance, medical diagnostics, or construction design, computerized tools are indispensable.
While human labor is often the bottleneck, it is also the most fungible and therefore the most valuable resource. As superior machinery replaces humans, these humans (in contrast to their supplanters) are capable of finding employment in other sectors, potentially satisfying a societal need that previously went unsatisfied. Thus, the effect of automation is not limited to whatever sector the change occurs in, but positively affects society as a whole. From this point of view, automation is the driving force that sets mankind free from the fundamental constraint imposed by nature: the scarcity and limited quality of human labor.
Cognitive automation, in the form of intelligent programs, is reaching the higher levels of human thought. Semantic search is at our fingertips, automatic translation of documents only a mouse-click away, and spam filters block even the richest Nigerian princes. AI researchers are producing neural networks that are capable of dreaming, recognizing images and speech, beating the world champions in Jeopardy!1 and Go2, and even writing scientific papers accepted to peer-reviewed journals3. As fewer traditionally human-dominated tasks appear immune to automation, it seems inevitable that this automation will become even more ubiquitous and affect society even more profoundly.
The Gap of Rigor
Another triumphant scientific breakthrough of the last century is the complete formalization of logic and the classification of valid laws of logical inference. By emphasising syntax rather than the semantics, formal logic is capable of encompassing all of mathematics by reducing even its most sophisticated proofs to tiny, individual steps of rigorously verifiable logic. Any proof that is not at least in theory reducible to formal logic is not accepted as valid by peers in the mathematical community. Moreover, there already are computer programs such as Coq and Mizar for mechanically verifying formal proofs. The QED Manifesto4 envisions a world in which all mathematical proofs are presented in a formal, computer-verifiable language, as this formal presentation offers the only reliable method to distinguish valid proofs from invalid ones with absolute certainty.
Unfortunately, the adoption of computer-verifiable proofs is slow at best. The underlying notions in any given mathematical theorem or proof are chosen precisely because they are semantically meaningful to the problem at hand. The mathematicians responsible for creating such “semantically deep” objects do so by stacking layer upon layer of abstractions and definitions on top of the indivisible units of the underlying formal system. A full formalization would require writing an exponential number of highly redundant atomic symbols, not to mention the effort on the part of the mathematician required to master a skill as tricky as writing formalized proofs. Such a devotion to formalism hardly seems worthwhile when other experts in the field are satisfied with much less; any surplus effort is more prudently expended on the next brilliant research idea.
Nevertheless, the benefit of formalized proofs should be obvious: they completely eradicate the possibility of error. As all humans are fallible, so are both the mathematicians that write proofs and the ones that verify them. Peer-reviewed and published mathematical proofs are bound to contain errors — and, indeed, they do. Currently, the only way in which such an error is discovered, is through the hard, virtuous work of another expert in the field. Formal proofs, however, offer the option of democratizing the process: they make proof verification available to anyone who is willing to download, install and run the software.5
Enter the potential of cognitive automation: deep neural networks may one day be trained to traverse the many layers of abstraction in mathematical proofs, interfacing with the mathematician in his own terms and definitions, while at the same time outputting a list of logical symbols that constitute a valid, verifiable proof. As the depths of abstraction increase to which mathematicians can descend while retaining a neural network-assisted link to formalized logic, who knows what exciting new branches of mathematics may be discovered, or which conjectures may finally be proven — or disproven?
The Importance of Law
Reason — the fundamental trait that sets man apart from animals — manifests itself in essentially two ways. On the one hand, human cleverness allows him to overcome the harsh conditions of nature; on the other hand, human argument allows him to cooperate with his fellow man and settle their disputes with words instead of violence. Words offer the means to the institution of law, which is the quintessential trademark of civilization — as opposed to the law of the jungle.
The importance of an ethical basis for institutional law cannot be overstated. Ethics underlies the legitimacy of the political system; without ethics, the entire state is no more than an infrastructure for organized theft.6 Even the thief, rapist and murderer, by committing their barbarities, profess and defend a (mistaken) conception of right and wrong. The ethical skeptic or nihilist cannot charge these criminals with an inhuman crime that is obviously wrong in and of itself, because to make this charge is to assert the validity of ethics. Most fundamentally, it is literally impossible to argue successfully for the superiority of other qualities of human interaction over ethicality. Any universally valid argument for the superiority of other qualities would itself be, by definition, part of ethics.
And yet, law is currently arbitrary; it reduces to the thoughts and ideas of defunct revolutionaries of the past. In the end, judges base their pronouncements on those of other judges, on the writs of politicians in and out of parliament, and on the ex-post manifestos of successful coups-d’etat. There is no process or incentive that ever weeds out past errors of judgment, except perhaps accidentally and based on popular sentiment. Conversely, the emotions of the masses may introduce irrational fallacies into law just as easily as they may eliminate them. Without rigorous ethical foundation, legislation relies only on gut feeling and is consequently entirely irrational. Irrational law is unjust by default and just by accident. Any political system based on institutionalized irrational law amounts to systemic injustice, and its existence is an affront to human dignity.
This need not be so. If ethics can be formalized, then laws can be formally proven to be valid. Automation can help judges to make provably just pronouncements. Members of parliament can justify their legislation to their constituents and to the rest of the world on the basis of a computer-verified proof of justice. The power of the executive can be delineated not by some arbitrary document nor by the subjective oversight of some supposedly independent power, but by the rigorous quality of sound ethical theorems. Human society can at last reach its full, unbridled potential. If only ethics could be formalized …
Towards a Formalization of Ethics
An argument is a list of propositions, each one of which is either a premise or else is held to follow logically from the preceding propositions, and which is designed to convince someone of final proposition, the conclusion. An argument is rigorous if each non-premise follows from the preceding propositions through the application of exactly one inference rule of the underlying formal logical system. Consequently, rigorous arguments are trivially verifiable by simply checking the inferences made. Unfortunately, a complete reduction of ethics to a formal logical system such as those used in mathematics and computer science would make this essay too long to be comprehensible. Instead, the goal of this section is to illustrate the intuition and convince the reader that such a formal reduction is indeed possible.
Commonplace definitions of “ethics” relate the term to normative concepts such as right and wrong, or proper behavior, but leave these normative terms undefined or only defined in a circular way. A formalization of ethics must start with a definition that contains this crucial concept of normativity and reduces it to other concepts. Let us use the following definition: Ethics is the set of valid arguments for or against human interactions applying universally to all persons, as well as a methodology for obtaining such arguments and distinguishing valid from invalid ones.7
The word “human” and “person” in the above definition do not refer to instances of the species homo sapiens; instead, they refer to members of the category of moral agents whose existence is implied by the possibility of a universally applicable argument. After all, an argument cannot appeal to any object incapable of receiving the argument; nor to anything incapable of understanding logic and distinguishing between valid and invalid; nor of acting on that understanding. As such, the abilities to communicate, to understand and to act are the key properties that set moral agents apart from other objects.
Immanuel Kant makes two important distinctions between types of propositions.8 First, a proposition can be either analytic, i.e., true or false depending solely on the meaning of the words; or synthetic, i.e., true or false depending on the state of reality. Second, a proposition can either be a priori, i.e., independent of empirical observation; or a posteriori, i.e., dependent on empirical observation. While the notion of an analytic a posteriori proposition is self-contradictory, the opposite notion of a synthetic a priori proposition is not. Indeed, the most well-known example is Descartes’ famous quip, “I think, therefore I am.” It is a priori because it cannot be logically contradicted, and yet it is synthetic because it conveys information about the universe.
Ethical propositions belong to the same category. On the one hand, they are a priori because they must apply universally to all moral agents. Moral agency is after all an abstraction defined independently of reality, as opposed to a model designed to approximate reality.9 On the other hand, ethical propositions are also synthetic because they apply to real instantiations of moral agents. In other words, in order to convey a normative imperative unto real world people, ethical propositions must be synthetic.
Phrased differently, ethics consists of principles and hypothetical arguments that exist only in mind-space and whose validity is independent of reality. However, anyone who wishes to escape their reach must first argue that these arguments do not apply to them. But this is unarguable because by presenting this argument, he proves his own moral agency and thus ensures that the arguments do apply. The use of this performative contradiction places this brand of ethics inside the more general category of argumentation ethics, as propounded by Frank van Dun10 and, independently, by Hans-Hermann Hoppe11.
In order for ethics to be relevant, there must exist another person, independent of the first, allowing for the possibility of interaction and discussion. It is thus possible to capture the fundamental principle of ethics in one proposition: there exists a discussion about proper interaction between two or more persons.
It is impossible to deny the existence of this discussion without making an argument for its non-existence. However, any such non-existence argument must take place in the context of a discussion and thus immediately defeats itself. Likewise, one cannot argue that invalid or illogical arguments ought to be accepted in this discussion: by making this argument, the arguer is presupposing the desirability of logic and validity. Not only that but he is also appealing to the ability of his discussion partners to distinguish valid from invalid and logical from illogical. Both are contrary to the content of the argument and thus invalidate it. As a consequence of all this, only valid arguments in the omnipresent ethical discussion can be used to derive ethical principles.
The minimality of this foundation of ethics cannot be overemphasized. Argumentation ethics is entirely independent of deniable axioms, human emotions, state officials, leaps of faith, and deities themselves. One who wishes to include any of these items in the foundation of ethics must first argue for their relevance. However, this argumentation cannot invoke said items for justification as it would be circular if it did. So, logically, any such argument would defeat itself by conceding the irrelevance of whatever extension it was trying to justify in the first place.
Persons and the Universe
The fundamental principle of ethics has been phrased only with respect to notions that are intuitively meaningful: action, interaction, exists, person. In order to properly formalize ethics, these notions must receive a rigorous definition as well. Importantly, these definitions must be abstractions and not models so as to ensure the a priori quality of ethical arguments.
A universe is a finite directed fractal graph, which at every level of consideration consists of nodes and edges. The nodes represent automata obeying physical laws and the edges represent channels of transmitted information — or, equivalently, causation. It is a fractal graph because what may be considered a node or an edge at one level may also be considered a subgraph at another, and vice versa. Something exists if it can be identified with a node in the universe. The universe is the unique universe in which the argumenter exists as a non-isolated node.
A person is a node in the universe which 1) communicates, i.e., exchanges information with other nodes; 2) simulates, i.e., makes models of the nodes in his vicinity and computes their perturbed states under suitable approximations of their governing physical laws so as to predict the consequences of changes in the environment; 3) is capable of reasoning, i.e., distinguishing truth from falsehood; and 4) acts, i.e., configures the nodes in his environment so as to realize a simulated reality. An action is any such configuration, whereas an interaction is a set of actions by distinct persons, each affecting the other and his environment.
Want and Action
A central notion implied by that of action is want, i.e., the situation the action attempts to realize. Crucially, this property is what sets persons apart from clever automata such as computers or more primitive life forms. It is a hard problem to distinguish, empirically or through thought experiments, between nodes that act and nodes that merely exhibit behavior inherent in their programming. Nevertheless, an appeal to inherent programming does not excuse crimes in the court of law as any such appeal is itself an action, thus defeating itself. Likewise, the inability to act cannot underlie a valid ethical argument as any such argument is itself an action.
The concept of action as opposed to programmed behavior ties in to the question of freedom of will. However, as far as ethics is concerned, it is unnecessary to make this distinction, or even to debate whether free will exists. Ethics is an abstract notion and if an ethical question arises in the course of hypothetical debate in order to establish the proper principle, then both parties can be explicitly assumed to be acting persons — or not, depending on the nature of the hypothesis. If an ethical question is raised in the court of law then both parties fit the category of acting persons by virtue of presenting their arguments.
Action is defined as bringing nearby nodes into a configuration that matches a simulated universe. Importantly, action is not meaningfully distinct from argumentation. Indeed, the very purpose of an argument is to precisely bring nearby nodes into a desirable configuration, except that in this case these nearby nodes happen to be persons capable of reason as opposed to merely reactive matter. More importantly, actions can be thought of as arguments because they affect nearby humans and convey information about the desirable configuration. Likewise, any interaction between two or more people can be thought of as a discussion.
Ethics is not an autistic hypothetical exercise. Plurality of actors must be explicitly assumed as a premise before any ethical theorem can be derived. Robinson Crusoe, alone on his island, has no need for ethics until he meets the natives.
More importantly, there is no need for ethics either as long as all actions by all parties are perfectly harmonious, i.e., wanted by all who are involved. The ethical question only arises when some actions by some persons are unwanted by others. Generally speaking these actions occur in pairs: the action and the reaction, each mutually exclusive with respect to the other and therefore both unwanted by the opposite party. Thus ethics essentially deals with conflict and prescribes its prevention and resolution through rationally defensible actions.
Conflict12 occurs whenever there is 1) scarcity, i.e., equivalent nodes of a particular type are finite and cannot be configured conformant to several simulations simultaneously; 2) plurality of wants, i.e., the simulated universes are distinct; 3) independence of will, i.e., the capacity for action of either party is independent of that of the other; and 4) access, i.e., both parties are capable of causing the configuration they desire. All four items are necessary qualities; drop one and there is no conflict.
In order to eliminate conflict there are thus four options. Scarcity is an unfortunate property of the universe and can perhaps be ameliorated by technology but never wholly eliminated. Wanting is in itself not an action and hence cannot be subject to reason, nor the prescription of an ethical argument. Independence is the premise of any discussion and in particular the discussion about ethics; consequently any argument that would undermine independence would defeat itself. The only option to resolve conflict without undermining the fundamental principle of ethics and which can be the subject of reason and choice is thus the restriction of access. Therefore, there is a possibility for the ethical solution to conflict, namely the reasoned restraint by one or both participants. The exact form of this restraint and this reason is yet to be argued.
While conflict of wants is inevitable and must be tolerated, conflict of actions is essentially the antithesis of discussion: one party rejects the arguments of the other party — outside of reasonable grounds — and resorts to physical intervention to accomplish his goals. Consequently, whenever there is active conflict, at least one party is guilty of undermining the discussion, contrary to its un-counter-arguable desirability. In other words, at least one party is being unethical. The next question is to determine who, i.e., to distinguish the party who is acting ethically from the party who is not.
Action implies a sense of appropriation. By employing scarce goods in order to attain an end, the actor broadcasts to the world an argument that those goods ought to be used for that purpose, as opposed to other potential purposes. Moreover, the actor reassigns those goods away from their previous use and to their new use; or else he is the first to assign a use to the previously unused goods.
In the latter case, the actor essentially transforms things into means. As long as this transformation is isolated, i.e., cannot affect the environments of other persons, the employment of these goods as means cannot be the subject of ethical argument or counterargument. He is thus free to do as he pleases. The act of appropriation through mixing labor with unowned resources is called homesteading; the person who does this is a homesteader.13
A different reasoning applies when the goods in question are capable of affecting another actor, and in particular when this second actor wants to appropriate the resources himself, in order to employ them for his own ends. Time is on the side of the original homesteader as he performed his actions — and broadcasted his argument — before the ethical question was raised and thus before the discussion was started. In order to formulate an ethical argument in the discussion with the original homesteader, the latecomer must first recognize the agency of his discussion partner, and respect the homesteader’s application of the previously unowned goods to whatever ends they are applied to. Any subsequent appropriation on the part of the latecomer undermines homesteader’s capacity for argument and with it the foundations of the discussion. Consequently, ethics prescribes reasoned restraint on the part of the latecomer.
However, if both parties consent, then the burden of reasoned restraint may pass from the latecomer unto the homesteader. Equivalently, contract may transfer property rights, i.e., the right to employ a particular scarce good to any use whatsoever, from the original homesteader to the latecomer, or from the latecomer to a third party. Thus, by induction, ownership of property is just if and only if it traces back through links of voluntary contract, to the original homesteader.
Another exception is when the argument for reasoned restraint as would be made by the owner, cannot be made without itself undermining the discussion. For example, no one can be ethically compelled to take their own life or take actions that would result in the same, on the basis of an otherwise would-be violation of property rights. Similarly, if in the course of human action, another person is created from matter that is owned by the first person, such as is the case when children are conceived and born and grow up, the property rights of the first person cannot be used to undermine the personhood of the newly created person. In other words, argumentation ethics guarantees self-ownership just as surely as it guarantees property rights.
From self-ownership and property rights follows the non-aggression principle, which states that any physical invasion of a person’s property or body is ethically wrong unless it is consensual. The non-aggression principle serves as the foundation for the well-established edifice of libertarian legal theory, which covers freedom of speech, privacy, the right to keep and bear arms, and a whole host of civil liberties and principles of criminal law.14
The foundation for ethics is the omnipresent discussion about ethics, in which certain propositions must be true by virtue of their negations being self-defeating and thus unarguable. While this discussion is abstract, relating to the universe and persons as nodes and edges in a fractal graph, its logical consequents are no less true than those of mathematics as both can potentially be rigorously formalized; nor are its propositions any less applicable to real human life than sociology or psychology. Most importantly, unlike sociology, psychology or mathematics, the logical proofs arising from the ethical discussion confer a normative quality on their interpreter, by virtue of his capacity for understanding them.
The central notion in this discussion are its participants, who are necessarily actors, i.e., persons who act, are independent, number two or more, and are potentially in a state of conflict with respect to scarce goods. By virtue of using scarce goods as means to an end, the actors make claims to scarce goods. In general only that one claim that precedes all others cannot be logically invalidated. Informed and voluntary consent to contract may transfer the one un-invalidatable claim to alienable scarce goods unto others, giving rise to property rights and, by proxy, all other human rights.
All pieces of the puzzle are finally in place. The ethics presented in the previous section can be cast into a perfectly formal, symbolic language in which every step is a rigorous application of basic laws of logic. There is thus an objective method by which to decide which ethical propositions are true and which are false — and automatic proof checkers that offer this functionality already exist.
Judgment varies from case to case and while it may be contentious which ethical principle applies, the validity of two or more contending principles should be beyond doubt. Moreover, which of two contending principles applies should be purely a function of the evidence presented, which in today’s world can also be digitized and whose processing can also be automated. Consequently, judges have recourse to a mechanistic, optimizable, computerizable and auditable process by which to produce a judgment, which should in the end reduce to a provably correct ethical theorem. Perhaps one day judges themselves can be replaced by faster, harder-working, more environmentally friendly and less error-prone computer programs.
The spread of provable ethics should not stop at the judiciary. Legislators, too, offend against reason when they pretend to write into law a mere proposition and attribute its legitimacy not to any valid argument but instead to a quorum of votes. Contrary to popular conception, law does not come into being by the pen of the parliamentarian; law is discovered, like mathematics, and spreads organically from thinker to thinker through discussion and by virtue of the validity of its proof.
Nor should provable ethics remain contained within the judicial and legislative branches. As ethics concerns the moral quality of all human interaction, the people who make up the executive branch are not exempt. Not only should their actions be held to the highest possible, provable and verifiable standards; their legal and practical power should not exceed what is logically mandated and allowed by ethics to begin with.
International conflicts, like interpersonal conflicts, have a unique and provably ethical solution. It is only the public disbelief of this fact that continues to lend power, credence and legitimacy to the warlords across the world who commit and enable unspeakable acts of inhuman atrocity. By dismantling the myths of ethical pluralism and ethical nihilism, provable ethics can undercut the real source of power that fuel the many wars, feuds and conflicts raging across the world, and thus end their destructive reign of terror once and for all.
Not even the foundations of the state are immune to ethical scrutiny — scrutiny which is finally entirely independent of the state and in no way relies on its existence. The constitutions of the various nations of the world — including the Universal Declaration of Human Rights — should be culled until only those phrases remain that are completely, provably compatible with ethical principles. Democracy itself, hailed often, proudly and wrongly as the greatest achievement of mankind since the invention of the wheel, should be seen for the disaster it is: democracy is the means to trump a valid argument. It should be discarded but well-remembered for its destructive potential along with all the other defunct ideas from the black book of human history.
The Road to Utopia
Having established a humble picture of utopia, it is time to turn to another, related question: how to bring it about in the most ethical way possible. While the answer is easy when one is allowed to assume unlimited power — i.e, “immediately” — no such divine force is thrust upon ethical revolutionaries. They must instead face the dilemma of choosing which injustices to suffer before the master plan is hatched.
Except, a divine force is thrust upon ethical revolutionaries. This force does not ordain them to, as it were, break the eggs to make the omelet; no ideology absolves its believers of their sins. Nor does it suffer them to be lazy; despite its objective correctness, the ideology of provable ethics will not spread of its own accord. The power in the hands of ethicists is reason, the ability to make and distinguish valid and invalid arguments; and discussion, the ability to confer arguments unto others and receive them in turn. It allows the revolution to charge its ideological opponents with an incontrovertible argument to either join the revolution, or be reduced to indignified animals for rejecting it irrationally.
However, this essay merely argues that a formalization of ethics is possible; it does not present one outright. There are many holes to be filled and leaps of understanding to be formalized that are intuitively accessible but lacking in rigor. The skeptic can delay the inevitable dilemma until such time as he is presented with a more rigorous formalism. And any reasonable delay-seeking counter-argument is truly a gift, because it leads to a more rigorous ethical argument or else exposes its falsity in the first place. Until at one point, if there is no falsity to be exposed, the argument is completely formalized. At this point, the critic must accept the conclusion or else forsake all semblance of rationality.
Fortunately, however, despite the many trials and tribulations that await the doctrine of provable ethics, there is just cause for optimism. Think about it: the fundamental principle of ethics is undeniably well in place. For how does the skeptic hope to refute any part of this essay without presenting rational arguments and engaging in discussion?
- Jeopardy!: http://www.nytimes.com/2011/02/17/science/17jeopardy-watson.html?pagewanted=all&_r=0
- Go: http://www.bbc.com/news/technology-35785875
- Automatically generated papers: https://pdos.csail.mit.edu/archive/scigen/ (To be fair though, although some papers were accepted to peer-reviewed conferences, this project is intended as a joke.)
- The QED Manifesto in Automated Deduction – CADE 12, Springer-Verlag, Lecture Notes in Artificial Intelligence, Vol. 814, pp. 238-251, 1994. http://www.cs.chalmers.se/Cs/Research/Logic/TypesSS05/Extra/wiedijk_2.pdf
- Of course, any proof-verification software worth its salt is itself accompanied by a formal proof of correctness, verifiable independently by a host of other proof-verification software packages. This way, society merely has to trust that there is no world-wide conspiracy against proof verifiers.
- In the words of Saint Augustine of Hippo: “Absent justice, what are states but giants robberies?” -The City of God/Book IV/Chapter 4
- While the two terms are often used interchangeably, this essay distinguishes ethics from morality, the latter being the broader category dealing with any type of action, not necessarily involving other persons.
- Immanuel Kant. Kritik der reinen Vernunft. 1781
- In the famous words of George Box, “All models are wrong, but some are useful.” Likewise, all abstractions are correct, but only some are useful.
- Frank van Dun. “Het fundamenteel rechtsbeginsel” (Translation: “The Fundamental Principle of Law”) Murray Rothbard Instituut, 2008. (Republication of the 1982 edition.)
- Hans-Hermann Hoppe. “The Ultimate Justification of the Private Property Ethic” (September 1988). Liberty 2 (1): 20–22.
- Although not part of his main publication, this definition is due to Frank van Dun and is an often recurring feature in his presentations.
- This principle of appropriation from nature traces back to John Locke, “Two Treatises on Government”. 1689
- For an excellent step-by-step reduction of well-established freedoms and civil liberties to property rights, see Murray N. Rothbard, “The Ethics of Liberty” NYU Press, 2003.
4 thoughts on “Formal Ethics, Provable Justice”
Have you taken into account the posible implications of the Gödel’s incompleteness theorem on the possibility of finding a consistent formulation for ethics? And, if we cannot find a consistent formulation for ethics, wouldn’t this essay, whatever (inconsistent) ethics formulation is inforced, lead to a distopia?
Hi Enrique, thanks for the question. I have given some thought to the implications of Gödel’s incompleteness theorem. I’m afraid I don’t have a complete answer because Gödel. However, I can do my best to offer a sound one.
It’s important to bear in mind exactly what Gödel’s theorem does and does not say. It says that any sufficiently powerful logical system cannot be simultaneously complete (anything that’s true can be proven) and sound (anything that can be proven is true). It does not say that any sufficiently powerful logical system is necessarily inconsistent, unless you demand it also be complete. It is always possible to drop axioms from the system until your logical span is free of contradictions; Gödel says this strategy comes at the cost of allowing true (and false) propositions that cannot be proven. One of the propositions that becomes unprovable if you do this is the statement “this logical system is consistent”.
So maybe there are propositions about actions that are undecidable. However, they have no normative weight because they are not universal; a rational actor can reject them without leading to contradictions. You cannot charge a moral agent with irrationality for not deriving a theorem that is unprovable anymore than you can blame him for failing to compute whether your program halts. Note how I presciently defined ethics as the set of valid arguments pertaining to actions and not as the set of true propositions pertaining to actions. The truth value of a proposition might be undecidable, thus disqualifying it from ethics. In contrast, the validity of an argument is easily decidable.
Hi Alan. First, thank you for your thoughtful reply. Second, sorry for my missuse of the term “consistent”. Of course, the proposed ethics are consistent, and probably sound, indeed… But, as you also admit, incomplete. There would possibly be then agents performing undecidable actions (under the ethics derived from the decided set of axioms), which would be considered as out of the ethics. These actions may be considered inside the ethics if the axiom set is extended. So, where do we stop extending it? Wouldn’t ethics itself be doomed to halt?
Hi, recently I read Frank van Duns “The logic of liberty”. The paper is quite surprising, since I never saw some ethics in predicate logic before. (although his syntax is awful.) You mentioned automated theorem proving above. Do you know whether there are any approaches to formalize ethics using such a proof assistant? Beside mathematics and theoretical computer science they have already been used for formalizing some economics* and (philosophical) theology*. Therefore ethics wouldn’t be surprising.
* Isabelle archive of formal proofs.