How long for rationalists?
BTW, try Googling the bold-faced phrase near the beginning of the text, as an exact string. There are about 25 hits. All the sites which contain the full text are junk sites.
Short summary: This post gives an unsystematic and fragmented list of poorly described historical examples of procedures for answering moral questions.
Pythagoras and Plato sought to combine moral and mathematical elements of reality in their work on ontology. This was very influential and the work of both is still consulted to this day, although, the social and political implications of their methods are often rejected by more modern philosophers.
Pythagoras isn't really consulted in this regard except by those doing work in Ancient History of Philosophy. Also, I don't really know what the first sentence means. Honestly, in some of these cases maybe arguments could be made in favor of the writer's assertions but a lot of these claims are so unclear and unusual that anyone new to these issues would come away with wrong ideas.
Some consider the debate to continue to this day in economics, with the neoclassical economics based firmly on Aristotle's methods via Friedrich Hayek and Karl Popper,
"Methods of Aristotle" goes undefined throughout. This really could mean nearly anything. But whatever the interpretation I know of no insightful way to distinguish neoclassical economics from Islamic or feminist economic by referencing Aristotle.
Islamic economics and feminist economics which reject some aspects of Aristotle's logic, e.g. law of excluded middle, and seek to build on some intuitive and morally defensible ontology, as Plato did.
Wtf? I'm not an expert in Islamic or Feminist economics but... they reject the law of the excluded middle? They deny that all propositions are either true or not true? Maybe there is a keen insight here, if so someone explain it to me. I reads like a non-sequitur.
Buddhism also stresses notions of right livelihood which seem to be possible to measure and compare in a quasi-formal manner.
They're not.
The Noble Eightfold Path is a set of priorities, ordinal not cardinal, not strictly quantities, but still, a useful framework for any more formal or weighted value theory.
The Eightfold Path is neither an ordinal nor cardinal set of priorities- its a conceptual division. And I have no idea how one would use it as a framework in this regard.
During The Enlightenment the various traditions became more unified:
No. The Enlightenment took us from one major tradition (Thomistic Scholasticism) to three or four different theories (utilitarianism, Kantianism, natural rights, self-interest/ contractualism). While there was certainly diversity among scholastics (some favoring Plato, Some Thomas/Aristotle etc.) there was little to no inventiveness in moral philosophy, every theory was just a different way of relating morality to the Christian God.
Immanuel Kant, in his "categorical imperative", sought to define moral duty reflectively, in that everyone was obligated to anticipate and limit the impacts of one's own actions, and "not act as one would not have everyone act.". This can be seen as a restated Golden Rule.
You could see it that way but you would be seeing it wrong. I can explain in detail why this is wrong if need be. Suffice to say that the CI tells you to do different things in some circumstances and is motivated by an entirely different set of concerns than the Golden Rule. Also, the CI has nothing to do with the "impacts" of one's actions.
Anyway, those are the areas I feel most confident commenting on. Others might have more to say.
Wtf? I'm not an expert in Islamic or Feminist economics but... they reject the law of the excluded middle? They deny that all propositions are either true or not true? Maybe there is a keen insight here, if so someone explain it to me.
I could be mistaken, but I think that's just imported postmodern claptrap: "Truth is relative. What's true for me might not be true for someone else. Therefore some propositions are both true and not true." Not exactly keen or insightful.
No, there are good reasons to reject the law of excluded middle other than that particular flavor of relativism. I think the jury's still out on whether anything of worth can come out of paraconsistent logic (or intuitionism that disallows the law for infinite sets, or other such logics) but trying to reject the principle of explosion and resolving the liar's paradox seem like the sorts of things a professional logician might reasonably spend time on.
I completely agree. But do you think it's reasonable for economists to reject the results of other economists on the grounds that the result depends on the law of the excluded middle?
Speaking for myself, I wouldn't have a problem with an intuitionist/constructivist economist who rejected the formal deductive validity of proof that relied on the LoXM. But it wouldn't follow from that that the predictions the other economist were wrong, and frankly thats the criteria by which economic theories should be evaluated anyway since perfect deductive validity isn't important when your axioms aren't always true either.
As a point of historical curiosity, I'd be interested to know if there ever was an explicitly constructivist economist.
Of course there are. If I understand the abstract correctly, this paper argues for a particular formalization of game theory (often a branch of economics) on the grounds that the players (intuitionistically) play strategies that are computable from only a bounded amount of lookahead.
www.math.wisc.edu/~lempp/conf/wroc/stecher.pdf
Pythagoras isn't really consulted in this regard except by those doing work in Ancient History of Philosophy. Also, I don't really know what the first sentence means.
Pythagoras and his followers were the first philosophers to clearly state that mathematics (though they were probably referring to what anthropologists call "sacred geometry") is a secure basis for philosophical and moral reasoning. Sacred geometry was Pythagoras's ontology, and his influence on Plato is especially clear in the latter's Meno dialogue, where Meno's slave "recollects" his innate knowledge of the perfect (geometric) Forms. Bertrand Russell confirms that Pythagoras was a key influence on Plato and on Western philosophy overall.
"Methods of Aristotle" goes undefined throughout. This really could mean nearly anything.
It probably refers to "rationalism" as most pilosophers would define the term (i.e. based on logic and the axiomatic method), contrasted to empiricism and other traditions. This would substantiate the references to Aquinas and to the Mutazilite tradition in Islam.
Wtf? I'm not an expert in Islamic or Feminist economics but... they reject the law of the excluded middle?
Ever heard of fuzzy logic? Very little of the reasoning ordinarily used by humans is actually of the "either true or false", "necessary and sufficient conditions" type. If moral reasoning is to be "intuitive", it must refer to the way human beings actually reason, not to formal logic. As neoclassical economics does with its "axioms of rationality" and "proofs of market efficiency"
The Eightfold Path is neither an ordinal nor cardinal set of priorities- its a conceptual division.
The references I can find state that the Eightfold Path is an ordered set of priorities, from "wisdom" to "concentration". Some of these priorities even have inner structure with ordered subpriorities.
Also, the CI has nothing to do with the "impacts" of one's actions.
It most certainly does when you compare it to the way normative ethics as usually practiced distinguishes good from bad actions--normative morals, i.e. "rules".
Also, the CI has nothing to do with the "impacts" of one's actions.
As Jack also mentions, the very definition of the categorical imperative is that consequences are completely irrelevant. Were consequences relevant, it would be a hypothetical imperative.
"Do not kill," is a CI. "Do not kill if you want to avoid being an evil person" is an HI.
Saying that the CI has something to do with the impacts of one's actions is as accurate as saying that a square has five sides.
That's not entirely fair. Kant said that morality was not determined by consequences; but that statement may be incoherent. Attempts to use the categorical imperative result in looking at consequences in one way or another - even if the user is unaware they are doing so, because they are referencing values evolved into them by their consequences to the user's ancestors (and selected-against non-ancestors).
Again agreeing with Jack; it's true that much of Kant's argument about the CI is based on consequences. Conceptually, however, the CI and its association with objective morality do require it to be purely non-consequence-based. If it were consequence based, then if the consequences were different, it wouldn't necessarily hold, so it would not be "categorical."
I agree that, fundamentally, any intelligible concept of ethics will rest on consequences. But the idea behind the CI is that it is a priori, which is why it's such a terrible and convoluted idea.
Thats a really interesting notion. However, it is more of an objection to Kant's position than it is an objection to Psychohistorian and my interpretation of Kant. It might be the case that you can never get away from the impacts but Kant didn't think that and what Kant thought was what was at issue.
Pythagoras and his followers were the first philosophers to clearly state that mathematics... etc.
Pythagoras was really influential. Yes. But that is non-responsive. He was influential on Plato and people read Plato- but no one today reads Pythagoras... which the article claimed.
(Re: Aristotle's method)
It probably refers to "rationalism" as most pilosophers would define the term (i.e. based on logic and the axiomatic method), contrasted to empiricism and other traditions. This would substantiate the references to Aquinas and the Mutazilite tradition in Islam.
Rationalism as understood by most philosophers is a thesis about the need and reliability of sense experience in knowledge. And the the rationalist and empiricist camps didn't exist until the Scientific Revolution. And the rationalist tradition certainly isn't particularly associated with Aristotle, who invented empirical science and was Descarte's arch enemy. Also, any value for "methods of Aristotle" substantiates an Aquinas reference. What on earth rationalism has to do with Karl Popper I have NO idea (when he said falsification he meant empirical falsification!). But then, your interpretation of the essay makes about as much sense as any other interpretation.
Ever heard of fuzzy logic? Very little of the reasoning ordinarily used by humans is actually of the "either true or false", "necessary and sufficient conditions" type. If moral reasoning is to be "intuitive", it must refer to the way human beings actually reason, not to formal logic. As neoclassical economics does with its "axioms of rationality" and "proofs of market efficiency"
The law of non-contradiction doesn't hold that all propositions are "either true or false", it holds that all propositions are either true or not true. What you are talking about is the principle of bivalence-- related but different. In any case, there is still no reason to associate a rejection of the principle of bivalence with feminist or Islamic economics. Also, a logic can either be bivalent or not. Whether or not the logic is bivalent is mostly irrelevant to whether or not one can get interesting results from some set of axioms. Feminist economics, I assume, doesn't axiomatize. But that doesn't mean they hold to a particular position on bivalence/whatever. I don't know why feminist economists would spend time talking about intuitionist logics if they don't have an axiomatized system.
The references I can find state that the Eightfold Path is an ordered set of priorities, from "wisdom" to "concentration". Some of these priorities even have inner structure with ordered subpriorities.
The fact that you read a list of the eight parts of the path and that they were written such that one part followed the other isn't evidence that they're an ordered set of preferences. Any list of anything is going to have a beginning and an end. That doesn't mean the order presented has any significance. There aren't eight paths. There is one path conceptualized in terms of eight different areas of existence/experience. Right on the wikipedia page there is a nice picture of a wheel with eight spokes. Thats the idea. In any case, the more philosophical branches of Buddhism would totally reject the idea that any of the Buddha's teachings are a formalistic approach describing the truth of anything. Everything is just a heuristic or pedagogical instrument and one shouldn't get too attached to any of it.
(Re: the CI having nothing to do with impacts)
It most certainly does when you compare it to the way normative ethics as usually practiced distinguishes good from bad actions--normative morals, i.e. "rules".
I don't know what you're talking about. The Categorical Imperative is a rule. Its the rule. The only rule. The impact of a given action has exactly zero to do with it's morality according to Kant.
Feminist economics, I assume, doesn't axiomatize.
Why would you assume that? If you're willing to reject the principle of bivalence (and thus "logic" as ordinarily understood), you're free to take some "core" of morality as axiomatic and use "fuzzy" reasoning to reach formal conclusions. Admittedly, feminist economics probably doesn't do that, at least not yet. But an AI built to follow feminist or Islamic principles could.
I don't know what you're talking about. The Categorical Imperative is a rule. Its the rule. The only rule. The impact of a given action has exactly zero to do with it's morality according to Kant.
You're clearly thinking about "moral philosophy" as practiced by Western academic philosophers, not "ethics", "morals" and "rules" as most people actually understand these terms. Yes, Kant was trying to define a rule-based morality, and he stated as much. But the Categorical Imperative is not more of a rule than the Utilitarian Imperative is--"choose actions which maximize world Gross National Happiness (or some other index of total well-being)". It is actually closer to "ethics" as a form of dispute resolution between conflicting rights (or "principles of rational agency" as Kant would say), rather than "morality" as understood by most people, i.e. divine command theory/moral absolutism: "I am right and you are wrong and you should do what I say".
Nobody cares about what Kant wrote or thought about his theories, unless they're a scholar who's specifically interested in that. Besides, most LWers know that a lot of Western philosophy is hopelessly garbled and should be reanalyzed from scratch if it is to be practically useful.
Besides, most LWers know that a lot of Western philosophy is hopelessly garbled and should be reanalyzed from scratch if it is to be practically useful.
I don't think most people here think that. I'm pretty sure that you'll find the following two opinions much more prevalent:
Western philosophy is to some extent useful and to that extent it should be taken at face value
Western philosophy is to some extent hopelessly garbled and to that extent it should be thrown out entirely, not "reanalyzed".
False dichotomy. But that's par for the course for Aristotelian philosophers.
Besides, throwing out Western moral philosophy entirely without further comment would not be making it "practically useful". And it would be distinctly unhelpful to its current practitioners, many of whom have a legitimate interest in the questions it seeks to address.
Besides, throwing out Western moral philosophy entirely without further comment would not be making it "practically useful".
Indeed. I see no profit in making something hopelessly garbled into something practically useful, rather than inventing something new to serve that purpose. For similar reasons we're mostly atheists, rather than saying we're Christians and then redefining "God" and various metaphysical 'beliefs' to mean something coherent.
For similar reasons we're mostly atheists, rather than saying we're Christians and then redefining "God" and various metaphysical 'beliefs' to mean something coherent.
And yet we mostly recognize the usefulness of various forms of religion. So, perhaps we should describe ourselves as "religious" as much as Confucians do, or at least as following some moral code and practicing a form of ethics.
The most obvious interpretation of the article is that it is a historical/genealogical account of formalized ethics. After all, the first sentence is:
The search for a formal method for evaluating and quantifying ethicality and morality of human actions stretches back to ancient times.
So its bad when the article then goes on to describe this search incorrectly. I said that it did so and was asked to be explicit. I was. Yeah, maybe there will one day be a Feminist or Islamic AI that acts according to an axiomatic system and non-bivalent logic. But that has absolutely nothing to do with describing the history of the academic fields of feminist and Islamic economics.
Along the same lines, of course I'm thinking about moral philosophy as practiced by Western academic philosophers and not the loose amalgamation of authoritative dictations and ugly prejudices that most people call morality! We're talking about attempts at formalizing ethics, remember? Specifically, we were talking about Kant's attempt. If we want to give a history of such attempts and then totally botch our description of Kant's attempt we've given a bad history no matter what non-philosophers think about Kant.
Kant's Categorical Imperative has nothing to do with the impacts of actions. I don't really know what you're getting at with divine command theory. Its true divine command theory also isn't about the impacts of actions but Kantianism isn't more teleological than divine command theory. Any claim that Kantianism is concerned about impacts requires a huge explanation before it can count as something other than a misdescription.
and not the loose amalgamation of authoritative dictations and ugly prejudices that most people call morality! We're talking about attempts at formalizing ethics, remember?
And yet this "loose amalgamation" seems to work fairly well as a means of resolving disputes and deciding "how we should live". Even the "authoritarive dictations" of moral absolutists are de facto integrated into political debate. One could argue that any meaningful attempt at "formalizing ethics" must account for the views of the man-in-the-street, or at least a significant portion of them. Isn't this what CEV is all about?
Kant's Categorical Imperative has nothing to do with the impacts of actions. ... Any claim that Kantianism is concerned about impacts requires a huge explanation before it can count as something other than a misdescription.
This is a reasonable argument and Psychohistorian has explained it clearly, but the original article only states that Kant's CI is "reflective", much like the Golden Rule and the implied argument of "ecological footprint" supporters: 'we only have a single Earth, so no one could possibly be entitled to more than X of the Earth's ecology'. Also, both John S. Mill and R.M. Hare made forceful claims that Kant's CI must necessarily involve an evaluation of "universalized" impact.
And yet this "loose amalgamation" seems to work fairly well as a means of resolving disputes and deciding "how we should live".
If your baseline is no norms or guidance at all, then it works fairly well. We should have higher expectations. Not sure if you're going anywhere with this.
This is a reasonable argument, but the original article only states that Kant's CI is "reflective", much like the Golden Rule and the implied argument of "ecological footprint" supporters: 'we only have a single Earth, so no one could possibly be entitled to more than X of the Earth's ecology'.
I have no idea what is meant by reflective, here. But here is the full quote:
Immanuel Kant, in his "categorical imperative", sought to define moral duty reflectively, in that everyone was obligated to anticipate and limit the impacts of one's own actions, and "not act as one would not have everyone act."
Kant thought we couldn't know the impacts of our actions, so I don't know how it is his definition of moral duty involved anticipating and limiting the impacts of our actions.
Also, both John S. Mill and R.M. Hare made forceful claims that Kant's CI must necessarily involve an evaluation of "universalized" impact.
Yeah, and they might be right. There are a bunch of examples of Kant thinking he knew something a priori when he definitely didn't. He thought he knew Newton's Laws of Motion a priori, too.
Yeah, and they might be right. There are a bunch of examples of Kant thinking he knew something a priori when he definitely didn't.
Interesting point. So, when I read a paper about ethics and see a casual reference to "Kant's categorical imperative", is the author implicitly stating that Kant was right and Mill and Hare are wrong? If not, then the issue is genuinely uncertain--so what's the big deal about the OP's description?
So there is a distinction between the Categorical Imperative and the formulation of the Categorical Imperative (of which Kant as three). You can argue that the first formulation (the universal maxim one) doesn't return answers for some or all actions unless what Kant is really doing is taking insights from imagining a possible world in which the maxim is universalized and mistaking them for insights about the rationality/self-consistency of the maxim when universalized. But the CI in itself is just the principle of "pure practical reason" from which particular rules are derived.
Take Euclid. He thought that all his conclusions followed deductively from his axioms and that his depictions were just illustrations and played no role in the formal proof. Most people dispute this. Euclid's particular geometry might make undeclared assumptions and use the visual models to draw conclusions that don't follow formally. But we would still never write, "Euclid sought to describe plane geometry as beginning with a set of axioms and from there, proved propositions about planer figures with the help of undeclared assumptions and visual aids."
Take Euclid. He thought that all his conclusions followed deductively from his axioms and that his depictions were just illustrations and played no role in the formal proof. ... But we would still never write, "Euclid sought to describe plane geometry as beginning with a set of axioms and from there, proved propositions about planar figures with the help of undeclared assumptions and visual aids."
Really? Euclid's axiomatic system was only clarified in the late 19th century by Hilbert, and the logic of his visual models is a subject of ongoing research. So this looks like it could be a sensible description of Euclid in an article about how geometrical reasoning might be formalized, since a system which took Euclid's pretenses at face value would face unexpected (and unacceptable) limitations. Now I agree that the OP has other problems, but perhaps this is simply a difference in perspective.
They point is Euclid wasn't trying to prove propositions with the help of undeclared assumptions and visual aids. He was trying to formalize it deductively and thought he had. The fact that he doesn't actually do that is a flaw not a feature of the Elements. Similarly, if indeed one of Kant's formulations of the CI fails to tell us how to act in an a priori way then one wouldn't conclude that Kant sought to explain morality as a concern about impacts. Rather, one would conclude that Kant had failed to show morality isn't a concern about impacts.
The fact that he doesn't actually do that is a flaw not a feature of the Elements.
I'm sorry, this conclusion doesn't follow. According to modern mathematicians, Euclid's contributions to mathematics were twofold:
It is true that Euclid's axioms had a number of gaps which Euclid himself would probably have remedied if he had known about them (e.g. the assumption that a line has at least two points). But the status of his visual aids is far less clear: Euclid himself had no notion of formal proof, and his use of visual aids is in fact quite rigorous. So describing them as a flaw of the Elements seems unjustified: we do not know what Euclid would have done if he'd known about our modern notions of proof, but most likely he would have used them anyway, and he could still be credited with developing the axiomatic method.
Similarly, Kant's contributions from the POV of modern ethicists were:
The technicalities of what Kant meant exactly by "a priori" and "pure practical reason", and whether the notion of "impact" is consistent with them are largely irrelevant to Kant's accomplishment. Even if Kant's CI turned out to be largely concerned with impact, it would still be widely cited as an example of moral duty, and one which may be in some sense logically justified by the principles of rationality.
You're clearly thinking about "moral philosophy" as practiced by Western academic philosophers, not "ethics", "morals" and "rules" as most people actually understand these terms.
You (or the article you posted) were writing about moral philosophy as described by Western philosophers. You were not writing about moral philosophy as viewed by the man on the street. If nobody cares about Kant or his theories, why are you posting an article that explicitly references Kant and his theories?
"may come to be seen as a sort of" ... "to the degree it requires" ...
recalls for me these two shameful examples given in Orwell's Politics and the English Language:
- I am not, indeed, sure whether it is not true to say that the Milton who once seemed not unlike a seventeenth-century Shelley had not become, out of an experience ever more bitter in each year, more alien [sic] to the founder of that Jesuit sect which nothing could induce him to tolerate.
On the one side we have the free personality: by definition it is not neurotic, for it has neither conflict nor dream. Its desires, such as they are, are transparent, for they are just what institutional approval keeps in the forefront of consciousness; another institutional pattern would alter their number and intensity; there is little in them that is natural, irreducible, or culturally dangerous. But on the other side, the social bond itself is nothing but the mutual reflection of these self-secure integrities. Recall the definition of love. Is not this the very picture of a small academic? Where is there a place in this hall of mirrors for either personality or fraternity?
The machines are getting smarter. I skimmed through the whole thing before fingering it as botspam.
Having taught at a university, I can say I'd have been thrilled to get an essay this good from any of my students. My main quibble is that the final paragraph gives the impression of being a conclusion, when it is not. Also, the topics probably should have been covered in at least chronological order, rather than random order.
tl;dr version please? There's a good reason why all scientific articles start with an abstract.
While it could be seen as no more than a basic primer in moral philosophy, it is arguably required reading to anyone unfamiliar with the philosophical background of such concepts as Friendly AI and Coherent Extrapolated Volition.
This is a terrible primer for moral philosophy and if this counts as canon for Friendly AI debates the field is in far worse shape than I thought. It isn't even a decent piece of writing.
Well, this post has now been voted down to -5, but it's still showing as "0" and it hasn't disappeared off the "Recent Posts" header. This is probably not the behavior we want, I think?
Mmm... I'd probably want stuff to not disappear from new/recent posts, even if voted down. Instead, let them fall out of the popular (and fall lower in the promoted list, if a promoted one ended up being voted down that much)
ie, to me, new/recently posted means just that, a non filtering list of simply "what was posted recently", while things like "popular" and so on are more appropriate places for such filtering to occur.
I'm not sure. Surely posts that have been voted down should still be visible to those of us who'd like to read even unpopular posts. Perhaps deletion is the right answer if it really is junk, as RichardKennaway suggests. However, bogus seems to be an actual user who makes reasoned contributions, so I'd hesitate to call it 'spam' or something.
I suggest the post be considered for deletion by the admins. It's junk.
But perhaps bogus (ha!) has something to say. bogus, what is the provenance of that text, and why did you post it? According to Wikipedia, user "24" was banned for gross abuse, and "124" is also under suspicion.
I can't help but think this is machine-generated. Anyone know the link to that utility MIT concocted for detecting machine-generated text?
Hmm... I think this one at Indiana University is the one I was thinking of: Inauthentic paper detector
This post comes out as inauthentic, with a 35% chance of being authentic.
However, Robin Hanson's most recent post comes out as inauthentic, with a 16% chance of being authentic, so maybe this doesn't work as well as I remember.
That authenticity detector is partly based on article length, I believe. I tried testing some posts, and they came out as inauthentic, I then just pasted a series of posts after one another, and the authenticity increased significantly.
Yes - since it's based partially on length and repetition, one could initially fool it by pasting the same machine-generated text twice in a row. They put in a cheap hack to prevent this by explicitly checking for it; I imagine it's still easy to fool.
I tried the three Less Wrong posts before this one, and it classified two of them as inauthentic and one of them as too short to test. I haven't found anything that it considers authentic, so I'd call it a broken detector.
In fairness, it was designed specifically for scientific papers, so I'm not sure if blog posts should be expected to have the same sort of structure. I tried some old philosophical academic papers of mine, and came up in the 80% range (authentic).
Background: This article is licensed under the GNU Free Documentation License and Creative Commons Attributions-Share-Alike Unported. It was posted to Wikipedia by an author who wished to remain anonymous, known variously as "24" and "142". It was subsequently removed from view on Wikipedia, but its text has been preserved by a number of mirrors. While it could be seen as no more than a basic primer in moral philosophy, it is arguably required reading to anyone unfamiliar with the philosophical background of such concepts as Friendly AI and Coherent Extrapolated Volition.
The search for a formal method for evaluating and quantifying ethicality and morality of human actions stretches back to ancient times. While any simple view of right, wrong and dispute resolution relies on some linguistic and cultural norms, a 'formal' method presumably cannot, and must rely instead on knowledge of more basic human nature, and symbolic methods that allow for only very simple evidence.
By contrast, modern systems of criminal justice and civil law evaluate and quantify social and moral norms (usually as a fine or sentence or ruling on damages) rely usually on adversarial process and forensic method, combined using some quasi-empirical methods and many outright appeal to authority and ad hominem arguments. These would all be unacceptable in a formal method based on something more resembling axiomatic proof, which by definion relies on some axioms of morality.
Religious moral codes provide such axioms in most societies, and to some degree, following those strictly could be considered formal in that no more trusted or respected method existed. But our modern concept of what is formal and thus universally trustworthy and transparent is derived from that of the ancient Greeks:
Pythagoras and Plato sought to combine moral and mathematical elements of reality in their work on ontology. This was very influential and the work of both is still consulted to this day, although, the social and political implications of their methods are often rejected by more modern philosophers.
Thomas Aquinas, Francis Bacon and some of the Asharite philosophers shared a belief in some kind of over-arching ethical reality provided by a deity. But while Aquinas and Bacon integrated this with methods of Aristotle and ultimately inspired Jesuit and other Catholic methods of assessing and dispensing justice, resulting in Catholic canon law and other forms of Christian church law, the Asharite influence on Islam rejected parallel Mutazilite work on Aristotle, and eventually resulted in the "classical fiqh" and the shariah now being revived in some parts of the Islamic World. Thus it could reasonably be said that Catholic and Islamic thought diverged on Aristotle's ideas in the middle ages.
Some consider the debate to continue to this day in economics, with the neoclassical economics based firmly on Aristotle's methods via Friedrich Hayek and Karl Popper, against Islamic economics and feminist economics which reject some aspects of Aristotle's logic, e.g. law of excluded middle, and seek to build on some intuitive and morally defensible ontology, as Plato did. This is probably no less of a controversy today than it was in Plato's time, or among the Asharites:
Today, few accept that economics is a means to any ethical or moral end, but more of a technology that serves the ends of those who control and refine it. It remains however that economics does "evaluate and quantify" relationships of such importance, e.g. food, labour, that most humans literally cannot live without an economy around them. Thus an economy embodies assumptions about ethics and morality, and Karl Marx thought that this was itself proof that capitalist economics had subsumed the role of the old feudal methods. This view is current to this day in Marxist economics.
However, the longest-lived view of formal methods as applied to morality comes not from Western but Eastern traditions. Confucianism with its stress on honesty and transparency and etiquette, and moral example of rulers and elders, has at times been seen as a formal method among the Chinese, its "axioms" often respected as much or more than any from science.
Buddhism also stresses notions of right livelihood which seem to be possible to measure and compare in a quasi-formal manner. The Noble Eightfold Path is a set of priorities, ordinal not cardinal, not strictly quantities, but still, a useful framework for any more formal or weighted value theory.
During The Enlightenment the various traditions became more unified:
Immanuel Kant, in his "categorical imperative", sought to define moral duty reflectively, in that everyone was obligated to anticipate and limit the impacts of one's own actions, and "not act as one would not have everyone act.". This can be seen as a restated Golden Rule. In the 20th century it was restated as the ecological footprint, a measure of one's use of the Earth's natural capital, which later became a keystone of green economics.
Other related practices are means of measuring well-being and assessing the implied value of life of various professional ethical codes and infrastructure decisions. While these systems rely on empirical methods for gathering data, and are more interested in "is" than "should", they are at least "transparent" and "repeatable" in a sense that could be called "pre-formal" or "pre-requisite to formal". Some think that they verge at times on the reliability of the quasi-empirical methods in mathematics, in that no conceivable disproof seems possible, but evidence "for" is not disputed - an example being the observation of Marilyn Waring that actions which prepare for war have measurably higher economic values than those within family.
A formal method could reconcile many points of view by excluding forensic or audit methods which passed morally-undesirable outcomes, e.g. war or genocide, or worse which valued them highly. It could not validate any one view a "true" but it could find a "best" or "best next step" for some given time horizon or limited list of models or choices to evaluate. Most proposals for moral purchasing employ some such process. Given a very large number of socially-shared semi-formal economically-committed methods, one might take a mean or other stochastic measure of ethical and moral acceptability to those participating, and thus produce very nearly a species-wide informal method that would have as much reliability as one could expect from any "formal" method. Such are the goals of some NGOs in civil society and peace movement and labour movement and anti-globalization movement circles.
An alternative but less popular view is that "human nature" can be so well understood and modelled mathematically that it becomes possible to assess with formal and mathematical methods, the cognitive bias or moral instinct, e.g. altruism of humans in general, perhaps with measurable variations due to genetics. This view has been popular since the emergence of the theory of evolution, and E. O. Wilson and George Lakoff are among those who have asserted a strong "biological basis" for "morality" and "cognitive science of mathematics" respectively.
Some combination of these views may effective at posing a starting point for models of moral cores and instincts and aesthetics in human beings. However few see them as routes to new moral codes that would be more reliable than the traditional religious ones. A notable exception is B. F. Skinner who proposed exactly such replacement in his "Walden Two", a sort of behaviorist utopia which had many characteristics in common with modern eco-anarchism and eco-villages. Most advocates of such co-housing and extended family living situations, e.g. Daniel Quinn or William Thomas, consider informal, political, "tribal" methods sufficient or more desirable than those involving any kind of "proof".
If so, the long search for a formal method to evaluate and quantify ethical outcomes, even in economics, may come to be seen as a sort of mathematical fetishism, or scientism, or even commodity fetishism to the degree it requires the reduction of quality of life to a series of simple quantities.