The American Heritage Dictionary (2011) defines “altruism” as “selflessness.” If one accepts that standard definition, then it seems reasonable to view an “altruistic act” as one that fails to produce a net gain in personal benefit for the actor subsequent to its completion. (Here, we privilege psychological altruism as opposed to biological altruism, which is often dismissed by the “selfish gene” theory of Darwinian selection and notions of reproductive fitness.) Most people, however, assume psychologically-based altruistic acts exist because they believe an act that does not demand or expect overt reciprocity or recognition by the recipient (or others) is so defined. But is this view sufficiently comprehensive, and is it really possible to behave toward others in a way that is completely devoid of self? Is self-interest an ineluctable process with respect to volitional acts of kindness? Here, we explore the likelihood of engaging in an authentically selfless act and capturing true altruism, in general. (Note: For those averse to mathematical jargon, feel free to skip to the paragraph that begins with “[A]t this stage” to get a basic understanding of orthogonality and then move to the next section, “Semantic States as ‘Intrinsic Desires’,” without losing much traction.)
Imagine for a moment every potential (positive) outcome that could emerge as a result of performing some act—say, holding the door for an elderly person. You might receive a “thank you,” a smile from an approving onlooker, someone reciprocating in kind, a feeling you’ve done what your parents (or your religious upbringing) might have expected you to do, perhaps even a monetary reward—whatever. (Note: We assume there will never be an eager desire or expectation for negative consequences, so we require all outcomes to be positive, beneficial events. Of course, a comprehensive model would also include the desire to avoid negative consequences—the ignominy of failing to return a wallet or aiding a helpless animal (an example we will revisit later)—but these can be transformed into positive statements that avoid the unnecessary complications associated with the contrapositive form.)
We suppose there are n outcomes, and we can imagine each outcome enjoys a certain probability of occurring. We will call this the potential vector , the components of which are simply the probabilities that each outcome (ordered 1 through n) will occur:
and where does not have to equal 1 because events are independent and more than a single outcome is possible. (You might, for example, receive both a “thank you” and a dollar bill for holding the door for an elderly woman.) So, the vector represents the agglomeration of the discrete probabilities of every positive thing that could occur to one’s benefit by engaging in the act.
Consider, now, another vector, , that represents the constellation of desires and expectations for the possible outcomes enumerated in . That is, if , then catalogs the interest and desire in outcome . (It might be convenient to imagine as a binary vector of length n and an element of , but we will be better to treat vectors as a subset of the parent vector space to which belongs.) In other words, : either you desire the outcome (whose probability is denoted by) or you don’t. (There are no “probabilities of expectation or desire” in our model.) We will soon see how these vectors address our larger problem of quantifying acts of altruism.
The point in is determined by , and we want to establish a plane parallel to (and including) with normal vector . Define a point X generated by a vector where the scalar and . If is a normal vector of , then the normal-form equation of the plane is given by , and its general equation is
We now have a foundation upon which to establish a basic, quantifiable metric for altruism. If we assume, as we did above, that an altruistic act benefits the recipient and fails to generate any positive benefits for the actor, then such an act must involve potential and expectation vectors whose scalar product equals zero, which means they stand in an orthogonal (i.e., right-angle) relationship to each other. It is interesting to note there are only two possible avenues for – orthogonality within our model: (a) the actor desires and/or expects absolutely no rewards (i.e., ), which is the singular and generally understood notion of altruism, and (b) the actor only desires and/or expects rewards that are simply impossible (i.e., where ). (We will assume .) In all other cases, the scalar product will be greater than zero, violating the altruism requirement that there be no benefit to the actor. Framed another way, (the vector of) an altruistic act forms part of a basis for a subspace in .
At this stage, it might be beneficial to pause and walk through a very easy example. Imagine there are only three possible outcomes for buying someone their morning coffee at Starbucks: (1) the recipient says “thank you,” (2) someone buys your coffee for you (“paying it forward”), and (3) the person offers to pay your mortgage. A reasonable potential vector might be [0.9, 0.5, 0]—i.e., there’s a 90% chance you’ll get a “thank you,” a 50% chance someone else will buy your coffee for you, and a zero-percent chance this person will pay your mortgage. Now, assume your expectation vector for those outcomes is [1, 0, 0]—you expect people to say “thank you” when someone does something nice for them, but you don’t expect someone to buy your coffee or pay your mortgage as a result. The scalar product is greater than zero (), which means the act of buying the coffee fails to meet the requirement for altruism (i.e., the potential vector is not orthogonal to the plane that includes Q and X = tq). In this example, as we’ve seen in the general case, the only way buying the coffee could have been an altruistic act is if (a) the actor expects or desires no outcome at all or (b) the actor expected or desired her mortgage to be paid (and nothing else). We will discuss later the reasonableness of the former scenario. (It might also be interesting to note the model can quantify the degree to which an act is altruistic.)
The above formalism will work in every case where there is a single, fixed potential vector and a specified constellation of expectations; curious readers, however, might be interested in cases where there exists a non-scalar-multiple range of expectations (i.e., when X for some scalar t), and we can dispatch the formalism fairly quickly. In these cases, orthogonality would involve a specific potential vector and a plane involving the displacement of expectation vectors. The vector form of this plane is , and direction vectors , are defined as follows:
with defined similarly for points Q and R; are scalars (possibly understood as time per some unit of measurement for a transition vector), and points S and R of the direction vectors are necessarily located on the plane in question. Unpacking the vector form of the equation yields the following matrix equation:
whose parametric equations are
It’s not at all clear how one might interpret “altruistic orthogonality” between a potential vector and a transition or range (i.e., subtraction) vector of expectations within this alternate plane, but it will be enough for now to consider its normal vectors—one at Q and, if we wish, one at X (through the appropriate mathematical adjustments)—as secondary altruistic events orthogonal to the relevant plane intersections:
Semantic States as ‘Intrinsic Desires’
To this point, we’ve established a very simple mathematical model that allows us to quantify a notion of altruism, but even this model hinges on the likelihood that one’s expectation vector equals zero: an actor neither expects nor desires any outcome or benefit from engaging in the act. This seems plausible for events we can recognize and catalog (e.g., reciprocal acts of kindness, expressions of affirmation, etc.), but what about the internal motivations—philosophers refer to these as intrinsic desires—that very often drive our decision-making process? What can we say about acts that resonate with these subjective, internal motivations like religious upbringing, a generic sense of rectitude, cultural conditioning, or the Golden Rule? These intrinsic desires must also be included in the collection of benefits we might expect to gain from engaging in an act and, thus, must be included in the set of components of potential outcomes. If you’ve been following the above mathematical discussion, such internal states guarantee non-orthogonality; that is, they secure a scalar for because for some internal state k. This means internal states belie a genuine act of altruism. It is important to note, too, these acts are closely associated with notions of social exchange theory, where (1) “assets” and “liabilities” are not necessarily objective, quantifiable things (e.g., wealth, beauty, education, etc.) and (2) one’s decisions often work toward shrinking the gap between the perceived self and ideal self. (See, particularly, Murstein, 1971.) In considering the context of altruism, internal states combine these exchange features: An act that aligns with some intrinsic desire will bring the actor closer to the vision of his or her ideal self, which, in turn, will be subjectively perceived and experienced as an asset. Altruism is perforce banished in the process.
So, the question then becomes: Is it possible to act in a way that is completely devoid of both a desire for external rewards and any motivation involving intrinsic desires, internal states that provide (what we will conveniently call) semantic assets? As I hope I’ve shown, yes, it is (mathematically) possible—and in light of that, then, I might have been better served placing quotes around the word myth in the title—but we must also ask ourselves the following question: How likely it is that an act would be genuinely altruistic given our model? If we imagine secondary (non-scalar) planes composed of expectation vectors from arbitrary points (with ) parallel to the x-axis, as described above, then it is easy to see there are a countably infinite number of planes orthogonal to the relevant potential vector. (Assume because if q is the zero vector, it is orthogonal to every plane.) But there are an (uncountably) infinite number of angles and , which means there exists a far greater number of planes that are non-orthogonal to a given potential vector, but this only considers rotations in as a two-dimensional slice of our outcome space . As you might be able to visualize, the number of non-orthogonal planes grows considerably if we include rotations in . Within the context of three dimensions, and to get a general sense of the unlikelihood of acquiring random orthogonality, suppose there exists a secondary plane, as described above, for every integer-based value of (and ) with rotations in ; then the probability of a potential vector being orthogonal to a randomly chosen plane of independent expectation vectors is highly improbable: p = 1/178 = 0.00561797753, a value significant to eleven digits. If we include rotations to those already permitted, the p-value for random orthogonality decreases to 0.00001564896, which is a value so small as to be essentially nonexistent. So, although altruism is theoretically possible because our model admits the potential for orthogonality, our model also suggests such acts are quite unlikely, especially for large n. For philosophically sophisticated readers, the model supports the theory of psychological altruism (henceforth ‘PA’) that informs the vast majority of decisions we make in response to others, but based on p-values associated with the prescribed model, I would argue we’re probably closer to Thomas Hobbes’s understanding of psychological egoism (henceforth ‘PE’), even though the admission of orthogonality subverts the totalitarianism and inflexibility inherent within PE.
One final thought explicates the obvious problem with our discussion to this point: There isn’t any way to quantify probabilities of potential outcomes based on events that haven’t yet happened, even though we know intuitively such probabilities, outcomes, and expectations exist. To be sure, the concept of altruism is palpably more philosophical or psychological or Darwinian than mathematical, but our model is successful in its attempt to provide a skeletal structure to a set of disembodied, intrinsic desires—to posit our choices are, far more often than they are not, means to ends (whether external or internal) rather than selfless, other-directed ends in themselves.
Some Philosophical Criticisms
Philosophical inquiry concerning altruism is rich and varied. Aristotle believed the concept of altruism—the specific word was not coined until 1851 by Auguste Comte—was an outward-directed moral good that benefited oneself, the benefits accruing in proportion to the number of acts committed. Epicurus argued that selfless acts should be directed toward friends, yet he viewed friendship as the “greatest means of attaining pleasure.” Kant held for acts that belied self-interest but argued, curiously, they could also emerge from a sense of duty and obligation. Thomas Hobbes rejected the notion of altruism altogether; for him, every act is pregnant with self-interest, and the notion of selflessness is an unnatural one. Nietzsche felt altruistic acts were degrading to the self and sabotaged each person’s obligation to pursue self-improvement and enlightenment. Emmanuel Levinas argued individuals are not ends in themselves and that our priority should be (and can only be!) acting benevolently and selflessly towards others—an argument that fails to address the conflict inherent in engaging with a social contract where each individual is also a receiving “other.” (This is the problem with utilitarian-based approaches to altruism, in general.) Despite the varied historical analyses, nearly every modern philosopher (according to most accounts) rejects the notion of psychological egoism—the notion that every act is driven by benefits to self—and accepts, as our model admits, that altruism does motivate a certain number of volitional acts. But because our model suggests very low p-values for PA, it seems prudent to address some of the specific arguments against a prevalent, if not unshirted, egoism.
1. Taking the blue pill: Testing for ‘I-desires’
Consider the following story:
Mr. Lincoln once remarked to a fellow passenger…that all men were prompted by selfishness in doing good. His [companion] was antagonizing this position when they were passing over a corduroy bridge that spanned a slough. As they crossed this bridge they espied an old razor-backed sow on the bank making a terrible noise because her pigs had got into the slough and were in danger of drowning. [M]r. Lincoln called out, ‘Driver can’t you stop just a moment?’ Then Mr. Lincoln jumped out, ran back and lifted the little pigs out of the mud….When he returned, his companion remarked: ‘Now Abe, where does selfishness come in on this little episode?’ ‘Why, bless your soul, Ed, that was the very essence of selfishness. I should have had no peace of mind all day had I gone on and left that suffering old sow worrying over those pigs.’ [Feinberg, Psychological Altruism]
The author continues:
What is the content of his desire? Feinberg thinks he must really desire the well-being of the pigs; it is incoherent to think otherwise. But that doesn’t seem right. Feinberg says that he is not indifferent to them, and of course, that is right, since he is moved by their plight. But it could be that he desires to help them simply because their suffering causes him to feel uncomfortable (there is a brute causal connection) and the only way he has to relieve this discomfort is to help them. Then he would, at bottom be moved by an I-desire (‘I desire that I no longer feel uncomfortable’), and the desire would be egoistic. Here is a test to see whether the desire is basically an I-desire. Suppose that he could simply have taken a pill that quietened the worry, and so stopped him being uncomfortable, and taking the pill would have been easier than helping the pigs. Would he have taken the pill and left the pigs to their fate? If so, the desire is indeed an I-desire. There is nothing incoherent about this….We can apply similar tests generally. Whenever it is suggested that an apparently altruistic motivation is really egoistic, since it [is] underpinned by an I-desire, imagine a way in which the I-desire could be satisfied without the apparently altruistic desire being satisfied. Would the agent be happy with this? If they would, then it is indeed an egoistic desire. if not, it isn’t.
This is a powerful argument. If one could take a pill—say, a tranquilizer—that would relieve the actor from the discomfort of engaging the pigs’ distress, which is the assumed motivation for saving the pigs according to the (apocryphal?) anecdote, then the volitional act of getting out of the coach and saving the pigs must then be considered a genuinely altruistic act because it is directed toward the welfare of the pigs and is, by definition, not an “I-desire.” But this analysis makes two very large assumptions: (1) there is a singular motivation behind an act and (2) we can whisk away a proposed motivation by some physical or mystical means. To be sure, there could be more than one operative motivation for an action—say, avoiding discomfort and receiving a psychosocial reward—and the thought-experiment of a pill removing the impetus to act does not apply in all cases. Suppose, for example, one only desires to avoid the pigs’ death and not the precursor of their suffering. Is it meaningful to imagine the possibility of a magical pill that could avoid the pigs’ death? If by the “pill test” we intend to eviscerate any and all possible motivations by some fantastic means, then we really haven’t said much at all. We’ve only argued the obvious tautology: that things would be different if things were different. (Note: the conditional A –> A is always true, which means A <–> A is, too.) Could we, for example, apply this test to our earlier coffee experiment? Imagine our protagonist could take a pill that would, by acting on neurochemical transmitters, magically satisfy her expectation and desire for being thanked for purchasing the coffee. Can we really say her motivation is now altruistic, presumably because the pill has rendered an objective “thank you” from the recipient unnecessary? In terms of our mathematical model, does the pill create a zero expectation vector? It’s quite difficult to imagine this is the case; the motivation—that is, the expectation of, and desire for, a “thank you”—is not eliminated because it is fulfilled by a different mechanism.
2. Primary object vs. Secondary possessor
As a doctor who desires to cure my patient, I do not desire pleasure; I desire that my patient be made better. In other words, as a doctor, not all my particular desires have as their object some facet of myself; my desire for the well-being of my patient does not aim at alteration in myself but in another. My desire is other-regarding; its object is external to myself. Of course, pleasure may arise from my satisfied desire in such cases, though equally it may not; but my desire is not aimed at my own pleasure. The same is true of happiness or interest: my satisfied desire may make me happy or further my interest, but these are not the objects of my desire. Here, [Joseph] Butler simply notices that desires have possessors – those whose desires they are – and if satisfied desires produce happiness, their possessors experience it. The object of a desire can thus be distinguished from the possessor of the desire: if, as a doctor, my desire is satisfied, I may be made happy as a result; but neither happiness nor any other state of myself is the object of my desire. That object is other-regarding, my patient’s well-being. Without some more sophisticated account, psychological egoism is false. [See Butler, J. (1726) Fifteen Sermons Preached at the Rolls Chapel, London]
Here, the author errs not in assuming pleasure can be a residual feature of helping his patients—it can be—but in presuming his desire for the well-being of others is a first cause. It is likely that such a desire originates from a desire to fulfill the Hippocratic oath, to avoid imposing harm, which demands professional and moral commitments from a good physician. The desire to be (seen as) a good physician, which requires a (“contrapositive”) desire to avoid harming patients, is clearly a motivation directed toward self. Receiving a “thank you” for buying someone’s coffee might create a feeling of pleasure within the actor (in response to the pleasure felt and/or exhibited by the recipient), but the pleasure of the recipient is not necessarily (and is unlikely to be) a first cause. If it were a first (and only) cause, then all the components of the expectation vector would be zero and the act would be considered altruistic. Notice we must qualify that if-then statement with the word “only” because our model treats such secondary “I-desires” as unique components of the expectation vector. (“Do I desire the feeling of pleasure that will result in pleasing someone else when I buy him or her coffee?”) We will set aside the notion that an expectation of a residual pleasurable feeling in response to another’s pleasure is not necessarily an intrinsic desire. I can expect to feel good in response to doing X without desiring, or being motivated by, that feeling—this is the heart of the author’s argument—but if any part of the motivation for buying the coffee involves a desire to receive pleasure—even if the first cause involves a desire for the pleasure of others—then the act cannot truly be cataloged as altruistic because, as mentioned above, it must occupy a component within q. The issue of desire, then, requires an investigation into first causes (i.e., “ultimate”) motivations, and the logical fallacy of Joseph Butler’s argument (against what is actually psychological hedonism) demands it.
3. Sacrifice or pain
Also taken from the above link:
A simple argument against psychological egoism is that it seems obviously false….Hume rhetorically asks, ‘What interest can a fond mother have in view, who loses her health by assiduous attendance on her sick child, and afterwards [sic] languishes and dies of grief, when freed, by its death, from the slavery of that attendance?’ Building on this observation, Hume takes the ‘most obvious objection’ to psychological egoism.…[A]s it is contrary to common feeling and our most unprejudiced notions, there is required the highest stretch of philosophy to establish so extraordinary a paradox. To the most careless observer there appear to be such dispositions as benevolence and generosity; such affections as love, friendship, compassion, gratitude. […] And as this is the obvious appearance of things, it must be admitted, till some hypothesis be discovered, which by penetrating deeper into human nature, may prove the former affections to be nothing but modifications of the latter. Here Hume is offering a burden-shifting argument. The idea is that psychological egoism is implausible on its face, offering strained accounts of apparently altruistic actions. So the burden of proof is on the egoist to show us why we should believe the view.
Sociologist Emile Durkheim argued that altruism involves voluntary acts of “self-destruction for no personal benefit,” and like Levinas, Durkheim believed selflessness was informed by a utilitarian morality despite his belief that duty, obligation, and obedience to authority were also counted among selfless acts. The notion of sacrifice is perhaps the most convincing counterpoint to overriding claims to egoism. It is difficult to imagine a scenario, all things being equal, where sacrifice (and especially pain) would be a desired outcome. It would seem that a decision to act in the face of personal sacrifice, loss, or physical pain would almost certainly guarantee a genuine expression of altruism, yet we must again confront the issue of first causes. In the case of the assiduous mother, sacrifice might service an intrinsic (and “ultimate”) desire to be considered a good mother. In the context of social-exchange theory, the asset of being (perceived as) a good mother outweighs the liability inherent within self-sacrifice. Sacrifice, after all, is what good mothers do, and being a good mother resonates more closely with the ideal self, as well as society’s coeval definition of what it means to be a “good mother.” In a desire to “do the right thing” and “be a good mother,” then, she chooses sacrifice. It is the desire for rectitude (perceived or real) and the positive perception of one’s approach to motherhood, not solely the sacrifice itself, that becomes the galvanizing force behind the act. First causes very often answer the following question: “What would a good [insert category or group to which membership is desired] do?”
What of pain? We can imagine a scenario in which a captured soldier is being tortured in the hope he or she will reveal critical military secrets. Is the soldier acting altruistically by enduring intense pain rather than revealing the desired secrets? We can’t say it is impossible, but, here, the aegis of a first cause likely revolves around pride or honor; to use our interrogative test for first causes: “Remaining true to a superordinate code is what [respected and honorable soldiers] do.” They certainly don’t dishonor themselves by betraying others, even when it’s in one’s best interest to do so. Recalling Durkheim’s definition, obedience (as distinct from the obligatory notion of duty) also plays an active role here: Honorable soldiers are required to obey the established military code of conduct, so the choice to endure pain might be motivated by a desire to be (seen as) an obedient and compliant soldier who respects the code rather than (merely) an honorable person, though these two things are nearly inextricably enmeshed. To highlight a relevant religious example, Jesus’ sacrifice on the cross might not be considered a truly altruistic act if the then-operative value metric privileged a desire to be viewed by the Father as a good, obedient Son, who was willing to sacrifice Himself for humanity, above the sacrifice (and pain) associated with the crucifixion. (This is an example where the general criticism of Durkheim’s “utilitarian” altruism fails; Jesus did not receive from His utilitarian sacrifice in the way mankind did.) These are complex motivations that require careful parsing, but there’s one thing we do know: If neither sacrifice nor pain can be related to any sort of intrinsic desire that satisfies the above interrogative test, then it probably should be classified as altruistic, even though, as our model suggests, this is not likely to be the case.
Given the arguments, it is still unclear why we should consider psychological egoism to be obviously untrue. One might appeal to introspection or common sense, but neither is particularly powerful. First, the consensus among psychologists is that a great number of our mental states, even our motives, are not accessible to consciousness or cannot reliably be reported…through the use of introspection. While introspection, to some extent, may be a decent source of knowledge of our own minds, it is fairly suspect to reject an empirical claim about potentially unconscious motivations….Second, shifting the burden of proof based on common sense is rather limited. Sober and Wilson…go so far as to say that we have ‘no business taking common sense at face value’ in the context of an empirical hypothesis. Even if we disagree with their claim and allow a larger role for shifting burdens of proof via common sense, it still may have limited use, especially when the common sense view might be reasonably cast as supporting either position in the egoism-altruism debate. Here, instead of appeals to common sense, it would be of greater use to employ more secure philosophical arguments and rigorous empirical evidence.
In other words, we cannot trust thought processes in evaluating our motivations to act. We might think we’re acting altruistically—without any expectations or desires—but we are often mistaken because, as our earlier examples have shown, we fail to appreciate the locus of first causes. (It is also probably true, for better or worse, that most people prefer to think of themselves more highly than they ought—a process that better approaches exchange ideas of the ideal self in choosing how and when to act.) Jeff Schloss, the T.B. Walker Chair of Natural and Behavioral Sciences at Westmont College, suggests precisely this when he states that “people can really intend to act without conscious expectation of return, but that [things like intrinsic desires] could still be motivating certain actions.” The interrogative test seems like one easy way to clarify our subjective intuitions surrounding what motivates our actions, but we need more tools. Our model seems to argue that the burden of proof for altruism rests with the actor—“proving,” without resorting to introspection, one’s expectation vector really is zero—rather than “proving” the opposite, that egoism is the standard construct. Our proposed p-values based on the mathematics of our model strongly suggest the unlikelihood of a genuine altruism for a random act (especially for large n), but despite the highly suggestive nature of the probability values, it is unlikely they rise to the level of “empirical evidence.”
Though I’ve done a little work in a fun attempt to convince you genuine altruism is a rather rare occurrence, generally speaking, it should be said that even if my basic conceit is accurate, this is not a bad thing! The “intrinsic desires” and (internal) social exchanges that often motivate our decision-making process (1) lead to an increase in the number of desirable behaviors and (2) afford us an opportunity to better align our actions (and ourselves) with a subjective vision of an “ideal self.” We should note, too, the “subjective ideal self” is frequently a reflection of an “objective ideal ([of] self)” constructed and maintained by coeval social constructs. This is a positive outcome, for if we only acted in accordance with genuine altruism, there would be a tragic contraction of good (acts) in the world. Choosing to act kindly toward others based on a private desire that references and reinforces self in a highly abstract way stands as a testament to the evolutionary psychosocial sophistication of humans, and it evinces the kind of higher-order thinking required to assimilate into, and function within, the complex interpersonal dynamic demanded by modern society. We should consider such sophistication to be a moral and ethical victory rather than the evidence of some degenerate social contract surreptitiously pursued by selfish persons.
Bernard Murstein (Ed.). (1971). Theories of Attraction and Love. New York, NY: Springer Publishing Company, Inc.