The Mathematics Of Altruism

TheMadFool

Altruism is the principle and moral practice of concern for happiness of other human beings or animals, resulting in a quality of life both material and spiritual. — Altruism Page Wikipedia

In an extreme case, altruism may become a synonym of selflessness, which is the opposite of selfishness. However, because altruism ultimately benefits the self in many cases, the selflessness of altruistic acts is brought to question. — Altruism Page Wikipedia

Definition of "Selfless": concerned more with the needs and wishes of others than with one's own; unselfish — Google Definitions

Altruism in biological observations in field populations of the day organisms is an individual performing an action which is at a cost to themselves (e.g., pleasure and quality of life, time, probability of survival or reproduction), but benefits, either directly or indirectly, another individual, without the expectation of reciprocity or compensation for that action. — Altruism Page Wikipedia

A related concept in descriptive ethics is psychological egoism, the thesis that humans always act in their own self-interest and that true altruism is impossible. Rational egoism is the view that rationality consists in acting in one's self-interest (without specifying how this affects one's moral obligations). — Altruism Page Wikipedia

The takeaway from the above is the Argument Against The Possibility Of True Altruism:

1. True altruism is when an altruist doesn't, in any way, shape or form, benefit from an act that fae undertakes and that act benefits others

2. It's impossible for a person to act in a way that doesn't benefit faerself

Ergo,

3. True altruism is impossible

What I'm going to do in this thread is to bring a mathematical perspective to altruism and, with that, I'm going to (try and) prove that true altruism is not only possible but was/is/will be a real, alive and well, phenomenon in our world.

Firstly, there seems to be discrepancy in the definition of selflessness and altruism. Going by the Wikipedia page on altruism, the philosophical view of selflessness is in accordance with premise 1 above i.e. selflessness = True altruism. The lexical definition of selflessness is a bit toned down in that all that's required of selflessness isn't the complete absence of benefit to the self but only that one be "concerned more with the needs and wishes of others than with one's own". The philosophical definition of [i[]selflessness[/i] doesn't tolerate any concern for the self but the lexical definition does and only requires that one value others more than oneself. This difference is important because it gives us the impression that we're dealing with two different kinds of selflessness, one being true altruism (philosophically) and the other in line with the lexical definition (dialed down selflessness). Note here an important distinction between the two definitions of selflessness viz. the lexical definition of selflessness is possible and actual (there are people who care more about others than themselves) and the philosophical definition of selflessness/true altruism (framed in the way it is, it seems impossible)

Secondly, I would like at this point to introduce what I call the Benefit Calculus which is the mathematical portion of my argument. It involves:

(i). Quantification of benefit. This is, at its core, a claim that benefit(s) accrued from our actions can be measured and assigned a number, a number for the sake of simplicity will be whole numbers (no fractions/decimals). So, it's possible to say that a person John got 8 benefits and a person Mary got 2 benefits.

(ii). The simple mathematical operations of subtraction and addition. Here benefits can be compared. For instance if John has 8 benefits and Mary has 2 benefits then, then we can say that John has 6 more benefits than Mary because 8 - 2 = 6 and we can also say things like Mary benefited less than John because 2 benefits < 8 benefits.

Suppose now that there are two people X and Y. X is the budding altruist and is therefore, selfless in the lexical sense i.e. X is "concerned more with the needs and wishes of others ( Y ) than with one's own (X)" and so he decides to do something that benefits Y and it needs no mentioning that X too benefits from the act but here's the deal: according to the Benefit Calculus, the benefit accrued by X is a and the benefit to Y is b and it must be the case that b > a; after all X is] being selfless in the lexical sense (concerned more about Y than X faerself).

So we have the following inequality based on the Benefit Calculus

Y's benefit > X's benefit
...............b > a..............[lexical definition of selflessness]
It follows that,
.........b - a > 0..............[philosophical definition of selflessness = true altruism]

In other words, that Y benefits more than X from X's actions means that, according to the Benefit Calculus, Y has a (positive) benefit of b - a and X has a benefit of 0. In other words, an altruist's (X) action than benefits others ( Y ) and also faerself (X) but in such a way that Y's benefits are greater than X's is equivalent to Y benefiting an amount equal to b - a and X not benefiting at all (X's benefit is 0). I suppose it all boils down to, for all X (altruist) and Y where X's actions accrue a benefit a to X and a benefit b to Y such that b > a, b ( Y ) > a (X) is mathematically indistinguishable from (b - a) ( Y ) > 0 (X).. The lexical definition of selflessness and the philosophical definition of selflessness (true altruism) are mathematically equivalent and we know that the lexical definition of selflessness is real in that there are people selfless in that sense. Ergo, it follows, true altruism is not just possible but actual too!

Echarmion

↪TheMadFool

The whole idea of "absolute altruism" or "true selfishness" is somewhat strange. It seems to presuppose an atomistic view of both persons and their intentions where there are no lasting relations between either.

Your calculation actually is quite apt here, because in a sense the notion is based on a commercialised view of human intentions, where you could calculate something like a distinct "altruism value".

If we take persons to exist in a web of relations to one another, with complex intentions that take the web into account, the problem of "true" or "absolute" altruism vanishes. Because it's then obvious that such an act is merely an abstraction, with real acts always affecting relations among the web in different ways.

TheMadFool

commercialised view of human intentions — Echarmion

Are you referring to my attempt to, in what in the eyes of many will appear not only disgusting but also in complete contradiction to the spirit of morality, reduce altruism and by extension, all of morality, to nothing more than a simple calculation, the likes of which we breeze through with the least bit of care in our daily lives?

I get, or I think that I do, where you're coming from though. My stance on altruism in this thread is consequentialist in character in that there's a quantitative element [the idea of greatest benefit seems to parallel that of the greatest good] to it and the riddle of whether it's right/wrong to hang an innocent person to prevent a riot where many more deaths will occur isn't lost on me.

At this point, all I can say is that quantification (in your terms "commecialisation") is baked into the very notion of good and bad (morality) for the selling point of morality is that good is better than bad and "better" is a word that is, from its definition, inherently quantitative.

web of relations — Echarmion

I understand that there's a complexity to human relations, relations not confined to human-human, and that interferes with, even precludes, the Benefit Calculus if not in principle, on grounds of impracticality. Nonetheless, in my humble opinion, the Benefit Calculus is a rough approximation of how people navigate the moral dimension under the consequentialist banner.

Outlander

fae — TheMadFool

How would you like if i made an interesting post and just included an inrefertial (nonsensical and made up) word in it for no ryhme of reason. English language forum. Thanks.

Echarmion

Are you referring to my attempt to, in what in the eyes of many will appear not only disgusting but also in complete contradiction to the spirit of morality, reduce altruism and by extension, all of morality, to nothing more than a simple calculation, the likes of which we breeze through with the least bit of care in our daily lives? — TheMadFool

No, I am referring to the general idea of thinking about human interactions as governed by opposing, atomistic intentions such as self-interest vs. altruism. So that one might end up with an intention made up of "pure altruism", which would be equal and opposite to "pure self-intetest".

And this leads to the sense of morality you describe here:

At this point, all I can say is that quantification (in your terms "commecialisation") is baked into the very notion of good and bad (morality) for the selling point of morality is that good is better than bad and "better" is a word that is, from its definition, inherently quantitative. — TheMadFool

But perhaps morality isn't about quantifying, as in a commercial relationship, the loss and profit.

TheMadFool

No, I am referring to the general idea of thinking about human interactions as governed by opposing, atomistic intentions such as self-interest vs. altruism. So that one might end up with an intention made up of "pure altruism", which would be equal and opposite to "pure self-intetest". — Echarmion

Sorry, I don't follow. Are there molecular intentions as contrasted with atomic ones? My guess is you're making a reference to the complexity of the moral sphere and that my take on it is too simplistic and fails to capture or address morality's breadth and depth.

Well, I agree with you that there's more to morality in particular and human personality in general but the point is, if I may be so bold as to say so, the underlying idea of altruism is rather simple - others must be more important than yourself. Whether this fails to acknowledge the intricacies of the "web of relations" or not is a different story. All I'm concerned with, at the moment, is showing how, within the framework of existing moral paradigms, true altruism isn't just possible but is alive and well, needing a mathematical perspective to be seen.

TheMadFool

↪Outlander

Fae = He/She
Faer = Him/Her
Faers = His/Hers
Faerself = Himself/Herself

I picked up these unisex/gender ambiguous pronouns from a website.

Mijin

The problem with the wiki, and the OP, is the conflation between whether an action has benefit to the individual, and whether it was motivated by benefit to the individual.

The fact that I can think of a benefit of some action does not prove that that's the reason the individual performed that action.

I'll give a trivial example to illustrate this.

If a flame touches your hand, there is a reflex action to jerk your hand away. This happens *before* the sensation of touching the flame even reaches your brain.

What's the benefit of this action? Well obviously it minimizes the extent of any potential burn to the body.

What motivated me to jerk my hand away?
Nothing. Because, while there's a reason the reflex was selected by evolution, no part of my body or mind needs to know why that action should be performed, any more than I would need to instinctively know why my femur has the shape it has. It just is. Individuals with a femur like mine disproportionately survived. And individuals with a reflex like mine disproportionately survived.

You might say that this is a silly example; since we're talking about something that doesn't go through the brain, this is entirely a phenomenon of the body. Sure. But I want to be sure first that we're all on the same page that there is a distinction between why something evolved, what the benefits are for an action, and the motivation for an action.
I can give examples of conscious actions in my next post :)

Echarmion

Sorry, I don't follow. Are there molecular intentions as contrasted with atomic ones? My guess is you're making a reference to the complexity of the moral sphere and that my take on it is too simplistic and fails to capture or address morality's breadth and depth.

Well, I agree with you that there's more to morality in particular and human personality in general but the point is, if I may be so bold as to say so, the underlying idea of altruism is rather simple - others must be more important than yourself. Whether this fails to acknowledge the intricacies of the "web of relations" or not is a different story. All I'm concerned with, at the moment, is showing how, within the framework of existing moral paradigms, true altruism isn't just possible but is alive and well, needing a mathematical perspective to be seen. — TheMadFool

Well, what I argue is that it's problematic to make the distinction between yourself and others in this way. Neither the sentence "others must be more important than yourself" nor the sentence "I am more important than others" are true.

In a community of mutually dependent beings, like humans are inclined to be, doing something for others is also always doing something for yourself. It is only in large, individualistic societies that you can come up with the notions of a "purely" self-interested or altruistic act. But even then you're imagining yourself as a being with no social relations, which probably isn't true.

Banno

↪TheMadFool

No True Scotsman is altruistic.

TheMadFool

doing something for others is also always doing something for yourself — Echarmion

This is premise 2. It's impossible for a person to act in a way that doesn't benefit faerself of the argument in the OP and I don't contest it. What I believe is possible is that one can act in ways that benefit others more than oneself and, as I go on to argue, that is mathematically equivalent to an act that doesn't benefit oneself at all.

Imagine X acts in a way that produces a benefit b to Y and a to X and that Y's benefit [ b ] > X's benefit [ a ] such that a and b are non-zero. Let a = 2 and b = 8 for the sake of simplicity and take note of the fact that the mathematical relaltionship between 8 and 2 will be maintained for all values of a and b provided b > a

Argument A
(i). 8 > 2 [ Y's benefit is 8 while X's benefit is 2]
(ii). 8 - 2 > 2 - 2
(iii). 6 > 0 [Y's benefit is 6 while X's benefit is 0]

(iv) If [Y's benefit is 8 and X's benefit is 2] then [Y's benefit is 6 and X's benefit is 0]

Argument B
(i) 6 > 0 [Y's benefit is 6 and X's benefit is 0]
(ii) 6 + 2 > 0 + 2
(iii) 8 > 2 [Y's benefit is 8 and X's benefit is 2]

(iv) If [Y's benefit is 6 and X's benefit is 0] then [Y's benefit is 8 and X benefits 2]

Combining the two arguments,
(v) Y benefits 8 and X benefits 2 if and only if Y benefits 6 and X benefits 0

The general formulation of (v) would be,
(vi) Y benefits b and X benefits a such that b > a [altruism] if and only if Y benefits b - a and X benefits 0 [true altruism]

In other words,

(vii) Mathematically, Y benefits more than X [possible and in accordance to your claim that "...doing something for others is also always doing something for yourself"] if and only if Y benefits and X doesn't benefit at all [true altruism]

In other words, if a person can act in a way that benefits others more than faerself, this act is mathematically equivalent to true altruism.

No True Scotsman is altruistic. — Banno

This can be a charge we can level against advocates of true altruism but it's irrelvant insofar as my argument is concerned as, according to my argument, altruism = true altrusim (mathematically).

The Mathematics Of Altruism

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