Tuesday, October 30, 2012

The Dualism of Practical Reason: Sidgwick

The Dualism of Practical Reason from "Some Fundamental Ethical Controversies" by Sidgwick 

Sometimes we are faced with decisions in which we must choose between our own good and the good of others.  Of course, there are happy situations where the two converge, but the difficult moral situations are those in which the two interests do not aligne, and a choice must be made.  It is in these types of situations where Sidgwick says we experience the dualism of practical reason.

What does the dualism of practical reason mean?  To figure this out lets take the concepts in isolation.  Practical reason is the type of reasoning we use to decide what to do.  For (a very simple) example, if I'm hungry, my practical reason tells me I should make a "samich" rather than drink wine.  Or if I want to graduate, practical reason tells me I need to write my papers at night rather than go out drinking.  We also employ practical reasoning in more complex situations that involve values.  Suppose I value virtue (whatever that is).  Practical reason is what I employ to decide which actions will bring about virtue. Essentially, practical reason is what we use to determine how we should go about achieving some end--usually normative.  

Dualism, in this context, refers to the idea that our practical reason is divided between two sometimes conflicting ends.  These two ends are the good of other and our own good.  For Sidgwick the goal of seeking our own good/happiness is just as reasonable as seeking the good/happiness of others.  Because both goals are reasonable, in situations where these goals conflict, our practical intuition will be split.  That is, our practical reason will be in a stalemate with itself and so cannot be used to determine what to do.  In such cases, what we do will be a function of the relative strength of non-rational impulses.  In other words, what we decide to do will be determined by whatever desire is strongest, not what is rational.

For most of moral philosophy prior to Sidgwick moral theorists thought two things: (a) morality is rational and (b) what is right and good for the individual to do will converge with what is right and good for society.  Despite his desire that both be so, Sidgwick concludes that they can't both be true because of the dualism of practical reason.  Lets look at that in a little more detail...

The Dualism of Practical Reason:  The Problem of Rational Egoism
For many traditional moral theorists, it is a "dictate of reason" to prefer the general good to that of yourself.  That is, in cases where you stand to benefit at the expense of others, to do so would be immoral and irrational (because morality and reason are intertwined).

The problem is that some people might refuse to acknowledge the reasonableness of this principle.  A person might say that it is more or equally rational to prefer my own good as the end of my actions.  So, the only way such a person could act for the general good (in cases of conflict) is to act irrationally.   

It seems, that if we are honest with ourselves, we must acknowledge that reason "assigns a different end to the individual and to the [group]."  That is, it is just as reasonable to sacrifice one's own happiness to the group as it is to prefer one's own happiness to the group's.  If we want to maintain that morality is rational, that is, we can determine what to do in moral situations by appeal to our practical reason, we will find that what we ought to do sometimes conflicts.

Internalism vs Externalism
So, there are a couple of philosophical things going on here which has to do with what is called "internalism" and "externalism".  I wrote a post last year on this topic (see the Williams article) if you want more depth, but I'll quickly sketch it out here.  The issue is about what constitutes a reasonable end.

So far we've just said that both preference of one's own happiness (because it is important to you) and preference of the general good are both reasonable ends for our practical reason to realize.  But are they equally reasonable?

An internalist says that the reasonableness of an end of action is determined, well...internally.  That is, if I think that my well-being is more important to me than the general well-being, then that's good enough for it to constitute a reasonable reason for my action.  My subjective desires and beliefs about what's important determine what's reasonable for me to do.  You can't tell me "no, you are mistaken that your personal well-being is important to you".  How could I be mistaken about what is important to me?  That doesn't seem to make any sense.  So, so long as we say it is rational for an individual to pursue what is important to that particular individual, then actions toward those goals will be rational.

The externalist says, ho..ho..ho..hold on a second!  Not all reasons (i.e., ends) for action are reasonable, and furthermore reasons aren't merely internal desires for things.  Reasons stand outside of us.  Ok, yes x, y, z is important you but that doesn't make it objectively important or an objective reason for action.   There are reasons for action that everybody would agree are reasonable.  For example (from Parfit), if you are in a burning building and you can safely leave, you have a good reason to leave.  Everyone would agree to the reasonableness of your not wanting to get burned to deph.  You have a reason (in the external sense) to x-scape from the burning building.

So, the externalist says that there are different degrees of reasonableness ranging from the subjective to the objective.  Rationality is acting on the reasons to which everyone would subscribe.   Everybody has a reason to care about the general well-being (because they are a part of it) but only you (and maybe your momma) care about your particular well-being above the general well being.  Acting on objective reasons over subjective (ie. internal) reasons is a more rational thing to do.  Since (if!) morality is rational, then we should prefer the general good over our own in cases where they conflict.  Or at least in cases where I benefit at the expense of er'body elks.

Internalists deny the existence of external reasons, they say all reasons are internal, but that doesn't necessarily mean that people only have selfish motives for action.  Some people might, as part of their psychology prefer the good of others to their own.  So, their reason for acting benevolently will arise from wanting to see this preference realized.  Internalism doesn't condemn us to crass egoism.  People's actions will simply be a function of their internal preferences.  We just have hope that most desire the good of others!

Dualism of Practical Reason 2
There is another moral theory that demonstrates the split of our practical reason.  In Kant's moral philosophy we are always to act accordian to reason because it is supposed that reason alignes perfectly with the good.  That is, the right and the good perfectly overlap.

For Kant, the right is a matter of following absolute (rational) moral principles.  The problem is, it doesn't take much imagination to come up with situations where following the moral principles would cause us to act in a way we'd call--by any reasonable sense--immoral.  

The standard example is that of lying.  Kant says we should never lie.  Well, what about if I'm in WW2 Germany and I'm hiding Jews (down the well) and a gestapo agent asks me if I'm hiding any Jews down the well?  Our moral sensibilities seem to tell us that in such cases the moral position is to lie.

Sidgwick's point is this: even supposing we could rationally intuit or deduce a set of moral principles, there will inevitably be situations where these principles conflict and we will have to chose one over the other.  So, our practical reason will be split.  Furthermore, in such cases we need an "master" principle of morality.  One that tells us how to order the other principles when they conflict.

So, lets grant that Kant came up with the set of rational principles.  In situations where following them would seem to be causing great harm, it appears that our practical reason will be split.  Do we follow the rules just for the sake of following the rules or do we abide by another rule that says we should minimize general harm and maximize general happiness? 

 Only the most martinet of people follow rules "because that's the rule and following rules is what is good".  Most reasonable people acknowledge that when rules--no matter how rational--cause more harm then good, we should at least consider the principle of harm/utility.  So, even if we have a system of rational rules, our reason will still be split; that is, there will still be a dualism of practical reason. 

Saturday, October 27, 2012

Sidgwick on Philosophical Moral Intuitions

Sidgwick on Philosophical Intuitions (Book 3, Ch. 13)

Yo, check it.  Weez gonna learn about Sidgwick's philosophical intuitions.  Sidgwick (aka Jesus--in my opinion) had this idea that moral truths can be found in the "Common Sense" morality of the everyman.  Well, not exactly.  More precisely, he thought that if one could systematically analyze the common sense moral principles that are floating around and reject the incoherent (i.e., tautological) axioms, and clarify those that are left--then we can discover the self-evident moral axioms to which every rational person will agree.

What he ends up with are the principles of Justice, Prudence, and Rational Benevolence.  And he regards the apprehension of "these abstract truths, as the permanent basis of the common conviction that the fundamental precepts of morality are essentially reasonable."  What's important to extract from this conclusion is that the fundamental principles of morality are rational and self-evident.

By 'rational' he means that each on its own is internally consistent (but not necessarily consistent with the others--this will come up later).  By 'self-evident' he means that neither one needs to be justified to be accepted as true.  We somehow are just able to grasp their truth.

So, lets take a closer look at these famous universal axioms of morality...

Justice:  Justice can be divided into two main ideas, both of which are too general to serve as particular rules, but are recognized as giving general guidance.
(1)  Golden rule-ish justice:  "whatever action any of us judges to be right for himself, he implicitly judges to be right for all similar persons in similar circumstances."
(2)  Legal Justice: impartiality in the application of general rules; i.e., treat like cases alike.

Prudence (Rational Self-Love):  One ought to aim at one's own good.  With the qualification that, given greater probability of realizing a future good over a present good, we ought not pursue the present good if I causes us to lose the future good.  In other words, suppose you will get 1000 units of happiness from finishing your paper on time and 10 units of happiness from going on facebook.  Going on facebook will prevent you from finishing your paper on time.  So, stay the fuck off facebook!

Rational Benevolence: The good of one individual is of no more importance that the good of another individual, from the point of view of the impartial universe, (unless you live in 'merica, cuz God thinks 'merca in #1--that's a scientifical fact)

Ok, so now that we know what the universally true moral axioms are, lets qualify them.  While these are absolute practical principles, they are too abstract and too universal in scope to determine what we ought to do in any particular case; "particular duties have still to be determined by some other method."  Nevertheless, (it is supposed) they are useful guides to which all particular moral rules can be logically traced.

I think there's a question here about how significant Sidgwick's 3 principles are.  I guess from the point of view of the philosophical task of demonstrating--contra the skeptic--that there are universal moral principles, we might say that Sidgwick is successful.  

But from the point of view of utility, I'm not sure that these principles offer us much guidance when we have tough moral decisions.  Of course, Sidgwick acknowledges their generality, but perhaps his project (at this point) is not to present a practical set of principles, rather his enterprise is one of description. 

As Sidgwick later points out, the 3 principles aren't necessarily logically consistent with each other.  That is to say, in situations where prudence conflicts with rational benevolence there is no rational argument to prefer the one principle to the other, or to shew that one can be derived from the other:

But in the rarer cases of a recognized conflict between self-interest and duty, practical reason, being divided against itself, would cease to be a motive on either side; the conflict would have to be decided by the comparative preponderance of one or other of two groups of non-rational impulses.

By 'non-rational impulses' he means 'desires' for things other than self-interest and duty to society.

Why These and not Other Ones?
So, given all the possible moral principles that exist, why are these the self-evident ones and not some others?  Recall that Sidgwick is looking for the founding principles of morality.  If a principle is foundational that means it can't be deduced.  If we deduce it from some other premises then it would seem that the premises were foundational rather than the conclusion--in fact, this is true by definition.  So, Sidgwick needs principles that aren't rationally deduced, yet self-evidently true to er'body.

Consider some other rules like, "you ought not to lie" or even "you ought not to kill".  These principles are not self-evident.  They seem to require some rational justification, and they aren't universally accepted without qualification--whereas Sidgwick's principles don't require justification.  His principles are as self-evident as a mathematical principle (such as the sum of any two even numbers will equal an even number).

The upshot here is that foundational principles will not be deducible from other principles.  This in turn which means that if there are universal foundational principles they will only be accessible through our intuitions (how else could we know them?).  The best place to look for universal moral intuitions is in the "common sense"  (i.e., informal, everyman's) morality.  Of course, the common sense morality isn't a systematic moral system but a mishmash of confused and conflicting principles.  However, if you go through through it systematically (as he does in an earlier chapter) and tease out the content-ful from the vacuous, you will end up with Sidgwick's 3.  That is, all of the principles in common sense morality are either vacuous or can be deduced from Sidgwick's 3.

The Origens of Moral Principles 
This this bring up the issue of where moral principles come from (Jesus...duh!).  So, of course, Sidgwick, like virtually all moral philosophers is hopelessly misguided on this question because he doesn't realize that er'thing he needs to know about morality he can find in the Bible...or the Koran...or the Vedic texts,  or the Tipitaka...etc...

Anyhow, for Sidgwick, because we can't by definition reason our way to foundational moral principles, the only way to access these self-evident moral truths is through our intuitions (not in a new-age-y sense, but a more sophisticated philosophical sense, the details of which don't really matter at this point).  

But this raises an objection which goes like this:  intuitions are just a psychological fact.  The mere fact that our psychologies align on these principles only tells us something about the psychology of humans, it doesn't tell us anything about the objective world in regards to morality.  That is, psychological convergence doesn't necessarily imply truth, only that we share some psychological intuitions--which isn't surprising considering we share the same evolutionary past.

Sidgwick's reply to this is that the critique is engaging in a sort of genetic fallacy/burden of proof-y argument.  It goes like this.  The other principles in common sense morality (those that he discarded) where shown to be either false or vacuous without appeal to their origens.  So, we should apply the same sort of standard to the 3.  If they are false we should be able to shew it by pointing out that they have internal some logical problem or that they are vacuous.  In short, a principle's origen is irrelevant to its truth value.

There are obviously some assumptions about human reason but setting that aside, I think Sidgwick has a strong case here.  Lets suppose someone is a liar but occasionally tells the truth.  When they say something is that is true, we don't automatically say it's false just because it came from a source that often produces false statements.  That would be committing the genetic fallacy.  Instead we ought to evaluate statements and principles on their own merit.

There is another objection to Sidgwick.  This objection agrees with his invokation of the genetic fallacy but says that he has drawn the wrong conclusion.  Sidgwick's conclusion excludes other possible self-evident principles.  In other words, he was on the right track but he missed some!

Fairly recently there has been a huge collaborative project between moral psychologists, cognitive scientists, and moral philosophers to empirically discover the foundations of morality loosely organized by Haidt.  The most current version of the "moral foundations" theory looks something like this:  there are 6 foundations of morality.  They are liberty/vs oppression, don't harm others/care for others, sanctity/purity, fairness/don't cheat/proportionality, loyalty (to group and individuals), and respect for authoritar.

The moral foundations theory explains cultural differences in moral rules as arising from the assignment of different values to each foundation.  For example, Western liberal countries have the liberty/vs oppression foundation very high and the sanctity/purity quite low (there are, however, regional variations--predominately between the north and the south).  More traditional cultures place a higher value (than Western cultures) on sanctity/purity and respect for authoritar.
(Fun activity! find out your own value weights!) http://www.yourmorals.org/

I think you might be able to make the case that Sidgwick's 'prudence' could be rolled into liberty/vs oppression, rational benevolence could be rolled into "don't harm others/care for others", and Justice could be accommodated in "fairness/don't cheat/proportionality".   The fit might not be exact but with a little exigenical liberty and charity I think it could be done.

The problem will be accounting for the other three:  purity, loyalty, and respect for authoritar.  Did Sidgwick's intuitions miss out on something?  Did he dismiss something from the common sense morality that he shouldn't have?  Or is there some way to fit these remaining 3 into Sidgwick's?

My inclination is that the psychologists and cognitive scientists probably have a model (based on resources and method) that better reflects global intuitions than does Sidgwick's arm-chair theory.

What does this mean for Sidgwick's theory?  Maybe we can say that he got some things right, but he missed a couple of things too.  Maybe what I need to do is to go back to the text and look at what he dismisses.

Another possibility is that the moral foundations project has a different concept of "foundational moral principle" than does Sidgwick.  
Stitch and Machery have done some interesting work on the nature of moral concepts to show that often different theories are talking past each other.  For example, the moral foundations theory people might mean by "foundational moral concept" motivating force in an agent's decision making, while Sidgwick might mean the fundamental premises to which all rational moral decision making can be traced.  

So, one possibility is that we are comparing apples and oranges.  We'd need to do some work to determine precisely what each means by "fundamental moral concept" to properly evaluate whether the two theories are different. 

Assuming similar notions of what it is to be a fundamental moral concept, one implication of accepting the "moral foundations theory" is that it weakens Sidgwick's claim that all moral rules are derived from just 3 self-evident moral principles.

Sidgwick derives further confidence in his conclusion from the history of (Western) ethics where we find many of the same principles (Clarke, Kant, Mill).  The difference between Sidgwick and these other schools of ethics are that they try to shew that the moral axiom are logically linked.  That is, by pursuing the good of all we make ourselves better off or that by pursuing our own good, we make society better off.  Sidgwick's main point is that all attempt to logically connect these principles fail.  The fact that there are self-evident moral truths don't necessitate that they be logically connected.

Friday, October 12, 2012

Moore's Criticism of Mill's Proof of Utilitarianism

Moore's Criticism of Mill's Proof of Utilitarianism
Ok, in the previous post we looked at Sidgwick's criticisms of Mill's proof of utilitarianism.  As the title might suggest, we will now turn to Moore's criticisms.  For a more detailed explanation of Mill's proof, check out the previous post.  For this post I'll just present Mill's proof in its skeleton form so we are easily able to refer back to specific premises.

(I will write a post within a week about how Mill might reply to Sidgwick and Moore)
Favourite Quote:
"Happiness, as we saw, has been defined by Mill, as 'pleasure and the absence of pain'.  Does Mill mean to say that 'money,' these actual coins, which he admites to be desired in and for themselves, are a part either of pleasure or of the absence of pain?  Will he maintain that those coins themselves are in my mind, and actually a part of my pleasant feelings?  If this is to be said, all words are useless:  nothing can possibly be distinguished from anything else; if those two things are not distinct, what on earth is?  We shall hear next that this table is really and truly the same thing as this room; that a cab-horse is in fact indistinguishable from St Paul's Cathedral..." (Moore, p.71)

Quick Sketch of Mill's Proof

Proof of Part 1: Happiness is a Good

(P1)  The only evidence that something is desirable (i.e. good) is that people desire it.
(P2)  People desire their own happiness.
(P3)  Thus, a particular person's happiness is desirable to them (and therefore an end),
(P4)  Thus, happiness (as conceived by each person) is an end and (therefore) a good to that person.
(C1)  So, the general happiness is a good to the aggregate of all people.

Proof of Part 2:  Happiness is the only good.
All desires are either a means to happiness or a component of a compound notion of happiness.  Since we identify ends by whether they are desirable, (C2) happiness is the only thing desired as an end in itself.

Grand Conclusion
Because happiness is the sole end of human action "and the promotion of it the test by which to judge of all human contact," it must be the standard of morality (Mill, p. 125).  In other words, utilitarianism is true.  

Moore's Criticisms of Mill's Proof
Moore identifies most of the same problems that Sidgwick does, however, his account of why Mill went wrong differs.

Argument 1: Naturalistic Fallacy Via Fallacy of Equivocation
Recall that Sidgwick also accuses Mill of the fallacy of equivocation (failing to hold constant the meaning of a term through out the premises to the conclusion).  Moore makes the same claim against Mill but explains the equivocation as causing Mill to commit the naturalistic fallacy.  

The naturalistic fallacy is committed anytime the property of moral good is equated with a natural property, and Mill commits this fallacy when he tells us that 'good' means 'desirable'.  To make his argument, Moore relies on the same disanalogy Sidgwick recognized in Mill's analogy between 'visible' and 'desirable'.  Mill tells us that to know what is is visible we observe what is able to be seen and so, to know what is desirable we observe what people desire.  The problem is that 'visible' means 'able to be seen' but 'desirable' doesn't mean 'able to be desired': it means something ought to be desired or is worthy of being desired.

However, if we simply follow Mill's analogy and interpret 'desirable' as the descriptive 'able to be desired' then it follows that just about anything can be good.  Because, it seems just about anything can, in a descriptive sense, be desired--including 'bad' things.  Well, that's not going to help Mill's case....

But that's not the main problem.  The main problem that arises from attributing the descriptive interpretation to 'desirable' is that what we ought to do (the normative rule of action) collapses into the descriptive claim about what we do do.  

In other words, he established his normative (i.e. , what we ought to do) conclusion that "the general happiness is good because it is desirable"  through the descriptive claim that people do desire their own happiness.  But if we hold the descriptive meaning constant throughout the premises and apply it to the conclusion, then the conclusion itself becomes descriptive--i.e., the general happiness is good because we are able to desire it.  

But that doesn't tell us that we ought to desire it or that it ought to be desired, which is what Mill wants to say.  Furthermore, as we have seen, being able to desire something doesn't imply it is what we ought to desire, nor does it make it the standard by which to judge all human conduct.  

By equating 'desirable' with 'the good' and holding Mill to the descriptive meaning of desirable (established in the premises), he cannot derive the normativity he wants in his conclusion.   His alternative is to equivocate on the meaning of 'desirable', which invalidates his argument because it commits the fallacy of equivocation.  

Argument 2:  Means-Ends vs Psychological Hedonism

Like Sidgwick, Moore also rejects Mill's psychological hedonism--i.e., that the only thing we desire  (i.e., the sole end of action) is pleasure/happiness because everything is either a means to or a component of happiness.  Moore's two general arguments are that (a) Mill psychological model of the relationship between desires and pleasure is wrong and that (b) Mill conflates what it is to be a means and what it means to be an end.

The first part of Mill's objection is to counter Mill's psychological model.  For Moore pleasure is what motivates action toward some particular object; and that particular object is included in the ultimate end of my desire.  For Mill when I desire some object, it's actually not that object that I desire but only the anticipated pleasure I will get from it.  But for Moore the way it works is that the idea of that object causes in me a thought of pleasure which in turn causes me to desire the object.  So, as well as the pleasure I hope to attain, I also desire the object.  Therefore, pleasure isn't the only thing we desire because we also desire the object. 

The second argument concerns a confusion of means and ends.  Recall that Mill acknowledges that some might counter his psychological hedonism by pointing out that people pursue things like virtue, power, fame, money etc as ends in themselves.  His reply is that in such cases those 'ends', through habit or education, have become components of a compound notion of happiness, thereby supporting his hypothesis that the only thing people desire is happiness.

To illustrate Moore's objections, lets take money as an example.  Recall that for Mill happiness is 'pleasure and the absence of pain'.  Some people view money as an intermediate means to some pleasure.  But as Mill suggests, for some people, money can be an end it itself.  That is, they just want money for money's sake.  Not to buy anything...but just to have it: think Scrooge McDuck or Mr. Burns.  

In the latter case money has become part of that person's compound notion of happiness.  And, if money is part of someone's compound notion of happiness then money is pleasure because happiness is pleasure.  But in what sense can money be pleasure?  This doesn't seem to make sense at all.  Mill is just defining words to suit his purpose.

Mill told us that everything except pleasure is but a means, which seems to imply that everything except pleasure is precluded from being an end.  But now he tells us that some other things that were previously means--that by any reasonable use of language are distinct from pleasure--can also be ends.  

So, either Mill must maintain the ridiculous position that money is pleasure or that there are things besides pleasure that people desire as ends.  If he doesn't want to appear kressy he's going to have to take the latter, but then he has to give up psychological hedonism.

Tuesday, October 9, 2012

Sidgwick's Criticisms of Mill's Proof of Utilitarianism

Sidgwick's Criticisms of Mill's Proof of Utilitarianism 
Ok, apparently I can only write if it's in my blog so, instead of staring at a blank screen trying to rewrite my paper, I'll write down the basic ideas up in herr first.

Here we will examine Sidgwick's criticisms of Mill's Proof of Utilitarianism.  With that in mind, it will probably do some good to lay out Mill's (in)famous proof which I've done in more detail elsewhere.  I'm too lazy to figure out how to put a link to it but it was last month.  What I've laid out below should be sufficient for our purposes.  But first a lets clarify the terminology...

Utilitarianism:  From the most general point of view utilitarianism is a consequentialist theory, which means the the goodness/rightness or badness/wrongness of an action/thing is measured according to the consequences it produces.  More specifically, it is the moral theory that the 'rightness' of an action is measured in direct proportion to the happiness it produces.  In other words, if you want to know how 'right' or 'good' an action is, you need to count up how much happiness it produced.

Happiness:  Generally speaking, Mill equates happiness with pleasure or diminution of pain.

Moral good: is what ever the ultimate end our actions is (ought to be?)--that is, happiness.

Mill's Proof of Utilitarianism
The utilitarianism is about ultimate ends--and that end is happiness.  To prove that something is an ultimate end we need to determine if that thing is desirable.  The principle that Mill seeks to prove is that "happiness is desirable, and the only thing desirable, as an end; all other things being desirable as means to that end."

Mill's conclusion about happiness being the only desirable end can be divided into two main sections.  The first is to prove that happiness is an end, and second that happiness is the ultimate end.  Since knowing whether something is an ultimate end depends on whether it is desirable, the proof will require establishing that happiness is not only desired and an end but is the only thing desired as an end.

With this in mind, lets lay out the first part of the proof:
(P1)  The only evidence that something is desirable (i.e. good) is that people desire it.
(P2)  People desire their own happiness.
(P3)  Thus, a particular person's happiness is desirable to them (and therefore an end),
(P4)  Thus, happiness (as conceived by each person) is an end and (therefore) a good to that person.
(C1)  So, the general happiness is a good to the aggregate of all people.

Up to here Mill's given a proof for the first half of what he needs--that happiness is desirable as an end.  But he still needs the second half of the proof--that happiness is the only thing desirable as an end, and that all other things are desirable only in so far as they are a means to happiness.

This argument I've covered this in a previous post so I'll go though it quickly.  The basic idea behind this part of the proof is psychological hedonism: the idea that all possible objects of desire are in fact merely a means to happiness or a component of a compound notion of happiness.

The argument goes like this:  Sure it's true that people desire things other than happiness such as virtue, fame, honour, power, and so on, but they only desire these things because they are means to achieving the ultimate end of happiness.

Someone might reply that, wait, that's too easy.  You're just defining the problem in such a way that your desired conclusion isn't falsifiable.  To this Mill introduces the compound notion of happiness.  This is the idea that different things can be included in different people's notion of happiness.  Sure, he says, there are things like virtue that you pursue in their own right from which you do not expect a happiness pay-off.  But what has happened is that being virtuous has come to be included (by habit and/or education) in your concept of happiness.  Now, unless you live virtuously, you will not be able to be happy.

So, virtue-- just like eating donuts--has come to comprise the cluster of things that are contained in your concept of happiness.  By desiring virtue as an end, you are not desiring something distinct from happiness because virtue is just an aspect of happiness for you.  Finally, with psychological hedonism Mill has proven the second half of the conjunction:  (C2) since everything either is desirable as a means to happiness or is contained within it, happiness is the only thing desirable as an end.

Lets turn to Sidgwick's criticisms of Mill's proof.

Sidgwick's Criticism of Mill's Proof

Argument 1: The Aggregation Step
Sidgwick's first criticism concerns Mill's aggregation step which is the move from (P4) to (C1).  The general argument is that just because individuals desire their own respective happiness it does not follow necessarily that the aggregate of people (i.e. humanity together) desires the general happiness.  If there is no desire for the general happiness, then it cannot be and end nor a good.

Lets grant Mill that everyone desires their own happiness and that their particular happiness is a good to them.  Now consider two people, Bob and Mary, who live on an island.  Bob desires his own happiness and considers it a good and Mary desires her own happiness and considers it a good.  If we somehow add together their concepts of happiness into a "general happiness" it does not follow that Bob and Mary desire the general happiness; in fact, they (still) only desire their particular happiness.

Neither Bob nor Mary necessarily have a desire for the general happiness.  Add together happinesses on a society or world-wide scale and the problem becomes even more pronounced--people's desires for happiness only correspond to their own.  Since no individual desires the general happiness (just their respective individual happiness), there exists no desire for it, so--contra Mill--the general happiness is not an end, and therefore not a good.

Argument 2:  Fallacy of Equivocation
The fallacy of equivocation is committed when a key term (that has more than one meaning) doesn't maintain a consistent meaning throughout the argument.  Mill tells us in (P1) that we can know what is desirable by observing what people desire.  He uses an analogy to make this point:  the proof that something is visible is that people see it, and the proof that something is audible is that people hear it.  So, it follows that we can know that something is desirable if people desire it.  But the analogy doesn't work.  'Desirable' doesn't usually mean 'able to be desired', it usually means that there is something we ought to desire or that is worthy of desire.  In short, it is usually employed as a normative term, but 'able to desire' is a descriptive term.

So, what's the problem?  Well, Mill's conclusion--utilitarianism--is a normative theory; it purports to tell us that we ought to desire the general happiness.  But his supporting premises contain 'desirable' in the descriptive sense, i.e., (P2) people do desire their happiness.  Therefore, Mill is not justified in  arguing for a ethical conclusion from psychological facts.  More generally stated: the proof suffers from the fallacy of equivocation because 'desirable' isn't used consistently throughout the premises and the conclusion.

Argument 3:  Vs Psychological Hedonism In order to prove (C2) that happiness is the only thing desirable as an end, Mill appealed to psychological hedonism: i.e., the theory that all possible objects of desire are in fact either a means to happiness or a component of a compound notion of happiness.  Sidgwick rejects this psychological model and consequentially the conclusion (C2) that follows from it.

Lets do a quick analysis of Mill's psychological model.  For Mill, the relationship between "desiring a thing and finding it pleasant" is one of equivalence; "they both name the same psychological fact" (Mill, pp. 125-126).  But is this true?  Perhaps, if by decree we define our words this way, but this semantic equivalence doesn't accord with common or psychological usage.  Sidgwick suggests one possible disequivalence is that phrases like "at his pleasure" or "as he pleases" denote something akin to voluntary choice rather than the chooser's objective being some "prospective feeling" (Sidgwick, p. 44).

Butler psychological model suggests a more extreme disequivancence between desiring a thing and finding it pleasant.  On his model, we necessarily desire things other than pleasure.  Pleasure is the consequence of pursuing things like honour, power, and virtue.  If we do not already have the additional desire for (in addition to the desire for pleasure)  the thing that gives us pleasure, we can not pursue the pleasure (quoted in Sidgwick, Ibid).  

While Sidgwick doesn't endorse Butler's view that we could never pursue pleasure at all without first desiring some other object, he agrees with the general point against Mill:  Not all of our desires are directed at pleasure.

So, if we accept some version of this psychological model it is not clear that everything we desire we also will find pleasant.  It then follow that  (C2) cannot be derived from the proof--i.e., happiness might not be the only desirable end.