my lip: 20(9/11)_59mm

 

上唇と下唇それぞれの厚さの平均値をご存知でしょうか?一般的に上唇は8mm、下唇は10 mmが唇の平均的な厚さであると言われています。

絶対値としての厚みでは上下合わせて1.8cmが平均なので、2.5cm以上の厚さになるとたらこ 唇と捉えられる人が多くなってくるでしょう。

 

最も美しい唇のバランスは上が1に対して下が1.5と言われています。つまり

唇の厚さの黄金比=上唇:下唇=1:1.5

です。美容業界ではこの比率の唇が最も美しいバランスであると言われています。メイクの勉 強などでこの比率に見えるようにすると教わった人もいるかも知れません。

一旦話がそれますが、最も美しい顔というのは最も平均的な顔であると言われています。つま り平均値を取れば自然と最も美しくなるはずなのです。

冒頭で説明したように唇の平均的な厚さは上8mmに下10mmで、これだと黄金比になってい ないところが少し不思議です。上を基準にすると下が12mmになるはずなのですが、実際の 下唇の平均の厚さは10ミリです。

 

実際の唇の厚さの平均値から出した白銀比

逆に実際の平均的な唇の厚さを最も美しいものとすると、黄金比とは違った比率が現れます。 上唇が8mm、下唇が10mmのこの比率を黄金比になぞらえて白銀比としましょう。

唇の厚さの白銀比=上唇:下唇=1:1.25

実際に人から見られた時に1.5と1.25のどちらが良い印象を与えるかはデータがありま せんがおそらくメイクをして黄金比、していない素顔の状態で白銀比になるのがベストなので しょう。

 

唇の縦横比も重要です。横幅が狭ければ、実際には対して厚みの無い唇でもタラコに見られて しまう可能性があります。では理想の唇の縦横比はいくつなのでしょうか?

唇の縦横比=縦:横幅=1:3

口を閉じた状態で縦と横の比率が1:3くらいになるのが美しいと言われています。

実際には顔全体とのバランスも更に考慮に入れなければなりません。唇としての上下左右のバ ランスが完璧でも人によっては口が大きく見える人も小さく見える人もいるはずです。

 

 

 

参謀とは

軍隊における役職の一つ。

「謀に参ずる」という語意の通り、当該軍隊の作戦立案・遂行において指揮官を補佐する職である。 後方参謀、情報参謀など担当する職務によっては軍官僚としての性格を持つ場合も多く、作戦立案のみに従事するわけではない。

転じて、スポーツチームや企業・団体における指導者や経営者に助言をしたり、作戦を組んだりする「知恵袋」的な存在を”参謀”と言い習わすことがある。

PRIMER ON THE ELEMENTS AND FORMS OF UTILITARIANISM 2013/03/22

PRIMER ON THE ELEMENTS AND FORMS OF UTILITARIANISM

Phil. 213

R. N. Johnson

via: http://web.missouri.edu/~johnsonrn/utilnote.html


Utilitarianism (ωφελιμισμός) consists of two doctrines:

A theory of what is good,(αγαθό) and a theory of what is right.(δίκαιο/ορθό)

Utilitarianism’s theory of what is right is consequentialism, or the doctrine that the morally (ηθικά) right option (επιλογή) in any circumstance (περίπτωση) is that option which brings about the most (πιο) good, or the best (καλύτερες) consequences; (συνέπειες) any other option is wrong (λάθος).

Utilitarians refer to the option that brings about the best consequences, or “maximizes the good”, as being the optimific alternative.

Hence, the right option is the optimific option.

Hereafter, I will use this locution.

Note that an option which produces the most good also, and by definition, produces the least bad consequences.

Hence, there can be a right alternative even if the only alternatives produce bad consequences (e.g., other things equal, the right dentist to go to is the one who produces the least pain.)

Utilitarians all agree that what is good is “utility“—human well-being or welfare.

However, they disagree about what human well-being or welfare is.

Classical utilitarians were hedonistic: They held that human well being consists of pleasure. [see: http://eidetisch.tumblr.com/tagged/pleasure]

In holding this view, they DID NOT, of course, deny that human well-being consists of community, self-development, wealth, and so on.

[NB] What they claimed was that each of these things were either a means to, or associated with, pleasure, and it is this association with pleasure which makes them count as parts of human well-being.

However, because of the difficulty of measuring, and so maximizing, amounts of  pleasure, few now hold this doctrine, and there are a variety of theories of what is good among contemporary utilitarians. We will discuss this below.

Utilitarians  also all agree that what is right is the optimific alternative.

They are all consequentialists in this sense. [see: http://eidetisch.tumblr.com/tagged/consequentialism]

However, they disagree about what things should be evaluated according to the consequentialist criterion — particular actions, character traits, rules and standards of behavior or large-scale institutions.

Again, the classical utilitarian view held that particular actions are what must be evaluated according to the consequentialist criterion.

Hence, they held that what makes an action right is that it produced the best consequences.

However, many disagree with this, as we will see; there are a variety of forms of consequentialism that utilitarians hold.

The utilitarian view can be applied either to all spheres of practical life, or can be restricted to some particular sphere.

Utilitarianism as a comprehensive doctrine expresses an outlook that can be applied to all practical spheres, for instance, both to the private actions of individuals and to the political structures of societies.

Hence, comprehensive utilitarianism is the view that what makes actions right or wrong is determined by the utilitarian standard, and this very same standard also tells us which forms of government, societal institutions, laws and policies are just or unjust.

But when utilitarianism expresses a view only about the latter, it is merely a politicaldoctrine, and we will call it political utilitarianism.

Rawls and other political philosophers mainly are concerned with political utilitarianism.

Rawls refers to the subject of a political theory as the “basic structure” of society—its form of government, institutions and policies—rather than to the actions of the individuals who live in the society. […]

 I.  THE THEORY OF RIGHT: Varieties of consequentialism

A. Act consequentialism

An act consequentialist holds the following account of right action:

 (AU): Ø-ing is right if and only if Ø-ing is optimific.

 Act consequentialism tell us that what determines whether a given action is right is that action’s consequences.

It tells us that the one and only right action to perform in any given situation is that action which produces the best consequences of all those actions that are available to the agent at a given time and place.

Any action that produces less than the best consequences is therefore wrong.

— Hence, lying is wrong in a given situation if and only if telling the truth or remaining quiet produces better consequences. [“intrinsic”/”non-intrinsic”]

— By the same token, lying is right in a given situation if and only if lying produces better overall consequences than either telling the truth or remaining quiet.

One DIFFICULTY with act consequentialism is that it seems quite possible for it to conflict dramatically with our conscience and many of our deeply held convictions.

For instance, we believe that in most cases torture is wrong even if it produces the best consequences. […]

In general, it seems quite possible that our deeply held beliefs about what we ought or ought not do could conflict with what the act consequentialist standard tells us to do.

IN RESPONSE TO this problem, many utilitarians have opted for rule consequentialism instead.

B. Rule consequentialism

A first approximation of rule consequentialism would be:

 (RU1): Ø-ing is right if and only if Ø-ing is in accordance with a set of rules conformity to which is optimific.

Notice that whether or not a particular action is right for a rule consequialist does notdepend on its consequences.

Rather, it depends on whether the action is in accordance with a set of rules of conduct.

Which set of rules?

That set conformity to which has the best overall consequences. […]

For example, suppose the following rules are members of the set of those rules conformity to which is optimific:

“Tell the truth”, “Don’t steal”, “Don’t torture” and “Help others in need” and “Develop your talents”.

SUPPOSE further than in a particular case, lying would have the best consequences overall of all alternative actions that I could perform.

— On the act consequentialist view, lying would in this case be the right thing for me to do.

— But on the rule consequentialist view, it would be the wrong thing for me to do.

It would be wrong because it is not in accordance with the set of rules conformity to which is optimific.

RU1 does not, however, specify whose conformity is at issue.

Is it the agent’s conformity that matters for determining the optimific set of rules?

Or is it everyone’s or general conformity?

Most commonly it is taken to be the latter.

Hence, we should refine RU1 as:

 (RU2): Ø-ing is right if and only if Ø-ing is in accordance with a set of rules general conformity to which is optimific.

RU2 embodies the intuition that an action is wrong if it is in accordance with a rule which, if everyone followed it, would have bad consequences.

Consider this example (from D. Lyons, Forms and Limits of Utilitarianism)

SUPPOSE you and a friend are walking beside an orchard. Your friend says “Let’s pick a couple of apples”. You well object, “No. That would be wrong, because it would be stealing”. However, your friend responds, “Two fewer apples out of this huge orchard won’t harm the owner, and we will get great pleasure out of them.”

The intuition behind RU2 is that violating the rule “Don’t steal” is wrong, not because in this case stealing will produce bad consequences.

Nor is it wrong because your violating this rule will produce bad consequences (it is not your conformity with the set of rules that matters here as to which set of rules is optimific).

Rather, we think “What if everyone did that?”

That is, if everyone were to follow the rule “pick apples for yourself in these circumstances”, then orchard owners would go broke.

Hence, we think it is wrong for us to steal apples in this case because if everyone were to follow this as a rule in such a case, it would have bad consequences.

C. Indirect Consequentialism.

Now one quite obvious objection to consequentialism is that it would be undesirable to always try to calculate which action or rule is optimific.

[NB] Moreover, many of our ordinary intuitions about what is right and wrong imply that we ought to perform actions that are not optimific. […]

For instance, we often think that we ought to tell the truth or be fair to people, even if doing so would not be optimific, and even if doing so would be in accordance with a rule general conformity to which would be optimific.

IN ORDER TO MEET both of these objections, many utilitarians, following Henry Sidgwick, a famous 19th century utilitarian, are indirect consequentialists.

[INDIRECT CONSEQUENTIALISM] Indirect consequentialists argue that consequentialism is only a theory about which actions are right or wrong.

It is not a decision procedure for determining which action is right or wrong.

The idea is this: A decision procedure for determining which action is right recommends a kind of action, for deciding is an action.

Hence, calculating the consequences of an act or of a rule is itself an action.

So whether it is right to calculate must itself be determined by the consequentialist standard.

Once we see this, we can see that very often, perhaps always, it will not be optimific to try to determine which action is optimific, and so it will be wrong to do so.

This may seem paradoxical at first.

Surely, we might think, if the right action maximizes good consequences, then we should try to determine which action maximizes good consequences.

But indirect consequentialists deny just this claim.

Hence, many utilitarians even go so far as to say that we ought to determine what the right action is by non-utilitarian standards, since using such standards as decisions procedures is itself optimific.

And, they add, utilitarianism even explains why we have the non-utilitarian intuitions about particular actions that we do: Because having those intuitions itself is optimific!

D. Arguments for consequentialism.

Kymlicka offers TWO arguments for utilitarianism, the egalitarian argument and the teleological argument, and rejects them both.

Recall that, as Kymlicka sees it, all viable political philosophies have at bottom the value of egalitarianism, or “treating people as equals”.

What they all differ over is the (very substantial!) issue of what “treating people as equals” entails.

Hence, consequentialism can be seen as one way of cashing-out the value of “treating people as equals”.

(i) The egalitarian argument.

Some might argue for consequentialism on the basis of the claim that it is entailed bythe principle of treating people as equals:

1. Ø is right if and only if Ø treats everyone as equals.
2. Ø treats everyone as equals if and only if Ø takes into account everyone’s preferences equally. 
3. Ø takes into account everyone’s preferences equally if and only if Ø maximizes overall utility.

 

 Therefore,

 4. Ø is right if and only if Ø maximizes overall utility.

On this view, egalitarianism (premise 1) is supposed to yield consequentialism.

But does it?

Let us, with Kymlicka, assume that premise 1 is correct—a conceptual truth—though it is completely uninformative.

— We then ask, What does it mean to treat people as equals?

— The second premise tells us what this means: It is to take into account everyone’s preferences equally.

But though this is informative, it is quite controversial indeed.

In fact, it is false.

Ø may well take into account everyone’s preferences equally, yet among those preferences might be preferences that a minority population is discriminated against. [NB][“equals” / “everyone’s preferences equally” / cf. “general will”][vulnerability of …]

So Ø might have to take into account external preferences, or preferences that others’ preferences should or should not be satisfied. […]

Moreover, a majority might prefer that a single person’s goods be taken away and used as public goods. [NB] […]

So in taking into account everyone’s preferences equally, Ø might take into account selfish preferences, or preferences for more than one’s fair share. [NB]

These are both counter-examples to 2.

[NB] Both show that Ø might take into account everyone’s preferences equally and yet not treat everyone as equal. [NB]

So premise 2 is false, and the argument for 4 is no good.

(ii) The teleological argument.

The more traditional understanding of consequentialism holds that treating people as equals, our moral ideal, does not entail consequentialism, but rather consequentialism entails treating people as equals. […]

[“right”: “maximize utility” —> “treat people as equals”]

Treating people as equals is one of the best ways, indeed maybe the best way, to maximize utility, on this view. [“equality” / “utility”]

1’. Ø is right if and only if Ø maximizes utility.
2’. Ø maximizes utility if and only if Ø takes everyone’s preferences into account equally. 
3’. Ø takes everyone’s preferences into account equally if and only if Ø treats people as equals.

 

 Therefore,

 4’. Ø is right if and only if Ø treats people as equals.

Although Kymlicka does not discuss it, it is quite clear that the very same objections we had to premise 2 above would apply equally well to premise 3’ here. […] [?]

[todo] [“Ø takes everyone’s preferences into account equally if and only if Ø treats people as equals.” vs. “Ø treats everyone as equals if and only if Ø takes into account everyone’s preferences equally. “]

So this is a bad argument for treating people as equals, premise 4’, for the very same reasons that the egalitarian argument above is a bad argument for consequentialism.

But set that aside.

The problem with Kymlicka’s presentation is that this is not any kind of argument at all for consequentialism.

It is, rather, an argument for treating people as equals, and a bad one at that.

This argument quite clearly takes consequentialism (premise 1’) as a premise of an argument, not as a conclusion of any argument.

Kymlicka’s objections are, in fact, to premise 1’.

He claims that

(a) maximizing utility cannot be a duty, for if P has a duty, then there is some Q to whom that duty is owed, and no one is owed the duty of maximizing utility. […]

(b) At best, maximizing utility is a non-moral requirement.

Perhaps it is an aesthetic requirement. […]

And Kymlicka seems to hold that 1’ is not a moral duty because it is not a requirement to treat people specially, but a requirement to the good (whatever it may be) specially.

But surely Kymlicka is begging the question against the teleological utilitarian.

[NB] Kymlicka claims that moral duties are duties to treat people specially (“equally”), and teleological utilitarians deny it, or at least deny that this is a fundamental duty. [thesis]

So Kymlicka’s argument relies on (a), that consequentialism cannot define our duties, because maximizing the good is not owed to anyone. […]

But a teleological theorist will reply that, of course maximizing utility is not owed to anyone.

Rather, it is what justifies our owing things to others.

That is, it is no argument against 1’ to say that no one is owed the duty of maximizing utility.

For premise 1’ does not aspire to say such a thing.

[NB] Rather, it aspires to say what justifies our duties.

This is not to offer any positive argument for 1’.

But it at least shows that Kymlicka is wrong to say that this all amounts to an argument for consequentialism, and he is wrong to object to it on these grounds.

[Kymlicka vs. teleological consequentialism] However, Kymlicka does have a better OBJECTION against teleological consequentialism: It gives us the right answer (we should treat people as equals) for the wrong reason (it maximizes utility).

Why is this the wrong reason?

Because we think that we should treat people as equals whether or not it maximizes utility.

(iii) The conceptual argument.

Kymlicka briefly refers Hare’s claim that he could not understand what “right” could mean if it did not mean “productive of the best overall consequences”.

What this suggests is that consequentialists actually rely on a far more simple, and common, philosophical argument for their position, viz., a conceptual argument.

Roughly, the claim here would be that what the term “right” means is nothing other than “productive of the best consequences”.

Actually, this amounts only to a conceptual assertion at this point.

What such an argument would have to show is something like this: People use the term “right” in such a way as to show that what they mean to pick out all and only those actions which are productive of the best consequences.

Clearly, this is a problematic strategy, as it stands, since as we have already seen, one reason for rejecting act consequentialism is the obvious fact that we do not use the term “right” in this way.

We often use it to pick out actions that are not productive of the best overall consequences.

There is much more that a consequentialist might say in this regard.

It will suffice for the time being to note that often utilitarians have not used any normative arguments for their position, but have relied on a (dubious) conceptual assertion.

 II. Theory of the Good: Varieties of Utility

 A. Hedonism

Hedonism was the classical utilitarians’ answer to the question

 “What is good?”

It is pleasure and pleasure alone.

They had a very simple argument for this position:

1. Y is the good if and only if  Y is desirable as an end in itself.
2. Only pleasure is desirable as an end in itself. 
3. Therefore, only pleasure is Y.

Although the argument is simple, there are a number of concepts we need to fully understand it.

Premise 1 is fairly uncontroversial: It seems to be a conceptual truth. […] [“good” / “pleasure” / “desirable” (“as an end in itself”)]

To say that Y is good is to say that Y is desirable, and to say that Y is desirable is to say that Y is good.

But things can be good in two quite different ways: Y can be an instrumental good or good as an end in itself.

This distinction is based on why a thing is desirable—the reason it is desirable.

And what we will refer to as “the” good will not be what is merely instrumentally good, but what is good as an end in itself.

And this is to say that it is desirable simply because of what it is, and there need be no other reason for its goodness.

Instrumental goods are desirable because they bring about or produce (i.e., are instrumental to) something else which is desirable.

Money and surgery are examples of instrumental goods; they are desirable because they can get us desirable things such as cars or health.

But on their own, they are not desirable. [“usefull” / “αξία χρήσης”]

If money could not be exchanged for desirable items such as cars, there would be little reason to regard it as desirable; it would be just so much paper and metal.

Likewise, if surgery wasn’t instrumental to one’s health, one would not find surgery at all desirable.

Moreover, whether a given thing is indeed instrumentally good depends on whether what it produces is indeed desirable. [ΝΒ]

If A produces B, but B is not desirable, then A is not instrumentally good because it produces B. [ΝΒ]

Now in a relation such as that between A and B, we call A the means to B, and B the end of A.

Hence, the relationship between A and B is a means/end relationship.

So we can say that instrumental goodness is equivalent to goodness as a means.

[ΝΒ] It follows, then, that something is good as a means only if what it is a means to is good.

In other words, instrumental goodness is dependent on the goodness of ends, and if nothing is good as an end, then nothing is instrumentally good either. [ΝΒ]

Notice that A may be good as a means to B, yet B is good because it is in turn a means to C, which is also good as a means to D, and so on.

For instance, money is good because it is a means to getting good things such as a car.

But getting a car is in turn good because it is a means to easy transportation, which is also good.

And easy transportation is good because it is a means to saving time, and so on.

Notice that, because instrumental goodness is dependent on goodness as an end, A will be good only if B is good.

And B is good only if C is good, and so on.

But at some point there must be something which is just good and not merely good because it produces something else which is good.

Not everything can be instrumentally good.

For A is instrumentally good only if there is something else that A leads to that is good, and what A leads to is B, yet B is also an instrumental good, and so good only if there is something else that it leads to that is good, and so on.

[ΝΒ] If there were no end to this chain of instrumental goods, then it could not be established that A is good.

So there must be an end to it if anything is to be instrumentally good.

[ΝΒ] And whatever that is must be something that is desirable in itself.

We will call that which is desirable in itself, or desirable for its own sake, the good, to signify that it is the ultimate good thing, that in virtue of which everything else is good.

While money, cars, easy transportation and saving time may well be good as an end, they are not good as ends in themselves, since their goodness as an end depends on their being a good means to something else. [ΝΒ]

And the good will be something that is good as an end in itself.

Now we can fully understand THE HEDONIST’s position.

She thinks that the only thing that is desirable in itself is pleasure.

Pleasure is the only thing that we desire for its own sake alone, and not because it leads to something else that is desirable. [cogito-cogitatum] […]

It is important to notice that hedonists do not claim that it is one’s own pleasure that is the good. [intersubjectivity]

That theory of the good would be a form of egoism.

Rather, hedonists claim that anyone’s or, indeed, anything’s pleasure is good.

It doesn’t matter who or what has the pleasure, since what is desirable as an end is not some particular person’s or thing’s pleasure.

What is desirable as an end is simply pleasure itself.

Hedonism is a perfectly impartial (αμερόληπτη) view about what is good.

No one’s (or thing’s) pleasure is more important than anyone else’s, and each person’s (or thing’s) pleasure counts equally.

B. Preference satisfaction.

The problem with hedonism, as Robert Nozick has argued (Anarchy, State and Utopia), and Kymlicka nicely shows, is quite simple: If pleasure alone is desirable as an end, then we will be indifferent to whether we get it through real activities, such as writing novels, having families or skiing, or whether we get it through an “experience machine” that is capable of producing any pleasure directly by electrical stimulation or injection of drugs. […]

But we are not indifferent to this choice.

We want to write novels and ski; we don’t just want the pleasure of writing novels and skiing.

Most people would prefer to do things such as write novels or succeed in their careers, not simply have the pleasure of writing a novel or succeeding in a career. […] [cogito/cogitatum]

Moreover, most people prefer many things that will be painful.[…] 

Hence, to make such people better off would be to promote novel-writing and success in careers, even if doing so would produce less pleasure.

[NB] So not all things which are desirable as ends are equivalent to pleasure or even pleasurable. […]

It is for SUCH reasons that most utilitarians nowadays have abandoned hedonism as a theory of the good.

Human well-being should be determined in accordance with maximizing, not pleasure, but preferences. [NB]

Some people might prefer pleasure, others may not.

So making someone better off may well not involve creating more pleasure for them.

C. Informed preference satisfaction.

But even the view that the good is preference satisfaction is problematic.

The objection to simple “preference-satisfaction” theories of the good is that sometimes what we prefer is obviously not beneficial to us.

Sometimes we are better off not having a preference satisfied.

Suppose I prefer to drink the glass of liquid in front of me because I prefer a gin and tonic and believe that the glass contains a gin and tonic.

But, unbeknownst to me, the glass is filled with gasoline, not gin and tonic.

If my preference is satisfied, I will drink what is in the glass.

But in so doing, my welfare will quite obviously not be enhanced, but decreased.

Clearly, my preferences are at best a prediction of my welfare, not my welfare itself. […]

What I prefer is what I believe will be desirable or good, and I may well be wrong about this. [false consciousness] […]

[NB] So my welfare consists, not in the satisfaction of my preferences, but in the satisfaction of those preferences I would have were I to have all the relevant information about what I prefer. […]

In believing that the glass of liquid in front of me contains a gin and tonic, I do not have all the relevant information.

So my preference for it is not to be counted as something the satisfaction of which would enhance my welfare.

Moreover, I may prefer something because I fail to imagine fully what getting it will be like.

For instance, I may prefer to go to law school, even though I have all the relevant true beliefs about what being a lawyer is like.

I know that it will be boring, for instance. But since I fail to imagine fully this boredom, I still prefer to go to law school. And once finished, I may well find that it is boring in a way that I had not fully imagined. I hadn’t imagined that it would be so boring! Hence, going to law school fulfilled a preference I had, and it was moreover an informed preference, but it fails to enhance my welfare because the preference was formed without full imaginative engagement on my part. [???]

[NB] Many utilitarians take these considerations to favor a “fully informed” preference view of the good.

[NB] Hence, a person’s welfare consists, not in pleasures nor mental-states of various kinds, nor in preference satisfaction, but in the satisfaction of fully informed preferences, or those preference we would have were we to have all and only true beliefs about the objects of our preferences, formed with full imagination and with no other irrationalities. […]

[NB] For short, we will say that a person’s welfare consists in the satisfaction of those preferences she would have were she fully rational. […] [“preferences”] [“rational”]

D. Incommensurability problems.

One persistent problem for a utilitarian who claims that the good consists in satisfaction of preferences is that of aggregating these preferences.

If our goal is to maximize overall preferences, then our goal is to try to amass the largest package of overall preferences.

But consider this simple example: Is writing a novel plus skiing a more valuable package of preferences than having a nice car plus hang-gliding?

The hedonist has at least an answer to this: It is if and only if the former consists of more pleasure than the latter.

[NB] That is, a hedonist has a common denominator of all preferences, viz., pleasure.

But there is no common denominator for someone who simply holds that the preferences themselves are the measure of utility. […]

So there seems to be no answer to the question whether one set of preferences is preferable to another set of preferences.

They seem to be incommensurable.

Although utilitarians admit that there is a problem with aggregating preferences, they do not admit that it undermines utilitarianism.

Indeed, it does not.

For even if we cannot tell whether writing a novel plus skiing is a more valuable package of preferences than having a nice car plus hang-gliding, we can tell that writing a novel plus skiing is a more valuable package of preferences than working all the time at a dead end job plus having no leisure time.

That is, as Kymlicka puts it, the latter is a less fine-grained distinction among sets of preferences, one we can indeed make, even if we cannot make the former, more fine grained distinction.

© Robert N. Johnson, 1996