## Saturday, October 15, 2011

### Go Traveller on Thy Way

For a Tablet at Silbury-Hill
by Robert Southey

This mound in some remote and dateless day
Rear'd o'er a Chieftain of the Age of Hills,
May here detain thee Traveller! from thy road
Not idly lingering. In his narrow house
Some Warrior sleeps below: his gallant deeds
Haply at many a solemn festival
The Bard has harp'd, but perish'd is the song
Of praise, as o'er these bleak and barren downs
The wind that passes and is heard no more.
Go Traveller on thy way, and contemplate
Glory's brief pageant, and remember then
That one good deed was never wrought in vain.

## Friday, October 14, 2011

### Slippery Slope, Camel's Nose, Thin End of the Wedge

There are a number of things called 'slippery slope arguments'. One of these, broadly causal, is a practical argument: if we do A, then there is a probability that should not be neglected that it will lead to unfavorable B. This is, for instance, what Eugene Volokh is looking at in his paper on the mechanisms of the slippery slope (PDF). These are in many ways the simplest and most straightforward members of the tribe: the strategy for responding to such a slope is either (1) to deny that there is a significant probability that A will lead to B; (2) to deny that B is unfavorable; or (3) to combine A with a compensating proposal that will fix the problem. And (3) is generally the most useful response; it makes the matter simply a problem of design, thus allowing compromises.

It seems to me, however, that most slippery slope arguments, even those put in causal language, are actually not really causal in precisely this way. Rather, they are justificatory. And I think these are in general the version that is least amenable to easy analysis and evaluation. The temptation is to try to put it down in premise-premise-conclusion form, and I think there are good reasons to be wary of such a glib approach. For it is glib in at least this sense, that it assumes the argument is deductive in structure. Or in Locke's terms, which are actually useful for once, it pretends that the argument must be ad judicium, when it is really ad ignorantiam; that, in particular, it is an argument in the premise-conclusion sense rather than a challenge.

Challenges are a class of argument that are common in rational argument, although often overlooked; it is difficult to find anyone besides Locke who even acknowledges that they exist. But that they do exist is clear. Here is a famous example from Berkeley's Principles of Human Knowledge (1.10):

Now, if it be certain that those original qualities are inseparably united with the other sensible qualities, and not, even in thought, capable of being abstracted from them, it plainly follows that they exist only in the mind. But I desire any one to reflect and try whether he can, by any abstraction of thought, conceive the extension and motion of a body without all other sensible qualities. For my own part, I see evidently that it is not in my power to frame an idea of a body extended and moving, but I must withal give it some colour or other sensible quality which is acknowledged to exist only in the mind.

This is undeniably an argument; indeed, it is probably the argument in PHK most people have historically found persuasive, despite the fact that he gives more sophisticated arguments. And, as with all of Berkeley's arguments, it is beautifully constructed. He gives a reason for the challenge (first sentence), the challenge (second sentence), and a reason for thinking it is genuinely challenging (third sentence). But how would one put this into premise-conclusion form without distorting the argument? To be sure, the first sentence is a conditional, but the third sentence is ineliminably in first person and if it were just taken flatly wouldn't be much of an argument at all, even combined with the first sentence -- certainly not one that would have much force for anyone but Berkeley himself. Any significant force the argument has comes from the second sentence. But the second sentence is not a premise; it is quasi-imperative in nature. It's not a premise, it's a request.

And this, I think, is the key. Challenges are part of a broader class of rational acts that we might call 'search requests'. In these arguments, key information is not provided; rather, what we have in its place is a request for one's interlocutor(s) to do something and return with information, which will be the premise (or complete it). What differentiates this challenge-argument of Berkeley's from other search requests is that it is specifically (1) an objection to an opposing position; (2) in which the person giving the request is fairly confident that the information returned due to the request will be unfavorable to that position. Berkeley is quite confident that no one will be able to "by any abstraction of thought, conceive the extension and motion of a body without all other sensible qualities." From this one can see that the possible good responses to such an argument are (1) reject the request for some good reason (e.g., if it weren't actually relevant) or (2) accept it and return information contrary to expectation (i.e., favorable to the position expected to). Another way to put it is that the argument here is itself simply a demand for an argument, combined with a reason for thinking the demand cannot be met: to counter it, you have to give an argument that you really and truly can "conceive the extension and motion of a body without all other sensible qualities."

I said above that I think most slippery slope arguments, regardless of how they are phrased, are really justificatory: the warning they raise in particular is that it's unclear how a justification (for an action or a position) used in this case would not also apply (perhaps equally, but perhaps with minimal adaptation) in situations where it would give bad results. Putting it this way shows the affinity between slippery slope arguments on the one hand and arguments by analogy and parity arguments on the other; this would be fruitful territory for exploring. But it's still the case that slippery slope arguments are admonitive challenges, not analogies or arguments based on parity.

### Opinion Polls

But you mortals--you do not know how to act honorably except in response to flitting vulgar favors and empty gossip; you have abandoned the excellence of your conscience and your virtue and demand your rewards from the idle chatter of outsiders.

Boethius, Consolation of Philosophy, Relihan, tr. Hackett (Indianapolis: 2001) p. 44.

## Wednesday, October 12, 2011

### Two Poem Drafts

Two hagiographical ones. The Martha in question is Martha of Bethany, of course, the Martha of the Bible; old French legend says that she went to France and rescued a town from a terrible dragon-like creature called the Tarasque. There are a number of versions of the story. In one, St. Martha faces and converts the Tarasque and brings it back, now tame, to the town; the townspeople, terrified, kill it. The Tarasque dies like the good Christian it now is, refusing to protect itself less it harm anyone else, and Martha rebukes the people sharply in a sermon on mercy that converts the town to Christianity. As penance they name their town Tarascon and keep the memory of the dragon alive. In other versions Martha simply undoes the power of the Tarasque by prayer, allowing the townspeople finally to defend themselves against it.

St. Martha, Subduer of Dragons

No fearful tears are in your eyes:
They are both bright and clear
and look upon this weary world
with power free of fear.
Along a hard and worried road
but tasted of the tree of life--
You serve amid the pots and pans
the might of dragon-flame!

St. Michael, Defender of the Tempted

Prince of hosts! Defend us now
as battles 'round us rage;
support us in the march and fight
in warfare that we wage
against all crowns and thrones that serve
the spirit of the age!

You are one like unto God;
God's image are we too,
and though the prince of darkness rule,
God has his word renewed
through broken bone and flowing blood
of Faithful One, and True.

Then fight with us by God's good grace,
and as the dragon was cast down,
cast down oppressor's pride;
the liar walks with cloth of light --
reveal his wicked lie!

Upon the name, the Holy Name,
and carry soldiers from the field
who by dark arrows fall.
Cast back the serpent's malice cold
ere it envenom all!

### Music on My Mind

Anthony D'Amato, "My Father's Son". A bit gloomy, but that's generally a sign I'm in an excellent mood. And it's always worth reminding ourselves that we all struggle with inherited dispositions to vice -- drunkenness and cowardice in the case of the narrator in the song, but they are legion, and most are more subtle -- and we fight them simply by always rising up again when we fail and fall.

## Tuesday, October 11, 2011

### AFAIK and Modal Logic

In comments on another blog, an interesting question about the modal logic of phrases like 'as far as I know' (AFAIK), with someone making an argument with the following structure:

If all that is A is B, then C. Therefore, if all that we know to be A is B, then, as far as we know, C.

This is certainly not formally valid. If, for instance

A = true
B = what we know is true
C = we (collectively) know all truths

then we get an ontological argument that we are (collectively) omniscient, based entirely on the true premises that (1)if everything that is true is what we know to be true, we (collectively) know all truths; and that (2) what we know to be true is what we know is true. Since we don't know all truths, even collectively, this pretty much guarantees that the argument is invalid.

But it did start me thinking on the side question of how the AFAIK modality works. So let's go through some standard kinds of principles in modal logic and see if we get anything that sounds about right, and also see if any interesting side issues arise that shed light on the whole thing.

(1) Distribution: [AFAIK](p ->q) -> ([AFAIK]p->[AFAIK]q)
If p's being true implies (as far as I know) q's being true, then p's being true (as far as I know) implies q's being true (as far as I know).

This seems a reasonable enough principle, but there is a bit of room to think it doubtful, because if something is true as far as I know, this does not mean that I know that it is true. In fact, p's being true as far as I know doesn't seem to rule out q's being false as far as I know; this would be a puzzling situation to be in, but it's not clear that it's contradictory. Certainly such puzzles do seem to arise: where, as far as you know, X is true and, as far as you know, Y is true, but X and Y can't both actually be true. This is one way we can characterize paradoxes, for instance. The problem arises because clearly if I say "p is true as far as I know" I am saying, "Given everything I know, p seems to be true". It's probabilistic and defeasible: p doesn't definitely follow from everything I know (because then I would just say that I know p is true), it just seems to. And we know for a fact that things can seem to follow from what you know that are just plain inconsistent -- these aporia, anomalies, and paradoxes lead us to look a little deeper, and try to expand our knowledge so that we don't just have to go on what seems to be true.

So maybe we should say that Distribution fails for AFAIK, and that we need a different principle, e.g.,

That seems to get around the problem pretty reasonably. On the other hand, usually when Distribution-like principles fail, you can actually tweak things a bit (e.g., introduce a condition, or slightly modify the implication, or what have you) so that you restore Distribution, or something very, very close to it. And there are many advantages of doing so, because systems that make use of Distribution-like principles tend to be pretty straightforward, all things considered. So maybe we shouldn't give it up. I'm not sure off the top of my head, though, what would get around the fuzziness of AFAIK.

Further, it's interesting to note that AFAIK is not, like knowledge or necessity, a stable operator: what is true as far as I know changes over time, and varies from circumstance to circumstance. Therefore it doesn't seem that a situation in which [AFAIK](p->q) really does imply that in a situation where [AFAIK]p , it would also be true that [AFAIK]q. For instance, I tell you today that as far as I know, if John is in a place called Paris, John is in France. This can certainly be true. But then I get a letter from John postmarked Paris, Texas. What is true as far as I know has changed, and it's true that [AFAIK](John is in a place called Paris) but not true that [AFAIK](John is in France). This is, of course, easily handled; [AFAIK] would have to be treated as time-relative. It really doesn't mean 'as far as I know' (simply) but rather 'as far as I know at a given time'. And actually, this makes a lot of sense, whether one wants Distribution or not.

(2) M-Boxish: [AFAIK]p ->p
'If p is true as far as I know, p is true.'

This clearly doesn't work unless I am omniscient. What this shows is that AFAIK doesn't work like standard necessity. It doesn't seem like it would be any Box-like modality at all.

(3) M-Diamondish: p->[AFAIK]p
'If p is true, p is true as far as I know'

Again, this doesn't work unless I am omniscient. What this shows is that AFAIK doesn't work like standard possibility. But I think one could argue that this is a less obviously absurd position; which might be taken as a reason to think that it's some kind of Diamond modality -- possibility like, but not possibility in our usual sense. So let's deal with this a bit more. Since AFAIK obviously has something to do with knowledge, we should ask ourselves what relation it has with knowledge, which is very Box-like.

(4) Epistemic D-Diamondish: [KIp]->[AFAIK]p
'If I know that p is true, p is true as far as I know'.

Now we have something that seems right. The reverse, of course, (which I would, on the same principles of naming I've been using, call Epistemic CD-Diamondish) doesn't work unless I'm omniscient, for much the same reason M-Diamondish doesn't.

Of course, this is exactly what we would expect: AFAIK is an epistemic modality, dealing with knowledge; but it is definitely weaker than K (which is knowledge).

What it suggests to mind immediately is that AFAIK may very well work like 'Permissible' in deontic logic.* And if we can salvage distribution it in fact just is the same as the logical systems typically used for deontic logic -- either D or D4, to be precise, depending on whether we accept that claim, "If I know something, I know that I know it," -- if we don't accept it, we're in D, and if we do, we're in D4. And even if we have to modify Distribution, we're still going to be left with the conclusion that AFAIK is Permissible-like.

This actually makes a lot of sense, if you think about. If I say 'P is true as far as I know', this is actually not too far from saying, 'Given what I know, it's OK (permissible) for me to conclude that P is true'. One might want to argue that the former claim is a little bit stronger than the latter claim, and I think there's something to be said for that, too. If that's so, we might have to look for what, precisely, distinguishes AFAIK from a 'It-Is-Permissible-for-Me-to-Conclude' modality. I would suggest, if we go that route, that we look at the fact that AFAIK seems to suggest that there's at least a reasonable argument from what we know to the conclusion (it's just not an absolutely certain argument). AFAIK would then be something like there-is-good-reason-for-me-to-conclude, which is slightly stronger than it-is-OK-for-me-to-conclude. We certainly do make such distinctions on occasion. On the other hand, there are plenty of contexts where this would be splitting hairs. I'm not sure the best way to go here.

So what do you think?

---
* Incidentally, looking at this SEP article again, which is by Paul McNamara, I have to say that it is extraordinarily good. If I've not recommended it before, I recommend it.

## Monday, October 10, 2011

### Happy Thanksgiving!

If you live in Canada, of course. I've always liked the French name for it, though: Jour de l'Action de GrÃ¢ce. Canadian Thanksgiving has fallen on the same day as the U.S. Columbus Day since the early 70s. I had thought it was to facilitate the synching of business calendars, but this was cynical; it seems to have been a completely coincidental effect of the U.S. Uniform Monday Holiday Act, which moved several federal holidays to Mondays in order to increase three-day weekends. Really, someone should write a book on the history of holiday legislation; it's just chock full of interesting things.

### Thus Have You Seen the Fall of Pride

A Lamentable Song of the Death of King Leir and His Three Daughters

King Leir once rulÃ¨d in this land
With princely power and peace;
And had all things with hearts content,
That might his joys increase.
Amongst those things that nature gave,
So princely seeming beautiful,
As fairer could not be.

So on a time it pleas'd the king
A question thus to move,
Which of his daughters to his grace
Could shew the dearest love:
"For to my age you bring content,"
Quoth he, "then let me hear,
Which of you three in plighted troth
The kindest will appear."

To whom the eldest thus began;
"Dear father, mind," quoth she,
"Before your face, to do you good,
My blood shall render'd be
And for your sake my bleeding heart
Shall here be cut in twain,
Ere that I see your reverend age
The smallest grief sustain."

"And so will I," the second said;
The worst of all extremities
I'll gently undertake:
And serve your highness night and day
With diligence and love;
That sweet content and quietness
Discomforts may remove."

"In doing so, you glad my soul,"
"But what sayst thou, my youngest girl,
How is thy love ally'd?"
"My love" (quoth young Cordelia then)
"Which to your grace I owe,
Shall be the duty of a child,
And that is all I'll show."

"And wilt thou shew no more," quoth he,
"Than doth thy duty bind?
I well perceive thy love is small,
When as no more I find.
Henceforth I banish thee my court,
Thou art no child of mine;
Nor any part of this my realm
By favour shall be thine.

"Thy elder sisters loves are more
Then well I can demand;
To whom I equally bestow
My kingdome and my land,
My pompal state and all my goods,
That lovingly I may
With those thy sisters be maintain'd
Until my dying day."

Thus flattering speeches won renown,
By these two sisters here;
Yet was her love more dear:
For poor Cordelia patiently
Went wandring up and down,
Unhelp'd, unpity'd, gentle maid,
Through many an English town:

Untill at last in famous France
She gentler fortunes found;
Though poor and bare, yet she was deem'd
The fairest on the ground:
Where when the king her virtues heard,
With full consent of all his court
He made his wife and queen.

Her father king Leir this while
With his two daughters staid:
Forgetful of their promis'd loves,
Full soon the same decay'd;
And living in queen Ragan's court,
The eldest of the twain,
She took from him his chiefest means,
And most of all his train.

For whereas twenty men were wont
To wait with bended knee:
She gave allowance but to ten,
And after scarce to three;
Nay, one she thought too much for him;
So took she all away,
In hope that in her court, good king,
He would no longer stay.

"Am I rewarded thus," quoth he,
"In giving all I have
Unto my children, and to beg
For what I lately gave?
I'll go unto my Gonorell:
My second child, I know,
Will be more kind and pitiful,
And will relieve my woe."

Full fast he hies then to her court;
Where when she heard his moan
Return'd him answer, that she griev'd
That all his means were gone:
But no way could relieve his wants;
Yet if that he would stay
Within her kitchen, he should have
What scullions gave away.

When he had heard, with bitter tears,
"In what I did let me be made
Example to all men.
I will return again," quoth he,
"Unto my Ragan's court;
She will not use me thus, I hope,
But in a kinder sort."

Where when he came, she gave command
To drive him thence away:
When he was well within her court
(She said) he would not stay.
Then back again to Gonorell
The woeful king did hie,
That in her kitchen he might have
What scullion boys set by.

But there of that he was deny'd,
For once refusing, he should not
Come after to her gate.
Thus twixt his daughters, for relief
He wandred up and down;
Being glad to feed on beggars food,
That lately wore a crown.

And calling to remembrance then
His youngest daughters words,
That said the duty of a child
Was all that love affords:
But doubting to repair to her,
Grew frantick mad; for in his mind
He bore the wounds of woe:

Which made him rend his milk-white locks,
And all with blood bestain his cheeks,
To hills and woods and watry founts
Till hills and woods and sensless things,
Did seem to sigh and groan.

Even thus possest with discontents,
He passed o're to France,
In hopes from fair Cordelia there,
To find some gentler chance;
Most virtuous dame! which when she heard,
Of this her father's grief,
As duty bound, she quickly sent
Him comfort and relief:

And by a train of noble peers,
In brave and gallant sort,
She gave in charge he should be brought
To Aganippus' court;
Whose royal king, with noble mind
So freely gave consent,
To muster up his knights at arms,
To fame and courage bent.

And so to England came with speed,
To repossesse king Leir
And drive his daughters from their thrones
By his Cordelia dear.
Where she, true-hearted noble queen,
Was in the battel slain;
Yet he, good king, in his old days,
Possest his crown again.

But when he heard Cordelia's death,
Who died indeed for love
Of her dear father, in whose cause
She did this battle move;
He swooning fell upon her breast,
From whence he never parted:
But on her bosom left his life,
That was so truly hearted.

The lords and nobles when they saw
The end of these events,
The other sisters unto death
They doomed by consents;
And being dead, their crowns they left
Unto the next of kin:
Thus have you seen the fall of pride,
And disobedient sin.

This is a ballad from Thomas Percy's Reliques of Ancient Poetry.

## Sunday, October 09, 2011

### The Mystery of Acts Themselves

D. G. Myers has an excellent post on sin and repentance in Judaism:

Since Pollack was the one to bring up theology, however, it might do some good to clarify his own. In a word, his theology is confessional. Or, to be less coy about it, his thinking is not Jewish at all, but Christian. It is the Christian who demands prior belief as a condition of performing religious acts. For the Jew, things are rather different. As Arthur A. Cohen explains, "All Jewish beliefs interpret and elaborate the mystery of acts themselves, determining finally that many, even those regarded as critical, derive their justification from no rationalization, no human logic, but merely because they are the will and ordinance of God."

For the Jew, in other words, the act is prior, and belief trails along afterwards, picking up wrappers and butts of meaning, which usually turn out to be worthless—every Jewish authority interprets the act differently—eventually concluding that it is done because Jews do it.

One of the things that I think is difficult for most people to understand is that this is the natural way of looking at the matter. Most religions have no theology in a proper sense; it is the acts that matter. This tends not to be quite true of monotheistic religions, which generally have some kind of theology distinguishing them from polytheistic neighbors, but the weight put on this tends to be a fairly minimal: it is just enough theology to make sense of the acts in general, and everything else is, so to speak, private interpretation. This is true of Sikhism, and true to a somewhat greater extent of Islam, and truer still of Judaism. Christianity is the deviation from the norm, and, within Christianity, magisterial Protestantism is generally the strongest deviation (a result of Protestant emphasis on primitive Christianity and the Protestant tendency to interpret that as consisting of what is largely distinctive of Christianity). It is this, of course, that characterizes the Christian and quasi-Christian themes that float around American (and much Western) culture; our familiarity with them leads us not to see how truly strange they are.

This sort of difference is inherent to the relationship between Judaism and Christianity. They are the only direct survivors of religion in the first-century Roman Empire, an era of extraordinarily diverse religious experimentation, and rather notably they both derive directly from big-tent versions of first-century Judaism. In the history of Judaism in our sense, the evolution and history has all been quite straightforward: it derives from fairly mainstream first-century Judaism, closely associated with the Temple but not so closely as to wither when the Temple was destroyed, and while details depend on particular rabbinical traditions, the overall shape of it is exactly what you would expect to grow out of this. If there is any surprise, it is that in the early first century one would probably have expected it to be more Hellenized than it turned out to be, because Hellenistic Judaism was still thriving. Christianity, on the other hand, begins with a highly improbable mix of Messianic, ascetic, and Hellenistic strands of first-century Judaism, and develops out of that in further freakishly improbable ways (largely due to its unique emphasis on proselytizing, which constantly puts it into new situations and leads it to face new cultures by assimilating what it can and actively opposing what it can't). The craziness of Christianity -- its intrinsic tendency to take an originally Jewish base and give it the most unlikely interpretations while nonetheless insisting upon them as essential -- is hidden only by its numbers.

### Impeded Function

John Danaher at "Philosophical Disquisitions" has a nice post discussing what are variously called physiological, physical, perverted faculty, or (in this case) impeded function arguments against gay sex. There are a few minor problems with the discussion. For instance, it turns out to be remarkably difficult to find any natural law theorists who put much weight on this argument. A small handful have, but it really is a small handful: they would be virtually insignificant if they didn't have a few very clever philosophical analyses to their names. (I haven't read this one in particular, but the most famous seems to be Richard Connell's "A Defense of Humanae Vitae," in Laval Philosophique et Theologique vol 26, no. 1 (February 1970).) When it is used by others, it is used almost exclusively to establish a much weaker conclusion than Danaher's (4); in particular, it is used to argue for something like the claim that gay sex is wrong unless there is excellent reason to do it. That is, it is used to claim that when it comes to sexuality there is a moral presumption in favor of sex acts in which there is a possibility of procreation and a moral presumption against sex acts in which there is no such possibility. Other arguments are usually brought in to try to strengthen this to any sort of absolute prohibition. So we should be rather careful about suggesting that natural law theorists usually put much weight on the impeded function argument. It is, to be sure, a popular argument, but it is popular in the way that popular utilitarian arguments are popular: whatever flaws there might be, any such use of utilitarian arguments for or against something can't be treated as generally representative of utilitarian arguments on that subject; they are simply (at best, assuming no gross distortion, which is always a danger with popularizations of arguments) the most accessible fragments of the more accessible versions of utilitarianism. So here.

In any case, even if we take the pure form of the argument, we have to be careful about counterexamples. Take, for instance, the example used of blindfolding and sight. Your eyes have as their natural function letting in the light, and closing your eyes or blindfolding impedes that. It's not so clear, however, that this sort of counterexample works; first, because eyes are part of a sensory system that is in actual life fairly integrated, and whose function is (one would suppose) to gather information about the environment. This overarching function will sometimes be impeded by blindfolding but sometimes won't; and, moreover, it isn't clear that this, rather than sight as such, is the function of the eyes, with letting in the light simply being the particular means of fulfilling that function. At least, it needs to be argued rather than left to unstated assumptions. Likewise, just as your eyelids close to protect your eye, closing your eyes to protect your eyes actually furthers the functions of sight by protecting them from what is dangerous to them. And it is certainly the case that there are plenty of circumstances in which one will think there is really, and perhaps morally, something wrong with a person who goes around blindfolded or with eyes closed: driving, for instance, or walking across the street, or the like. One could, of course, account for these in other ways, but that these other ways are superior would, again, need to be argued rather than assumed. Similar problems arise with many other alleged counterexamples -- showing that they are actually counterexamples is much trickier than Danaher makes it sound.

A problem related to both of these issues is that Danher's (5) is unnecessarily ambiguous between "An action is not always immoral if it impedes the natural function of a bodily organ" and "No action is immoral merely because it impedes the natural function of a bodily organ". Establishing the latter would be a decisive refutation, but it is tricky to establish, and structurally cannot be established by counterexamples alone; the former can be established by well-developed counterexamples. But if we go the former route, it clearly leaves open the possibility of a probabilistic version of the impeded function argument, and a probabilistic version of the argument is difficult to refute by counterexamples alone. The problem with counterexamples in this sort of context is that they depend crucially on precise issues of interpretation and application, and they get their force entirely from the supposition that the proponent of the argument assumes it to be demonstrative rather than probabilistic, presumptive, defeasible under precisely determinable conditions, or any of the other ways arguments can be taken.

And a final worry is the oddity of Danaher's proposed alternative, (13). The impeded faculty argument is not that all biological functions should be fulfilled as much as possible, but simply the more moderate view that they should not be deliberately foiled in those acts in which they are, in fact, biologically involved. But (13) makes a worrisome confusion between biological functions and "basic goods", understood in a consequentialist way, which is, frankly, a bizarre kind of consequentialism. It would imply, for instance, that it is always morally acceptable to destroy or suppress parts of your brain geared toward and necessary for human sympathy if under the circumstances doing so would make it easier to get more of (all three of) sex, food, and sleep.

But while there is some looseness in the precision and nuances that aren't fully addressed, the basic argument Danaher is presenting is an important and essentially correct one. In genuinely traditional natural law the relevant principles of natural law are species-level and therefore, while they establish important priorities, if they are left unsupplemented do not establish anything definitive about individual actions. In genuinely traditional natural law, of course, they are not thought to be unsupplemented; but this gets into rather difficult and sometimes murky territory. But that is as it should be. Sex impinges on so many facets of life that it seems a bit foolish to assume that there are any definitive arguments to exceptionless conclusions on the subject that can be set down in short syllogisms. And one of the things the counterexample approach, and Danaher's presentation of it, does do well is raise over and over again the worry that things are much more complicated than they might initially have seemed to the proponent of the impeded function argument.

### Our Four-Dimensional World

I have an office key that mysteriously works this way, too (the lock on the door is sideways and down by my waist, which somehow throws me off every time, and it's usually 7 am, and I've usually been up since 5).