Sereno, Brewer, and O'Donnell: "Context Effects in Word Recognition" (2003)

This paper is a mystery to me. It presents EEG evidence that ambiguous words are more difficult to process in a "biasing context," but it lumps together the figures for the sentences that primed the dominant of the word, and those for the sentences that primed the subordinate meaning.

I have no idea why anybody would ever want to do that, and it puzzles me even more since the two conditions seem to have been kept apart in the actual execution of the experiment.

Independent Variables

The materials used for the experiment are not reprinted in the paper except for the following twelve example sentences:

Word type	Context	Set	Example sentence
Ambiguous	Neutral	1	James peered over at the bank.
High-frequent	Neutral	1	She looked over the book.
Low-frequent	Neutral	1	To our surprise we saw a hawk.
Ambiguous	Neutral	2	The counted the number of feet.
High-frequent	Neutral	2	Sally knew about the drug.
Low-frequent	Neutral	2	They navigated through the cove.
Ambiguous	Biased	1	They measured in terms of feet.
High-frequent	Biased	1	The pharmacist distributed the drug.
Low-frequent	Biased	1	Pirates headed out to the cove.
Ambiguous	Biased	2	The mud was deep along the bank.
High-frequent	Biased	2	She read the new book.
Low-frequent	Biased	2	Flying to its nest was a hawk.

It would seem that the natural statistical tool for such a design would be a three-dimensional analysis -of-variance with 12 = 3 x 2 x 2 data cells; but as mentioned above, the authors seem to just throw the "Set" variable out the window for no particular reason (even though it seems like the most important one). Instead, they perform a two-dimensional analysis with 6 = 3 x 2 cells.

Dependent Variables

Even though the stuff that the authors are interested in is the amount of electrical activity at the scalp of the head, they actually consider two different dependent variables, both of them rather complicated. They come to the same conclusions in both cases.

The reason that they don't simply end up with a single number right away is that they used 129 electrodes and measured the electrical activity 256 times during each trial. This means that they start out with a huge amount of raw data, and they need some kind of dimensionality reduction to make sense of it.

To bring it down to edible size, they thus performed a principal component analysis; this is a method for bending and stretching the axes of the data space in such a way that all linear correlations between the dimensions disappear (as far as I understand). The problem of doing this turns out to be equivalent to finding the eigenvectors of a certain matrix; and once you have done it, the dominant eigenvector will then tell you how to reduce the data set into a single dimension in the most informative way.

They report that this principal component analysis was "spatial," and that they did it using a so-called quartimax rotation. I'm not quite sure what either of that entails exactly.

At any rate, the two dependent variables they consider are, if I'm not mistaken,

1. the amount of variance that the first (most important) component accounted for, i.e., the amount of variance in the dimension of this eigenvector relative to the total variance of the data set (measured in percent);
2. the mean value of the data when projected into this dimension (measured in microvolts).

How the former of these can be a negative number beats me (cf. their Fig. 1). But maybe I should just push some more big, red buttons and not worry so much.

Mud On the Bank

Here's how the authors sum up their results in the discussion section:

First, we found significant frequency effects in both neutral and biasing sentence contexts […] Second, although there was no context effect for HF [= high-frequent] words, LF [= low-frequent] words were (marginally) facilitated in a biasing context […] Finally, and critically, we examined context effects on ambiguous words. In a neutral context, ambiguous words behaved like HF words; in a biasing context, they behaved like LF words. A neutral context neither facilitated nor inhibited emergence of the dominant (HF) meaning, but a subordinate-biasing context selectively activated the subordinate (LF) meaning (the fate of the dominant meaning is less certain). We believe the pattern of results unambiguously establishes the existence of context effects very early on in the ERP record. (p. 331)

The fact that the ambiguous words behaved like the high-frequent unambiguous words should not be too surprising: the frequency of the high-frequent words were calibrated so as to match the dominant meaning of the ambiguous words as exactly as possible. So the key observation is that the ambiguous words "behaved like LF words" in the biased context.

This means that their ambiguous words required about as much mental effort to process on average as an unambiguous word with the same frequency as the least common meaning of the ambiguous word. But it seems to me that this piece of information is almost completely useless as long as these numbers are based on an average over both the sentences that were biased towards the dominant meaning and the sentences that biased towards the subordinate.

Xenophon: Hiero

Marble bust of Xenophon (from Wikimedia).

In this dialogue by Xenophon, the tyrant Hiero of Syracuse tells the poet Simonides that his job offers far less joy than the ordinary life of a citizen. Simonides responds by instructing Hiero to become a generous and kind ruler, so that his subjects will come to love him.

Live by the Sword

The core of Hiero's complaints is fear: Fear of rebellion, conspiracy, assassination, and treason. When a citizen kills an enemy in battle, Hiero explains, he can publicly boast and rejoice; but when a tyrant executes a conspirator, he needs to hush down the incident and justify his actions, anxious of the resentment it might provoke (II, 15–17).

All of this means that the tyrant must sleep with one eye open, suspicious of everybody:

Drink and sleep I avoid as a snare. To fear a crowd, and yet fear solitude, to fear to go unguarded, and yet fear the very men who guard you, to recoil from attendants unarmed and yet dislike to see them armed—surely that is a cruel predicament! (VI, 3–4)

Consequently, the tyrant lives "in a perpetual state of war" (IV, 11).

The worst about all this, Hiero continues, is that cementing your own despotic power also means burning your bridges:

[“]For how could any despot ever find means to repay in full all whom he has robbed, or himself serve all the terms of imprisonment that he has inflicted? Or how could he forfeit a life for every man whom he has put to death? Ah, Simonides,” he cried, “if it profits any man to hang himself, know what my finding is: a despot has most to gain by it, since he alone can neither keep nor lay down his troubles with profit.” (VII, 12–13)

Death, it thus seems, is the only possible exit.

"Draw on your private property"

Simonides doesn't buy this. He insists that a tyrant can come to live a life without fear, but it requires that he makes himself well liked:

Take heart then, Hiero; enrich your friends, for so you will enrich yourself. Exalt the state, for so you will deck yourself with power. (XI, 13)

Specifically, this means using his private capital to initiate public construction projects, to equip the citizen army, to hire local rather than foreign horse-breeders, and to generally ensure the economic prosperity of the elite citizens of his polis (XI, 2–5).

Drawing of a coin showing Hiero (from an 1875 Swedish history book)

So the solution, it appears, is to throw around money like it's candy: "For in my opinion the sums that a great despot spends on the city are more truly necessary expenses than the money he spends on himself" (XI, 1).

Policy Recommendations

What are we to make of all of this? Surely Xenophon is not a friend of democracy, and we can't take this dialogue as arguing against the institution of tyranny as such.

Perhaps, instead, the idea is to inspire rulers into the kind of "philosophical tyranny" that Plato tried to bring about in Syracuse without much success. The dialogue could be an elaborate excuse for talking some sense to tyrants who rule in a too short-sighted or egotistical fashion.

If so, then all the lamenting about the fear of rebellion and assassination in the beginning of the dialogue might be a preface intended to show the intended reader that there really isn't any happiness to be expected from excessive power-grabbing and exploitation of the citizenry.

In this way, the text would be parallel to other ancient texts claiming that true happiness comes from wisdom, moderation, and self-discipline rather than unhindered access to food, sex, and power.

Croft: Radical Construction Grammar (2001), ch. 1

I read the first chapter's of William Croft's textbook on "radical" construction grammar with a vague sense that he was repeating himself a lot. Then I came across the two quotes below, and the penny finally dropped.

First, pages 32–33:

Dryer suggests that the following four things might be proposed to exist in the domain of grammar (adapted from Dryer 1997b: 116–17):

(23)	categories and relations in particular languages similarities among these language-particular categories and relations functional, cognitive and semantic explanations for these similarities categories and relations in a cross-linguistic sense

Syntactic theorists, including many functionalist theorists, assume the existence of (23d), that is universal categories and relations. These universal categories and relations are then instantiated in the grammars of particular languages. In other words, (23a) is just an instantiation of (23d). In this view, (23b)—the fact that categories across languages are similar, not identical—is due to language-particular peculiarities that do not affect the overall architecture of Universal Grammar.

But in fact there is a wide range of cross-linguistic variation in syntactic categories and roles and other basic syntactic phenomena, as we have already seen, and will see in later chapters.

Then, page 45:

In this section, I argue that the same solution offered by Dryer for cross-linguistic categories should be applied to categories within a language. The following four things might be proposed to exist in a particular language grammar:

(55)	categories and relations defined by particular constructions similarities among these construction-particular categories and relations functional, cognitive and semantic explanations for these similarities categories and relations in a cross-constructional sense

All of the syntactic theories referred to in §1.1 assume the existence of (55d), which I will call global categories and relations. These global categories and relations are then instantiated in particular constructions in a particular language. In other words, (55a) is just an instantiation of (55d). In this view, the fact that categories across constructions are similar, not identical, is due to construction-specific peculiarities that do not affect the overall architecture of the language's grammar.

But in fact distributional criteria in general do not match, within or across languages.

So, it's the book as performance art: He forces us to notice an analogy between two things by pasting the same text into the chapter twice.

That's an efficient rhetorical strategy (and good zen-buddhist practice). It's a pity that it's so boring to read.

Geskell and Marslen-Wilson: "Lexical Ambiguity Resolution and Spoken Word Recognition" (2001)

If you pronounce the phrase

• worn building

and you do this relatively quickly, there is a good chance that it comes out as something close to

• ['wɔɹm'bɪldɪŋ]

instead of

• ['wɔɹn'bɪldɪŋ].

This phenomenon is known as consonant assimilation. In this particular case, it happens because the peripheral consonant /b/ in the beginning of building makes it difficult to pronounce a coronal consonant such as the /n/ in worn, compared to another peripheral consonant such as the /m/ in warm. Your lips simply have to move less to say things like em-beh than to say things like en-beh.

The lip position used for an [m] is close to that used for a [b]
(picture from an online book by Michael Gasser)

In principle, this means that the sound string ['wɔɹm'bɪldɪŋ] involves an ambiguity for the hearer: Was the intended original message worn building or warm building? Both are plausible given the observed signal because they are both occasionally pronounced in the same way.

Assimilation effects can thus — in certain, relatively rare, cases — add another decoding problem to the already quite substantial ambiguity of words like warm.

Noisy Channel Hearing

The raises a question about the psycholinguistics of hearing: What would happen if we plugged a sound ambiguity like this into an experimental paradigm designed to track the process of word sense selection? Would people perhaps show traces of an active inference from sound to word, and competition between various hypotheses?

This is the question investigated by this paper by Gareth Gaskell and William Marslen-Wilson. Their idea is to play back an ambiguous sound string to their subjects, and then check if they are faster at recognizing a word on a computer screen if that word could have been the source of the sound string before consonant assimilation. For instance:

• Voice: The ceremony was held in June and the sunny weather added to the air of celebration. An article about the bribe made the [Screen: bride] local paper.
• Voice: The conditions in the outback were difficult for driving. In the intense heat, the mug cracked up [Screen: mud] completely.
• Voice: We were impressed by her stylish delivery and intonation. Jane finished off the seam beautifully. [Screen: scene]

These test sentences are then compared to another condition in which the phonetics of the sentences do not warrant any backwards inference to a different sound form:

• Voice: The ceremony was held in June and the sunny weather added to the air of celebration. An article about the bribe turned up [Screen: bride] in the local paper.
• Voice: The conditions in the outback were difficult for driving. In the intense heat, the mug turned to [Screen: mud] dust.
• Voice: We were impressed by her stylish delivery and intonation. Jane finished off the seam deftly. [Screen: scene]

These sentences cannot have come about by assimilation effects, so there is no basis for a reconstructive inference. For instance, bribe turned is not easier to pronounce than bride turned, so there is no reason to hypothesize that bribe as a distorted form of bride.

In the Face of Overwhelming Evidence

The main result of the whole paper is that there is indeed a significant difference between the cases where the phonological context supports an inference (e.g., mug cracked) and the cases where it doesn't (e.g., mug turned). This is, however, only the case if the discursive context also strongly suggests the same reconstructive inference (Experiment 3).

It's also worth noting that the effects are tiny. On average, subjects took 522 milliseconds to recognize the phonologically warranted form (e.g., mud from mug cracked) and 537 milliseconds to recognize the phonologically unwarranted (e.g. mud from mug turned). This is a difference of 15 milliseconds, or a drop of 2.8% in decision time. It's statistically significant, but it's not big.

They also found that if you remove the discursive bias from the materials, this effect disappears (Experiment 1 and 2). There is, for instance, no priming effect in the following sentence:

• Voice: An article about the bribe turned up [Screen: bride] in the local paper.

It is thus only when both discursive and phonological context supports the inference that it leaves a measurable trace.

It is conceivable that there is an activation effect in the other case as well, but that it simply is so miniscule that we can't see it. But at any rate, this finding makes sense if we think about the inference as a kind of naive Bayes collection of evidence in favor of a hypothesis.

Mieroop: A History of the Ancient Near East (2004)

Two pieces of information from this textbook surprised and fascinated me:

The first is that the Babylonian scribes during the Uruk period apparently used different number systems for different things (ch. 2.2). They would thus have one system for discrete objects (including human beings) based on symbols for the numbers

1/2 (or 1/10), 1, 10, 60, 600, 3600, 36000.

Another system would be used for things that would come in volume, like grain. This system was based on the unit symbols for the numbers

1/2, 1, 10, 60, 120, 1200, 7200.

A third system would be used to express areas.

What's particularly whacky about this practice is that dried fish would count as discrete objects, while fresh fish would not. Once you dried a fish, you would thus count it using a different number system.

20th century BCE list of stones, plants, fish, birds, and clothing (from the Cuneiform Digital Library Initiative).

A second this is the role of lists in the ancient educational system. There are hundreds and hundreds of so-called lexical lists remaining from the period, recording the names of, for instance, types of swine, often in several languages or with pronunciation guides.

It would seem that copying lists like this would be a core exercise for scribes during this period, perhaps also because they might not always have spoken the official language of the administration as mother tongue.

But there seems to be a particular philosophy expressed by this practice as well, a kind of "ordered universe" conception, with every object occupying its place in the great chain of being. This would might also explain certain aspects of the story of Noah, which seems to have roots in ancient Babylonia, too.

Klepousniotou: "The Processing of Lexical Ambiguity" (2001)

Following up on a related experiment by Lyn Frazier and Keith Rayner, this paper by Ekaterini Klepousniotou presents some evidence that not all types of ambiguity are equally hard to process.

Specifically, she reports a significant difference between, on one hand, the mass/count ambiguity of foodstuff words like potato, and, on the other hand, "deeper" ambiguities like that of fan ("enthusiast" vs. "air-blower").

Filed Down

These differences are found using a priming paradigm in which the subject must make a decision as to whether a string (e.g., prock) is a real English word or not. This task is posed immediately after the subject has read a sentence which primes one specific meaning of the term.

For instance, in the section of the experiment concerned with homonyms, you might for instance get one of the following prime–target pairs:

• The carpenter smoothed the wood. — file
• I have the papers in my office. — file

These two sentences differ as to whether they prime the less frequent or the more frequent meaning of the word file (i.e., "hand tool" or "dossier").

I am afraid Klepsousniotou's frequency calibration of the experiment was done on the basis of data from 1967. This may have had a quite important effect on the outcome of the experiment.

Somewhat surprisingly, Klepsousniotou reports that there was no significant difference between the priming of more frequent meanings and less frequent meanings (p. 213). This contradicts data from other experiments which were specifically designed to show that subordinate meanings are more difficult to access.

A Typology of Lemons

She does, however, find an on-average difference between ambiguities of the type above and ambiguities based around foodstuff metonymies (the result of what Langacker calls "grinding").

The following pair of prime–target pairs would thus both be quicker to process than the file examples above:

• I baked one for lunch. — potato
• I ate some mashed with gravy. — potato

And sure enough, the phrases a potato and some potato hardly seem to invoke different senses of the word potato. It would seem a bit weird to insist that the bare word, in the absence of any article, necessarily would have to be forced into the mold of a "mass noun" or a "count noun."

Mean reaction times for two ambiguity types and two target frequencies (cf. p. 213).

But anyway, now we have some empirical evidence that confirms this hypothesis: Subordinate meanings of strongly ambiguous words (e.g., spring = "source," punch = "drink," racket = "noise," etc.) are more difficult to settle on than mass readings of food words (e.g., some olive, some lemon, some rabbit, some cabbage, some apple, etc.).

Budgell: The Spectator 197 (1711)

In a comment on the conversational culture of his day, Eustace Budgell uses this issue of The Spectator to complain about lawyers who seem to make "Matter for Disputation out of every thing that occurs." He takes this to be a misplaced professional habit:

They are shewing in common Talk how zealously they could defend a Cause in Court, and therefore frequently forget to keep that Temper which is absolutely requisite to render Conversation pleasant and instructive.

Budgell in 1720 (from Wikipedia)

He complains that this esprit de contradiction is spreading like a disease among the young men hanging around the coffee houses (like himself):

Upon my calling in lately at one of the most noted Temple Coffee-houses, I found the whole Room, which was full of young Students, divided into several Parties, each of which was deeply engaged in some Controversie. […] In short, I observed that the Desire of Victory, whetted with the little Prejudices of Party and Interest, generally carried the Argument to such an Height, as made the Disputants insensibly conceive an Aversion towards each other, and part with the highest Dissatisfaction on both Sides.

That's not the style of a proper Gentleman. So he hastens to add some sound advice on how to be an agreeable and polite conversationalist:

Avoid Disputes as much as possible. […] But if you are at any time obliged to enter on an Argument, give your Reasons with the utmost Coolness and Modesty, two Things which scarce ever fail of making an Impression on the Hearers. Besides, if you are neither Dogmatical, nor shew either by your Actions or Words, that you are full of your self, all will the more heartily rejoice at your Victory. Nay, should you be pinched in your Argument, you may make your Retreat with a very good Grace: You were never positive, and are now glad to be better informed.

Notice the ambiguity here: While Budgell is seemingly trying to curb the antagonistic attitude shown in disputes, he is, at the same time, proposing advice for how to win. His comments on the error of losing your temper in an argument contains the same ambivalence:

… if you contend for the Honour of Victory alone, you may lay down this as an Infallible Maxim. That you cannot make a more false Step, or give your Antagonists a greater Advantage over you, than by falling into a Passion.

When an Argument is over, how many weighty Reasons does a Man recollect, which his Heat and Violence made him utterly forget?

Or again, in his advice on taking the role as arbitrator:

That nothing procures a Man more Esteem and less Envy from the whole Company, than if he chooses the Part of Moderator, without engaging directly on either Side in a Dispute. This gives him the Character of Impartial, furnishes him with an Opportunity of sifting Things to the Bottom, shewing his Judgment, and of sometimes making handsome Compliments to each of the contending Parties.

The subtext seems to be that arguments about weighty issues are something that "learned men" do, and that this class-based meta-function is more important than any actual content that could go on within the dialogue.

Gunter, Wagner, and Friederici: "Working Memory and Lexical Ambiguity Resolution as Revealed by ERPs" (2003)

When a word is unexpected in its context, it often elicits a measurable N400 response. This is the case even if the unexpected word is not impossible in the context, only surprising. An example of such a sentence might possibly be

• The plants flourished in the spring water.

But such shifts between hypotheses are difficult, and it would be reasonable to expect individual differences between how good people are at making such retrospective reinterpretations.

Somewhat surprisingly, this paper by Thomas C. Gunter, Susanne Wagner, and Angela Friederici presents some evidence that seems to suggest that people who score high on working memory tests tend to be worse at this kind of switching than people who score low.

Half Full or Half Empty?

The authors interpret this finding as evidence that the process of disambiguation is a matter of inhibition as opposed to activation.

But this seems rather nonsensical; there is no real-world difference between having too many feet and having too few shoes. Activating meaning A could just as well be described as inhibiting meaning B, unless some more precise anatomical theory is intended, and that doesn't seem to be the case in this paper.

But it seems fair enough to say that the test subjects who find the switching difficult must in some sense have been more "successful" in selecting a single hypothesis and getting rid of all the others. As far as I can see, the data in the paper tells us nothing about what the process behind this polarization is at the neurological level, only that it correlates positively with large working memory spans.

Materials

The materials that Gunter, Wagner, and Friederici used consisted in sentences with meaning oscillations of the following four kinds:

• Der Ton wurde vom Sänger gesungen (dominant to dominant)
• Der Ton wurde vom Töpfer gebrannt (subordinate to subordinate)
• Der Ton wurde vom Sänger gebrannt (dominant to subordinate)
• Der Ton wurde vom Töpfer gesungen (subordinate to dominant)

The most difficult switch is the one where the evidence first favors the dominant (more frequent) meaning, and then afterwards the subordinate (less frequent). Those are the cases that provoke larger N400 responses in people with long working memory spans.

A graph showing the averaged ERPs of the low-memory group (top) and the high-memory group (bottom) immediately after reading the disambiguating final verb (from experiment 1, p. 647).

This is not a matter of timing, the authors argue. Even when they added several intervening words, the effect persisted (experiments 2 and 3). It is thus not that the subjects with short working memory spans were slower at making a decision, but rather that they never made up their mind quite as forcefully and irreversibly as the subjects with long memory spans.

The authors report having used 88 different items in the experiment (p. 653), but they only quote two: The clay/tone example above, and the sentence

• Der Ball wurde vom Spieler/Tänzer geworfen/eröffnet

which they use to explain their experimental paradigm throughout the paper.

Gossuin de Metz: The myrrour (1527)

This is a translation of the 1245 book l'Image du Monde by the French priest Gossuin de Metz. It contains, among other things, short introductions to all the liberal arts, including grammar, logic, and rhetoric.

The quality of the scan of the book at Early English Books Online is quite bad, with splotches and dots all over. Combined with the odd and inconsistent spelling, this makes for a very difficult read.

Since I now plowed my way through the few pages on logic anyway, I thought I should put my own transcript here, and save some poor soul the labor some time in the future. The pages are unnumbered in the book, but the logic section stretches over what I guess would be pages 27–30.

Here is the text:

Logyke is the scyence wherby men do lerne to know the trovthe from the false sverly & trvly by probable argvmentys, and so to knowe the trovthe and the falshed of every proposycyon. A proposycvon is a reason of the indicatyff or shewing mode congrve and perfyte, sygnyfyenge trovthe or false, as god is beyng, a man is a beste, and a horse is rennynge, and svche other.

Also every syngvler proposycyon is an affyrmatyff or a negatyff, The affyrmatyff is he that affyrmeth the pryncypal verbe, As a man is a beste. The negatyfe is he that denyeth the pryncypall verbe, as a man is not a beste, so that the negatyffe come before the pryncypall verbe.

Also of syngle proposycyons, some be universals, some pertycvlers, some indiffinite, and some syngvlers.

An universall proposycyon is he that whan a nowne appellatyff that beryth the name of a thynge is his svbjectyfe determynyd with a sygne universall, as every man is a beste.

A partycvler proposycyon is he that whan a nowne that bereth the name of a thyng is his svbiectyfe determyned with a sygne pertycvler, as some man is a beste.

A proposycyon syngvler is he that whan a nowne that is the proper name of a thynge or a pronowne or adverbe demonstratyfe is svbjectyfe, as John is a man, wylliam is a beste, this men renneth, he ronneth, there is a beste, here is a man.

Also of proposycyons som be modallis & som be essencyallys.

A proposycyon modall is he that hath his svbiectyfe with a sygne modall, as this, possyble it is a man to go.

Sygnes modals be .iiii. that is to say, possyble, impossyble, necessarye, contyngent.

Also of proposycyons impossible and necessary there be thwayne that is so say, impossible by hym selfe, and impossible by accydent, impossible by hym selfe is that ever was fals, is false, and ever shall be fals, as no god is, impossible by accydent is that, that is fals & ever shalbe false, bvt yet ones it myght heve be or was trewe, as I have not be livyng. Necessary by hymselfe in like wise is that, that ever was trewe, is trewe, and ever shall be trew as god is, Necesary by accedent, is that that is trew and ever shalbe trew bvt yet [new page] ones is myght heve be or was fals, as my father hath begotte me, Contyngent is that that may be trewe or fals indyfferently, as I go, I speke, I shall go, I shall speke.

Also a dovble proposycyon is called an ypotytyk which hathe .ii. preposycyons inclvdyd in hym with some conivnctyon, As with &, if, or, & whyle, &, when they be ioyned with this worde &, they be called compylatyves, as thov arte arte a man, & that thov arte a beste, and with this worde, yf, cavsels, as yf I ronne, A man ronnyth and with this worde, or, dyffinytifes, As I go, or thov goest, & with this worde, whyle, temporell, as while I go thov syttest.

Illustration from book, placed between the chapter on rhetoric and the chapter on logic.

An argvment is the reason of a dovbtfvll thynge shewyng that whyche is dovbtfvll to be trewe or false, as John is a man, ergo John is a beste, So ever ye mvste note all that cometh before this worde, ergo is callyd the antecedens & that whiche folowth thys worde ergo is called the conseqvens, And note this ever for a pryncypall rvle to knowe a good argvment, when by no case possyble that can be pvtte the antecedens may be trewe and the conseqvens fals, than it is a good argvment, bvt yf any case in the wordle possyble may be pvt that the antecedens maye be trewe & the conseqvens fals, than it is no good argvment.

Also other rvles there be in Logyke to know a good argvmente whyche for yong lerners is conveinent to be had and to be u[se]d for to qvyckyn theyre wyttes bvt this forsayde rvle for them that have wytte and good capasyte is svffycyent to knowe every argvment whether it be good or badde.

Also Logyke techeth a man to know the dyffynicyon or the discrypcyon of every thyng which is no more in effect bvt rvles wherby to know trvly what the thyng is.

A dyffynycyon is that which sheweth what the thyng is by other thyngs essencyal.

A dyscrynpcyon is that whych sheweth what the thyng is by other thynges accydentall. As the dyffynycyon of a man is thys. A man is a body wyth lyfe sencyble & reasonable or every thynge whiche is a body with lyfe sensyble & reasonable is a man, and every man is a body wyth lyffe sensyble and reasonable.

Sensyble is as moche to say as that thynge that hathe the use or aptnes of the .v. sensys, as of tastynge, smellynge, herynge, seiyng, & tovchyng.

A dyscrypcyon is to know what the thynge is by thynges accyden[new page]tall, as the dyscrypcyon of a boke comonly is that thynge that is made with perchement or paper or with lettres that men may rede yet every thynge which is made with parmemente or paper with leters that men may rede is not a boke, nor every boke is not made with parchement or paper and lettres as a boke made with tables and ymages. Therfore in the dyscrypcyon we saye this worde comonly.

Accydentall thynges be those that my be somtyme take away from the thynge and yet the thynge to remayne as whytnes, blacknes, greatnes, or smalnes.

Essencyall thynges be those which never may be taken away from the thynge and the thynge to remayne, as the body of a man can never be takyn away from the man and the man to remayn.

Then follows the chapter on geometry.

Weber: From Max Weber (1948)

Max Weber in 1894 (image from Wikimedia).

The most thought-provoking piece in this anthology is chapter 10, "The Meaning of Discipline." The chapter an excerpt from Weber's Wirtschaft und Gesellschaft, and it contains a discussion of the way charismatic authority is consolidated into discipline once heroic or spirited leadership turns into everyday goverment and bureaucracy.

Everybody in the Army!

Weber is very clear about what he considers as the origins of discipline:

The discpline of the army gives birth to all discpline. (p. 261)

After discpline has been established in the army, however, it can spread to other sectors:

… discipline has always affected the structure of the state, the economy, and possibly the family. (p. 257)

For instance:

When infantry drill is perfected to the point of virtuosity (Sparta), the polis has an inevitably 'aristocratic' structure. When cities are based upon naval discpline, they have 'democratic' structures (Athens). […] The rule of the Roman participiate, of the Egyptian, Assyrian, and finally of all the modern European bureaucratic state organizations—all have their origin in discipline. (p. 257)

OK, that was a bit fast on the trigger, cowboy, but I see what you're saying.

Discipline in the Factory

The principles of "scientific management" may also be explained in this way, according to Weber. In this respect, he has foreshadowed countless modern commentators, so I'll quote this at some length:

No special proof is necessary to show that military discipline is the ideal model for the modern capitalist factory, as it was for the ancient plantation. In contrast to the plantation, organizational discipline in the factory is founded upon a completely rational basis. With the help of appropriate methods of measurement, the optimum profitability of the individual worker is calculated like that of any material means of production. On the basis of this calculation, the American system of 'scientific management' enjoys the greatest triuphs in the rational conditioning and training of work performances. The final consequences are drawn from the mechanization and discipline of the plant, and the psycho-physical apparatus of man is completely adjusted to the demands of the outer world, the tools, the machines—in short, to an individual 'function.' The individual is shorn of his natural rythm as determined by the structure of his organism; his psycho-physical apparatus is atuned to a new rythm through a methodical specialization of seperately functioning muscles, and an optimal economy of forces is established corresponding to the conditions of work. This whole process of rationalization, in the factory as elsewhere, and especially in the bureaucratic state machine, parallels the centralization of the material implements of organization in the discretionary power of the overlord. (p. 261–62)

This translation is in fact quite off on a number of points, so let me just paste the German original in here for reference:

Daß dagegen die »militärische Disziplin« ganz ebenso wie für die antike Plantage auch das ideale Muster für den modernen kapitalistischen Werkstattbetrieb ist, bedarf nicht des besonderen Nachweises. Die Betriebsdisziplin ruht, im Gegensatz zur Plantage, hier völlig auf rationaler Basis, sie kalkuliert zunehmend, mit Hilfe geeigneter Messungsmethoden, den einzelnen Arbeiter ebenso, nach seinem Rentabilitätsoptimum, wie irgendein sachliches Produktionsmittel. Die höchsten Triumphe feiert die darauf aufgebaute rationale Abrichtung und Einübung von Arbeitsleistungen bekanntlich in dem amerikanischen System des »scientific management«, welches darin die letzten Konsequenzen der Mechanisierung und Disziplinierung des Betriebs zieht. Hier wird der psychophysische Apparat des Menschen völlig den Anforderungen, welche die Außenwelt, das Werkzeug, die Maschine, kurz die Funktion an ihn stellt, angepaßt, seines, durch den eigenen organischen Zusammenhang gegebenen, Rhythmus entkleidet und unter planvoller Zerlegung in Funktionen einzelner Muskeln und Schaffung einer optimalen Kräfteökonomie den Bedingungen der Arbeit entsprechend neu rhythmisiert. Dieser gesamte Rationalisierungsprozeß geht hier wie überall, vor allem auch im staatlichen bürokratischen Apparat, mit der Zentralisation der sachlichen Betriebsmittel in der Verfügungsgewalt des Herrn parallel. (pp. 686–87)

I always get a sense that Weber wrote sentences like this when he was in the most gloomy mood, imagining a dismal future society of complete bureaucratization and control. As for Marx, Heidegger, and others, this sense of unease was ambiguous between a romantic protest against alienation and a more cynical mapping out of the mechanics of power.

Pragmatics at the Dentist

There is just one more thing I would like to quote, mostly out of a linguistic interest. This comes from the essay "The Protestant Sects and the Spirit of Capitalism."

This essay was written after Weber's book on protestantism. Its main claim is that membership of esoteric church communities was used as an indication of one's creditworthiness in the USA of Weber's day. This made sense both because of the moral doctrines of the communities, and because membership was expensive.

In the beginning of the essay, Weber relates the following anecdote:

The matter became somewhat clearer from the story of a German-born nose-and-throat specialist, who had established himself in a large city on the Ohio River and who told me of the visit of his first patient. Upon the doctor's request, he lay down upon the couch to be examined with the nose reflector. The patient sat up nce and remarked with dignity and emphasis, 'Sir, I am a member of the –––––– Baptist Church in –––––– Street.' puzzled by about what the meaning this circumstance might for the diease of the nose and its treatment, the doctor discreetly inquired about the matter from an American colleague. The colleague smilingly informated him that the patient's statement of his church membership was merely to say: 'Don't worry about the fees.' (p. 304)

The reason I found this such a nice example is that it shows how completely obscure pragmatic inferences sometimes are, and how wrong communication can go when the right common ground is absent.

Swift: A Modest Proposal (1729)

Contemporary portait of Swift (of disputed copyright)

In this hilarious booklet, Jonathan Swift starts by observing the dire conditions of his country's poorer classes:

It is a melancholy object to those, who walk through this great town, or travel in the country, when they see the streets, the roads and cabbin-doors crowded with beggars of the female sex, followed by three, four, or six children, all in rags, and importuning every passenger for an alms. These mothers instead of being able to work for their honest livelihood, are forced to employ all their time in stroling to beg sustenance for their helpless infants who, as they grow up, either turn thieves for want of work, or leave their dear native country, to fight for the Pretender in Spain, or sell themselves to the Barbadoes.

I think it is agreed by all parties, that this prodigious number of children in the arms, or on the backs, or at the heels of their mothers, and frequently of their fathers, is in the present deplorable state of the kingdom, a very great additional grievance; and therefore whoever could find out a fair, cheap and easy method of making these children sound and useful members of the common-wealth, would deserve so well of the publick, as to have his statue set up for a preserver of the nation. 

The solution is, of course, obvious — have the rich eat the kids of the poor:

I have been assured by a very knowing American of my acquaintance in London, that a young healthy child well nursed, is, at a year old, a most delicious nourishing and wholesome food, whether stewed, roasted, baked, or boiled; and I make no doubt that it will equally serve in a fricasie, or a ragoust. 

This will also have "the profit of a new dish, introduced to the tables of all gentlemen of fortune in the kingdom, who have any refinement in taste." Further, the skin of the children "will make admirable gloves for ladies, and summer boots for fine gentlemen."

In additional to this increase in wealth and leasure, it would have a beneficial effect on morals, since it would give "a great inducement to marriage" and to "the care and tenderness of mothers towards their children."

Hattiangadi: Oughts and Thoughts (2007)

Front cover (from amazon.com).

This book, based on Anandi Hattiangadi's doctoral dissertation, embodies pretty much everything that's wrong with analytic philosophy — the scholasticism, the narrowness, the in-breeding. Opening up the book on a completely random page, I find the following example:

Similarly, if we want to explain why Jones tokened a 'horse' thought, but Smith did not, we might cite the fact that there was a horse in front of Jones but not in front of Smith. However, if there is a horse in front of both of them, but Jones is in the light and Smith is in the dark, we will cite the fact that the horse in front of Jones was well lit. In that case, it looks like it is the light rays bouncing off the horse and into Jones's eyes that caused the 'horse' thought, since the in the absence of that condition, in Smith's case, a 'horse' thought was not caused. (p. 138)

And so on. You probably get the point.

Private Commitments And Bananas

The reason why I checked out the book from the library is that it contains a discussion of the issue of normativity in semantics. In fact, its last chapter before the conclusion is called "Is Meaning Normative?" (ch. 7).

Hattiangadi doesn't think so. Her argument comes in three species:

1. Meaning can't be based on prescriptions, promises, conventions, etc. because that would only work if you could already understand those prescriptions, promises, conventions, etc. So they would presuppose meaning (pp. 193–97).
2. If you assume that norms are somehow a matter of personal, private, inner commitments, there's a lot of stuff that doesn't make sense: "Eating a banana instead of an apple does not mean that I have failed to do what I ought to do in anything other than the trivial sense that I have violated the hypothetical imperative conditional on my intention" (p. 201). This argument often co-occurs with the character Matilda, who is a notorious liar.
3. Since norms and rules are only negative and restrictive, they won't generalize, for some reason: "The rule that tells me to apply 'horse' only to horses does not tell me that 'horse' applies to all horses" (p. 206).

Those all seem to be pretty bad arguments. The first one, in particular, is an exact parallel to the often-used argument against relativism which, like St. Anselm's proof of God's existence, can be used to support any theory of meaning or knowledge, however whacky.

Ainsworth: The Art of Logick (1653)

In this textbook on logic, Henry Ainsworth presents the topic as a kind of mental training, preparing the mind for other serious matters:

No discipline more helpeth the wit, or contemplative sharpness, i.e. the inclination of the temperature to contemplate distinctly and accurately. (p. 7)

This notion of mental training should be taken quite seriously:

The exercise then of Logick consisteth in this, that we frequently think on, & diligently meditate things conformably to the prescriptions and rules of Logick, that is, orderly and distinctly: This indeed is the chief, most principal, and the nearest Efficient Cause of this habit in us of this Art of Logick, and immediately ingenerates and expresseth Logick in us, whereas Wit and Precepts are Causes but remote. (pp. 12–13)

The book consequently closes with two chapters of suggested exercises.

Games and Meditations

These recommended exercises include both "solitary" and "social" exercises or games (p. 205).

For instance, Ainsworth suggests one problem type in which a teacher gives the pupil a theme (e.g., animal), and the pupil then responds by explaining the etymology, genus, parts, antonyms, etc. of the concept (p. 195).

A discussion-game for two is also discussed, after a due amount of prudent warnings (e.g., "Let not the matter propounded to be disputed of, violate Piety or Religion," p. 205).
Specifically for "social disputation," another bundle of ground rules are added:

1. Let there be brought unto disputation a good intention of the mind, which seeks not glory, but truth.
2. Let the mind be pure from all prejudices.
3. Let the disputers agree whither of them shall oppose or answer.
4. Let both parties bind themselves to the Laws and Rules of Logick.
5. Let them agree between themselves of certain foreknown principles.
6. Let brevity and plainness be kept in opposing, and answering all Ambiguities; and Ambages of Oratorious Declamations avoided. (p. 206)

After having drawn up these general rules, Ainsworth goes on to discuss the more specific "duties" of the person playing Opponent, and the person playing Answerer (p. 207–8; there is occasionally also a President, p. 208).

Other suggested exercises include solitary meditation on things learned (p. 212), and methodological analysis of written arguments, putting them into syllogistic form and the like (p. 217ff).

Foucault: Fearless Speech (2001)

Cover image (from amazon.com).

The title of this book is a bit misleading; it suggests a sexy collection of provocatively political manifestos but is in fact a piece of good, old-fashioned classicist scholarship, like much of the work Foucault did in his last years.

This particular study is concerned with the notion of parrhesia or "frank speech," which played an interesting role in both Athenian democracy and later Stoic self-improvement. Foucault combs meticulously through the works of Seneca, Epictetus, Plato, and others, in order to map out how the concept came to be first articulated and then problematized in the ancient and late-ancient literature.

The text is based on six tape-recorded lectures that he gave at UC Berkeley in 1983.

Although the first couple of chapters of the book treat the role of parrhesia in the context of political life, it really starts to pick up momentum as Foucault gets into the discussion of his latter-day pet topic, the care of the self.

The King Gets a Beating

As part of this discussion, he considers a dialogue by the Cynic philosopher Dio Chrysostom. This text dramatizes the alleged meeting between Diogenes (the philosopher said to live in a barrel) and Alexander the Great (pp. 124–133).

During the dialogue, Diogenes provokes Alexander by all sorts of means, including questioning his courage and his claims to the throne. This kind of deliberate provocation has some interesting parallels with the Socratic dialogue, but also some interesting differences from it:

… whereas Socrates plays with his interlocutor's ignorance, Diogenes want to hurt Alexander's pride. For example, at the beginning of the exchange, Diogenes calls Alexander a bastard and tells him that someone who claims to be a king is not so very different from a child who, after winning a game, puts a crown on his head and declares that he is king. Of course, all that is not very pleasant for Alexander to hear; But that's Diogenes' game: hitting his interlocutor's pride, forcing him to recognize that he is not what he claims to be—which is something quite different from the Socratic attempt to show someone that he is ignorant of what he claims to know. (p. 126; emphasis in original)

As the dialogue progresses, Alexander's patience and tolerance are put to increasingly harsh tests. In effect, Diogenes thus turns the conversation into a game with extreme stakes: Will Diogenes shut up out of fear for death, or will Alexander lose his temper and slaughter him because, after all, he did not have the self-confidence and fearlessness that marks a true king?

Everybody Wins?

The martial element of the dialogue is thus, in one sense, even stronger than in Plato:

Whereas the Socratic dialogue traces an intricate and winding path from an ignorant understanding to an awareness of ignorance, the Cynic dialogue is much more like a fight, a battle, or a war, with peaks of great aggressivity and moments of peaceful calm—peaceful exchanges which, of course, are additional traps for the interlocutor. (p. 130)

19th century depiction of the meeting (from Wikimedia).

The game finally ends when Alexander gets around to asking what the true mark of a king might be (now that Diogenes has disqualified practically everything that makes Alexander a king). Diogenes explains that a true king behaves like one, and is, in what I assume is Foucault's paraphrase, "noble by nature" (p. 132).

Thus:

Here the game reaches a point where Alexander does not become conscious of his lack of knowledge, as in a Socratic dialogue. He discovers, instead, that he is not in any way what he thought he was—viz., a king by royal birth, with marks of his divine status, or king because of his superior power, and so on. He is brought to a point where Diogenes tells him that the only way to be a real king is to adopt the same type of ethos as the Cynic philosopher. And at this point in the exchange there is nothing more for Alexander to say. (p. 132)

Just as in the Stoic ethos, the goal of the whole exercise thus seems to be a kind of independence from visible fame, power, and wealth. It's not that the real gratification lies in some afterlife as in the Christian tradition, but there is still a sense that one should avoid attachment to the wrong things, and to the wrong symbols.

Perceptual Hygiene

The last example in the book comes from a text by Epictetus, and describes a method for training oneself to meet impressions with the right state of mind. Inspired by sophistical question-and-answer games, Epictetus suggests that we should constantly keep an inner dialogue going regarding everything we see:

As we exercise ourselves to meet the sophistical interrogations, so we ought also to exercise ourselves daily to meet the impression of our senses, because these too put interrogations to us. So-and-so's son is dead. Answer, "That lies outside the sphere of the moral purpose, it is not an evil." […] He was grieved at all this. "That lies withing the sphere of the moral purpose, it is an evil." He has borne up under it manfully. "That lies within the sphere of the moral purpose, it is a good." Now if we acquire this habit, we shall make progress, for we shall never give our assent to anything but that of which we get a convincing sense-impression. (p. 163, cited from Epictetus: The Discourses as Reported by Arrian, III, 8)

Epictetus goes on to recommend doing this exercise constantly "from dawn till dark," interrogating your senses about everything you see. He compares this examination of one's impressions to the caution of a nightwatch — "Wait, allow me to see who you are and whence you come" (p. 161).

This is interesting for two reasons: First, it resonates a lot with contemporary notions of mindfulness as employed in New Age religions and self-help therapy. And second, it has an interesting and not completely obvious relationship with epistemological skepticism; many philosophical discussions of how one should distrust one's senses acquire a quite different ring when we put them in the context of such a clearly normative and ethical theory of perceptual hygiene.

The Dangers of Florid Prose

Just one last example: In his book On the Tranquility of Mind, Seneca reproduces a (possibly fictional) letter by a family member named Serenus. In the letter, Serenus complains that while he har largely overcome his desire for material wealth, public recognition, and an immortal legacy, he still occasionally falls back into old habits, feeling envy at "the sight of slaves bedecked with gold" and the like (p. 155, cited from Seneca: On the Tranquility of Mind, I, 4–17).

What I want to point out, however, is the way that Serenus explicitly links his desire for an eternal memory with a specific mode of writing:

And in my literary studies I think that it is surely better to fix my eyes on the theme itself, and, keeping this uppermost when I speak, to trust meanwhile to the theme to supply the words so that unstudied language may follow it wherever it leads. I say: "What need is there to compose something that will last for centuries? Will you not give up striving to keep posterity silent about you? You were born for death; a silent funeral is less troublesome! And so to pass the time, write something in simple style, for your own use, not for publication; they that study for the day have less need to labor." Then again, when my mind has been uplifted by the greatness of its thoughts, it becomes ambitious of words, and with higher aspirations it desires higher expression, and language issues forth to match the dignity of the theme; forgetful then of my rule and of my more restrained judgment, I am swept to loftier heights by an utterance that is no longer my own. (pp. 156–57)

In this way, Serenus (or Seneca) constructs a direct parallel between vain desires and ambitions to "high" writing. Apparently the assumption is that there is a kind of humbleness or honesty built into the "simple style" which at once is guaranteed to be "your own" and to keep you vigilant with respect to abiding by your (Stoic) principles of a philosophical life.

Final Remarks on Method

There is a place in the third volume of the History of Sexuality in which Foucault implicitly criticizes the Marxist conception of the dynamics of history for being to rigid, but it is quite obscure what exactly he imagines to put in its place.

This gets a little clearer in the brief remarks he makes on his project in these lectures. It's an important point, so I'll quote is quite extensively here.

During the first lecture, Foucault states:

I would like to distinguish between the "history of ideas" and the "history of thought." […] The history of ideas involves the analysis of a notion from its birth, through its development, and in the setting of other ideas which constitute its context. The history of thought is the analysis of the way an unproblematic field of experience, or a set of practices, which were accepted without question, which were familiar and "silent," out of discussion, becomes a problem, raises discussion and debate, incites new reactions, and induces a crisis in the previously silent behavior, habits, practices, and institutions. The history of thought, understood this way, is the history of the way people begin to take care of something, of the way they become anxious about this or that—for example, about madness, about crime, about sex, and themselves, or about truth. (p. 74)

In his concluding remarks at the end of the course, he elaborates:

Some people have interpreted this type of analysis as a form of "historical idealism," but I think that such an analysis is completely different. For when I say that I am studying the "problematization" of madness, crime, or sexuality, it is not a way of denying the reality of such phenomena. One the contrary, I have tried to show that is was precisely some real existent in the world which was the target of social regulation at a given moment. The question I raise is this one: How and why were very different things in the world gathered together, characterized, analyzed, and treated as, for example, "mental illness"? What are the elements which are relevant for a given "problematization"? And even if I won't say that what is characterized as "schizophrenia" corresponds to something real in the world, this has nothing to do with idealism. For I think there is a relation between the thing which is problematized and the process of problematization. The problematization is an "answer" to a concrete situation which is real. (pp. 171–72)

Homing in even more specifically on what must have been a Marxist critique, he continues:

But we have to understand very clearly, I think, that a given problematization is not an effect or consequence of a historical context or situation, but is an answer given by definite individuals (although you may find this same answer given in a series of texts, and at a certain point the answer may become so general that it also becomes anonymous). (p. 172)

These answers do not come "from any sort of collective unconscious" (p. 172):

And the fact that an answer is neither a representation nor an effect of a situation does not mean that it answers to nothing, that it is a pure dream, or an "anti-creation." A problematization is always a kind of creation; but a creation in the sense that, given a certain situation, you cannot infer that this kind of problematization will follow. Given a certain problematization, you can only understand why this kind of answer appears as a reply to some concrete and specific aspect of the world. There is the relation of thought and reality in the process of problematization. (p. 172)

I suspect this is about as clear as Foucault ever got on this issue, and about as clear as he could get.

Mills: Gender and Politeness (2003)

The most interesting argument in this book by Sarah Mills is that we cannot treat politeness as a matter of form. Meaning is extremely context-dependent, and people often spend quite a lot of time and mental resources trying to figure out how whether something was a sarcastic jab, a polite compliment, or something completely different.

The Indeterminacy of Politeness

Front cover, from amazon.com.

As an example of such a case of very real uncertainty, Mills relates a story of a woman who asks a man whether he has any change for the payphone just as he exits the booth (p. 84). He tells her that there is 80p of credit left in the phone, and that she can use that, and she replies

• Thank you VERY MUCH; thank you VERY MUCH.

The man, who was Libyan but experienced this incident in Britain, was later unsure what exactly to make of this comment. He wondered whether she thought that he "had been stupid to be so generous to a stranger" (p. 84). Possibly, she could also have been ironically remarking that the gift had been too small rather than too big. Or perhaps she really just meant to thank him.

A more straightforward example (p. 80) is that of a teacher telling her class,

• Can you PLEASE be quiet?

Obviously, this is not a matter of the teacher subserviently bowing and scraping for the kids, but rather quite forcefully giving an order. (I'm sure you have heard an equivalent of this exact sentence back in your school days.) Mills attributes this example to Mark Jary (1998).

In both cases, the linguist can't simply sit on a mountaintop and claim to have special insights into the meaning and force of the things that people say. If you want to know whether something appears as polite or impolite to the participants in a conversation, you need to ask them.

Deep and Shallow Conversational Themes

The fifth chapter of the book, also called "Gender and Politeness," largely takes the form of a prolonged criticism of the book Men, Women, and Politeness (1995) by Janet Holmes.

Mills correctly criticizes her for having a way too superficial conception of the relation between form and function, and for ignoring or explaining away data that doesn't fit her theory. On a theoretical level, nothing is done here which has not already been done better and more pointed by Deborah Cameron, but it's perhaps still worth the time to see in detail where the seams come apart.

By way of illustration, Mills analyses two telling examples of mismatches between stereotypically "mannered speech" and the real motivations of the participants. One example is about excessive thanking between women (pp. 227–31), and the other is about two women having a discussion while a largely quiet man is also present in the home (pp. 231–34).

Lovely, Lovely

In the first of these examples, a woman codenamed "D" gives a Maori shell as a present to her hosts, who proceed to thank. One participant, codenamed "M," for instance shoots off this tirade (p. 228):

• … oh, that's lovely. lovely, isn't it? […] oh, that's lovely, thank you very much, I love the colours …

On the face of it, this seems like a perfect example of stereotypical "women's speech," but in her interviews with the participants, Mills actually found that, during this exchange, the women were in fact trying to shut up D so that they could to get on with their lunch. This led to a kind of unfortunate spiraling effect, since D took thanking as an invitation to talking, and her talking led the other women to ramp up their thanking.

Again, had Mills been sitting in her office handing out judgments of what this or that utterance meant, she would probably only have added yet another layer of misunderstanding, and largely misread the subtext of the conversation.

Pointing the Camera the Wrong Way

The other example concerns a conversation between two participants, two women who are old friends, and the partner of one of them. The exchange centers around a misunderstanding — the woman codenamed A is visiting the couple, planning to go out with them, but the host couple then realize a bit too late that she didn't come by car as they first thought.

A then apologizes quite heavily (p. 232):

• I'm sorry, I've, um, messed up all the plans.

Mills comments:

Focusing only on the way that A explicitly apologizes, which conventional politeness theories such as Holmes do, would not allow us to focus on the way that in this interaction questions of the sex of the participants is not particularly salient. (p. 234)

Instead, the exchanges surrounding the misunderstanding all could instead be seen as a collaborative project of building and maintaining intimacy, so that

… they can present themselves as a group of friends who get on well together because they can resolve conflicts jointly, not allowing difficulties and misunderstandings to threaten anyone's face. (p. 234)

So, looking for superficial cues like I'm sorry would very likely lead an analyst to think that A was very explicitly gendering herself in this dialogue. But in fact, one could just as well focus on the quite forceful way that the other female speaker asserts herself during the dialogue, or the much more withdrawn role of the male participant. From that perspective, the use of apologies, teasing, and irony would be seen much more as a product of the local context.

Seneca: Letters to Lucilius (trans. E. Barker, 1932)

The letters from Seneca to Lucilius mostly contain an assorted bunch of moralistic advice on how to live a good, Stoic life. One thing in particular which struck me about them, however, was their very explicit ridiculing of superficial philosophical or logical arguments.

Bust of Seneca (from Wikimedia)

For instance, one central tenet of the Stoic creed is that one should not fear death; but Seneca rejects the notion that this change of attitude can be brought about by a kind of "logical hocus-pocus" (letter 82; p. 12). He thus writes:

Our founder Zeno uses the following syllogism:

'No evil is glorious;
Death is glorious,
Therefore death is not an evil.'

O my comforter! Dispeller of my terrors! After that I shall lay my head on the block with alacrity! Please talk more seriously, and don't make a dying man laugh. Upon my honour I should find it hard to tell you whether the man who imagines he has snuffed out the fear of death by this inference, or one who tries gravely to explode it, as if it really bore on the question, is the crazier. (letter 82, p. 11-12)

The message thus seems to be that it isn't enough to recognize the formal validity of this or that verbal argument — you have to internalize its message and learn to live by it.

"Breakfast, Lads!"

Seneca's own preferred medium for making such points is instead the short, forceful statement of fact that treats death without any special ornament or sentimentality. In another comment to the syllogism above, he thus comments:

A moving address indeed! After that who'd demur to hurl himself on the levelled spear-points and die where he stood? But what gallant words Leonidas spoke: 'Get a good breakfast, lads: there'll be no dinner till the next world.' The food didn't rise in their mouths or stick in their throats or slip from their fingers: they accepted for dinner as cheerfully as for breakfast. Once more, there's the Roman officer speaking to the men sent to pierce a huge hostile force and seize a position: 'We must get there, boys,' said he, 'but we needn't get back again.' You see how unaffected and masterful virtue is: pray is there a single soul the chicaneries of you and your friends could inspire and brace? (letter 82; pp. 17-18)

Apparently, death-talk should not only be staunch and "unaffected," but also positively folksy ("lads"). This is is a matter of style and ethics rather than logic:

What can you say to fire men's heart for a plunge into the thick of peril? With what pleading can you defeat this unanimity of dread, with what resources of genius the conviction of humanity that bars your way? Do I find you juggling with words and spinning miserable little syllogisms? (letter 82; p. 18)

In fact he does, and he has an opinion to offer on the relevance of such arguments:

Your arguments run to point. Yes, and so does an ear of barley. It's the very fineness of some points that makes them useless and ineffective. (letter 82; p. 18)

It's difficult not to read a gendered Victorian connotation into a word like "fineness," but I don't know what the Latin text said, or how it would sound to contemporary ears.

"Storm the Stronghold of the Passions"

Seneca makes a similar point when discussing the dismissive Stoic attitude towards money, and in particular, the false sense of pride and security that people may draw from their wealth. Again, he counters this notion with a syllogism in the classical form:

Good doesn't result from evils. Wealth does results from a sum of many poverties: therefore wealth is not a good. (letter 87, p. 58; italics in original)

But he has little hope that such arguments really convince anybody:

Are we likely to argue the pros and cons in syllogisms of the kind we've just seen? Are we likely by their means to succeed in making the Roman people seek poverty, the groundwork and source of their imperial power, and honour it, shrink in dismay from their own wealth, reflect that they discovered this wealth in the treasuries of the vanquished, that from it bribery, corruption, and political disorders have forced their way into the most irreproachable and austere of cities, that the spoils of other nations are too gloatingly paraded, and that what one people has wrestled from all, all may more easily wrest from one? No, it is our actions [that] must champion that law: we must storm the stronghold of the passions, not draw lines round them. Let us speak, if we can, more forcibly; if not that, more plainly. (letter 87; p. 59)

It thus seems that in Seneca's ethical idiom, there is a strong connection between (1) being a "man of action" rather than idle words; (2) having learned to live in accordance with one's ethical truth; and (3) talking in a certain "no-nonsense" style of frank, manly prose.

In a sort of roundabout way, the effect is thus that he comes to appear in line with the modern "one true sentence" philosophy of writing that we associate with Hemingway — another decidedly macho writer/soldier/moralist.

Ardeshir and Ramezanian: "A solution to the surprise exam paradox in constructive mathematics" (2012)

The surprise examination problem concerns a teacher who announces the following:

One of the next five days, you will have an exam; and I will pick the day of the exam such that when it comes, it will come as a surprise.

The problem with this announcement, according to one line of reasoning, is that it is in fact impossible to satisfy:

The teacher can't rationally place the exam on Friday, because it would then be completely predictable given that it hadn't occurred Monday through Thursday; but the teacher also can't place it on Thursday, because it would then be completely predictable given that it hadn't occurred Monday through Wednesday, and that the teacher will be rational on Friday; and similarly, it can't take place on Wednesday, etc. In this way, we end up concluding that the exam can't take place at all.

This impossibility argument rests on a number of assumptions: For instance, if the teacher is not guaranteed to be rational in the future, the argument collapses, just as in the case of the centipede game. Another assumption is that the teacher can only use pure (deterministic) strategies, a restriction that rules out the solutions to many games, including rock-paper-scissors.

Backwards Induction in Constructive Mathematics

However, the approach taken in the paper by Mohammad Ardeshir and Rasoul Ramezanian is to deny constructive validity of the argument above. They do so by translating the teacher's choice of examination day into a bounded and increasing series whose maximum identifies the day of the exam.

For instance, if the exam takes place on Thursday, the students might observe the following series:

1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, …

Since this series can is increasing and only takes values among the number {1, 2, 3, 4, 5}, it has a maximum according to classical reasoning. However, in constructive mathematics, this maximum is said not to exist because we can't explicitly identify which of the five numbers it is.

Given this translation, the teacher can now truthfully say:

I can construct a bounded and increasing series with values in {1, 2, 3, 4, 5} such that you cannot constructively infer its maximum from any finite segment.

That's doable; the standards of existence imposed by constructive mathematics are so high that as long as you haven't observed a 5 anywhere in the sequence, you have no constructively valid conclusion about the maximum. So even if the exam is placed on Friday, there is no specific natural number k such that you can with certainty infer the maximum of the series after having observed k items.

In other words, the students have no reliable algorithm for inferring what day the exam will be held. This conclusion does, however, rest crucially on the assumption that there can be arbitrarily large time lags between the jumps in the sequence.

Infinite Input Turing Machines

Towards the end of the paper, the authors introduce something called "Type 2 Turing machines." These are machines that can take infinite inputs and produce infinite outputs.

The reference they give for this concept is a textbook by Klaus Weihrauch. I will have to take a look at that at some point.