Friday, August 11, 2023


 One inevitable result of reading Sir Walter Scott is being exposed to words you haven't come across before. One recent example is 'umquhile'; it is a (now mostly obsolete) Scots word meaning 'late', in the sense of 'relatively recently deceased'. Very rarely it could be found in the variant, 'umwhile'. 

I've mentioned before the struggles that Scottish philosophers in the early modern period had with trying to write in English; Scots and English were dialects much farther apart then than they have since become. Many of the differences were just ordinary dialectal differences arising from having populations that rarely interacted,  but one of the more substantive differences was that Scots was much more directly influenced by legal language than English. This is the reason, for instance, why Scots then (and to a lesser extent even today) is a more latinate language than English -- Law-Latin was much more likely to contribute words to everyday vocabulary in Scotland than in England. But it wasn't just Latin in particular; 'umquhile' is from Middle English (originally meaning 'sometime' as an adjective, and loosely related to the later term 'erstwhile'), but was also primarily used in legal contexts; it's thus unsurprising to find the Scots using it in the early modern period.

As time has gone on, a few Scottish words have entered into English, but the general pattern has been for Scots to shift to accommodate English grammar and vocabulary. This is unfortunate, I think, as a general matter; but it's one of the historical reasons why anyone still reads David Hume today -- his historical works were popular among the English, and had a reputation of being a very readable, if occasionally eccentric, summary of English history. Writing in English rather than Scots in a popular niche with relatively little competition kept Hume's name alive. And Hume himself was aiming at it -- it's why he started spelling his name 'Hume' rather than the more correct 'Home', so that the English would pronounce it in a way that was approximately right.

Sir Walter Scott, like Robert Burns, is at an interesting position in all of this. Burns and Scott also often wrote in English for English audiences, but they both were trying to contribute as well to Scottish literature itself. As such, they have become major figures in the preservation of some of the vernacular Scots of their day, maintaining a significan proportion of Scots while being readable to those who read English rather than Scots. This balancing act must have been immensely difficult, especially in the early years of the Union, but both, in different ways, manage to do it very well. Scots is only a shadow of its former self, but it is a shadow of its former self; it has so far, even if only through hanging by its fingertips, avoided becoming the umquhile Scots language.

Thursday, August 10, 2023

Fallacies of Diagrammatic Reasoning

 In recent decades there has been an increasing recognition that we can reason directly with diagrams -- that the role of diagrams in reasoning need not merely be illustrative of some kind of non-diagrammatic inference but may also carry some genuine weight in the reasoning itself. (This is an idea that has gone in and out of style; the last time it had widespread acceptance was in the nineteenth century.) If we assume this, however, and recognize that we can go wrong in diagrammatic reasoning, it follows that there will be fallacies of diagrammatic reasoning. What are the fallacies that can arise directly in diagrammatic reasoning? I can think of at least four.

(1) Improper Form: A diagram may be irrelevant. Your diagram, as used in reasoning, may mischaracterize how different kinds of information used in the reasoning are related to each other, so that it mischaracterizes the situation; in this sense, the diagram is just the wrong diagram, however much it might look like it is right. Every kind of reasoning allows for some kind of fallacy of irrelevance, so it's unsurprising to find such a fallacy of irrelevance.

(2) Smuggled Assumption: When people attempt to come up with systems of diagrammatic reasoning, like Venn diagrams, or Lewis Carrol's literal diagrams, or Peirce's existential graphs, a great deal of  effort is put into constraining how a diagram is used so that the diagram does not add assumptions extraneous to reasoning. Diagrams are potentially very information-rich; this means it is easy for diagrammatic reasoning to add in an assumption that should not have been made. In geometrical diagrams, it is very easy to assume that you have shown that lines or arcs intersect when all you've actually done is show that your diagram doesn't rule out that they do. This is a smuggled assumption -- it looks like they intersect in your diagram, so you assume that they do, even though it may be the case that they just pass arbitrarily close to each other without intersecting. In this fallacy, an accidental feature of the diagram is treated as if it were non-accidental.

(3) Inconsistent Interpretation: When used in reasoning, one may end up giving more than one distinct interpretation to some diagrammatic feature. This means that it is possible for diagrammatic reasoning to have a kind of fallacy of equivocation.

(4) Incomplete Diagram: A diagram may not represent all the information that its use in reasoning requires it to represent. This is the opposite of the Smuggle Assumption fallacy; in that fallacy, the diagram is introducing assumptions that shouldn't be there, in this fallacy, the diagram is failing to introduce assumptions that should be there.

Beyond thinking of obvious cases of diagrammatic reasoning, it's worth noting that it's unsurprising that the kinds of fallacies you find in diagrammatic reasoning include versions of fallacies that we find in syllogistic reasoning, and it highlights something that is easily missed if you just assume that diagrams are mere illustrations: syllogistic systems are simultaneously verbal and diagrammatic. Indeed, this accounts for several features of Aristotle's syllogistic system, most notably those having to do with syllogistic figure.

If we look at a simple Barbara syllogism, which is First Figure, we explicitly locate subjects and predicates spatially:

All M is P.
All S is M.
All S is P.

If we change the locations around, we get a different (and invalid) argument; we have improper form, and are using (say) a Third Figure syllogism to do First Figure work.

Aristotle's actual syllogistic puts a huge amount of emphasis on converting Second Figure and Third Figure to First Figure. Later logicians added Fourth Figure; the primary reason for adding it is to account for all diagrammatic representations of subject and predicate, but medieval logicians also put considerable emphasis on transforming other figures to First Figure. This makes complete sense in diagrammatic terms; First Figure shows minor term and major term in the premises in the same spatial order as they are found in the conclusion, and this is a clear diagrammatic superiority of First Figure over the other figures.

In the nineteenth century, C. H. Hinton wrote a book, The Fourth Dimension, in which he claimed that other logicians had missed a valid syllogism in the Fourth Figure, IEO-4. He gave an example:

Some Americans are of African stock.
No one of African stock is Aryan.
Therefore Aryans do not include all Americans.

Hinton is right that this is valid, but wrong that it is Fourth Figure; he has misdrawn the diagram for a counterexample. It's actually Ferio (EIO-1). Hinton has confused the grammatical order of the conclusion with the logical order it should have in the syllogism; the conclusion is an O proposition, but it means "Some Americans are not Aryans", not "Some Aryans are not Americans", which would be required for it to be Fourth Figure. Thus he has treated an accidental feature of the words as a substantial element of the reasoning, and committed the fallacy of Smuggled Assumption.

Wednesday, August 09, 2023

This Scheme of Partial Pardons

 The World State
by G. K. Chesterton 

 Oh, how I love Humanity,
 With love so pure and pringlish,
And how I hate the horrid French,
Who never will be English! 

 The International Idea,
 The largest and the clearest,
Is welding all the nations now,
Except the one that's nearest. 

 This compromise has long been known,
This scheme of partial pardons,
 In ethical societies
 And small suburban gardens --

 The villas and the chapels where
 I learned with little labour
 The way to love my fellow-man
 And hate my next-door neighbour.

Sunday, August 06, 2023

Fortnightly Book, August 6

 In 1816, Sir Walter Scott embarked on a new project. The original intention was to write four stories in a four-volume work that would cover the various regions of Scotland; it would be called, Tales of My Landlord. The gimmick would be that the stories would be portrayed as being the stories of a landlord of an inn that were then compiled by a man named Pattieson and edited by 'Jedediah Cleishbotham'. (Scott did not publish his early works under his own name. The complicated metanarrative layers, which extend even deeper in the stories, seem to be a solution to a problem that Scott faced, namely, that he was writing historical fiction for Union Scotland on topics that were inevitably going to still be sore points among different factions of Scots; the layers allow Scott to distance himself from the inevitable controversies, and also to present more sympathetically figures with whom Scott himself had no sympathy.) The first of the tales, The Black Dwarf, devoted to the Scottish Borders, was finished by August, so Scott moved on to the second story, intended for southwestern Scotland, which came to be called The Tale of Old Mortality. However, as Scott wrote it, the story for Old Mortality expanded to take up three entire volumes, so the first series of Tales of My Landlord had only two stories in it. (Scott would over time add additional series to Tales of My Landlord, amounting to seven books in four series overall.)

The fortnightly book will be Old Mortality. The work explores the time of the Covenanters and in particular focuses on their major victory (Battle of Drumclog at Loudon Hill on June 1, 1679) and their major defeat (Battle of Bothwell Bridge on June 22, 1679), with a brief look at the Battle of Killiecrankie on July 27, 1689. As far as Scottish politics was concerned, the reign of Charles II had seen a power struggle between the Crown and the Kirk. For most of Charles's reign, this had been an indirect struggle; Charles needed the Scots and the Presbyterians had benefited from that need. In 1679, however, things began to get out of hand, as John Sharp, the Archbishop of St. Andrews, began to a spearhead a stronger imposition of Episcopalianism on the Lowland Scots, even billeting Highlanders in areas that were causing problems. In response a group of Covenanters attempted to assassinate the Sheriff of Cupar, who was one of Sharp's major supporters; they lucked out, however, because they came across Sharp himself instead. Sharp was assassinated, and the unrest boiled over as the government attempted to crack down. The book follows Henry Morton, from a Covenanter family, as he is reluctantly dragged into the tumult. 

'Old Mortality' is the common nickname for Robert Paterson (1716-1801), a stonemason who wandered the country setting up markers for the graves of Covenanters who had died in 'The Killing Time', as the Covenanters called the period, and he serves as one of the mediating figures in the history told in the novel, the historical figure to whom the fictional anecdotes of the novel are attributed.