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Here's a quote from a book on quotations by Paul F. Boller, Jr.:
…Admiral Lewis Strauss…chose…to quote Dr. William Neuman…cautiously warning against continued [nuclear] testing: "Our ignorance in this field is so great that we cannot say with any certainty that we have not already put so much strontium-90 into the stratosphere that harmful fall-out is not inevitable."2
Since nuclear testing is back in the news3, this quotation is accidentally topical, but what does it mean? Boller calls it a "triple-negatively worded statement", but I'm not sure how he arrived at the number three, since I count four negations, highlighted above: "-not" on the end of "cannot", "not", "not" again, and "in-" on the front of "inevitable". Given its complex structure and many negations, Neuman's statement is difficult to understand. Boller goes on to say that Neuman was "suggesting danger from nuclear tests", but is that right?
If you'd like to have a go at untangling Neuman's statement, stop here and do so. Click on the button below to see my analysis.
Let's start out by analyzing the overall structure of Neuman's statement. It's hard to understand partly because it has an internal sentence wrapped within two modifiers. Let's call this internal sentence "S1":
S1: We have not already put so much strontium-90 (Sr-904) into the stratosphere that harmful fall-out is not inevitable.
So, the entire statement can be abbreviated:
Our ignorance in this field is so great that we cannot say with any certainty that S1.
The two sentence modifiers are the phrases "our ignorance in this field is so great that" and "we cannot say with any certainty that". The second of these modifiers directly modifies S1:
S2: We cannot say with any certainty that S1.
S2 tells us that we can't be sure S1 is true. The other modifier modifies S2:
S3: Our ignorance in this field is so great that S2.
S3 is actually Neuman's full statement, and it explains why S2 is true, that is, it explains why we can't say S1 with any certainty. The reason we can't be sure about S1 is that we're too ignorant about the effects of nuclear testing. Neuman would have been more understandable if he'd made this proviso into a separate claim and eliminated the first negation. For instance:
It's hard to be sure that we have not already put so much Sr-90 into the stratosphere that harmful fall-out is not inevitable. This is because our ignorance in this field is so great.
So, let's unwrap S3 by removing the outer modifier and turn to S2. The remaining inner modifier simply says that it's hard to be sure about S1, but what is hard to be sure about? We've eliminated one negation by paraphrasing it away but three remain. Can we get rid of any more?
The most obvious simplification that can be made to S1 is to remove the double negation at its end―"not inevitable". To say that something is "not inevitable" is to say that it is "evitable", which is a real if uncommon English word meaning "avoidable"5. Therefore, we can simplify S1 to:
S1': We have not already put so much Sr-90 into the stratosphere that harmful fall-out is evitable.
However, it is likely, given Boller's report of what Neuman meant, that he should have written:
We have already put so much strontium-90 into the stratosphere that harmful fall-out is inevitable.
Even though both sentences have only a single negation, they do not mean the same thing. Compare the following two sentences:
Sentence 1 is denying that the turkey has been so long in the oven that burning is avoidable, which implies that if it were left longer in the oven burning would be avoidable. However, the longer the turkey is in the oven the more likely it is to burn6. So, sentence 1 implies something false. Sentence 2, in contrast, says something sensible, namely, that the turkey has been in the oven too long and burning can no longer be avoided.
Similarly, Neuman was apparently questioning whether nuclear testing had already put so much Sr-90 into the atmosphere that fallout couldn't be avoided. Therefore, he should have said something similar to the following:
We know so little that it's hard to be certain, but we may have already put so much Sr-90 into the atmosphere that fallout is unavoidable.
This has only one negation and it's perfectly understandable if a little wordy.
It appears that Neuman got so tangled up in his own modifiers and negations that he said something he didn't mean. This is why you should avoid using too many negations as you will not only confuse your readers, but you may also confuse yourself.
Notes:
Recent codifiers of scholarly usage tend to prefer repeating the short title2 to any use of the Latin abbreviations, and indeed there are indications that the whole apparatus is being simplified as well as Anglicized. But since thousands of books use the older systems dating back as far as the seventeenth century, it behooves the researcher to learn the classic symbols and usages.3
While not as common as they once were, abbreviations of Latin words and phrases still occur in the notes to some scholarly works. Moreover, such notes are ubiquitous in works from previous centuries. In order to detect misleading notes, you have to first understand what the notes mean.
Why Latin? For the same reason that people still wear those silly black robes and square hats during a graduation ceremony: tradition. No one now wears a gown and mortarboard outside of graduation, but in the middle ages it was standard scholarly attire4. To don this garb at graduation is to announce that you are now a scholar who is a part of a tradition stretching back many centuries to a time when people dressed funny5.
Latin used to be the language of scholarship, so that scholars who spoke different native languages could communicate in a common scholarly tongue. Today, that language is no longer Latin, but English, which is one reason why Latin in notes is diminishing if not disappearing entirely.
Why are the Latin words and phrases used in notes abbreviated? It's not to make them more mysterious, though it may have that effect, but to make them more compact so as to take up less space at the foot of the page―endnotes can afford to be more expansive. For the same reason, footnotes are often printed in a smaller font than the text, which can make them difficult to read. In notes, space is precious.
Here are the most common abbreviations, not in alphabetical order but roughly in frequency of occurrence and importance to understand:
8 Quoted in W. K. Hancock, Country and Calling, London, 1954, 95.9
This says that the quote in the text on the same page that is followed by a superscript "8" is from page 95 of the book Country and Calling by W. K. Hancock, which was published in London in 1954. So, the subsequent quote, followed by a superscript "9", is from the same page of the same book.
The purpose of "ibid." is to save the scholar and the reader from repeating the same citation as given in the previous note, but what do you do when you want to cite a work you've already cited but not in the immediately preceding note? That's where our next abbreviation comes in:
16. Methods of Ethics (Macmillan, 1874).…12
We can tell that this is the relevant work because the author, Henry Sidgwick, is mentioned in the text in both places. If multiple authors have already been noted, then "op. cit." would need to be preceded by the author's last name in order to indicate which work is cited.
6 Albert Einstein, "Autobiographical Note," in Albert Einstein: Philosopher-Scientist, ed. P. A. Schilpp (Evanston, Ill., 1949), p. 45.14
This tells us that the quote of Einstein on the same page comes from page 45 of Albert Einstein: Philosopher-Scientist, edited by P. A. Schilpp, and published in Evanston, Illinois in 1949. Several pages later, we see the note:
14 Einstein, loc. cit.15
This indicates that the claim followed by a superscript "14" on the same page comes from the same book and page as the previously cited quote from Einstein.
Robert J. Gula wrote forty-five years ago about "loc. cit." that: "This abbreviation used to be used in footnotes but has recently been replaced by ibid., or by the author's last name followed by the first words of the title [that is, the "short title"]."16 As mentioned above, "op. cit." is sometimes used this way, so "loc. cit." can be dispensed with, but you still may come across it, especially in older works such as Kuhn's.
30. … An instructive study of metaphor has been made by I. A. Richards,… Interpretation in Teaching (Harcourt, Brace, 1938), passim. … 18
This means that the "instructive study of metaphor" is found here and there throughout the book cited.
Those are the most common Latin abbreviations used in notes that don't also occur in the text itself, or in other contexts. In the next installment, we'll anatomize the structure of a citation.
Notes:
Anna Krylov, "Why I no longer engage with Nature publishing group", Heterodox STEM, 10/24/2025
…Scientific publishers play a key role in the production of knowledge…. The role of the publisher is to be an epistemic funnel: it accepts claims to truth at one end, but permits only those that withstand organized scrutiny to emerge from the other, a function traditionally performed by a rigorous peer-review and editorial process. This process should be guided by scientific rigor and a commitment to finding objective truth.Unfortunately, the Nature group has abandoned its mission in favor of advancing a social justice agenda. The group has institutionalized censorship, implemented policies that have sacrificed merit in favor of identity-based criteria, and injected social engineering into its author guidelines and publishing process. The result is that papers published in Nature journals can no longer be regarded as rigorous science. Three representative examples illustrate this decline:
- Institutionalized social engineering
The Springer Nature Diversity Commitment…openly pledges to "take action to improve diversity and inclusion in the conferences we organise, and in our commissioned content, the peer review population and editorial boards." Editors are "asked to intentionally and proactively reach out to women researchers" and authors are instructed to suggest reviewers "with diversity in mind." In other words, editorial choices and peer review are to be guided not solely by competence but by demographic attributes. …
- Ideological subversion of literature citations
Nature Reviews Psychology…now encourages authors to practice "citation justice"―that is, to social-engineer their manuscript's bibliography to promote members of favored identity groups, even if their works lack the requisite merit or relevance. "Citation justice" is particularly harmful because it undermines the rigor and reliability of published research. When references are chosen not for their scientific relevance or quality but to promote the work of preferred identity groups, the integrity of science itself is compromised….
- Institutionalized censorship
Nature Human Behavior has published a censorship manifesto…now widely criticized…in which they openly declare their intent to censor legitimate research findings that they deem potentially "harmful" to certain groups. Not only is it arrogant for editors to presume they have the expertise to make such judgments, the practice is antithetical to the production of knowledge.
Any of these policies, taken alone, would undermine the epistemic standards of scientific publishing as a pillar of the truth-seeking enterprise. Together they represent a profound corruption of purpose. The purpose of science is the pursuit of truth, not the advancement of diversity, equity, and inclusion. These examples disturbingly reveal that scientific publishing at Nature has become ideologically corrupt.
Disclaimer: I don't necessarily agree with everything in this article, but I think it's worth reading in its entirety. In editing the excerpt, I sometimes changed the paragraphing.
Andy, Betty, Charly, and Debby attended a party on Hallowe'en costumed as a mummy, a vampire, a werewolf, and a ghost, though not necessarily in that order. At the end of the party, there was a best costume contest that each of the four friends entered. As a result, each of the four costumes was ranked from best to worst. Given the following clues, can you figure out what costume each friend wore?
What costume was worn by each contestant and in what position did each finish?
Betty was first in the contest wearing the vampire costume; Debby came in second wrapped up like a mummy; Charly, made up as a werewolf, came in third; and, finally, Andy was dead last as a ghost.
This is the first entry in what I hope will be a series of entries on the misuse of notes―that is, footnotes or endnotes―in scholarly or pseudo-scholarly writing.
When I first started reading scholarly works, many decades ago, I recall being baffled by the notes. Some typical notes looked like the following:
14 Ibid.
18 Sutch, op. cit., 429.
19 New York, 1938.2
I recall struggling to understand this arcane language of scholars. It's bad enough that some notes included words taken from a dead language―Latin―but they were abbreviated as well. Moreover, scholarly notes were taught by the "sink or swim" method: you were thrown into the deep end of scholarship and either learned quickly to swim or drowned3.
Scholarly notes, whether at the foot of a page―"footnotes"―or the end of an article, chapter, or book―"endnotes"―are not just pedantry. If used correctly, notes serve useful purposes, but if used incorrectly they can mislead the reader. To understand how notes are misused, we must first understand how they are properly used.
What are notes for? Notes serve more than one purpose, in fact, they have three main uses:
1 Austen H. Layard, Discoveries in the Ruins of Nineveh and Babylon… London, 1853, 663.4
This footnote is a citation to the source of a lengthy quote included on the same page. The note gives, first, the author's name, then the title of the book, the place and year of publication and, finally, the number of the page where the quote occurs. The ellipsis after the title indicates that the full, lengthy nineteenth-century title has been truncated5.
22 And to think that Eeyore always maintained that Pooh had only fluff in his head!8
This is an amusing aside that will only be understood by readers familiar with Winnie the Pooh, otherwise adding nothing to the discussion of the example.
It should be noted that these three categories are not exclusive, and perhaps not exhaustive. Some notes combine two of these categories, and it's even possible that a single note could combine all three.
What these three types have in common is that they are written matter that the casual reader may skip without missing anything important to the main discussion. The notes are there for those who want to check sources―type 1―advanced readers who want technical information―type 3―or those who just wish to enjoy an amusing or interesting sidelight―type 2.
If all goes as planned, next month we'll take a brief look at the Latin phrases and abbreviations that have been traditionally used in notes. After that, we'll get into the ways that notes go bad.
Exercise: Test your understanding by classifying the following notes according to the three types above. Keep in mind that a note may be of more than one type and there may be borderline cases.
Notes:
A book I was reading recently mentioned a novel I'd never heard of by Anthony Boucher entitled "The Case of the Seven of Cavalry"1, a title that didn't make much sense to me. Is it a western? I know of Boucher as a writer of mysteries and science fiction, rather than westerns. So I checked and discovered that the title is actually The Case of the Seven of Calvary2. It is, in fact, a mystery novel as the beginning of the title―"The Case of the…"― would suggest. The actual title still didn't make much sense to me, but it made more sense than the misspelled one.
Unlike many other word pairs that are often confused, "cavalry" and "Calvary" are pronounced quite differently, at least if enunciated clearly, though some people manage to mispronounce the former as the latter. Following its usual descriptivist practice3, the online Merriam-Webster dictionary actually includes the pronunciation of "Calvary" as a variant pronunciation of "cavalry", though at least it labels it as "nonstandard"4, which means "wrong".
The main reason that the two words are confused is probably that they're anagrams of each other, that is, they have the same letters but in a different order, and if you're reading quickly it's possible to misread one for the other. Despite that similarity in spelling, the words are very different in meaning. "Cavalry", of course, is a noun that historically referred to a group of soldiers on horseback but, by extension, in the twentieth century it came to mean soldiers in tanks or other vehicles that replaced horses5.
"Calvary", in contrast, is a proper noun for a place, namely, a hill outside the wall of Jerusalem where Jesus was crucified, according to the gospel of Luke6. The name comes from the Latin word "calvaria" for the human skull7 and is translated from the Greek word "Golgotha", which itself translates an Aramaic word for "skull". The name is supposedly based on the hill's resemblance to a human skull8, but this is conjecture since no one now knows where this hill was located9.
Not a single one of the reference books I consulted mentions the confusion of "cavalry" and "calvary" despite the fact that this was not the first time, and probably not the second, that I've seen or heard them confused. However, my old copy of Microsoft's Word program automatically changes "calvary" to "cavalry" in phrases such as "send in the calvary" and "the calvary to the rescue" without even asking permission, which is annoying. Moreover, if you search for "calvary" in a search engine10, you may get suggestions that make sense only for "cavalry". All these facts suggest that the confusion is common.
Notes:
Notes: