Stoic logic and ECQ

Over on youtube, I received the following question:

How the stoic logic avoid the principle ex contradictione quodlibet?

There’s two formulations:

(1) a, \neg a\vdash b
(2) a and \neg a \vdash b

(2) it is not a valid sequent in stoic logic, since it requests two distinct sentences, but why (1) it is evidently invalid?

It was a great question, and one too complicated to answer in a youtube comment, so I’m answering it here instead.

The first thing to note in this context is how the Stoics define validity:

A valid argument, according to the Stoics, is an argument such that the negation of its conclusion is incompatible with the conjunction of its premises (Mates, p. 58).

However, Mates goes on to point out that:

This, however, need not be taken as the definition of validity but only as a statement of a property which belongs to all valid arguments (Mates, p. 60).

That is, the incompatibility condition is necessary for validity, but it need not be sufficient.

So let us consider (1) and (2) more closely: It’s clear that in (1) and (2), the conclusion is incompatible with the conjunction of the premises only because the conjunction of the premises (or the single conjunctive premise) itself is already incompatible. So in a sense, the conclusion is not incompatible with the premises — it’s nothing about the conclusion that is causing the problem. This is our first indication that even though these two sequents might meet the incompatibility criterion, it won’t be enough.

Another way to put it, in modern classical propositional logic, we have Deduction Theorems (for both \vdash and \vDash):


In Stoic logic, however, we don’t have the right-to-left direction; as Bobzien notes,

The Stoics considered all conditionals of the form ‘If A, A‘ as true (cf. Sextus, M. 8. 281, 466), but ‘arguments’ of the form ‘A\vdash A are neither axioms of the system, nor can they be derived; the latter is due to the requirement of a plurality of premisses (p. 181).

So this makes explicit why (2) is excluded; it simply doesn’t have enough premises. It also gives us a clue as to how we might be able to exclude (1): It simply doesn’t have the right form. All true (i.e., “sound” in modern vocabulary) arguments are either one of the five undemonstrated arguments, or derived from these five via one of the four themata. Arguments of the form (1) cannot be so derived. Note that we cannot use the first thema, RAA, which says that “If from two [propositions] some third is deduced, either of them with the opposite of the conclusion implies the opposite of the other” (Mueller, p. 201); because we have to start from a successful derivation before we can use RAA to turn it into another derivation.

Does this mean that the Stoic system is incomplete? That their system of argument forms and the rules for putting these argument forms together to derive new, valid arguments does not match up with their conditions for validity? After all, intuitively we have arguments that look like they should be valid, but are not derivable in the formal system.

Not necessarily. For if the “condition for validity” is merely necessary and not sufficient, then lacking a sufficient condition for validity, we don’t have a target class of formulas to match our derivation system up with. If the sufficient condition is: Incomptability of the negation of the conclusion with the conjunction of the premises and derivable from the five undemonstrated arguments, then by definition, this system, if sound, cannot be incomplete.

Alternatively, we can ask what other ways of characterising the conditional could meet the requirement we quote from Mates, but provide a definition of validity. Here, it’s worth looking at the variety of implications in play in the Stoic contexts, especially Chrysippus’s, whose “truth-conditions for the conditional were said to involve a connection…this connection was determined indirectly, based on the concept of conflict (maché), and there are some indications that the resulting concept is that of an implication stronger than strict implication” (Bozien, p. 186). If a genuine connection must be established — and by now it is a commonplace for scholars to argue that Chrysippus had a connexive or relevance understanding of implication — between the antecedent and the consequent, then having merely incompatible premises will not be enough to establish the incompatibility of the premises with the conclusion, hence allowing the Stoics to escape ECQ.


Bobzien, Susanne. 1996. “Stoic Syllogistic”, Oxford Studies in Ancient Philosophy XIV: 133-192.

Mates, Benson. 1953. Stoic Logic, University of California Press).

Mueller, Ian. 1979. “The Completeness of Stoic Propositional Logic”, Notre Dame Journal of Formal Logic XX, no. 1: 201-215.

Resolution Read, Week 30: A note on Wertz’s ” ‘Not both p and q, therefore if p then q’ is a valid form of arugment” (NDJFL, 1977)

I’ve been going through old issues of NDJFL to find articles written by women that I can tweet at Women in Logic. I’ve been reading (or, skimming) a lot of other articles, ones whose titles are relevant to my own research, or which merely catch my eye.

S. K. Wertz’s article in vol. 18, no. 4 was one of the latter. It’s two pages (so many of the early NDJFL papers are like 2 pages long, I’m jealous of when you used to be able to publish that sort of thing. Nowadays, you have to write a blog post instead.), and it’s about an argument put forward by Geoffrey Hunter in Mind (LXXXII, 1973).

Both Hunter and Wertz are concerned with arguments of the form:

(1) not both p and not q, therefore if p then q.

This argument form is purportedly valid, but Hunter believes he’s found a counterexample to it:

(2) Not both Geoffrey Hunter is a bachelor and Geoffrey Hunter is not married. Therefore, if Geoffrey Hunter is a bachelor then Geoffrey Hunter is married.

This appears to have a true antecedent and a false conclusion.

Wertz’s complaint against Hunter’s example is that bachelor = not married, so if “Geoffrey Hunter is a bachelor” is $p$, then “Geoffrey Hunter is married” should be \neg p, not q. He says that (2) then fails to be an instantiation of (1) because “(1) requires that the propositional variables be distinct” (p. 611, emphasis in the original).

But this is not true. In classical propositional logic, a valid argument form will remain valid whatever propositional letters are substituted. Let us then substitute in \neg p for q in (1):

(1′) not both p and not \neg p, therefore if p then \neg p.

or fully in symbolic form:

(1*) \neg(p\wedge\neg\neg p)\rightarrow(p\rightarrow\neg p).

which is equivalent to:

  1. \neg(p\wedge p)\rightarrow(p\rightarrow\neg p).
  2. (\neg p\vee\neg p)\rightarrow(p\rightarrow\neg p).
  3. \neg p\rightarrow(p\rightarrow\neg p).

And (5) is, clearly, a tautology.

So while Wertz is correct that Hunter’s “counterexample” fails because it fails to recognise the logical relationship between “Geoffrey is a bachelor” and “Geoffrey is married”, Wertz is incorrect in thinking he’s shown that (1) requires the propositional variables in the argument form to be independent.

Resolution Read, Week 20: “Intuition and Reason” by Christine Ladd Franklin

Even though it’s the middle of marking season, I actually have a bit of time to work on my own research (which is good, given the deadlines coming up in June and July…). I’ve been reading a lot of Christine Ladd Franklin’s work lately, for a handbook chapter on her that I’m writing, and today’s paper struck me as a good one for a resolution read, even though, technically, this doesn’t meet the resolution because it’s reading I have to do for a specific deadline/project.

Christine Ladd Franklin, “Intuition and Reason”, The Monist Vol. 3, No. 2 (January, 1893), pp. 211-219, from jstor.

Why? Because the paper is less about the faculties of intuition and reason, and which once “is the more noble guide to conduct” (p. 211), than it is about the “wholly unfounded” belief that some people have that men act according to reason and women according to intuition. As someone who worked in symbolic logic at the highest level, equal to the best logicians of her century, it’s not surprising that Ladd Franklin doesn’t want women relegated to the realm of intuition alone. She says:

It is time that the belief in the different quality of men’s and of women’s minds should follow the whole antiquated machinery of “faculties” into the limbo of old and worn-out fashions of thought and of speech (p. 211).

(She would be very disappointed to see how little we’ve come along in the last hundred and thirty years.)

What I find interesting is that even while she decries the existence of this antiquated viewpoint, she is happy to provide an explanation of where it came about. She says that men and women act equally from intuition and reason, depending on the context, but that women’s circumstances are such that they are more often in contexts where intuition rather than reason serves them better:

It is not true that the Creator has made two separate kinds of mind for men and for women; but it is true that society, as at present constituted, offers two somewhat separate fields of interest for men and for women, and that the nature of their conduct is of necessity determined by the character of the action which is demanded of them (p. 212).

There is a sort of feedback loop going on: Women are (or at least, traditionally/historically, for the majority of the history of logic prior to Ladd Franklin’s time) systematically excluded from the “public” spheres where reason, disputation, argumentation, debate, logic, etc. are central tools, because they are public. This means that women are afforded fewer opportunities of using these tools, which then allows men to conclude that women use these tools infrequently because they are incapable of using them, rather than that they do so simply because they don’t have as many opportunities. It’s a pernicious circle, one that women are still often trying to escape; and it’s no surprise at all, given Ladd Franklin’s history, that she’s speaking out against it.

If women are seen to be worse at reason and better at intuition, simply because they are given more opportunity to practice the latter than the former, then one would expect the converse to be true of men, and indeed, something fascinating in this paper is how Ladd Franklin zeroes in on the concept of “emotional intelligence” (although she doesn’t use this phrase) and uses it as an example of something where people assume that women are naturally better at it, but where in fact this is simply because

To the woman of the past, who was to a great extent confined to her own home, the temper of her house-mates was what her happiness depended upon more than anything else in the world. It was impossible that she should not acquire a keen intelligence in interpreting every slightest shade of expression upon the human face…Women’s interests have been so exclusively social that they have developed a sense for the physical expression of emotion which makes society for them a matter of complicated relations, of delicate susceptibility to play of feeling, which—except in the hyper-sensitive period of courtship—is not common among men [pp. 213-214]

She is quite dismissive of idea that men are simply less good at emotional intelligence, and argues that a man who “is markedly deficient in these qualities” (p. 214) should be censured.

In the end, she argues that intuition and reason not only are not distinct faculties or capacities, but they could not be, because the one is built on the other. She distinguishes three types of actions which fall under the umbrella of “intuitive”, and it depends on whether the principles of reason guiding the action are conscious or not. In one type, the reasoning is conscious, as in the beginner pianist who “goes through a painful process of syllogism before each key is struck” (p. 215); in the next, it is unconscious but can be “forced into consciousness”, as in the expert musician who reads his music and plays it without conscious effort (p. 215); and in the third, it is unconscious “and cannot by any effort be made conscious”, as in when we calculate the relative distances of objects (p. 215). Consequently, the question with which she opened the paper, “whether intuition or reason is the nobler faculty”, “is an exceedingly meaningless question” (p. 215).

As further evidence that women are by no means deficient in the capacity to reason, Ladd-Franklin points out that geometry was a standard part of the high school curriculum at the time, and that (and this surprised me!) “that there are in this country [the US] (according to the Report of the Bureau of Education) three times as many girls as boys who take the high school course” (p. 217). She points out quite cheekily that if women were naturally ill-disposed to pure reason, then there would be a

great hue and cry from the teachers of the geometry classes about the difficulty of teaching that subject to girls, and the girls ought to lament and moan over the impossibility of getting safely through with their demonstrations (p. 218).

But quite the opposite is the case: “Day after day an army of girls goes smiling into the class-room and comes smiling out, utterly unaware that an unnatural wrench has been given to their delicate minds” (p. 218). Given equal educational opportunities, there is no difference in cognitive facilities. (Here it’s useful to remember that Ladd-Franklin had herself been a high-school teacher in science and mathematics for a decade about twenty years prior to this paper. She’s speaking from personal experience here, as an anecdote she goes on to relate illustrates.)

All in all, a fascinating read.

A Jain argument for vegetarianism

For Easter break relaxation, I have been reading Gulam Mohammad Munshi’s translation of the Baitál Pachísí, a medieval collection of 25 stories about King Bikram and the Baitál (a type of Indian vampire). The framing of the collection is that Bikram has been charged with bringing Baitál back to a Brahman, but Baitál says he will only come with the king if the king doesn’t say a word. He then proceeds to tell amusing tales that each end with a riddle, and the king cannot help but answer the riddle, at which point Baitál escapes his clutches and returns to the tree Bikram originally found him in.

Most of the stories are merely silly and amusing, but some of them provide some really interesting insight into medieval Indian culture (particularly the recitation of various proverbs). In general, the characters are by default Hindu; however, occasionally a Jain turns up, such as in the tenth story, where Gunshekhar, the king of Baradmán in the country of Gaur, and his minister Abhaichand both follow the Jain religion. In this story, there is a very interesting argument for vegetarianism (combined with some very problematic ableism!) spliced in the rest of the antics:

And it is virtue to take care of every life, taking from an elephant down to an ant, beasts, birds and even men. There is no religion in the world equal to it. Those [men] who increase their own flesh by eating [the flesh] of other [animals] suffer hell at last. Therefore it is proper for a man to take care of lives. Those who do not feel pain for others and take lives and eat them, their ages are shortened upon the earth; and are often being maimed, lame, one-eyed, blind, dwarf, hump-backed and such deficient in body born. As they eat parts of beasts and birds’ bodies, in the same manner they lose their own parts of the body at last. And it is a great sin to drink intoxicating drinks. Therefore to drink liquors and eat meat is not proper.

Knowing basically nothing about Jainism, I have no idea if such an argument is typical or atypical, but I thought it was (a) interesting and (b) probably not widely known, which means it definitely merits a blog post.

Doctor Logic Awkwardly Does Logic: What Is Logic?

One year ago this week, I faced the sudden need to translate my logic classes into something that could be done via video. I had one laptop with a built-in webcam and a crappy headset with a crappy microphone, a whiteboard in an office with terrible lighting, and not even the faintest clue what programme I could use to record videos from linux — and thus was born Doctor Logic Awkwardly Does Logic, because oh my goodness my early videos were awkward.

Come October, and my introduction to logic class is entirely online, with entirely asynchronous lectures, for the whole year (we DID have remote, but synchronous, discussion groups). My uni provided me with a great mic and a good webcam, AND a drawing tablet so that I didn’t have to attempt to record a reflective whiteboard. I even mastered the art of zooming myself and recording the result, allowing me to take advantage of the zoom whiteboard! So while things were still awkward, they were not as awkward as they had been.

I’ve recorded videos in the morning, I’ve recorded them late at night, I’ve recorded in my office, in my bedroom, in my livingroom, in my kitchen, once I recorded from the upper bunk in my daughter’s bedroom because it was the only place in the house quiet enough to record that wasn’t the bathroom. I’ve recorded at a rate of slightly more than 1 per day every weekday (including holidays) for the last 5.5 months.

150 videos later, today I finished recording all the content I needed for that class. But — whatever videos I produced needed to be captioned for accessibility purposes, and the easiest way to get decent enough captions was to make use of youtube. So here’s a playlist of just over 20 hours’ worth of logic, in bite-size format.

It’s not your typical intro logic class. It’s got more zoom-bombing cats, more Latin, more Sanskrit, more history than your typical intro logic class — and 100% more awkwardness!

I’m now going to take a break for a few months, but maybe I’ll come back and do my advanced logic class sometime.

Resolution Read, Week 8: “Modal Semantics Without Possible Worlds” by John T. Kearns

John T. Kearns, “Modal Semantics Without Possible Worlds”, Journal of Symbolic Logic 46, no. 1 (1981): 77-86, available on JSTOR

I downloaded this paper last summer, thinking this might be a fun thing to add to my third year logic seminar this year. In the end, I downloaded too many such papers for the same reason, and this one ended up getting the chop, which is why I’m only getting around to reading it now.

In a nutshell, Kearns’s alternative is a 4-valued semantics involving “necessary truth” (T), “contingent truth” (t), “contingent falsity” (f), and “necessary falsity” (F). The language for this semantics is ordinary propositional modal logic with \neg, \vee and \square taken as basic, and \wedge, \rightarrow, and \Diamond defined in the usual way.

The truth tables for the connectives are not completely deterministic; there are a few clauses (in the tables for disjunction where certain pairs of inputs return two possible truth values, t and T. It’s worse in the case of \square, where ALL possible inputs return a pair of outputs, e.g.:

φ \square φ
T T,t
t f,F
f f,F
F f,F

The non-determinism of \vee and \square natural propagates to \wedge and \rightarrow.

In order to get a complete characterization, Kearns introduces “supplementations” which result in his semantics being a semantics for modal logic T. These supplementations come in the form of plausible modal principles that impose determinism on the tables (p. 79). These include principles such as “Any sentence which, according to the matrices, cannot come out false should be assigned value T (and anything that cannot come out truth would then get value F).

More specifically, Kearns gives an inductive definition of a notion of T-valuation. The 0th level is defined by the basic tables he first introduced. Then, given an nth-level T-valuation, the n+1st-level T-valuation assigns a sentence T if it is assigned either t or T in the nth-level valuation. A T-valuation, without specification, is then something that is an nth-level T-valuation for every n.

Though the paper says it’s about modal semantics, it goes on to give a natural-deduction proof system, based on a system P of tree-proofs for propositional logic with elementary and nonelementary rules. The elementary rules are ones “for which each premise is a sentence on the line of the inference figure which exemplifies the rule” (p. 79), and the non-elementary rules are ones “for which at leat one premise is a subproof whose conclusion is on the line of the inference figure exemplifying the rule” (p. 79); non-elementary rules are ones that cancel or discharge one of the hypotheses of a subproof premise.

A modal proof system can be obtained from P by adding introduction and elimination rules for \square, and a rule (which he calls “(T)”) that sort of corresponds to the K-axiom:

  • \square E: From \square φ, you can write down φ.
  • \square I: From φ, one can write down \square φ, provided that the proof of φ depends on no uncancelled hypotheses.
  • Rule T: From \square φ and \square(φ\implies\psi), you can write down \square\psi.

Kearns proves that this proof system is sound and complete with respect to the T-valuations he defines.

If we drop the assumption that \Diamond is defined in terms of \square and \neg, but instead give separate truth conditions for \Diamond and modify the previous semantics for \square, we can obtain semantics for S4 (p. 81):

φ \square φ \Diamond φ
t f,F T, t
f f,F T, t

The proof system that extends the system for T with a rule that says from \square φ you can write down \square\square φ (i.e., transitivity) is sound and complete with respect to these semantics.

Changing the matrices yet again gives semantics for S5 (p. 81):

φ \square φ \Diamond φ
t F T
f F T

The proof system that extends the system for T with a rule that says from \square φ you can write down \square\Diamond φ is sound and complete with respect to these semantics.

So much for section 1 of the paper. My immediate question is: Can these semantics be generalized, and if so, how? One of the huge advantages of Kripke semantics is that it is very very easy to generate sound and complete semantics for a very wide range of interesting modal logics, in a uniform way. I’m not yet sure what the value of Kearns’s alternative is.

Section 2 is about introduction quantification into his approach. Here I think there is likely to be much more interesting material. Kearns begins by pointing out that when we add modality to propositional logic, we don’t generally have to specify in advance a specific modal concept that we are introducing. But, as he says, “it is more difficult to do this for a first-order language, because there are more choices that must be allowed for” (p. 82), and in order to discriminate between these choices, he introduces certain heuristics that we can use to keep various different types of modal concepts straight, and then says he’ll develop modal quantificational semantics for one pair of concepts.

He takes possibility as the basic notion and then distinguishes four notions of possibility: (1) absolute epistemic possibility, which characterizes sentences that are not contradictory; (2) relative absolute possibility, which characterizes sentences that are not excluded by our knowledge; (3) absolute metaphysical possibility; and (4) relative metaphysical possibility. Of these four types, he says nothing further about (3) and (4) and spends the rest of the paper focussing on (1), as it is “the simplest of the concepts of possibility” (p. 82) and hence the easiest to capture. [My own note: isn’t this what other people call logical necessity, and hence the account he develops should correspond to S5?]

Oh, hahah, he addresses this in the next sentence: “The concept of “necessity” which answers to absolute epistemic possibility is (ordinarily called) analyticity. In what follows we are to understand \square φ as “it is analytic that φ”, and \Diamondφ as “it is logically possible that φ”” (p. 82). Oh dear. The dual of “logically possible” is “logically necessary”, NOT “analytic”. Ahem.

The logical language is extended by the universal quantifier, with the existential defined in the ordinary way, and with as many individual constants as one desires; these constants are unambiguous. Domains are assumed to be non-empty, as is usual, though Kearns is at pains to point out that “It is not obvious that this is an accurate “representation” of the ordinary concept of analyticity” (p. 82), because it is up for debate whether “Something exists” is analytically true in ordinary English.

Naturally, “the biggest problem with quantification is determining whether and how a formula can have the values T and F with respect to individuals as values of its free variables” (p. 83). He tries not to give a complete answer to this question, but instead focuses on minimal assumptions that can be introduced, such that formulas can be analytic [i.e., necessary] or impossible of individuals, and that if a formula is analytic with respect to one individual, it is analytic with respect to all individuals. As a result, if φ(x) is analytic with respect to some individual x, then \forall x φ will also be analytic. Ahah! My side note above is answered: “When we consider the (ordinary) concept of analyticity as it applies to sentences, the S5 matrix is clearly correct” (p. 83).

The semantics are then given as follows: Given a non-empty domain D, an assignment function f assigns elements of D to the individual constants of L; however, “f will not asisgn sets to predicates” (p. 83). This is because “Instead, individuals in the domain will be treated as if they were constants” (p. 83), an explanation I confess I do not understand; I think what he’s saying is that every element of the domain can be named. However, if we have a domain D and assignment function f, we can then construct a pseudo-language L^f_D (p. 83):

  • Every wff of L (our basic predicate language) is a pseudo-wff of L^f_D;
  • If φ is a pseudo-wff of L^f_D containing free occurrences of an individual variable x and a is an individual in D, then φ[x;a] is a pseudo-wff;
  • Nothing else is a pseudo-wff.

Valuations are then assigned to these pseudo-wffs, rather than to wffs in L; the important new clause is the clause for universally quantified pseudo-wffs:

  • \forall x φ is T iff φ[x:a] is T for every individual a in the domain.
  • \forall x φ is t iff φ[x:a] is t for every individual a in the domain.
  • If \forall x φ is f, then φ[x:a] is f for some individual a in the domain, but for no individual in the domain does it have value F.
  • If \forall x φ is F, then φ[x:a] is F for some individual a in the domain.

Because the last two clauses are not iff claims, we have indeterminacy yet again. As a result, a system of nth-level valuations must be introduced, analogously to the propositional case.

An adequate proof system is obtained first by extending the propositional system P to system Q with the expected rules for \forall E and \forall I, adding the rules from propositional S5, and adding a final rule, a rule of analyticity, which says that if you have \square φ(a/x) [that is, the result of substituting constant a into φ for all free occurrences of x], you can write down \square\forall x φ, provided that a does not occur in φ. This proof system is sound and complete with respect to the semantics.

There then follows a short conclusion, where Kearns argues that his approach is better than the possible worlds approach for anyone who thinks that possible worlds do not exist, not even as convenient fictions.

He then concludes:

However, for the present I will not enlarge further on the philosophical advantages of my semantics. The reader is left to her own speculations on these matters (p. 86).

Very well, then, Mr. Kearns. I will speculative away! [but in another blog post].

Resolution Read Week 6: “Personification’s Gender” by James J. Paxson

It’s my first resolution read of the year! I’m revising a paper and a referee requested I say something more about a question I’ve always wondered about, namely — why is Reason/Rationality always depicted as a woman in medieval art and literature, when reason/rationality/logic was an almost exclusively male domain? I figured there had to be something out there somewhere that addressed the broader question — why are abstract ideas personified as female — and so asked on twitter for literature, hoping the answer would be more interesting than “they’re grammatically feminine” [1]. One recommendation I got was for today’s resolution read:

James J. Paxson, “Personification’s Gender”, Rhetorica 16, no. 2 (1998): 149-179,

The abstract starts off with “The fact that classical and early medieval allegorical personifications were exclusively female has long perplexed literary scholars and rhetoricians” (p. 149). Excellent! I’m not the only one who’s been wondering!

A few points from the abstract/opening paragraphs: (1) Paxson doesn’t think the answer is grammatical gender. (2) It isn’t until the thirteenth century that “we first encounter prominent male personifications” (p. 151), including in the Roman de la Rose, which is interesting for my present purposes as one of the people I’m writing about in my paper is Christine de Pisan and the Querelle.

After pointing out the ubiquity of female personifications, and the fact that “female personifications are a given in medieval literature” (p. 151), Paxson looks to classical rhetoric to try to find an explanation for this. He quotes On Style by Demetrius (poss. 1st C AD) as making female body part of the definition of personification:

Another figure of thought — the so-called “prosopopoeia” — may be employed to produce energy of style, as in the words, “Imagine that your ancestors, or Hellas, or your native land, assuming a woman’s form, should address such and such reproaches to you” (p. 152).

Paxson argues that Demetrius and other early rhetoricians who used feminine examples when defining personification had “a cumulative effect on later writers, the allegorists, whose stock in trade was a canny reflection on tropological discourse and the imagery of bodies” (p. 153).

But the main conclusion that Paxson is arguing for in his paper is that “gendered personification in ancient and medieval literature in part reflects R. Howard Bloch’s description of a persistent and powerful (though not omnipresent) discourse of misogyny” (p. 154), which is fascinating for my purposes, because it may shed light on why medieval male authors were happy to depict Reason as a woman while simultaneously excluding women from the realm of rationality. A subsidiary conclusion he’ll argue for is that “personified characters in classical or early medieval literature were women because Personification as a concept (and itself personified) could be thought of as having the gendered qualities of the feminine” (p. 157).

Paxson argues that the grammatical explanation cannot be the whole story, because “personification already involves the radical suspension of fixed ontic categories such as bodily/abstract, human/non-human, or living/non-living” (p. 164), so it cannot be that personifications are female simply because the word for what is being personified is grammatically feminine. The process of personification by its very nature reverses many polarities, so why should it not reverse the gender polarity as well? But if grammatical gender is not the sole motive factor in personifying abstractions as female, then there must be another factor. Paxson groups previous theories of what this other factor is into two broad categories — the on “negativises women (they are morally fallen and mortal” while the other “idealizes or deifies them (women are the vehicles of cosmic and sacred generativity)” (p. 161). He then ties this binary view of women to Bloch’s account of misogyny in the Middle Ages (p. 161).

His own account will be based “on the associative or performative macrometaphors of rhetoric itself in order to more effectively connect femininity and key tropes like personification” (p. 165). The process of personification, he argues (pp. 165-166), is a feminine and feminising process — it is words putting on make-up and fancy clothing, it is words playing duplicitous roles that do not reflect their own nature — and thus it is natural that the outcome of this process be female. This is not merely a modern description of what happened historically, visible only retrospectively, but can be read in classical and early medieval rhetoricians; in particular, Paxson cites Quintilian (pp. 166-167), who struggled with establishing rhetoric’s legitimacy in a masculine enterprise, and also Tertullian (pp. 169-171), who was intimately interested in role/function of Eve/Woman. Eve herself is the original metaphor, for the (Christian) Roman rhetoricians, and thus from the beginning of the world rhetorical tropes and women were closely connected. The roots of rhetorical misogyny are therefore closely linked to the misogyny engendered by Eve’s role as the first sinner.

Paxson concludes that in the late Roman era:

Rhetoric, as Maud Gleason argues, found itself divided by a line partitioning a positive, masculine, energetic, honest, and ascetic cultural practice from a negative, feminine, languourous, deceptive, and indulgent one (p. 167).

(This is also interesting for my purposes, because we have clear evidence that medieval women were formally taught rhetoric, and that it was an acceptable thing for a woman to study, unlike logic, which was in a sense “too masculine”. But we all know that anything that women are allowed to do eventually becomes devalued, so there’s an interesting compounding interplay going on here — rhetoric can be studied by women and taught to women because it is a more effeminate subject; but rhetoric becomes more effeminate precisely because it is something that women can study and be taught.) He says that “the interchangeability of the feminine with trope amounts to a grafting of a meta-rhetorical, performative language about cosmetics and concealment onto those individuals who personally and by common cultural practice might indulge in cosmetic self-embellishment” (p. 171) — this self-embellishment isn’t restricted to women, but men who indulge in it are considered “effeminate”, i.e., are feminised. If rhetorical tropes are essentially feminine, then, Paxson argues, we should not be surprised that personification, which is a rhetorical technique involving one thing becoming something else, putting on a mask, pretending, etc., i.e., is one thing dressing up as another, should result in feminine/female outcomes. It becomes perfectly understandable that “the female entity Personification determines the femaleness of the many personifications in medieval allegory” (p. 175).


[1] This explanation Paxson says has been put forward by Joan Ferrante, Woman as Image in the Middle Ages: From the Twelfth Century to Dante (Columbia University Press, 1975): pp. 37-64, and, according to Helen Cooper in “Gender and Personification in Piers Plowman“, The Yearbook of Langland Studies 5 (1991), p. 31, “was once attributed by Edmund Silk to an anonymous writer of the ninth century” (p. 160), who explained Boethius’s personification of Philosophy as a woman by noting that philosophia is a feminine noun in both Latin and Greek. Other people who followed this grammatical line, according to Paxson, include Joseph Addison (in the 18th century), E. H. Gombrich and Maureen Quilligan (in the 20th century).

What came of my 2020 resolution

I’m not big on resolutions, but after a few years of making not-resolutions revolving around writing and submitting, for 2020 I opted to switch things up a bit and instead give myself permission to do some reading instead.

If it had been an actual resolution, I’d be looking back on 2020 and laughing at how badly I failed. But since it was not-a-resolution, I can instead look back and be happy at these papers that I read — and commented on! — that I would not have otherwise read:

Resolution Read Week 2: Hao Wang (1957), “The Axiomatization of Arithmetic”, Journal of Symbolic Logic 22, no. 2: 145-158.
Resolution Read Week 3: Mark Erickson, Paul Hanna, & Carl Walker, (2020), “The UK higher education senior management survey: a statactivist response to managerialist governance”, Studies in Higher Education.
Resolution Read Week 6: Eileen O’Neill, “Early Modern Women Philosophers and the History of Philosophy”, Hypatia 20, no. 3 (Summer, 2005): pp. 185-197.
Resolution Read Week 7: Edmund Michael Lazzari, “Would St. Thomas Aquinas Baptize an Extraterrestrial?” New Blackfriars 99, no. 1082 (2018): 440-457, DOI:10.1111/nbfr.12319.
Resolution Read Week 8: Christian Weidemann, “Christian Soteriology and Extraterrestrial Intelligence”, Journal of the British Interplanetary Society 67, nos. 11/2 (2014): 418-425.
Resolution Read Week 25: Daniel Kilham Dodge, “Puritan Names”, New England Quarterly 1, no. 4 (1928): 467-475,
Resolution Read Week 26: Floyd C. Medford, “The Apocrypha in the Sixteenth Century: A Summary and Survey”, Historical Magazine of the Protestant Episcopal Church 52, no. 4 (December, 1983): 343-354.
Resolution Read Week 28: A. McKenzie and J. Punske, “Language Development During Interstellar Travel”, Acta Futura 12 (2020): 123-132, DOI: 10.5281/zenodo.3747353.
Resolution Read Week 29: Philip Goff, “Universal Consciousness as the Ground of Logic”, in Panentheism and Panpsychism: Philosophy of Religion Meets Philosophy of Mind, Innsbruck Studies in Philosophy of Religion vol. 2, (Mentis, 2020): 107-122.
Resolution Read Week 36: Michael V. Fox, “Love, Passion, and Perception in Israelite and Egyptian Llove Poetry”, Journal of Biblical Literature 102, no. 2 (1983): 219-228.
Resolution Read Week 37: James G. Murphy, “Contemporary Jesuit Epistemological Interests”, in Anna Abram, Michael Kirwan, and Peter Gallagher, eds. (2017). Philosophy, Theology and the Jesuit Tradition: ‘The Eye of Love’ (Bloomsbury T&T Clark: 139-158).

So, that’s 11 more papers than I would have read otherwise! On wonderfully wide and disparate topics. I’m glad I read them all, and think I will make this not-a-resolution for 2021 again.

Wot I Wrote, 2020 edition

2020 was a hard year in terms of writing; I felt like I was under-writing pretty much every month. Didn’t write as much fiction as I would’ve liked. Didn’t write as much nonfiction as I needed to. Blog posts were down. On the upside, I wrote a lot more poetry this year than any other year in recent memory, and my writing for admin purposes was also down!

You can definitely tell which months were the hard months, though:
Bar graph of monthly word counts(Total wordcount: 316379 words.)

April was the “oh my god, Durham wants to move all teaching online permanently as of Oct. 2020, and while moving things online is necessary for Covid purposes, doing it as a long-term strategy is such a bad idea” month, where pretty much ALL I did was union activism and struggling to survive under lockdown.

August was the month where G was back in F2F school for part of it, and then was at climbing camp the other month; plus I took a week of vacation (!) and also worked outside for 5-6 hours every day. September she was back in school again, too, and I mostly was able to work outdoors. August and September were the months where I “rewrote” (as in, literally retyped) Pride and Prejudice, making as minimal changes possible in order to set the story on a peregrinatory space university. November was the month where I took that rewrite and started turning it into a proper story. I got my 50k for NaNoWriMo in, and then it’s been lying fallow ever since.


I accomplished four big non-fiction things in 2020: In March, thanks to a very generous PC chair who gave me one extension because of the strikes and then another extension because of trying to work at home in lockdown with a stressed out partner and a stressed out self and a child at home, I completed a paper, “William of Sherwood on Necessity and Contingency”, which was accepted and then presented at Advances in Modal Logic in August.

In February I finished off a paper on 19th-century Irish SF writer Jane Barlow, for a special issue of a journal; I got an R&R for it in March and was like “oh, sure, I’ll get it done by the end of April!” In July, I finally had a chance to sit down and work on it. I substantially revised it and think it came out a lot better…but it ended up getting new reviewers the second time around, who wanted another R&R, and the editorial policy of the journal was that two R&Rs = a rejection. So that was sad.

However, while working on that revision in July, I wrote completely unexpected paper, “Against the Theistic Multiverse”, which came out in Kriterion in August.

Finally, just before the end of the academic year, I finally, finally finished up a paper I’d been working on for almost two years, and had presented on twice over the summer, and sent it off, on “What Problem Did Ladd (Think She) Solve(D)?” It’s still under review.

Most of the rest of my nonfiction words went to updating my logic textbook.


I feel like I just didn’t write any fiction this year (don’t let the numbers fool you). I wrote one short story early on in lockdown which I think really worked; but so far none of the places I’ve sent it have agreed! Otherwise, I didn’t do anything substantial; everything else was small poems and flash fic and stuff.

However, I did much better on the submissions side of things. I had 73 complete submissions (6 are still pending), with 13 resulting in acceptances, for total earnings of $36.56 😉 — my highest number of submissions, my highest number of acceptances, and my highest percentage of acceptances (18%! Compared to 9% (2019), 11% (2018), and 11% (2017).

In January, “What Lies Beneath the Waves” was published in With Painted Words; you can read more about it here.

In February, one night G asked me, “Mummy, could we maybe someday sit down and write a story together?” OF COURSE, dear child! Together we drafted An Awfully Big Adventure, and got my mom to do some illustrations, and we published it in August!

In March, I wrote a poem, “Crisis Mode”, and posted it on FB and twitter; and a twitter friend of mine recorded himself reading it.

In April, my drabble Candace Swallowed the Sea” was given an Honorable Mention in the Quarantine Quanta drabble contest. April also saw the publication of “In Lieu of Gifts”, a poem I wrote about having a birthday in lockdown. I think it was also in April that three of my drabbles came out in Black Hare Press’s Oceans anthology, which I wrote about here.

A story that I wrote maybe two years ago, for G, “Metamorphosis” finally found a home in Manawaker Studio’s Flash Fiction podcast, and came out over summer. Another story I wrote for G, “Madame Sophie and the Ghost” was accepted early in 2020 and came out at the end of this year, in Stories for the Thoughtful Young. I still need to write my “about the story” posts for both of these!

During the strikes in February and March, I put together an idea of editing an anthology of poems, stories, songs, artwork, etc., coming out of the people involved in and affected by the strikes. The result of that came out in September, Striking Bodies, Striking Minds. It includes a previously unpublished poem of mine, “Out in the Snow”.

A friend started up a quarterly poetry journal over summer, with the first issue due out on the winter solstice. The theme was “sparks”, and I revised a poem and sent it off to him, and you can now read “Light Like Silk” in the inaugural issue of Ink Drinkers Poetry.

Wrapping up the year, Dreich accepted four of my poems, “(my) Love is (not) Patient” (written for G…), “At Her Mother’s Grave”, “My Love For You Floods Me”, and “Lupanar”, Dreich (a haiku about a brothel) for their “What you can do with love” themed chapbook scheduled to come out in February 2021. I’m super pleased to be sharing page space with a friend, whose first published poem this will be!

Finally, coming in on a day when we were heartsick with worry because one of our cats was missing (he came back home early this morning!!), one of my favorite stories, which I wrote about 2 1/2 years ago and which has been rejected sixteen times (including twice at the very final cut!) was accepted for inclusion in vol. 2 of Grace & Victory’s A Quiet Afternoon series. I am so damn pleased about that.

Gosh. When I write it all up, it doesn’t seem like it was that little…


I’ve continued to do short story reviewing over at, some (but not very much) blogging here, and some (even less) for the Dictionary of Medieval Names from European Sources blog.

I’m sure I wrote some other things. But not enough to matter.

Wot I Read, 2020 edition*

This post is why I switched this blog from blogger to wordpress. I’d taken detailed notes about all the books I read up until about late March/early April, and then one day discovered that the draft post had gotten erased and blogger doesn’t do backups. So this is “wot I read, 2020 edition (April – December)”.

It’s a shame because I read some really good books that I had a lot of opinions on in the early part of the year, but that was pre-UCU strike and pre-Covid and like hell I’m going to remember any of them now. The few I can, I’ve put in.

I also wasn’t as thorough at keeping track of the books I read aloud to G., so they aren’t all in the list.


  1. Adeyomi, Tomi, Children of Blood and Bone (finished January? 2020): I think? I know I read it around Christmas one year, and it doesn’t turn up in previous summaries, so it must have been 2020. Absolutely glorious, can’t wait to read the next one.
  2. Benaway, Gwen, ed., Mother, Maiden, Crone (finished February 2020): Read my review.
  3. Blyton, Enid, The Faraway Tree: Read aloud to G. This was my first Blyton.
  4. Brownlow, Dominic, The Naseby Horses (finished September 21, 2020): I bought this from a small press that put a call out on twitter for orders because they were struggling with the pandemic. It took me absolutely ages to finish, because I simply could not get the content to “stick”. I’d read a few pages and have no idea what happened. I ended up rereading many bits of it because each night I couldn’t remember where I’d ended so I’d start up at a part I didn’t remember only to realise I’d read it the night before.
  5. Byatt, A. S., The Children’s Book (finished July 29, 2020): This was very good. It read so much like nonfiction.
  6. C, V, BIaRG (finished December 2020): I read this with a view towards potentially publishing it; but it needs serious revisions.
  7. Cade, Octavia, The Stone Wētā (finished November 18, 2020): As I described it on FB: “Do you like fiction about climate change? Or fiction about scientists? Or fiction were basically every major character is a woman? Or all three?”
  8. Callendar, Kacen, Queen of the Damned (finished spring? 2020): This was a review I lost when I lost the earlier blog post. I had complex thoughts about it, much of which revolved around the use of Dutch-like personal names and words in a way that just didn’t seem to fit any other aspect of the story.
  9. Cisco, Michael, The Narrator (finished December 17, 2020): I don’t remember who recommended this, or where, but I’m so glad I got it. It was a strange, difficult book. I have never read anything which has so little plot; it was literally events strung one after another. Eerie and tricky and strange.
  10. Clark, David G., Callum Colback, Joe Butler, and Alex Hareland, eds., Beneath Strange Stars (finished March 2020): Read my review here.
  11. Cleary, Beverly, Ramona Quimby, Age 8: Read aloud to G.
  12. Cleary, Beverly, Ramona Forever: Read aloud to G.
  13. Cleary, Beverly, Ramona the Pest: Read aloud to G.
  14. Cleary, Beverly, The Mouse and the Motorcycle (finished December 2020): Read aloud to G.
  15. D, RJ, HCW (finished September 10, 2020): Being coy about this one because it’s not published — yet! And I am going to be the one to publish it. It’s marvelous and I’m so excited.
  16. Fitzwalter, A. J., No Man’s Land (finished September ?, 2020): One thing that came out of WorldCon in NZ this year was a distressing lack of focus on SFF focusing on NZ authors. I found a couple of lists of recent SFF books by NZ authors and bought a bunch of them, to help make up for that. This was one of them. It wasn’t the sort of book I’d probably pick up on my own, but I enjoyed it quite a bit.
  17. Ghalayini, Basma, ed., Palestine+100 (finished February 2020): Read my review here.
  18. Harrison, M. John, Settling the World: Selected Stories 1970-2020 (finished November 2020): Read my review here.
  19. Hendrix, Grady, My Best Friend’s Exorcism (finished August 2, 2020): Reading this was quite the trip. The 80s that was depicted was the 80s I grew up in; though the MCs were a decade older than me. But my dad had books on cult ministry on his shelves, and demonic possession was something we talked about when I was a child, and basically every single aspect of this story rang true to me.
  20. Holst, Elna, Lucas (finished June 29, 2020): This is a queer sequel to Pride & Prejudice, focusing on Charlotte Lucas. It was…fine. A bit too explicit for my general reading tastes, and also indulged in some unnecessary tropes (e.g., miscarriage due to an accident/fall). I wanted it to be great; in the end, it was merely fine.
  21. Jones, Diana Wynn, A Sudden Wild Magic (finished April 21, 2020): I was gifted this book by a SCAdian friend ages and ages and ages ago and despite all my friends raving over DWJ, I’d never read it, but early in lockdown I was running out of books so I decided to pull some unread ones off my shelf. And…wow, I really did not like this book, it was just so…male. It was not the story for me. But the bizarre part was that as I read it, I grew increasingly convinced that I had actually read it before, within the last decade or 15 years or so, and I clearly disliked it so much, I’d erased the memory of it!
  22. Jones, Diana Wynn, Howl’s Moving Castle (finished September 6, 2020): A friend had a duplicate copy and offered it up to whomever asked for it first, so I got it. This one I liked much better than ASWM. G and I then watched the movie a few months later, and the movie was good, but the book was better.
  23. Jones, Heather Rose, Floodtide (finished October 27, 2020): I needed some comfort reading during the beginning of a very stressful term, so I went straight to Alpennia. I think this one might be my favorite of all of them.
  24. Kitson, Helen, The Last Words of Madeleine Anderson (finished August 19, 2020): In August I saw a tweet from a small press owner saying “please buy my books, so I can afford to publish more” so I figured, what the heck, I looked through her catalogue and found two that looked interesting and bought them. This was one. It’s what I’d describe as an “airport book” — the sort I’d be happy to buy at an airport and read while traveling, but probably wouldn’t ever reread. I found a lot sympathetic in this book and a lot to laugh at too. Did not regret buying.
  25. Knight, Zelda and Ekpeki Oghenechovwe Donald, eds., Dominion: An Anthology of Speculative Fiction From Africa and the African Diaspora (finished July 2020): Read my review here.
  26. Knox, Elizabeth, The Vintner’s Luck (finished August 16, 2020): I can’t remember know how this got recommended to me, but it was one of the most unique books I’ve read in a long time. The characters and the story were beautiful and unusual and it’s one of those books that still lingers with me.
  27. L, S, G (finished December 2020): I’m in discussions with the author about publishing this!)
  28. Lancaster, A. J., The Lord of Stariel (finished October 22, 2020): I enjoyed this book so much, I ordered its two sequels before I’d even finished book one. It was a real feel-good, fun read, and the main characters — Hetta, Wyn, Marius, Jack — were all fully fledged, real, and distinctive.
  29. Lancaster, A. J., The Prince of Secrets (finished November 4, 2020): A good follow-up to the previous, although one of the things I really liked about the previous book (how distinctive a character Wyn was, and the way he and Hetta interacted) was rather washed away by both Wyn and Hetta transforming rather into coquettes.
  30. Lancaster, A. J., The Court of Mortals (finished November 13, 2020): I loved the shift to more mundane political intrigue; I was less happy with the “oh noes, oh noes, we have all this sexual angst because we’re forbidden to marry each other by our respected rulers”.
  31. L’Engle, Madeleine, The Arm of the Starfish (finished September 27, 2020): I needed a book to cry over, and this is always the one for me. Every single damn time I read it, I think, maybe this time, Joshua won’t die.
  32. L’Engle, Madeleine, Camilla (finished March? 2020): This was the first time I’ve reread this book since starting to write fiction again seriously. It is masterfully constructed.
  33. L’Engle, Madeleine, A Live Coal in the Sea (finished March? 2020): I always learn a lot about relationships whenever I reread this.
  34. Li, Jin and Dai Congrong, eds., The Book of Shanghai (finished June 2020): Read my review here.
  35. Mark, Jan, Ennead (finished April 30, 2020): A friend recommended this on FB, and it sounded interesting. I haven’t read much classic SF; it really is a very different beast from today’s SF.
  36. Miller, Linsey, Belle Revolté (finished August 26, 2020): I’m not sure if the author intended to subtweet casualisation in academia with this book, but I totally read it that way and it was a good read.
  37. Montgomery, L. M., Rilla of Ingleside (finished April? 2020): I reread this after a friend said she was rereading it, and finding a lot of parallels between Rilla’s experience of WWI and the uncertainty of lockdown. I felt a lot of those resonances, too, when I reread it.
  38. Montgomery, L. M., Emily of New Moon (finished October 4, 2020): I needed some comfort reading, and this is always worth a re-read.
  39. Montgomery, L. M., Emily Climbs (finished October 6, 2020): Re-reading this one always reminds me of how keenly Montgomery understands what it’s like to be a writer. It always reminds me how miserably writing is recompensed; in the early 20th C Emily was getting $2-3/poem, and her first story sold for $40. That’s…about the going rate in the early 21st C. Hideous.
  40. Montgomery, L.M., Emily’s Quest (finished October 13, 2020): I find reading this one is always so strange. It’s so drawn out, and so lonely, and so muted compared to the others. It makes me wonder how much the sentiments expressed in there are ones from Montgomery’s own early adulthood.
  41. Montgomery, L.M., Pat of Silver Bush (finished December 23, 2020): I needed a comfort reread.
  42. Montgomery, L.M., Mistress Pat (finished December 26, 2020): What I really appreciate about Montgomery’s books is the way that she portrays complex, but deeply loving, family relationships.
  43. Newman, Kim, The Secrets of Drearcliff Grange School (finished May 29, 2020): It was odd reading a speculative fiction book written/marketed as a popular fiction book. It was a fine read.
  44. Nijkamp, Marieke, ed., Unbroken: 13 Stories Starring Disabled Teens (finished September 2020: Read my review here.
  45. Osawa, Hirotaka, ed., Intelligence, Artificial and Human: Eight Science Fiction Tales by Japanese Authors (finished January 2020): Read my review here.
  46. R, K, CoLaS (finished December 2020): I hoped to publish this one, but the author has decided to consider options elsewhere. I hope someone does publish it, because I loved it!
  47. Sittenfeld, Curtis, Eligible (finished September 11, 2020): I wanted to love this, so much. But, I just couldn’t. It tried so hard to be politically correct, and on the one hand I appreciate an author of a mainstream chick lit book doing this; but on the other hand, it felt like he made a bunch of racists, classist, sexist characters just so he could point out that this was wrong, rather than just…not? So I’m not sure whether it did more good than harm.
  48. Wakes, Damon L, Ten Little Astronauts (finished January 2020): Read my review here.


  1. Adamson, Peter, History of Philosophy Without Any Gaps: Medieval Philosophy (finished spring 2020): I started reading this in October 2019, and live-tweeted it. The thread took about 5 months and was over 200 tweets long, and I didn’t break it! It’s a good book.
  2. V, C, S (finished Oct 2020): This is a book I’m looking at publishing, so no further details!
  3. V, C, FtCoA (finished Oct 2020): This is also a book I’m looking at publishing, so no further details!