Tuesday, 23 June 2015

A very brief, incomplete, and stopgap account of women in medieval logic

This afternoon Catarina commented on FB about the glaring lack of women logicians in the currently-being-edited Cambridge Companion to Medieval Logic. It's a topic that I've recently bumped heads with myself when trying to tread the line between encouraging my department to draw their curricula from a wide variety of sources, not just in terms of gender but also in terms of time and geography, while also ensuring that no rigorous quota for women authors was instituted as departmental policy, for while there are certainly a number of good secondary authors on medieval logic who are women, were I to ever teach a course dedicated to medieval logic, semantics, and philosophy of language, I didn't want to be put into a place of being required to teach women who don't exist.

But is it true that they don't exist? The conversation on the FB pointed out at the commonly held view of women being barred from higher education is a false one [1], with women being allowed at Italian universities, which even had female professors such as Maria di Novella, who became professor of mathematics at Bologna at the age of 25. (On the question of the percentage of women students in Italy, J.J. Walsh in The Thirteenth: Greatest of Centuries comments that matriculation lists tell us "very little that is absolute with respect to the sex of the matriculates" because "not a few girls are called by men's names and without the feminine termination which is so distinctive among the English speaking peoples [and] in olden times this was still more the case". Putting on my onomastic hat, I must point out that this is incorrect. While, yes, many names which are considered strongly gendered nowadays were used by both men and women in the Middle Ages, it was in English, not Italian, contexts where the gender of the person is not indicated by a feminine ending. Furthermore, the matriculation lists would've been written in Latin, an inherently gendered language. It is in general extremely easy to determine the gender of the bearer of a name recorded in Latin; it is only in cases where the Latinization is very light, such as in the Latinization of some names of Germanic origin, that it can be ambiguous. Germanic names, however, never had the strong foothold in Italy that they did in France and Germany, with names of Latin or Etruscan origin making up the majority of the name-pool. And even then, a trained onomastic will know that a Latinized name ending in -burg (as opposed to the explicitly marked -burgus or -burga / -burgis) is much more likely to be female than male, whereas one ending in -wald (again as opposed to the explicitly marked -waldus or -walda) is more likely to be male than female.) Unfortunately, I believe Bologna is treated in vol. 1 of Rashdall's Medieval Universities, which is the volume I don't own, so any further discussion of female professors there will have to be relegated to another post. In vol. 3 of Rashdall, there is a brief mention of women in connection to the University of Salamanca, founded c. 1227-8:

Salamanca is not perhaps precisely the place where one would look for early precedents for the higher education of women. Yet it was from Salamanca that Isabella the Catholic is said to have summoned Doña Beatriz Galindo to teach her Latin long before the Protestant Elizabeth put herself to school under Ascham [p. 88].

Beatriz Galindo was born sometime around 1465 in Salamanca, and studied grammar at one of the university's dependent institutions. She taught philosophy and medicine at Salamanca, and a commentary on Aristotle, Notas y comentarios sobre Aristóteles, is attributed to her (cf. S. Knight & S. Tilg, The Oxford Handbook of Neo-Latin, p. 367, and J. Stevenson, Women Latin Poets, p. 204). Little on the Notas appears to be available in English.

The answer to the question of whether there were women logicians in the Middle Ages depends, of course, on how 'logician' is defined (and also on how 'Middle Ages' is defined, but I'll let myself interpret that period very liberally here). One way would be to take it narrowly, and look for women who taught logic at the university level, or who wrote treatises with topics and titles that are clearly connected to the logical canon: Treatises on syllogisms, on the Organon, on consequences, on insolubles, on sophisms, on supposition, on syncategorematic terms, on obligationes. On that view, finding someone who qualifies may indeed be difficult.

A more fruitful approach would be to treat the subject broadly, as indeed it was treated in the Middle Ages, where dialectic included grammar and rhetoric along with logic, look at women who employed or commented on logical techniques, or who participated in philosophical methodology more broadly, or who even, by other means, provide us with evidence concerning the educational milieu and opportunities for women. On this view, we would be remiss if we didn't mention such women as:

  • Dhuoda: Dhuoda, aka Dodana or Duodena, lived in the 9th C. She married the son of a cousin of Charlemagne around 824, and their first son, William, was born two years later. Another son, Bernard, was born 15 years later, and during the next two years, Dhuoda wrote a moral handbook for her sons, the Liber Manualis (a rather poor scan of a portion of the Liber Manualis is available here). The Manual was a guide to good conduct, and is the only known work by a Carolingian woman known to have survived. It is useful as a guide to the type of education that a woman of relatively high social status would have had during this period (there is evidence that she is familiar with the grammarian Donatus, cf. ch. 8 of M. Thiébaux, The Writings of Medieval Women: An Anthology, and she also cites Isidore's etymology of oratio 'prayer' as oris ratio 'the reason of the mouth'). The Manual has chapters on such diverse topics as "the mystery of the Trinity", "how to pray and for whom", "social order and secular success", "interpreting numbers", and "the usefulness of reciting the Psalms". From the point of view of someone who is interested in medieval female logicians, philosophers, or mathematicians, that section on "interpreting numbers" looks of relevance. Alas, it in fact turns out to be an interesting excursus into numerology! (Numerological reasoning is also found in books 1, 4, and 6.)
  • Hildegard of Bingen: Hildegard von Bingen as born in Germany at the end of the 11th C. She was broadly educated, writing both fiction and non-fiction, including works in botany and medicine. Her significance in the context of medieval dialectics likes not on the side of logic but rather in rhetoric: As a theologian, she not only wrote letters and poems but also was a traveling preacher. Her contributions to and her place in the history of rhetoric are well documented.
  • Eloise d'Argenteuil: Eloise hardly needs introduction to logicians, as her name is well-known as it has been co-opted as the name of the existential player in two-player logic/semantic games. While we have no explicitly logical writings (in the narrow sense defined above) by her, you cannot work so closely with a logician for as long as she without absorbing some of its influence (being married a logician myself, I can attest to this; as can he, most likely), and, after Abelard's death, Peter of Cluny in a letter to her complimented her on the fact that she had "left logic for the gospel, Plato for Christ, the Academy for the clositer" (quoted in H. M. Jewell, Women In Dark Age And Early Medieval Europe c.500-1200). A complete understanding of the academic and social milieu of logic and philosophy in the mid 12th century would not be possible without knowledge of her writings.
  • Christine de Pizan: Christine de Pizan was born in Venice in the middle of the 14th C, but spent most of her adult life in France, later living and working amongst many of the French ducal and royal courts. She's best known for her courtly poetry, but she also wrote books of practical advice for women, and her two most important prose works are The Book of the City of Ladies and The Treasure of the City of Ladies. In the former, she enters into a dialogue with the allegorical figures of Reason, Justice, and Rectitude, all in the female perspective. Both books are written in a highly skilled dialectical style, the study of which would provide interesting insight into the relationship between women's education and the classical disciplines of logic, rhetoric, and dialectic as taught in Italy and Paris at the end of the 14th C. So far, I have found very little that explicitly discuss this question; two articles I have found (but haven't yet had a chance to read) are J. D. Burnley, "Christine de Pizan and the So-Called Style Clergial", The Modern Language Review 81, no. 1 (Jan. 1986): 1-6, and C. M. Laennec, "Unladylike Polemics: Christine de Pizan's Strategies of Attack and Defense", Tulsa Studies in Women's Literature 12, no. 1 (1993): 47-59.
  • Julian of Norwich: Julian of Norwich was born in Norwich around 1342, thus almost exactly Christine's contemporary, and is the first woman known to have written in Middle English. She is best described as a mystic theologian, rather than a philosopher, and so may be considered outside the relevant scope. However, her "Long Text" (~63,000 words, called such in contrast with the earlier "Short Text" of ~11,000 words) is a treatise reflecting on a set of divine visions that she had after an illness in 1373. While the Short Text was primarily a simple account of the visions, in the Long Text she seeks to understand their meaning and signfication. While there is little in terms of explicit discussion of theories of signification, the fact that questions of meaning pervade the text is clear. "Woldst thou wetten this lord mening in this thing?" she asks, and answers that "love was his mening". As with Christine above, I have found very little secondary literature which discusses the semantic or significative theory underpinning Julian's "Long Text", but I suspect that a close examination of this text in such a light would prove extremely fruitful and interesting. (But see footnote 6 of V. Gillespie and M. Ross, "'With Mekeness Aske Perseverantly': On Reading Julian of Norwich", Mystics Quarterly 30, nos. 3/4 (2004): 126-141, and the reference cited therein.)

These women may not be logicians strictly speaking, but reading them and their works can inform our knowledge of developments in dialectic and its applications in the Middle Ages.

Finally, I'd like to share a brief reference I found in the lyrics of the troubadours to women and dialectic. In the 13th C Occitan romance Flamenca, two young women, Flamenca and Margarida, are engaged in rewriting some poetry for Margarida to send to her lover, and in the process, Flamenca speaks highly of Margarida's skill in 'dialectic':

Flamenca said to her, "Who has taught you,
Margarida, who has shown you---
by the faith you owe me---such dialectic? (5441-5443)

(From Thiébaux, op. cit., p. 244.)

This post is but a smattering of information that was easily available via books I have on hand and the internet; but I hope it will provide a beginning for a larger account of the contributions of women to dialectic in the Middle Ages!


[1] It was, however, true for England until the early 19th C; see A. Cobban, English University Life in the Middle Ages, pp. 1-2.

© 2015, Sara L. Uckelman.

Tuesday, 2 June 2015

(Im)Possible Conference in Turin


Graduate Conference

June 29-30, 2015
Center for Logic, Language, and Cognition
University of Turin
Palazzo Badini 
Lecture Hall (ground floor)
via Verdi 10, Turin

With the generous support of: COMPAGNIA DI SANPAOLO


9.00 – Greetings: Gianmaria AJANI (Rector, Università di Torino), Massimo FERRARI (Director of the Department of Philosophy and Education, Università di Torino), Alberto VOLTOLINI (Coordinator of the FINO PhD Programme, Università di Torino).

9.45 – Opening Lecture
Mark SAINSBURY (University of Texas at Austin)
Intentionality, intensionality, and nonexistence: An outline

11.15 – Coffee break 

Daniel DOHRN (Humboldt-Universität Berlin)
The case for imagination as a guide to possibility

Daniele SGARAVATTI (Università di Roma III)
Thinking about something: On a transcendental argument by E.J. Lowe

13.15 – Lunch break

Samuele CHILOVI (Universitat de Barcelona)
Maurice dispelled

Raphaël MILLIÈRE (École Normale Supérieure Paris)
Thinking the unthinkable: Berkeley’s challenge and pragmatic contradiction

16.30 – Coffee break

Thibaut GIRAUD (Institut Jean-Nicod Paris)
Logically impossible objects in classical logic

Alexander DINGES (Humboldt-Universität Berlin)
Innocent implicatures 


9.45 – (Im)Possible Lecture
Graham PRIEST (University of Melbourne, University of St. Andrews)
Thinking the impossible

11.15 – Coffee break 

Filippo CASATI (University of St. Andrews)
Nobject, one can even think of something that is not an object

Agnese PISONI (Università di Genova)
Thinking on the (im)possibility of time without change

13.15 – Lunch break

Martin VACEK (Slovenská Akadémia Vied)
Impossible worlds and the incredulous stare

Cristina NENCHA (Università di Torino)
Was David Lewis an anti-essentialist?

16.30 – Coffee break 

17.00 – Closing Lecture
Timothy WILLIAMSON (University of Oxford)
Counterpossible conditionals

Wednesday, 20 May 2015

CFP: SoTFoM III and The Hyperuniverse Programme, Vienna, September 21-23, 2015.

The Hyperuniverse Programme, launched in 2012, and currently pursued within a Templeton-funded research project at the Kurt Gödel Research Center in Vienna, aims to identify and philosophically motivate the adoption of new set-theoretic axioms.

The programme intersects several topics in the philosophy of set theory and of mathematics, such as the nature of mathematical (set-theoretic) truth, the universe/multiverse dichotomy, the alternative conceptions of the set-theoretic multiverse, the conceptual and epistemological status of new axioms and their alternative justificatory frameworks.

The aim of SotFoM III+The Hyperuniverse Programme Joint Conference is to bring together scholars who, over the last years, have contributed mathematically and philosophically to the ongoing work and debate on the foundations and the philosophy of set theory, in particular, to the understanding and the elucidation of the aforementioned topics. The three-day conference, taking place September 21-23 at the KGRC in Vienna, will feature invited and contributed speakers.

Invited Speakers

T. Arrigoni (Bruno Kessler Foundation)
G. Hellman (Minnesota)
P. Koellner (Harvard)
M. Leng (York)
Ø. Linnebo (Oslo)
W.H. Woodin (Harvard)
I. Jané (Barcelona) [TBC]

Call for papers
We invite (especially young) scholars to send their papers/abstracts, addressing one of the following topical strands:

– new set-theoretic axioms
– forms of justification of the axioms and their status within the philosophy of mathematics
– conceptions of the universe of sets
– conceptions of the set-theoretic multiverse
– the role and importance of new axioms for non-set-theoretic mathematics
– the Hyperuniverse Programme and its features
– alternative axiomatisations and their role for the foundations of mathematics

Papers should be prepared for blind review and submitted through EasyChair on the following page:

We especially encourage female scholars to send us their contributions. Accommodation expenses for contributed speakers will be covered by the KGRC.

Key Dates:
Submission deadline: 15 June 2015
Notification of acceptance: 15 July 2015

For further information, please contact:

sotfom [at] gmail [dot] com

or alternatively one of:

Carolin Antos-Kuby (carolin [dot] antos-kuby [at] univie [dot] ac [dot] at)
Neil Barton (bartonna [at] gmail [dot] com)
Claudio Ternullo (ternulc7 [at] univie [dot] ac [dot] at)
John Wigglesworth (jmwigglesworth [at] gmail [dot] com)

Friday, 1 May 2015

Final CFP - LORI-V (extended deadline: May 25)

Call for Papers

The Fifth International Conference on Logic, Rationality and Interaction (LORI-V)
October 28-31, 2015, Taipei, Taiwan

The International Conference on Logic, Rationality and Interaction (LORI) conference series aims at bringing together researchers working on a wide variety of logic-related fields that concern the understanding of rationality and interaction (http://golori.org). The series aims at fostering a view of Logic as an interdisciplinary endeavor, and supports the creation of an East-Asian community of interdisciplinary researchers.

Submitted papers should be at most 12 pages long, with one additional page for references, in PDF/DOC format following the Springer LNCS style: http://www.springer.com/computer/lncs?SGWID=0-164-6-793341-0.

Please submit paper by May 25, 2015 via EasyChair for LORI-V: https://easychair.org/conferences/?conf=lori5

Accepted papers will be collected as a volume in the Folli Series on Logic, Language and Information, and a selection of extended papers will later be published in special issues of Synthese and the Journal of Logic and Computation.

To encourage graduate students, those whose papers are single-authored and are accepted will be exempt from the registration fee, and up to 10 students will also have free accommodations during the conference dates.

Invited Speakers

Prof. Maria Aloni (Department of Philosophy, University of Amsterdam, The Netherlands) 
Prof. Joseph Halpern (Computer Science Department, Cornell University, USA)
Prof. Eric Pacuit (Department of Philosophy, University of Maryland, USA)
Prof. Liu Fenrong (Department of Philosophy, Tsinghua University, China)
Prof. Branden Fitelson (Department of Philosophy, Rutgers University, USA)
Prof. Churn-Jung Liau (Institute of Information Science, Academia Sinica, Taiwan)

Organizers: LORI, National Taiwan University (NTU) and National Yang Ming University (YMU), Taipei, Taiwan, LORI

Questions about paper submission please contact: Prof. Wiebe van der Hoek (wiebe@liverpool.ac.uk) or Prof. Wesley Holliday (wesholliday@berkeley.edu)

Questions about conference details please contact conferenceonlogic@gmail.com

Monday, 27 April 2015

Entia Nomina V CFP

The “Entia et Nomina” series features English language workshops for young researchers in formally oriented philosophy, in particular in logic, philosophy of science, formal epistemology or philosophy of language. The aim of the workshop is to foster cooperation among young philosophers with a formal bent from various research groups. The fourth workshop in the series was Trends in Logic XIV and took place at Ghent University in 20014The fifth workshop in the series will take place from 9 to 11 September 2015 in Krakow, Poland.

The Entia et Nomina V workshop will be preceded by the 4th workshop of The Budapest-Krakow Research Group on Probability, Causality and Determinism (http://bp-k.tumblr.com/).

Extended abstract submission deadline: May 15, 2015.
More details and full CFP at:

The European Society for Analytic Philosophy - new webpage

By Catarina Dutilh Novaes

The European Society for Analytic Philosophy was created in 1990, with the mission to promote collaboration and exchange of ideas among philosophers working within the analytic tradition, in Europe as well as elsewhere. It has thus been responsible for organizing major conferences every 3 years, the highly successful ECAP’s.

The current Steering Committee (of which I am a member), under the leadership of current president Stephan Hartmann, is seeking to expand the ways in which we can serve the (analytic) philosophical community in Europe. We will of course continue to organize ECAP, which will take place in 2017, and for which we already have a fantastic lineup of invited speakers (check it out!). But we are also considering various ways in which we can provide valuable services to the ESAP members, such as negotiating journal access with publishers (this is still in the making), among other initiatives. In particular, the brand-new website of ESAP is now online, and the goal is, among others, to concentrate useful information for (analytic) philosophers working in Europe all in one place.

However, we are only getting started, and at this points suggestions on how ESAP can truly support and galvanize the analytic philosophy community in Europe (as well as strengthening ties with colleagues elsewhere) are much welcome! We haven’t even started with an official membership system yet, precisely because we first want to have a number of services in place so as to make membership to the ESAP an attractive proposition. What are the initiatives and services we could provide that would really make a difference and facilitate the activities of our members?  Comments with suggestions below would be much appreciated!

Thursday, 23 April 2015

Jamesian epistemology formalised: an explication of 'The Will to Believe'

Famously, William James held that there are two commandments that govern our epistemic life.
There are two ways of looking at our duty in the matter of opinion, --- ways entirely different, and yet ways about whose difference the theory of knowledge seems hitherto to have shown very little concern. We must know the truth; and we must avoid error, --- these are our first and great commandments as would be knowers; but they are not two ways of stating an identical commandment [...] Believe truth! Shun error! --- these, we see, are two materially different laws; and by choosing between them we may end by coloring differently our whole intellectual life. We may regard the chase for truth as paramount, and the avoidance of error as secondary; or we may, on the other hand, treat the avoidance of error as more imperative, and let truth take its chance. (Section VII, James 1896)
In this note, I give a formal account of James' claim using the tools of epistemic utility theory. I begin by giving the account for categorical doxastic states --- that is, full belief, full disbelief, and suspension of judgment. Then I will show how the account plays out for graded doxastic states --- that is, credences. The latter part of the note thus answers a question left open in (Pettigrew 2014). (Konek forthcoming) gives a related treatment of imprecise credences.

It is not entirely clear whether James intends, in The Will to Believe, to speak of beliefs and disbeliefs or of credences.  He certainly talks of ''options'' between ''hypotheses'', which suggests the choice between two categorical states --- belief in one hypothesis or belief in the other. But he also talks of different strengths of a ''believing tendency'' and suggests that only a hypothesis with the ''maximum of liveness'' (presumably the maximum ''believing tendency'') counts as a belief (Section I, James 1896). In any case, in this note, we treat both.

Thursday, 16 April 2015

Dynamic epistemic logic solves the birthday puzzle

Many of you will have come across the 'birthday puzzle' that went viral this week:

Proving that philosophical logicians can make real contributions to serious, societal problems, my colleague Barteld Kooi has made a video where he explains how the puzzle can be solved with the help of dynamic epistemic logic. (Barteld is one of the most prominent researchers working in the field -- in particular, he is one of the authors of Dynamic Epistemic Logic (2008) and one of the editors of the much more reasonably priced Handbook of Epistemic Logic (2015).) Here is the video:

Moreover, logician and ninja-woman Audrey Yap of University of Victoria has also provided a solution to the puzzle using similar tools, which is represented in a series of pictures; the series can be found in this post by Richard Zach.

Homework for M-Phi readers (please comment below for your answers): how are the two solutions, Barteld's and Audrey's, related? Are they similar, are they different? If different, how so? Let us know!

Friday, 10 April 2015

Aristotle's definition of the syllogism -- a dialogical interpretation

By Catarina Dutilh Novaes
(Cross-posted at NewAPPS)

(I am currently finishing a paper on the definition of the syllogism according to Aristotle, Ockham, and Buridan. I post below the section where I present a dialogical interpretation of Aristotle's definition.)

Aristotle’s definition of ‘syllogismos’ in Prior Analytics (APri) 24b18-22 is among one of the most commented-upon passages of the Aristotelian corpus, by ancient as well as (Arabic and Latin) medieval commentators. He offers very similar definitions of syllogismos in the Topics, Sophistical Refutations, and the Rhetoric, but the one in APri is the one having received most attention from commentators. In the recent Striker (2009) translation, it goes like this (emphasis added):
A ‘syllogismos’ is an argument (logos) in which, (i) certain things being posited (tethentôn), (ii) something other than what was laid down (keimenôn) (iii) results by necessity (eks anagkês sumbainei)(iv) because these things are so. By ‘because these things are so’ I mean that it results through these, and by ‘resulting through these’ I mean that no term is required from outside for the necessity to come about.
It became customary among commentators to take ‘syllogismos’ as belonging to the genus ‘logos’ (discourse, argument), and as characterized by four (sometimes five) differentiae:

(i)            there are at least two premises which are posited
(ii)          the conclusion is different from the premises
(iii)         the conclusion follows necessarily from the premises
(iv)         the premises imply the conclusion by themselves; they are jointly necessary and sufficient for the conclusion to be produced.

My starting point is the idea that the best way to understand Aristotle’s project in the APri is as the formulation of a formal theory that could be suitably applied in particular in contexts of dialectical disputations. In other words, dialectical (or more generally, dialogical) considerations are always in the background in the development of the syllogistic theory (as also argued by (Kapp 1975)). True enough, he states at the very beginning of APri that the framework applies both to demonstrative and to dialectical syllogisms. But in both cases we may think of a multi-agent, dialogical situation (e.g. demonstration in the context of teaching), even if there are important differences between dialectical and demonstrative contexts. However, while the dialectical context is inherently dialogical and multi-agent, the demonstrative context need not be.

As Aristotle presents it in Chap. 1 of Book I, the distinction between dialectical and demonstrative syllogisms seems to pertain exclusively to the status of the premises: if known to be true, and more primary than the conclusion, then the syllogism will be demonstrative; if merely ‘reputable’ (endoxa), then the syllogism is dialectical. But with respect to the pragmatics of the two situations, there are other relevant differences. In particular, demonstrative syllogisms used in the context of teaching will presuppose an asymmetric relationship between the interlocutors (teacher and pupil), whereas in a dialectical context, although questioner and answerer have different roles to play, their statuses are usually comparable – they are peers. Indeed, the overall goals of a demonstration are quite different from the goals of a dialectical disputation, even though both can rely on syllogistic as a background theory of argumentation.

Be that as it may, each of the clauses formulated by Aristotle and numbered above can be given compelling dialogical, if not dialectical, explanations (on occasion I will also refer to demonstrative contexts). Let us discuss each of them in turn.

(i) Multiple premises. This requirement excludes single-premise arguments as syllogistically correct. Indeed, in the formal theory subsequently developed in APri, the arguments considered are almost exclusively those that we now refer to as syllogistic arguments, namely composed of two premises and one conclusion, all of which are categorical sentences of the A, E, I, O forms. But as often noted, this definition excludes for example the conversion rules (from AiB infer BiA and vice-versa; from AeB infer BeA and vice-versa), creating some difficulty to account for the nature of the validity of these rules. Moreover, consider the following description of the general enterprise by Striker:
Aristotle intended his syllogistic to serve as a general theory of valid deductive argument, rather than a formal system designed for a limited class of simple propositions. (Striker 2009, 79)
If we follow Striker (as I think we should!), the specific features of the theory later developed in APri should not be taken to explain the general definition at the starting point: this would amount to putting the cart before the horse. Indeed, it is the formal theory that is meant to offer a regimented account of the conceptual starting point, which is the general notion of a valid deductive argument. So this specific feature of the formal apparatus cannot be summoned to explain this aspect of the definition.

What could then explain the requirement that there be multiple premises? As noted by Striker (2009, 79), the verb ‘to syllogize’ originally meant something like ‘to add up’, ‘to compute/calculate’, and so it immediately suggests the idea of ‘putting things together’, of a fusion of more than one element (a point often made by the ancient commentators).

Plato already used the term ‘to syllogize’ in the sense of ‘to infer’ or ‘to conclude’, which Aristotle seems to have adopted. Indeed, from a dialectical/dialogical perspective as illustrated in Plato’s dialogues, the multiple premises requirement makes good sense. In a typical dialectical situation, the questioner (e.g. Socrates) elicits a number of discourse commitments from the answerer, and then goes on to show that they are collectively incoherent – for example, because they entail something absurd – thus producing a refutation. Typically, a refutation will not come about with only one discursive commitment: it is usually the interaction of multiple commitments that gives rise to interesting (and sometimes embarrassing!) conclusions.

Notice also the use of the terms ‘posited’ and ‘laid down’, which have a distinctive dialectical flavor. They introduce the dimension of a speech-act, of an agent actually putting forward premises to an interlocutor or audience, again suggesting multi-agent situations. Later authors such as Boethius will make the multi-agent dimension even more explicit, adding that the premises are not only laid down by the producer, but also granted by the receiver.

(ii) Irreflexivity. Aristotle’s requirement that the conclusion be different from the premises seems puzzling at first sight, since it entails that the consequence relation underlying syllogistic is irreflexive. This is in tension with the currently widely accepted view that reflexivity is a core feature of deductive validity.

However, here again, taking into account the various contexts of application of syllogistic arguments, irreflexivity makes good sense for each of them (as argued in (Duncombe 2014)). Indeed, in a demonstrative context, the function of a syllogism is to lead from the known to the unknown, and so obviously premises and conclusion should be different. In a dialectical context, it makes no sense to ask the opponent to grant as a premise precisely that which one seeks to establish as a conclusion; this would amount to an instance of petition principii. So the irreflexivity of the syllogistic consequence relation is exactly what one would expect, given the applications Aristotle seems to have in mind when developing the theory. (There are issues of propositional identity that arise in connection with this requirement (e.g. are logically equivalent propositions such as AiB and BiA ‘the same’?), but we will set those aside for the present purposes.)

(iii) Necessary truth-preservation. Aristotle distinguishes syllogistic arguments from those whose premises make the conclusion likely but not certain, such as induction or analogy. It is in this sense that his main target seems to be the notion of a valid deductive argument, but from the start necessary truth-preservation will be a necessary but not sufficient condition for deductive validity (in particular, in light of the three other clauses).

There is much to be said with respect to why the ‘results by necessity’ clause makes sense in the different contexts of application of syllogistic arguments, in particular demonstrative and dialectical contexts, but let us keep it brief for the present purposes. In a dialectical context, an argument having this property will force the opponent to grant the conclusion, if she has granted the premises, so it is a strategically advantageous property for the one proposing the argument. In a demonstrative context, Aristotle’s whole theory of demonstration is premised on the idea of deriving rock-solid conclusions from self-evident axioms, and thus again necessary truth-preservation becomes advantageous.

(iv) Sufficiency and necessity of the premises. This is perhaps the most obscurely formulated of the four clauses in the definition, and indeed Aristotle goes on to offer a gloss of what he means, which is however still not very illuminating. In the Topics, his phrasing is more transparent, as described by Striker:
The definition as given in the Topics is clearer in this respect: it has the clause ‘through the things laid down’ instead of ‘because these things are so’. In this passage, Aristotle adds the remark that this clause should also be understood to mean that all premises needed to derive the conclusion have been explicitly stated. (Striker 2009, 81)
This clause has been variously interpreted by commentators. It seems to amount to some sort of relevance requirement: it must be precisely in virtue of the premises that the conclusion comes about. To be sure, the premises may be false or uncertain (at least outside demonstrative contexts), but the conclusion must be produced through them. Some commentators, in particular in the Arabic tradition, have interpreted this clause as a requirement for an essential connection between premises and conclusion. But the requirement can also be interpreted logically as stating that no premise is redundant for the conclusion to come about; all of them are de facto needed for the conclusion to result of necessity. (This is indeed one of the two main formulations of the requirement of relevance in modern relevant logics, known as ‘derivational utility’ (Read 1988, 6.4).) This requirement is also often discussed in connection with the fallacy of False Cause, which we will discuss briefly below.

Moreover, as Aristotle’s gloss suggests, this clause can also be read as the requirement that everything that is needed for the conclusion to result of necessity has been explicitly stated; there are no hidden premises required (“no term is required from outside”). And so, this clause may be read as the requirement that the premises laid down are exactly those needed for the conclusion to come about; no more, no less.

In demonstrative contexts, this clause is very natural: for Aristotle, a demonstration is an explication unearthing the causes of a given phenomenon, and so both redundancy and lack of explicitness go against this desideratum. In dialectical contexts however, both these requirements are less straightforward: the participants may have a fair amount of endoxa in common, which could plausibly be taken for granted without being explicitly put forward; and redundancy may be advantageous in purely adversarial contexts, as asking for various redundant premises may serve the strategic purpose of confusing one’s opponent. But in the Topics, Aristotle wants to move away from the purely adversarial dialectical disputes (though he also gives advice on how to perform well in such cases – see also the Sophistical Refutations) and towards a more cooperative model – dialectic as inquiry, where two parties together consider what would follow from given assumptions (Topics VIII.5). In such contexts, redundancy would be out of place, and relevance comes out as a notion related to cooperativeness.

Friday, 3 April 2015

On Quine's Arguments Against QML, Part 3: Ontology

Read part 1; read part 2.

The second objection that Quine levels against quantified modal logic in [1] is that its ontology is “curiously idealistic” and “repudiates material objects” [1, p. 43]. This consideration arises from the same starting point as the objection discussed in the previous subsection: The problem of quantifying into an intensional context

Consider the following:

(6) ∃x(x is red ∧ M(x is round))

Quine says that in order to interpret this sentence, we need supplementary criteria, and suggests one potential criterion:

(ii) An existential quantification holds if there is a constant whose substitution for the variable of quantification would render the matrix true [1, p. 46],

where a ‘matrix’ is simply “an expression which has the form of a statement but contains a free variable” [2, p. 126]. This criterion, he argues has the consequence that

there are no concrete objects (men, planets, etc.), but rather that there are only, corresponding to each supposed concrete object, a multitude of distinguishable entities (perhaps ‘individual concepts’, in Church’s phrase) [1, p. 47].

Thus, instead of having concrete objects such as Venus, Mars, and Pluto in our ontology, we have instead things such as Venus-concept, Evening-Star-concept, Morning-Star-concept, etc. Let us spell out his argument for this conclusion.

Suppose that Venus, Evening Star, and Morning Star are all constants in our language suitable for use in criterion (ii). Each of these constants bears a certain relationship to itself and to the other in virtue of the empirical data; Quine calls this relation ‘congruence’. The question is what these constants are names of; if they pick out concrete objects in the domain, then they should all pick out the same concrete object, namely, a planet. But we shall see that truths about congruence prevent us from taking as the values of these constants concrete objects.

Let C represent the relation of congruence; we have the following two truths:

(7) Morning Star C Evening Star ∧ L(Morning Star C Morning Star)

(8) Evening Star C Evening Star ∧ ¬L(Morning Star C Evening Star)

From these along with (ii), we can conclude that there are at least two distinct objects in the ontology which are congruent with ‘Evening Star’:

(9) ∃x(x C Evening Star ∧ L(x C Morning Star)

(10) ∃x(x C Evening Star ∧ ¬L(x C Morning Star)

But since there is but one planet Venus, it must be the case that the ontology is not made up of planets and other concrete objects, but rather concepts of planets, for only then could we find constants whose substitution for the variable would make (9) and (10) true.

A strange ontology this may be, but it does not immediately follow from this that QML is incoherent or that expressions involving quantification into modal contexts are nonsense. For let us recall what Quine’s modal logic is a modal logic of: Not logical necessity, not physical necessity, but analytic necessity. As discussed above, the notion of analyticity is defined in terms of synonymy. Synonymy—sameness of meaning or sameness of intension—is itself a notion concerning concepts, not objects. Therefore, in a modal logic designed to explicate a notion based on concepts rather than objects, we should not be surprised that the ontology of that logic is populated with concepts, rather than objects. What is surprising is that Quine does not apparently recognize this, despite the fact that he says, elsewhere, that “being necessarily or possibly thus and so is in general not a trait of the object concerned, but depends on the manner of referring to the object” [3, p. 148, emphasis added]. If the logic of necessity is thus not about properties of actual objects but of ways that objects are described, then we should in fact expect that the ontology of the logic to not be populated by actual objects, but rather by ways that objects can be described, i.e., by concepts.


  • [1] W. V. Quine. The problem of interpreting modal logic. Journal of Symbolic Logic, 12(2):43–48, 1947.
  • [2] Willard V. Quine. Notes on existence and necessity. Journal of Philosophy, 40(5):113–127, 1943.
  • [3] W. V. O. Quine. From a Logical Point of View. Harper & Row, 2nd edition, 1961.

© 2015 Sara L. Uckelman

Friday, 27 March 2015

On Quine's Arguments Against QML, Part 2: The problem of "quantifying in"

Read part 1.

The first of the two problems we look at is related to the problem of ‘quantifying in’. Versions of this argument can be found in [1,2,3]. Quine points out that modal contexts are intensional, by which he means simply that they are non-truth-functional [1, p. 122]; this is why the class of analytic truths is larger than the class of merely logical truths. Intensional contexts are opaque, and they “do not admit pronouns which refer to quantifiers anterior to the context” [1, p. 123]. To illustrate this, he gives his now-famous example of 9 and the number of planets. He says: “The identity

(3) The number of planets = 9

is a truth (so far as we know at the moment) of astronomy” [1, p. 119], [*]. Yet compare (4) “Necessarily something is greater than 7” and (5) “There is something which is necessarily greater than 7”:

(4) L¬∀x¬(x > 7)

(5) ¬∀x¬L(x > 7)

(4) “still makes sense”, according to Quine [1, p. 123], and further more it is true; take, for example, the number 9. But in contrast, (5) is “nonsense” [1, p. 124]. It is nonsense because L(9 > 7) is true, but L(The number of planets > 7) is false, even though 9 and the number of planets are the same (at least at the time he was writing). It is false because there is no analytic connection between ‘the number of planets’ and ‘> 7’.

The problem with this as an objection is that synonymy — and hence analyticity itself, since it is defined in terms of synonymy — is a contingent matter; it is accidental whether two terms are synonymous or not. In fact, the falsity of “The number of planets = 9” demonstrates the contingency of the matter; the fact that the IAU was able to redefine what it meant to be a planet, and hence change the number of planets in our solar system, shows that there is no necessary connection between the concepts ‘9’ and ‘the number of planets’. Their synonymy was only accidental.

At this point, an interesting parallel can drawn between this example and one that can be found in another area of modal logic, namely, the Aristotelian modal syllogistic. One of the long-standing difficulties commentators (ancient, medieval, and modern) have had with interpreting Aristotle’s modal syllogistic was the Two Barbaras problem: his insistence that NXN Barbara was valid while XNN Barbara was invalid. NXN Barbara is the first-figure syllogism Barbara with a necessary major, assertoric minor, and necessary conclusion, while XNN Barbara has an assertoric major and necessary minor. Commentators find common ground against Aristotle in two ways: Either they believe that neither form should be valid, or that if one is valid, there is no way to distinguish which one, and hence both should be. Here is an example in the form of NXN Barbara:

Necessarily all elms are deciduous.
All the trees in my yard are elms.
Therefore, necessarily all trees in my yard are deciduous.

One standard objection to the validity of such an argument is that the connection between being a tree in my yard and an elm tree is accidental; there is no deep underlying relation between these two concepts. This contingency in a sense “spills over” into the conclusion; it would be acceptable to draw an assertoric conclusion, but a necessary one is too strong.

Let us compare NXN Barbara with the following:

L(9 > 7)
The number of planets = 9
Therefore, L(The number of planets > 7).

In both cases, the way to rehabilitate the argument would be to necessitate the second premise; but in order to retain soundness this would require that ‘The number of planets = 9’ or ‘All the trees in my yard are elms’ be analytic (for only then would the result of prefixing them with ‘L’ be considered true, on Quine's account); but there is no reason to think that these premises are analytic.

The fact that the analogous argument is invalid, is, far from being a reason to reject quantifying into intensional contexts as incoherent, actually evidence that Quine is correctly analysing necessity-as-analyticity. This is exactly the sort of behaviour that we would want to see, since it is precisely because the identity statement is a merely accidental identity — as witnessed by the fact that while it used to be true, it is now in fact false — that we should reject the conclusion. Thus the problems that Quine sees arising from this example are not actually reasons for rejecting quantified modal logic, but rather reasons for embracing it: It is an advantage of Quine’s analytic approach to modal logic, not a disadvantage, that it makes such arguments invalid. Given that synonymy, and hence analyticity, is a matter of accident, we should not expect analytic identities to result in necessary conclusions, and if they did, we would have reason to question these conclusions on the same grounds that people question the validity of NXN Barbara.

References & Notes

  • [1] Willard V. Quine. Notes on existence and necessity. Journal of Philosophy, 40(5):113–127, 1943.
  • [2] Willard Van Orman Quine. Reference and modality. In From a Logical Point of View, pages 139–159. Harvard University Press, 2nd edition, 1980.
  • [3] Willard Van Orman Quine. Word and Object. MIT Press, 1960.
  • [*] Nowadays, of course, we know differently. It is rather amusing that two of the enduring platitudes in philosophy—that all swans are white and that there are nine planets — have both turned out to be false; Australia provided us with black swans, and the International Astronomical Union deprived us of Pluto.

© 2015 Sara L. Uckelman

Friday, 20 March 2015

On Quine's Arguments Against QML, Part 1: Modality and Analyticity

When teaching philosophical logic to undergraduates, I feel I have two responsibilities: (a) To teach them logic and (b) To teach them something of the historical development of the field. (Alas, given constraints arising from not enough time, (b) generally means saying something about 20th C developments, rather than what I'd really like to tell them about, namely, 13th and 14th C developments!) This means that when the part of the module where I teach quantified modal logic (QML) came around, I felt honor-bound to introduce them to Quine's arguments against it, and, further, to say something about how I view this arguments. This post and its successors arose from that project.

Philosophers often appeal to Quine's conclusions that QML is "meaningless" [1, p. 124] or has "serious obstacles" [2, p. 43] to justify why they do not consider QML. This, I think, does a great disservice, not only to QML, but also to other philosophers (particularly undergraduates) because it merely parrots his conclusions without engaging in them. Since I fall firmly on the side of thinking that QML is a worthwhile area of research which can be done coherently, the responsibility falls to me to explain where I think Quine's arguments against QML have gone wrong.

I have found that explanation rather easy: I don't think his arguments are wrong. I think where he has gone wrong is taking the phenomena that they demonstrate to be problematic, rather than recognizing that they are the natural consequences of his definition of necessity, in terms of analyticity. In the following posts, I will look at two of his arguments and show that what he is picking out by them are exactly what you would expect to happen in QML if necessity is defined as analyticity. In this, I will first look at what he says concerning the relationship between necessity and analyticity.

Because he wishes to define necessity in terms of analyticity, Quine first looks at the notion of analyticity in non-modal contexts. In such contexts, it is possible to identify a notion of logical truth which can be used as a touchstone against which to measure the concept of analytic truth. In a non-modal context, every logical truth, he says, is "deducible by the logic of truth-functions and quantification from true statements containing only logical signs" [2, p. 43], such as ∀x(x = x). [3] The class of analytic statements is "broader than that of logical truths" [2, p. 44], because it contains statements such as the following:

(1) No bachelor is married.

The truth of this statement is warranted on the basis of the relation of synonymity, or sameness in meaning (or intension, cf. [2, p. 44]), between ‘bachelor’ and ‘unmarried man’, and in fact synonymy proves to be the crucial concept in defining what it means for a sentence to be an analytic truth:

Definition A statement is analytic if by putting synonyms for synonyms (e.g., ‘man not married’ for ‘bachelor’, it can be turned into a logical truth [2, p. 44].

In order for this definition to prove fruitful, it must be spelled out precisely what is meant by ‘sameness of meaning’; this, however, is a complicated task, and one that many have struggled with to date without achieving full success. It is not necessary, thankfully, to have a complete answer here: If we suppose, as Quine does, that "there is an eventually formulable criterion of synonymy in some reasonable sense of the term" [2, p. 44], then we can appeal to this criterion even if we don’t yet know what it is.

That (1) is an analytic truth on this definition is clear by seeing that

(2) No man not married is married.

is a logical truth.

It is important for Quine that he provide a suitable definition of what counts as analytic because of the close relationship that he sees existing between analyticity and modality. He asserts that there is an analogy between necessity and analyticity in exactly the same way that there is between negation and falsity [2, p. 45]:

The contrast between ‘necessarily’ and ‘is analytic’ is exactly analogous to the contrast between ‘¬’ and ‘is false’. To write the denial sign before the statement itself. . . means the same as to write the words ‘is false’ after the name of the statement [1, p. 122].

When it comes to modality and analyticity, this close relationship is expressed in the following way:

Lemma The result of prefixing ‘L’ to any statement is true if and only if the statement is analytic [2, p. 45].

Given the usual connection between necessity and possibility, it follows that the result of prefixing ‘M’ to any statement S is true if and only if ¬S is not analytic.

References & Notes

  • [1] Willard V. Quine. Notes on existence and necessity. Journal of Philosophy, 40(5):113–127, 1943.
  • [2] W. V. Quine. The problem of interpreting modal logic. Journal of Symbolic Logic, 12(2):43–48, 1947.
  • [3] Whether = is, strictly speaking, a logical sign he does not discuss; and for our purposes it does not matter if we grant to him that it is.

© 2015 Sara L. Uckelman