Wednesday, 26 August 2015

Formal Methods in Philosophy: a Brief Introduction (Part II)

By Catarina Dutilh Novaes
(Cross-posted at NewAPPS)

This is the second and final part of my 'brief introduction' to formal methods in philosophy to appear in the forthcoming Bloomsbury Philosophical Methodology Reader, being edited by Joachim Horvath. (Part I is here.) In this part I present in more detail the four papers included in the formal methods section, namely Tarski's 'On the concept of following logically', excerpts from Carnap's Logical Foundations of Probability, Hansson's 2000 'Formalization in philosophy', and a commissioned new piece by Michael Titelbaum focusing in particular (though not exclusively) on Bayesian epistemology. 


Some of the pioneers in formal/mathematical approaches to philosophical questions had a number of interesting things to say on the issue of what counts as an adequate formalization, in particular Tarski and Carnap – hence the inclusion of pieces by each of them in the present volume. Indeed, both in his paper on truth and in his paper on logical consequence (in the 1930s), Tarski started out with an informal notion and then sought to develop an appropriate formal account of it. In the case of truth, the starting point was the correspondence conception of truth, which he claimed dated back to Aristotle. In the case of logical consequence, he was somewhat less precise and referred to the ‘common’ or ‘everyday’ notion of logical consequence.

These two conceptual starting points allowed Tarski to formulate what he described as ‘conditions of material adequacy’ for the formal accounts. He also formulated criteria of formal correctness, which pertain to the internal exactness of the formal theory. In the case of truth, the basic condition of material adequacy was the famous T-schema; in the case of logical consequence, the properties of necessary truth-preservation and of validity-preserving schematic substitution. Unsurprisingly, the formal theories he then went on to develop both passed the test of material adequacy he had formulated himself. But there is nothing particularly ad hoc about this, since the conceptual core of the notions he was after was presumably captured in these conditions, which thus could serve as conceptual ‘guides’ for the formulation of the formal theories.

Friday, 21 August 2015

Formal Methods in Philosophy: a Brief Introduction (Part I)

By Catarina Dutilh Novaes
(Cross-posted in NewAPPS)

There is a Bloomsbury Philosophical Methodology Reader in the making, being edited by Joachim Horvath (Cologne). Joachim asked me to edit the section on formal methods, which will contain four papers: Tarski's 'On the concept of following logically', excerpts from Carnap's Logical Foundations of Probability, Hansson's 2000 'Formalization in philosophy', and a commissioned new piece by Michael Titelbaum focusing in particular (though not exclusively) on Bayesian epistemology. It will also contain a brief introduction to the topic by me, which I will post in two installments. Here is part I: comments welcome!


Since the inception of (Western) philosophy in ancient Greece, methods of regimentation and formalization, broadly understood, have been important items in the philosopher’s toolkit (Hodges 2009). The development of syllogistic logic by Aristotle and its extensive use in centuries of philosophical tradition as a formal tool for the analysis of arguments may be viewed as the first systematic application of formal methods to philosophical questions. In medieval times, philosophers and logicians relied extensively on logical tools other than syllogistic (which remained pervasive though) in their philosophical analyses (e.g. medieval theories of supposition, which come quite close to what is now known as formal semantics). But the level of sophistication and pervasiveness of formal tools in philosophy has increased significantly since the second half of the 19th century. (Frege is probably the first name that comes to mind in this context.)

It is commonly held that reliance on formal methods is one of the hallmarks of analytic philosophy, in contrast with other philosophical traditions. Indeed, the birth of analytic philosophy at the turn of the 20th century was marked in particular by Russell’s methodological decision to treat philosophical questions with the then-novel formal, logical tools developed for axiomatizations of mathematics (by Frege, Peano, Dedekind etc. – see (Awodey & Reck 2002) for an overview of these developments), for example in his influential ‘On denoting’ (1905). (Notice though that, from the start, there is an equally influential strand within analytic philosophy focusing on common sense and conceptual analysis, represented by Moore – see (Dutilh Novaes & Geerdink forthcoming).) This tradition was then continued by, among others, the philosophers of the Vienna Circle, who conceived of philosophical inquiry as closely related to the natural and exact sciences in terms of methods. Tarski, Carnap, Quine, Barcan Marcus, Kripke, and Putnam are some of those who have applied formal techniques to philosophical questions. Recently, there has been renewed interest in the use of formal, mathematical tools to treat philosophical questions, in particular with the use of probabilistic, Bayesian methods (e.g. formal epistemology). (See (Papineau 2012) for an overview of the main formal frameworks used for philosophical inquiry.)

Tuesday, 18 August 2015

Book review: John P. Burgess' Rigor and Structure (OUP)

Rigor and Structure, Burgess tells us in the preface, was originally intended to provide for mathematical structuralism the sort of survey that A Subject with No Object (Burgess & Rosen, 1999) provided for nominalism. However, the book that Burgess has ended up writing is importantly different from his earlier work with Rosen. In large part, this is because, for Burgess, not only is mathematical structuralism true --- whereas he took nominalism to be false --- but moreover it is a ''trivial truism'', at least as a description of modern mathematics from the beginning of the twentieth century onwards (Burgess, 2015, 111). Thus, instead of providing philosophical arguments in favour of mathematical structuralism, Burgess instead devotes the first half of the book (Chapters 1 and 2) to providing an historical account of how mathematics developed into the modern discipline of which mathematical structuralism is so obviously a true description. And this is where the other component of the title enters the story. For it is Burgess' contention that modern structuralist mathematics --- which he explores in the second half of the book, that is, in Chapters 3 and 4 --- is an inevitable consequence of the long quest for rigor, which began, so far as we know, with Euclid's Elements, and was completed by work in the nineteenth and early twentieth century that led to the arithmetization of analysis, the axiomatization or arithmetic, analysis, and geometry, the formulation of non-Euclidean geometries, and the founding of modern algebraic theories, such as group theory.

Thus, in the first two chapters of Rigor and Structure, Burgess asks two questions: What is mathematical rigor? Why did mathematicians strive so hard to achieve it throughout the period just described? To answer the first question, Burgess turns initially to the pronouncements of mathematicians themselves, but he finds little that is precise enough to satisfy a philosopher there. So he turns next to Aristotle and, looking to the Posterior Analytics, extracts the following suggestion:

Mathematical rigor requires that:
  • ''every new proposition must be deduced from previously established propositions'';
  •  ''every new notion must be defined in terms of previously explained notions'';
  • there are primitive notions from which the chain of definitions begins;
  • there are primitive postulates from which the chain of deductions begins;
  • ''the meaning of the primitives and the truth of the postulates must be evident''.
(Burgess, 2015, 6-7)

Monday, 27 July 2015

Women in Logic: two new initiatives

For those who haven't yet come across these, I have two new initiatives relating to women in logic to advertise:

  • Women in Logic group on Facebook: "A group for women in Logic, philosophical, mathematical or computational. or any other kind of formal logic that you care about." Membership is not restricted to women.
  • Female Professors of Logic, an editable google spreadsheet. One outcome of this will be to give a list of people who should have wikipedia pages if they don't already.

Please share widely and contribute as you can.

© 2015 Sara L. Uckelman

Tuesday, 21 July 2015

Reductio arguments from a dialogical perspective: final considerations

By Catarina Dutilh Novaes

(Cross-posted at NewAPPS)

This is the final post in my series on reductio ad absurdum from a dialogical perspective. Here is Part I, here is Part II, here is Part III, here is Part IV, and here is Part V. I now return to the issues raised in the earlier posts equipped with the dialogical account of deduction, and of reductio ad absurdum in particular.


A general dialogical schema for reductio ad absurdum, following Proclus’ description but inspired by the Socratic elenchus, might look like this:
  1. Interlocutor 1 commits to A (either prompted by a question from interlocutor 2, or spontaneously), which corresponds to assuming the initial hypothesis.
  2. Interlocutor 2 leads the initial hypothesis to absurdity, typically by relying on additional discursive commitments of 1 (which may be elicited by 2 through questions).
  3. Interlocutor 2 concludes ~A.

The main difference between the monological and the dialogical versions of a reductio is thus that in the latter there is a kind of division of labor that is absent from the former (as noted above). The agent making the initial assumption is not the same agent who will lead it to absurdity, and then conclude its contradictory. And so, the perceived pragmatic awkwardness of making an assumption precisely with the goal of ‘destroying’ it seems to vanish. Moreover, the adversarial component provides a compelling rationale for the general idea of ‘destroying’ the initial hypothesis; indeed, while the adversarial component is present in all deductive arguments (in particular given the requirement of necessary truth preservation, as argued above), it is even more pronounced in the case of reductio arguments, that is the procedure whereby someone’s discursive commitments are shown to be collectively incoherent since they lead to absurdity. There remains the question of why interlocutor 1 would want to engage in the dialogue at all, but presumably she simply wishes to voice a discursive commitment to A. From there on, the wheel begins to spin, mostly through 2’s actions.

Monday, 20 July 2015

Conference on Belief, Rationality, and Action over Time

University of Wisconsin-Madison, September 5-7The goal is to get action theorists and epistemologists (especially formal epistemologists) together to think about topics related to diachronic rationality and belief.  All are welcome, but attendees are expected to have read the papers beforehand.  Register for free here.

Organizers:  Mike Titelbaum, Sergio Tenenbaum, Chrisoula Andreou, and Sarah Paul
Funded by the Canadian Journal of Philosophy, the University of Wisconsin, and a gift from Rodney J. Blackman. 

Friday, 17 July 2015

Dialectical refutations and reductio ad absurdum

By Catarina Dutilh Novaes

(Cross-posted at NewAPPS)

This is the fifth installment of my series of posts on reductio ad absurdum from a dialogical perspective. Here is Part I, here is Part II, here is Part III, and here is Part IV. In this post I discuss a closely related argumentative strategy, namely dialectical refutation, and argue that it can be viewed as a genealogical ancestor of reductio ad absurdum.


Those familiar with Plato’s Socratic dialogues will undoubtedly recall the numerous instances in which Socrates, by means of questions, elicits a number of discursive commitments from his interlocutors, only to go on to show that, taken collectively, these commitments are incoherent. This is the procedure known as an elenchus, or dialectical refutation.

The ultimate purpose of such a refutation may range from ridiculing the opponent to nobler didactic goals. The etymology of elenchus is related to shame, and indeed at least in some cases it seems that Socrates is out to shame the interlocutor by exposing the incoherence of their beliefs taken collectively (for example, so as to exhort them to positive action, as argued in (Brickhouse & Smith 1991)). However, as noted by Socrates himself in the Gorgias (470c7-10), refuting is also what friends do to each other, a process whereby someone rids a friend of nonsense. An elenchus can also have pedagogical purposes, in interactions between masters and pupils.

There has been much discussion in the secondary literature on what exactly an elenchus is, as well as on whether there is a sufficiently coherent core of properties for what counts as an elenchus, beyond a motley of vaguely related argumentative strategies deployed by Socrates (Carpenter & Polansky 2002). (A useful recent overview is (Wolfsdorf 2013); see also (Scott 2002).) For our purposes, it will be useful to take as our starting point the description of the ‘Socratic method’ in an influential article by G. Vlastos (1983) (a much shorter version of the same argument is to be found in (Vlastos 1982), and I'll be referring to the shorter version). Vlastos distinguishes two kinds of elenchi, the indirect elenchus and the standard elenchus:

Thursday, 16 July 2015

A precis of the dialogical account of deduction

By Catarina Dutilh Novaes

(Cross-posted at NewAPPS)

This is the fourth installment of my series of posts on reductio ad absurdum arguments from a dialogical perspective. Here is Part I, here is Part II, and here is Part III. In this post I offer a précis of the dialogical account of deduction which I have been developing over the last years, which will then allow me to return to the issue of reductio arguments equipped with a new perspective in the next installments. I have presented the basics of this conception in previous posts, but some details of the account have changed, and so it seems like a good idea to spell it out again.


In this post, I present a brief account of the general dialogical conception of deduction that I endorse. Its relevance for the present purposes is to show that a dialogical conception of reductio ad absurdum arguments is not in any way ad-hoc; indeed, the claim is that this conception applies to deductive arguments in general, and thus a fortiori to reductio arguments. (But I will argue later on that the dialogical component is even more pronounced in reductio arguments than in other deductive arguments.)

Let us start with what can be described as functionalist questions pertaining to deductive arguments and deductive proofs. What is the point of deductive proofs? What are they good for? Why do mathematicians bother producing mathematical proofs at all? While these questions are typically ignored by mathematicians, they have been raised and addressed by so-called ‘maverick’ philosophers of mathematics, such as Hersh (1993) and Rav (1999). One promising vantage point to address these questions is the historical development of deductive proof in ancient Greek mathematics,[1] and on this topic the most authoritative study remains (Netz 1999). Netz emphasizes the importance of orality and dialogue for the emergence of classical, ‘Euclidean’ mathematics in ancient Greece:

Greek mathematics reflects the importance of persuasion. It reflects the role of orality, in the use of formulae, in the structure of proofs… But this orality is regimented into a written form, where vocabulary is limited, presentations follow a relatively rigid pattern… It is at once oral and written… (Netz 1999, 297/8)

Wednesday, 15 July 2015

Problems with reductio proofs: "jumping to conclusions"

By Catarina Dutilh Novaes

(Cross-posted at NewAPPS)

This is the third installment of my series of posts on reductio ad absurdum arguments from a dialogical perspective. Here is Part I, and here is Part II. In this post I discuss issues pertaining specifically to the last step in a reductio argument, namely that of going from reaching absurdity to concluding the contradictory of the initial hypothesis.


One worry we may have concerning reductio arguments is what could be described as ‘the culprit problem’. This is not a worry clearly formulated in the protocols previously described, but one which has been raised a number of times when I presented this material to different audiences. The basic problem is: we start with the initial assumption, which we intend to prove to be false, but along the way we avail ourselves to auxiliary hypotheses/premises. Now, it is the conjunction of all these premises and hypotheses that lead to absurdity, and it is not immediately clear whether we can single out one of them as the culprit to be rejected. For all we know, others may be to blame, and so there seems to be some arbitrariness involved in singling out one specific ingredient as responsible for things turning sour.

To be sure, in most practical cases this will not be a real concern; typically, the auxiliary premises we avail ourselves to are statements on which we have a high degree of epistemic confidence (for example, because they have been established by proofs that we recognize as correct). But it remains of philosophical significance that absurdity typically arises from the interaction between numerous elements, any of which can, in theory at least, be held to be responsible for the absurdity. A reductio argument, however, relies on the somewhat contentious assumption that we can isolate the culprit.

However, culprit considerations do not seem to be what motivates Fabio’s dramatic description of this last step as “an act of faith that I must do, a sacrifice I make”. Why is this step problematic then? Well, in first instance, what is established by leading the initial hypothesis to absurdity is that it is a bad idea to maintain this hypothesis (assuming that it can be reliably singled out as the culprit, e.g. if the auxiliary premises are beyond doubt). How does one go from it being a bad idea to maintain the hypothesis to it being a good idea to maintain its contradictory?

Tuesday, 14 July 2015

Problems with reductio proofs: assuming the impossible

By Catarina Dutilh Novaes

(Cross-posted at NewAPPS)

This is a series of posts with sections of the paper on reductio ad absurdum from a dialogical perspective that I am working on right now. This is Part II, here is Part I. In this post I discuss issues in connection with the first step in a reductio argument, that of assuming the impossible.


We can think of a reductio ad absurdum as having three main components, following Proclus’ description:

(i) Assuming the initial hypothesis.
(ii) Leading the hypothesis to absurdity.
(iii) Concluding the contradictory of the initial hypothesis.

I discuss two problems pertaining to (i) in this post, and two problems pertaining to (iii) in the next post. (ii) is not itself unproblematic, and we have seen for example that Maria worries whether the ‘usual’ rules for reasoning still apply once we’ve entered the impossible world established by (i). Moreover, the problematic status of (i) arises to a great extent from its perceived pragmatic conflict with (ii). But the focus will be on issues arising in connection with (i) and (iii).

A reductio proof starts with the assumption of precisely that which we want to prove is impossible (or false). As we’ve seen, this seems to create a feeling of cognitive dissonance in (some) reasoners: “I do not know what is true and what I pretend [to be] true.” (Maria) This may seem surprising at first sight: don’t we all regularly reason on the basis of false propositions, such as in counterfactual reasoning? (“If I had eaten a proper meal earlier today, I wouldn’t be so damn hungry now!”) However, as a matter of fact, there is considerable empirical evidence suggesting that dissociating one’s beliefs from reasoning is a very complex task, cognitively speaking (to ‘pretend that something is true’, in Maria’s terms). The belief bias literature, for example, has amply demonstrated the effect of belief on reasoning, even when participants are told to focus only on the connections between premises and conclusions. Moreover, empirical studies of reasoning behavior among adults with low to no schooling show their reluctance to reason with premises of which they have no knowledge (Harris 2000; Dutilh Novaes 2013). From this perspective, reasoning on the basis of hypotheses or suppositions may well be something that requires some sort of training (e.g. schooling) to be mastered.

Monday, 13 July 2015

Problems with reductio proofs: cognitive aspects

By Catarina Dutilh Novaes

(Cross-posted at NewAPPS)

As some readers may recall, I ran a couple of posts on reductio proofs from a dialogical perspective quite some time ago (here and here). I am now *finally* writing the paper where I systematize the account. In the coming days I'll be posting sections of the paper; as always, feedback is most welcome! The first part will focus on what seem to be the cognitive challenges that reasoners face when formulating reductio arguments.


For philosophers and mathematicians having been suitably ‘indoctrinated’ in the relevant methodologies, the issues pertaining to reductio ad absurdum arguments may not become immediately apparent, given their familiarity with the technique. And so, to get a sense of what is problematic about these arguments, let us start with a somewhat dramatic but in fact quite accurate account of what we could describe as the ‘phenomenology’ of producing a reductio argument, in the words of math education researcher U. Leron:

We begin the proof with a declaration that we are about to enter a false, impossible world, and all our subsequent efforts are directed towards ‘destroying’ this world, proving it is indeed false and impossible. (Leron 1985, 323)

In other words, we are first required to postulate this impossible world (which we know to be impossible, given that our very goal is to refute the initial hypothesis), and then required to show that this impossible world is indeed impossible. The first step already raises a number of issues (to be discussed shortly), but the tension between the two main steps (postulating a world, as it were, and then proceeding towards destroying it) is perhaps even more striking. As it so happens, these are not the only two issues that arise once one starts digging deeper.

To obtain a better grasp of the puzzling nature of reductio arguments, let us start with a discussion of why these arguments appear to be cognitively demanding – that is, if we are to believe findings in the math education literature as well as anecdotal evidence (e.g. of those with experience teaching the technique to students). This will offer a suitable framework to formulate further issues later on.

Logical parenting, balloons, and Abelard's insights on quantifiers

My 3.5 year old daughter has apparently been learning about opposites at nursery, because all weekend she was popping out such gems as "You know what are opposites? Big and little!" (Hot and cold, up and down, in and out, etc., etc., etc.). Sunday evening while we were getting supper read, she proceeded to play underfoot with a balloon she'd been given at a birthday party earlier in the day. This was increasingly irritating until she came out with:

"Do you know what are opposites? No balloon and some balloon!"

Logical parenting: Ur doin it right.

Of course, I was curious to know if she could extrapolate, so I asked her what the opposite of "All balloons" was. Her reply was "No balloon", which I couldn't complain about, because, after all, I hadn't specified whether I was looking for the contradictory opposite or the contrary opposite. Being the proud parent I was, I relayed the story on FB, and was amused at the selection of half-joking, half-serious suggestions I got for the opposite of "all balloons": Negative balloons? Impossible balloons? The square root of minus one balloons? i balloons? But it also made me think: The usual Aristotelian quantifier opposed to 'all' is 'some____not'. But "Some balloons not" doesn't make any sense. You can have "all balloons", you can have "no balloons", you can have "some balloons", but you can't have "some balloons not" [1]; if you want to use that quantifier, there needs to be more than just a quantified subject, there has to be a predicate, too. The same is not true of the non-Aristotelian form of the negation, 'not all': While you can't have "some balloons not", you can have #notallballoons.

Reflecting on this on the way home this evening, I was reminded of how Abelard made this very distinction, between non omnis and quidam non, arguing that these two are not equivalent with each other: non omnis does not have existential import, while quidam non always does. Many people think that making a distinction between 'not all' and 'some____not' is only necessary in a context where 'all' has existential import; but perhaps Abelard's insight that non omnis and quidam non are not equivalent reflects something deeper than just logical machinery to deal with a problematic assumption about universal quantifiers.

[1] This is, essentially, just the well-known observation that there is no single natural language English term 'nall'.

© 2015, Sara L. Uckelman

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 ( 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:

Please submit paper by May 25, 2015 via EasyChair for LORI-V:

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 ( or Prof. Wesley Holliday (

Questions about conference details please contact

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 (

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!