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

Thursday, 12 March 2015

A Strange Thing about the Brier Score


This post was co-written by Brian Knab and Miriam Schoenfield.

In the literature on epistemic utility theory, the Brier Score is offered as a paradigmatically reasonable measure of epistemic utility, or epistemic accuracy. We offer a case meant to put pressure on the claim that the Brier score in fact reasonably captures epistemic utility or epistemic accuracy.


1. A Simple Case


Consider two people contemplating the origin of the universe.


The simple deist is confident that a being exists that designed the universe. She is aware that cosmologists have developed non-design theories about the origins of the universe. However, she's confident that the non-design thesis is false.


So, according to the simple deist: deism is true, and the non-design thesis (which we’ll call “adeism”) is false. Deism and adeism form a partition of her possibility space.


The simple adeist, on the other hand, is confident that deism is false. She's confident that the universe came about without any help from a designer at all, and that the non-design thesis is true.


So, according to the simple adeist : deism is false, and the non-design hypothesis is true. Deism, and adeism form a partition of her possibility space.


It turns out: There is a deisgner!  (So deism is true, adeism is false). Who is more accurate?  The deist, obviously.


The Brier Score straightforwardly confirms this -- the simple deist is more accurate, according to the Brier Score, than the simple adeist.


2. A Problem Case


Now, consider again two people contemplating the origin of the universe. Both of them are admittedly somewhat uncertain about the existence of a designer. Both of them are aware of a large number of non-design theories of the origin of the universe.


The sophisticated deist  is more confident in deism than adeism. She has, moreover, also carefully considered all of the available non-design hypotheses, and has concluded that only one of them could possibly be true.  The rest, she thinks, are non-starters.


The sophisticated adeist  is, on the other hand, more confident in adeism than deism. She has also carefully considered all of the available non-design hypotheses, and although she thinks it’s likely that one of them is true, she has no opinions concerning which is the true one.  In her estimation, the non-design hypotheses are all equally likely.


Now, suppose it turns out: Deism is true (and so every non-design hypothesis is false). Who is more accurate?


We think: the sophisticated deist!  After all the sophisticated deist has the following two advantages over the sophisticated adeist: she has a higher credence in the truth than the sophisticated adeist does, and she has less credence invested in falsehoods than the sophisticated adeist does. So what advantage does the sophisticated adeist have over the sophisticated deist?  The only remaining difference between them is the way in which they distribute their confidence among the false hypotheses.  But why should the way in which the adeist distributes her confidence among the various false hypotheses make her more accurate in a world in which deism is true?


From the first personal side of things: if I want to have an accurate attitude about the origin of the universe and my choices are between being a sophisticated deist or a sophisticated adeist, I’d prefer to be the sophisticated deist, in the world in which deism is true.


But, in certain situations, and given enough non-design theories, the Brier score delivers the opposite verdict. For example, let D be the design hypothesis, and suppose there are 58 non-design theories, T1, T2, ... T58. Thus our partition is



By the description of the case, the ideal credences, across this partition, are (1,0,0,0,0...0)


Suppose the sophisticated deist’s credences are



Then her Brier Score is


Suppose the sophisticated adeist’s credences are


Then her Brier Score is


That’s a small victory for the adeist, admittedly, but the point is a structural one.  The adeist  -- in spite of the fact that she is a good deal less confident in the truth and, overall, a good deal more confident in the false -- is more accurate than the deist, according to the Brier. (For a related point -- one which trades on this same structural feature of the Brier Score --  see Knab, “In Defense of Absolute Value.”)


3. Discussion


That, we think, is enough of a puzzle to put some pressure on the Brier understanding of epistemic accuracy. More generally, the Brier Score fails to satisfy what looks like a plausible desideratum:


Falsity Distributions Don’t Matter: For any partition of theories: T1...Tn, a probabilistic agent’s accuracy with respect to this partition at world w should be determined solely by the amount of credence she invests in the true theory at w, and the amount of credence she invests in false theories at w.  The way she distributes her credences amongst the false theories at w shouldn’t affect her accuracy.





Tuesday, 3 March 2015

Second MCMP Summer School on Mathematical Philosophy for Female Students

After the huge success of last year's event, the Munich Center for Mathematical Philosophy will be hosting the second installment of its Summer School for female students, from July 26th to August 1st 2015. From the website:
The summer school is open to excellent female students who want to specialize in mathematical philosophy. Since women are significantly underrepresented in philosophy generally and in formal philosophy in particular, this summer school is aimed at encouraging women to engage with mathematical methods and apply them to philosophical problems. The summer school will provide an infrastructure for developing expertise in some of the main formal approaches used in mathematical philosophy, including theories of individual and collective decision-making, agent-based modeling, and epistemic logic. Furthermore, it offers study in an informal setting, lively debate, and a chance to strengthen mathematical self-confidence and independence for female students. Finally, being located at the MCMP, the summer school will also provide a stimulating and interdisciplinary environment for meeting like-minded philosophers.
Instructions on how to apply can be found here. This is a fantastic opportunity for all female students interested in the more technical, mathematical areas of philosophy to strengthen their skills and become more familiar with work on the area. Although I missed last year's event (and will sadly miss this one too), I am told that the general atmosphere was very friendly and encouraging, and so extremely conducive to the stated aims of the Summer School. So time to get going with those applications!

Wednesday, 28 January 2015

Information, search, and causes – Workshop in Turin

Center for Logic, Language, and Cognition 
University of Turin – via Sant’Ottavio 20, Turin (Italy) 

6th February 2015 

ex Sala Lauree Giurisprudenza
Palazzo Nuovo (ground floor)

INFORMATION, SEARCH, and CAUSES
Rational and cognitive approaches 

PROGRAM
(here to download)

9.15 – 10.15 
David LAGNADO (UCL) 
Causal networks in evidential reasoning 

10.15 – 11.00 
Jonathan NELSON (MPI Berlin) 
Late-breaking results on stepwise approaches to sequential search 

Coffee break 

11.30 – 12.15 
Neil BRAMLEY (UCL) 
Acting informatively: How people learn 
causal structure through sequences of interventions 

Lunch break 

14.00 – 15.00 
Paul PEDERSEN (MPI Berlin) 
Dilation, disintegrations, dominance principles, and delayed decisions 

15.00 – 15.45 
Laura MARTIGNON (Ludwigsburg) 
Probabilistic information measures in the classroom 

15.45 – 16.30 
Flavia FILIMON (Humboldt University Berlin) 
Neural substrates of probabilistic perceptual decisions 
based on experienced probabilities vs. descriptive statistics 

Coffee break 

17.00 – 17.45 
Björn MEDER (MPI Berlin) 
Information search and presentation formats 

17.45 – 18.30 
Vincenzo CRUPI (Turin) 
Shannon and beyond: Generalized entropies and rational information search 


The Center for Logic, Language, and Cognition (LLC) of the University of Turin was established in 2014 as a joint initiative of the Departments of Philosophy and Education, Psychology, and Computer Science. The workshop arises from the activities of two ongoing research projects addressing related issues: priority program New Frameworks of Rationality, SPP 1516 (Deutsche Forshungsgemeinshaft, grant CR 409/1-2), and FIRB project Structures and Dynamics of Knowledge and Cognition (Italian Ministry of Scientific Research, Turin unit, D11J12000470001).

Friday, 23 January 2015

CfP: 2015 Logic Colloquium in Helsinki

First Announcement & Call for Abstracts

Logic Colloquium 2015
European Summer Meeting of the Association for Symbolic Logic

Helsinki, Finland, 3-8 August 2015
http://www.helsinki.fi/lc2015
The annual European Summer Meeting of the Association for Symbolic Logic, the Logic Colloquium 2015 (LC 2015), will be organized in Helsinki, Finland, 3-8 August 2015. Logic Colloquium 2015 is co-located with the 15th Conference of Logic, Methodology and Philosophy of Science,CLMPS 2015, and with the SLS Summer School in Logic

Plenary lectures

Toshiyasu Arai (Chiba)
Sergei Artemov (New York)
Steve Awodey (Pittsburgh)
Johan van Benthem (Amsterdam and Stanford)
Artem Chernikov (Paris)
Ilias Farah (York)
Danielle Macbeth (Haverford)
Andrei Morozov (Novosibirsk)
Kobi Peterzil (Haifa)
Ralf Schindler (Münster)
Saharon Shelah (TBC) (Jerusalem and Rutgers)
Sebastiaan Terwijn (Nijmegen)

Tutorials

Erich Grädel (Aachen)
Menachem Magidor (Jerusalem).

Special sessions

Set Theory, organized by Heike Mildenberger (Freiburg)
Model theory, organized by Dugald Macpherson (Leeds)
Computability Theory, organized by Russell Miller (New York) and Alexandra Soskova (Sofia)
Proof Theory, organized by Benno van den Berg (Amsterdam) and Michael Rathjen (Leeds)
Philosophy of Mathematics and Logic, organized by Patricia Blanchette (Notre Dame) and Penelope Maddy (Irvine)
Logic and Quantum Foundations, organized by Samson Abramsky (Oxford)

Travel Awards and Contributed Talks

Travel  awards  for students  and  young  researchers  have been  made available  by the  organizers.   In some  cases  full compensation  of expenses is possible.  The website includes detailed information about the awards, instructions of how to apply, and an electronic form which may be used for the application.
The Logic Colloquium will include contributed talks of 20 minutes' length. Abstracts on contributed talks are published in the Bulletin of Symbolic Logic.
The deadline for travel award applications and abstract submission  is Tuesday, May 3, 2015. Please see http://www.helsinki.fi/lc2015/submission.html for information about applying for travel awards and for submitting an abstract.

Review of Williamson's Tetralogue

By Catarina Dutilh Novaes

(Cross-posted at NewAPPS)

I've been asked to write a review of Williamson's brand new book Tetralogue for the Times Higher Education. Here is what I've come up with so far. Comments are very welcome, as I still have some time before submitting the final version. (For more background on the book, here is a short video where Williamson explains the project.)

============================

Disagreement in debates and discussions is an interesting phenomenon. On the one hand, having to justify your views and opinions vis-à-vis those who disagree with you is perhaps one of the best ways to induce a critical reevaluation of these views. On the other hand, it is far from clear that a clash of views will eventually lead to a consensus where the parties come to hold better views than the ones they held before. This is one of the promises of rational discourse, but one that is all too often not kept. What to do in situations of discursive deadlock?

Timothy Williamson’s Tetralogue is precisely an investigation on the merits and limits of rational debate. Four people holding very different views sit across each other in a train and discuss a wide range of topics, such as the existence of witchcraft, the superiority and falibilism of scientific reasoning, whether anyone can ever be sure to really know anything, what it means for a statement to be true, and many others. As one of the most influential philosophers currently in activity, Williamson is well placed to give the reader an overview of some of the main debates in recent philosophy, as his characters debate their views.

Bob represents those who hold what could be describe as ‘ancestral’ modes of thinking, including superstition, belief in witchcraft and so forth; Sarah is the staunch child of the Enlightenment, firmly convinced of the superiority of scientific knowledge over Bob’s ancestral beliefs; Zac is the relativist who abhors absolute views, and rejects the idea that anything can be true or false simpliciter; Roxana, a latecomer in the conversation, is the most unpleasant of them all (not that any of the other three is particularly pleasant), and represents rationality taken to its limit: she is the one who pursues the logical conclusions of each position to its (sometimes absurd) limits. As these people try to resolve their differences and convince each other of their own worldviews, Williamson explores the limits of rational debate and disagreement.

What is perhaps most noteworthy about this book is the dialogical form adopted. The dialogue as a literary form marked the very birth of Western philosophy with Plato’s dialogues, which in all honesty remain unsurpassed when it comes to complexity, philosophical sophistication, and pure literary beauty (the Gorgias is my favorite). In the circa 2.500 years since, a number of philosophical works have adopted the dialogical form, in some periods more than in others: dialogues were particularly important in the Latin medieval tradition, and the early modern period saw a resurgence of the genre with Leibniz, Hume, and Diderot, among others. (See V. Hösle, The Philosophical Dialogue, 2012.) But for the most part, philosophical literary forms such as the philosophical essay tend to be superficially non-dialogical, while in practice often corresponding to ‘internalized’ dialogues where arguments, counter-arguments, counter-counter-arguments etc. are presented by one and the same voice. Indeed, in recent decades no prominent philosophical work written in dialogical form seems to have appeared, with the very notable exception of Lakatos’ Proofs and Refutations (1976).

Williamson’s adoption of the dialogical form is a clear reference to Platonic dialogues, but it also makes sense given that his main topic here is disagreement and rational debate as such. The book presents itself as an introduction to recent philosophical themes for the non-initiated, while the initiated may enjoy seeing these topics embedded in apparently mundane discussions. In this sense, it is bound to be of interest to a wide range of readers. However, if it is really intended to be a “way into philosophy” for those new to the topic, it might have reached its goal more efficiently if it also contained further details and pointers to additional literature (as Lakatos does in footnotes in Proofs and Refutations). Instead, it is unclear how the interested reader is to proceed in order to delve further into these topics. Moreover, the characters are rather like caricatures of each of the positions, with no ambition to psychological complexity. This might sound like an unreasonable requirement given the stated goals of the book; but the truth is that anyone writing a philosophical dialogue will be confronted with the exceedingly high standards set by the founder of the genre, Plato. Nevertheless, Tetralogue remains a remarkable and courageous attempt to experiment with an eminently philosophical but somewhat ‘outdated’ literary form – the dialogue – to talk about disagreement and dialogue itself.

Friday, 16 January 2015

What meaning can and cannot be: Lessons from real life, Part 2

The problem of fictional discourse -- do statements involving fictional objects have truth-values or are they truth-valueless; if the former, how are these truth values determined? -- is one that goes back at least to Frege (his views on the compositionality of language and what the referent of a sentence is entail that sentences which have non-referring parts have no truth-value) and for which no adequate solution has yet been found, given, e.g., the publication of books such as Tim Crane's The Object of Thought in 2013. I'm not going to survey all the issues arising from these problems, but instead present a problem for some accounts of the truth values of fictional statements which is, so far as I am aware, not often considered.

In Part 1 last week, one of my example languages was Adûnaic, one of the languages developed by J.R.R. Tolkien. I picked Adûnaic because of the context in which it appears in its most full form, Lowdham's report to the members of the Notion Club (The Notion Club Papers are themselves full of extremely interesting ideas about the nature of language and how linguistic meaning can be acquired, and will be the focus of a future Lesson), but any of his languages -- Quenya, Sindarian -- or indeed any constructed language of sufficient sophistication -- e.g., Klingon -- will serve my purposes.

One thing that is remarkable about constructed fictional languages such as Klingon, Quenya, etc., is the academic scholarship that they have generated. There is the The Elvish Linguistic Fellowship (a special interest group of the Mythopoeic Society, "devoted to the scholarly study of the invented languages of J.R.R. Tolkien"), which publishes two print journals, Vinyar Tengwar and Parma Eldalamberon, and an online journal, Tengwestië; Helge Kåre Fauskanger's Ardalambion, an extensive collection of links regarding Tolkienian languages; the Klingon Language Institute; and even the journal Tolkien Studies, which will not specifically devoted to his constructed languages publishes articles on them, such as Christopher Gilson's "Essence of Elvish: The Basic Vocabulary of Quenya". One conclusion that can be drawn from this extensive academic activity is that these fictional languages are taken as worthy objects of study, When it comes to languages, one of the basic requirements that it has to meet in order for it to be something worth studying is that it be meaningful. (While people can, and do, create "nonsense" languages, which are not meaningful, these do not have a history of generating the sort of scholarship that fictional languages like Klingon and Sindarin have.)

There are two types of contexts in which these languages can be found: In the original context of construction (e.g., in Tolkien's writings for the Elvish languages; in Star Trek TV episodes and movies for Klingon), and in external contexts (e.g., a wholly new composition of poetry in Quenya, or translation of the Bible into Klingon). Both of these contexts cause problems for straightforward explanations of how these languages are meaningful.

Adûnaic is set apart from other fictional languages by the paucity of examples that we have in it. As Fauskanger notes, "There are no coherent Adûnaic texts. Except single words scattered around in Lowdham's Report, most of the corpus consists of a number of fragmentary sentences given in SD:247, with Lowdham's interlinear translation" [1]. Fauskanger supplements the translation that is found in Sauron Defeated with words whose meaning is known from other contexts, and gives it as follows:

Kadô Zigûrun zabathân unakkha... 
"And so / [the] Wizard / humbled / he came..."
...Êruhînim dubdam Ugru-dalad... 
"...[the] Eruhíni [Children of Eru] / fell / under [the] Shadow..."
...Ar-Pharazônun azaggara Avalôiyada... 
"...Ar-Pharazôn / was warring / against [the] Valar..."
...Bârim an-Adûn yurahtam dâira sâibêth-mâ Êruvô 
"...[the] Lords of [the] West / broke / the Earth / with [the] assent / of Eru..."
...azrîya du-phursâ akhâsada 
"...seas /so as to gush/ into [the] chasm..."
...Anadûnê zîrân hikallaba... 
"...Númenor / [the] beloved / she fell down..."
...bawîba dulgî... 
"...[the] winds [were] black..." (lit. simply "winds / black")
...balîk hazad an-Nimruzîr azûlada... 
"...ships / seven / of Elendil / eastward..."
Agannâlô burôda nênud... 
"Death-shadow / heavy /on us..."
...zâira nênud... 
"...longing [is] / on us..."
...adûn izindi batân tâidô ayadda: îdô kâtha batîna lôkhî... 
"...west / [a] straight / road / once / went / now / all / roads / [are] crooked..."
Êphalak îdôn Yôzâyan 
"Far away / now [is] / [the] Land of Gift..."
Êphal êphalak îdôn hi-Akallabêth 
"Far / far away / now [is] / She-that-hath-fallen"

Though this is fragmentary, it is clear that what is being expressed is in the context of the legends of Middle Earth, that is, Adûnaic is being used to write what is from our point of view fiction. This fragmentary poem is not intended to be read literally as expressing statements about the actual world. This feature -- the use of the language to say something within the context of a fiction -- is to some extent shared by "external" uses of fictional languages, which by and large are also used for non-literal or non-factive writing or speech: Almost no one writes lesson plans in Quenya, composes a shopping list in Klingon, or sends submits meeting minutes in Sindarin.

The question then, is: If these languages are meaningful, how are they meaningful? What do we mean when we say that these fictional languages are meaningful, or at least intended to have meaning? If we mean that the sentences that are expressed by these languages have truth-conditions (e.g., a truth-conditional account of meaning has been adopted), then we are stymied by the fact that there is no good account of the truth-conditions of fictional language. One might say that there are truth conditions, we simply do not know them, and hence (via an epistemic rather than ontological truth-conditional account of meaning) we do not know the meaning of these sentences, even though they are meaningful. This sceptical position, however, does not seem to take account of our behaviour regarding sentences in these languages: We evaluate translations from, e.g., Quenya into English as correct or incorrect, we write literary criticism about the propositions expressed, and in general, we sure act as if we know what these sentences mean, at least in part, even though by assumption we don't know the relevant truth conditions.

Of course, it always possible to stick to one's philosophical guns, and simply reply that we are mistaken when we think we know what the sentences mean: But that seems to be a pretty tough horn to impale oneself on, because it doesn't provide any account for our behaviour with respect to these sentences. There is clearly some factor that guides our behaviour: There must be something in which referees evaluating prospective articles for Tengwestië ground their reports. If this is not the meaning of the sentences, then whatever it is, it certainly seems to be something which is functionally equivalent to meaning.

Lesson: We treat statements in constructed languages as meaningful. But if these languages are only ever used in fictional contexts, then any truth-conditional account of meaning which denies truth values to fictional discourse will have difficulty accounting for the fact that we do treat these languages in that way (that is, as meaningful).


© 2015, Sara L. Uckelman

Call for Papers: LORI-V (Deadline May 18)

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.

We invite submission of contributed papers on any of the broad themes of LORI series; specific topics of interest include, but are not limited to, formal approaches to

* agency, * argumentation and agreement, * belief representation, * cooperation, * belief revision and belief merging, * strategic reasoning, * games, * decision making and planning, * knowledge and action, * epistemology, * dynamics of informational attitudes, * knowledge representation, * interaction, * norms and normative systems, * natural language, * rationality, * philosophy and philosophical logic, * preference and utility, * social choice, * probability and uncertainty, * social interaction, * intentions, plans, and goals

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 papers by May 18, 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 may later be published in a special issue of a prestigious journal.

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

For detailed conference information and registration, please visit the website: http://golori.org and click "LORI-V".

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

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

For questions about conference details, please contact conferenceonlogic@gmail.com

Friday, 9 January 2015

Mochizuki's proof of the ABC conjecture: still "in limbo"

By Catarina Dutilh Novaes

(Cross-posted at NewAPPS)

Here's a short piece by the New Scientist on the status of Mochizuki's purported proof of the ABC conjecture. More than 2 years after the 500-page proof has been made public, the mathematical community still hasn't been able to decide whether it's correct or not. (Recall my post on this from May 2013; little change seems to have taken place since then.)

Going back to my dialogical conception of mathematical proofs as involving a proponent who formulates the proof and opponents who must check it, this stalemate can be viewed from at least two perspectives: either Mochizuki is not trying hard enough as a proponent, or the mathematical community is not trying hard enough as opponent.
[Mochizuki] has also criticised the rest of the community for not studying his work in detail, and says most other mathematicians are "simply not qualified" to issue a definitive statement on the proof unless they start from the very basics of his theory.
Some mathematicians say Mochizuki must do more to explain his work, like simplifying his notes or lecturing abroad.
(Of course, it may well be that both are the case!). And so for now, the proof remains in limbo, as well put by the New Scientist piece. Mathematics, oh so human!

What meaning can and cannot be: Lessons from real life, Part 1

Nearly a decade and a half ago, before logic bewitched me and I fell under her spell, I started off graduate school intending to write a dissertation on something related to philosophy of fiction or fictional discourse (given that that's how specific my dissertation plans were for my first 1-2 years of grad school, I probably should've realized sooner that this was not the topic for me). This year I'm lucky enough to be teaching a 3rd-year undergrad course "Language & Mind" which has reminded me why I was interested in what philosophy can say about fiction, and vice versa, in the first place. For my inaugural contribution to M-Phi, this post will be the first in an (unbounded) series of reflections on what meaning can and cannot be, given the constraints of how language is actually used, both in real and fictional discourse.

It is one thing for a theory of meaning to give an account of simple declarative sentences which are grammatically correct and whose terms refer to existing, uncontroversial objects: "Snow is white" should not be a difficult sentence to analyse if one is to give a theory of meaning of English. It is yet another thing altogether to be able to handle the edge cases, the non-simple, the non-declarative, the non-grammatically correct sentences, the sentences which have non-referring terms, and unfortunately many theories of meaning stumble at these hurdles, providing answers that are hard to swallow. (Note: I am not one who generally thinks that when there is a clash between what a philosophical theory says and what my intuitions say, it is the intuitions that should win. I've been a philosopher long enough to know that my intuitions in some respect are utterly ruined. However, if my philosophical theory entails a conclusion that is at odds with how people think and act about the relevant subject matter, then I do feel entitled to ask my theory to explain why it is there is this discrepancy. In this, I think St. Anselm of Canterbury's approach to the division between logic and grammar was precisely right. To oversimplify it significantly: Grammar is about how people use language, logic is about how people should use language, but more than that, logic should also be able to explain why it is that grammar and logic diverge: Logic should be able to explain why the usus loquendi does not always match the usus proprie.) It is the edge cases that provide the true test for any philosophical theory, and thus it is edge cases that I'll be discussing in this series.

I started off the "Language & Mind" class with two questions, which have become the guiding questions of the class, and three quotes. The questions are:

  1. What is meaning?
  2. What are the preconditions for language to have meaning?

And the quotes:

Quote 1

Anadûnê zîrâ hikallaba //

Êphal ê phalak îdôn hi-Akallabêth.

Quote 2

A threigylgweith yd oed yn Arberth, prif lys idaw adyuot yn y uryt ac yn y uedwl uynet y hela.

Quote 3

I expect the average reader of this blog to recognize the language of at least one of these three, but I would be very surprised if anyone knew all three.

Quote 1 is Adûnaic, and translated into English reads:

Numenor the beloved, she fell down //

Far, far away now is She-that-hath-fallen.

Adûnaic is one of the languages created by J.R.R. Tolkien, the most full account of it appearing in "Lowdham's Report on the Adunaic Language", in Sauron Defeated, ed. Christopher Tolkien, p. 413-440. (An overview of the language can be found here). Tolkien's invented languages are well-known for the attention to detail and realistic grammatical and phonological structures that they have, unlike many other fictional languages which are made up in a piecemeal fashion without any attempt to make them mirror non-fictional languages in structure or complexity.

Quote 2 is Welsh, and translated into English reads:

Once upon a time he [Pwyll] was at Arberth, a chief court of his, and he was seized by the thought and the desire to go hunting.

This is the opening line of the story of Pwyll, Prince of Dyfedd, in the Mabinogion, a cycle of prose literature compiled in the 12th-13th C from oral tales.

Quote 3 is a votive inscription in Linear A, adapted from here. Linear A is one of the last remaining undeciphered writing systems of ancient Greece. This quote cannot currently be translated.

I chose these three quotes because each of them places different constraints on what meaningfulness can be, where it can come from, and how we must account for it.

The Adûnaic and Welsh quotes are clearly meaningful, as it is possible to translate them into meaningful sentences in English which can be understood even if the original quotes could not be. The status of the quote in Linear A is less clear: It could be argued (and indeed, students in my class did so!) both that Linear A, given that there is no one alive who can understand or decipher it, is therefore meaningless, and that if it were to be deciphered, then it would regain its previous meaningfulness; or it could be argued (and again, I had students willing to take up this side) that it is meaningful, even in the absence of anyone who can understand that meaning, and thus meaning is something which is intrinsic to a language itself, and not dependent on the people who use the language.

However, while Adûnaic and Welsh are certainly on the one hand opposed from Linear A, on other hand they are opposed from each other. Adûnaic, as a constructed rather than natural language, has a definitive moment of creation or inception, and even if it evolved as it was developed, its development is still governed by the arbitration of a single person. Now that that person is dead, that standard of arbitration is gone: There are questions about Adûnaic that are left essentially unanswerable, questions of both vocabulary, grammar, and pronunciation. Welsh, on the other hand, did not have its birth at the hands of a single person, and as a result, there is a standard that can be appealed to for arbitration, whether this be the sum of its uses in the medieval period (if it is Old or Middle Welsh that is of interest), its use amongst Welsh speakers today, the proclamations of some canonical language academy (Welsh doesn't have one; but French and other languages do). No one single person has the authority to say what is meaningful and correct and what is not, and yet these questions can still be answered, unlike the case of Adûnaic.

The lesson in this post will be short and simple, since the post itself has gotten rather long, and it is this: The varieties of language which a theory of meaning must account for is perhaps broader and more diverse than people who are used to thinking of what it means for an English sentence to be meaningful are aware. In a future post (perhaps the next one), we'll look closer at the case of Adûnaic, and the problems that a truth-conditional theory of semantics would face in accounting for the (apparent) meaningfulness of that language.


© 2015, Sara L. Uckelman.