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https://consequently.org/news/
Thu, 14 Nov 2019 20:01:45 +1100https://consequently.org/news/Teaching Logical Methods
https://consequently.org/news/2019/teaching-logical-methods/
Thu, 14 Nov 2019 20:01:45 +1100https://consequently.org/news/2019/teaching-logical-methods/<p>It’s been a <em>big year</em>. At the start of 2019, <a href="https://shawn-standefer.github.io">Shawn Standefer</a> and I decided to throw all our cards in the air and upend the curriculum for the <a href="https://consequently.org/class/2019/PHIL20030">Level 2 logic unit</a> in the philosophy program here at Melbourne. We wrote 200 pages of a draft textbook (while I really should have been finishing my <a href="http://consequently.org/writing/ptrm">other book</a>). Shawn designed and implemented a whole raft of multiple choice practice questions, and we worked on a range of class activities to help our class of 60 students grapple with the material. I recorded hours of video lectures covering the content. We stuffed all of this into the <a href="https://lms.unimelb.edu.au">LMS</a>. And we spent hours in the classroom teaching 60 students the ins and outs of proof theory and model theory for propositional logic, modal logic (including two-dimensional modal logic), and first-order predicate logic. Like I said, it was a <em>big year</em> putting all of this together. Now we’ve wrapped up our first semester teaching the new unit, so we can sit back, breathe and reflect on how things went.</p>
<p>While I was taking that breath and thinking about how things went, Liam Kofi Bright posted <a href="https://sootyempiric.blogspot.com/2019/11/just-humble-philosopher.html">a thoughtful reflection</a> on what he hopes to achieve when he teaches formal methods to his students at the LSE. Our aims for our logic class were similar to Liam’s, but we come at things from a slightly different angle. Since I found reading Liam’s reflections helpful, it makes sense to put my thoughts down in public, in case others might benefit in some way.</p>
<p>Our <a href="https://consequently.org/class/2019/PHIL20030">Logical Methods</a> unit is unashamedly a <em>logic</em> class. (We don’t try to teach the wide range of formal methods. There’s no probability calculus, decision theory or anything beyond <em>logic</em>.) Our subject is designed for philosophy students, though at least a third of the enrolment were students coming from other majors, and even other degree programs. Still, our aim was to give philosophy students the skills and the vocabulary from logic that they will find useful in the rest of their engagement with philosophy, but at the same time, get a sense of logic as a field of philosophical reflection all of its own. Yes, we wanted students to come away able to both construct proofs and make models in formal systems for propositional, modal and predicate logic, and to get a real feel for what we can <em>do</em> with proofs and with models, and how we can use tools from logic—from proof theory and from model theory—to understand and analyse arguments, and to explain and explore the connections between the claims we make. One of our aims was for students to acquire (or strengthen) some logical reflexes. To become familiar with basic inference principles, and to become comfortable with combining them. To get a sense of how to build a model and to construct a counterexample to an argument. To understand what kinds of moves are appropriate when reasoning about possibility or necessity, or with the quantifiers, and what kinds of mistakes you can make if you fail to pay attention to scope distinctions and ambiguity. These reflexes are useful when it comes to philosophical reflection, and it’s good to have a place to practice with them in their own right, before wielding them out in the Real World of other philosophy tutorials.</p>
<p>But in addition to those useful skills, we wanted to give the class a sense of some of the active debates in contemporary work in logic. Since Shawn and I are pluralists and not partisans by temperament, it was natural to us to introduce both intutitionistic logic (when we started venturing into propositional logic with Prawitz-style natural deduction as our account of proofs) and classical logic (when we introduced boolean valuations and truth tables as our account of models). This makes the mismatch between validity-as-given-by-proofs and validity-as-given-by-absence-of-counterexample a problem to be investigated. Do we close the gap by adding more proofs, or by adding more models, or do we live with this gap? That is a question that is worth asking, since working out an answer helps you articulate what sorts of things proofs and models are <em>for</em>. So, we tried to set up the curriculum so that students could understand proofs and models well enough to be able to both use those techniques whenever they’re doing reasoning, and then also to understand the kinds of questions that occupy those of us who work in these areas now.</p>
<p>In <a href="https://sootyempiric.blogspot.com/2019/11/just-humble-philosopher.html">his reflections</a>, Liam described the tension between the two distinct aims of helping students overcome ‘math anxiety’ on the one hand, and helping induce wonder and humility before the world’s complexities, on the other. There is something curious about the seeming opposition between these two goals, but as I thought about Liam’s piece, it struck me that I have never experienced these two goals to be in any way opposed in practice. If you think of logic as some finite collection of simple tools and techniques to be practiced and honed and mastered (like, say, learning the alphabet, or the addition and multiplication tables for the numbers from 1 to 12—or the truth tables for the boolean connectives), then once you’ve dealt with your math anxiety, there would be no humility before any awesome complexity, because the field would be all rather humdrum. But that’s not how logic has developed, and to stay at the level of multiplication tables (or boolean truth tables) is to miss out on what logic has become, and to be blind to the enormous range of the kinds of questions we are able to ask, and which we’re fortunate enough to occasionally be able to answer.</p>
<p>Liam’s reflections pointed me to a nice paper by <a href="https://www.nacadajournal.org/doi/abs/10.12930/0271-9517-10.1.47">Sheila Tobias</a> on “math anxiety”. According to Tobias’ research, the significant variables associated with students’ inability to do college level mathematics are (1) fear, (2) the belief that mathematics is a white male domain, and (3) the belief that you are either good at mathematics or good at languages and never both. These concerns ring true to my experience of dealing with student concerns about logic teaching. To those worries, I will add another concern that turns discourages many from doing logic: (4) the belief that <a href="http://web.apsanet.org/cswp/wp-content/uploads/sites/4/2015/08/bian-lin-et-al.-gender-stereotypes-abt-intell-ability-emerge-early-Science-Jan-2017.pdf">to do well in philosophy <em>or</em> mathematics you have to be <em>brilliant</em></a>. Worries like these have been on my mind for some time.</p>
<p>We’ve tried to design a subject that addresses concerns like these. We are nowhere near done with them–especially addressing the gender and race issues–but the results of our initial steps have been encouraging. Here is a little of what we’ve done so far.</p>
<ul>
<li><p><em>On the brilliance effect</em>: At every stage of learning a new technique or method or result, we try to operationalise what you need to learn, and to break these things down into practice tasks. When we teach the basics of natural deduction, there are separate tasks involving (<em>a</em>) reading proofs, (<em>b</em>) checking proofs to spot mistakes, (<em>c</em>) filling in the gaps in proofs, (<em>d</em>) making your own proofs. We don’t throw students into the deep end, hoping that they’ll “get it.” Whenever there are separable components to a skill, we break things down, bit by bit, and slowly build them up. We show what you need to learn in able to do something well, and then we give them tasks to practice. To master this stuff, you don’t need to just “get it”. There are skills to learn and practice, and you can get there if you put in the time and the work. Thanks to Shawn’s work on the Learning Management System, we have a range of practice exercises that students can hack away at, getting quick feedback on their work. Regular checkpoints show when a student has mastered reading proofs, or writing their own, checking truth in a model, or identifying facts about logical consequence.</p>
<p>This is one place where logic has it relatively easy, compared to other areas in philosophy. It’s a disciplinary norm to define things precisely and work things out piece by piece. It’s our job as educators to introduce those concepts in a manageable way. If we do that well, we <em>show</em> as well as <em>say</em> that these are tools and techniques that can be mastered by practice.</p></li>
<li><p><em>On the perceived difference between linguistic and mathematical expertise</em>: Here we try to use a range of different metaphors and explanatory strategies to explain what we’re doing when we’re doing formal logic. Thankfully, it is relatively easy to make clear that we’re not doing <em>mathematics</em> in the sense of doing a lot of calculations or heavy duty algebra. We’re up front that we teach <em>formal</em> logic, but we’re careful to explain that patterns are everywhere, and not just in mathematics classes. Here, the example of our colleagues in linguistics is helpful to us. We explain that we’re looking at human activities of speaking, thinking and representing, and identifying patterns and structures that recur in what we can <em>say</em> and <em>mean</em>, in order to activate the imagination and expertise of those who are confident with language.</p>
<p>Given that we have an interdisciplinary class (some from the Sciences, but most are Humanities students), we try to walk both sides of the street when it comes to explanatory metaphors. Instead of always talking about algorithms or programs, we describe things as recipes or routines. When we talk about model building, sometimes we emphasise the routine and the systematic, but we also describe specifying a model as an act of imagination, engaging our creativity. Given that the entire subject is built around the duality between proof theory and model theory, we take the perspective-switching nature of looking at a phenomenon from more than one side <em>seriously</em>, so it comes naturally to attempt to describe things in more than one way.</p></li>
<li><p><em>On gender and race</em>: Here we have much more to do than what we’ve done so far. We own the fact that we have taught the subject as two white males. It is a challenge for us to expand our citations beyond the usual small circle of white male experts, but we’ve expanded it just a little. We point to women logicians along the way, and our students’ final project involved the logic and metaphysics of putting together modal logic and first-order predicate logic, it focussed on Ruth Barcan Marcus and the Barcan formulas. So, we put her work front and centre as the culmination of the semester. There is much more to be done–especially on decolonising our curriculum–but the results of these tiny steps have been encouraging so far. With all the changes we made, our retention rate for non-male students was <em>significantly</em> higher than it has been in previous years. The class is still male dominated, but significantly less so than in previous occasions.</p></li>
<li><p><em>On fear</em>: We have not measured students’ anxiety or fears in any way, but we’ve attempted to address that fear in a number of ways. We are fortunate, at Melbourne, to have very good undergraduate students. They are smart, and they are engaged and they are willing to put in the work. So we explain that the subject will involve effort, but that the effort will pay off if they put in the time. We structured the assessments to be predictable and manageable. Not only were the practice tasks broken down into bite-size repeatable skills to master. We assessed them on the same basis. At four points through the semester, there was a multiple choice test, worth 15% of their final score, on just these skills. They weren’t all <em>easy</em> (they added up to some quite challenging tasks) but they were manageable, they were predictable and most importantly, they <em>weren’t an exam</em>. 60% of the assessment task could be done by grinding out effort. It is a way to manage the fear of not “getting it”.</p>
<p>The remaining 40% of the assessment was two projects. The second project was on quantified modal logic and Ruth Barcan Marcus, as I mentioned, and the first was on truth tables and proofs for three-valued logics, and the ways these could be used to model different sorts of phenomena. Both of these projects were clearly related to the work they’d done in class, but they allowed students to reach beyond what they’d practiced, and learn to apply their skills in different environments. The results have been much better than we had expected they’d be. The students loved being stretched, they took things seriously, and wrote quality work. Passing turned out to be relatively easy, if they put in the effort to grind. Then with the fear of passing dealt with, they could make the effort to excel if they wanted to. From the looks of it, almost all of them <em>really</em> wanted to excel, and many of them have.</p></li>
</ul>
<p>So, that’s been our experience of teaching logical methods in 2019. It’s been a wild ride, and it’s been such a pleasure to be on that ride with <a href="https://shawn-standefer.github.io">Shawn</a> and 60 willing students. Thanks to friends and colleagues, like <a href="http://davewripley.rocks">Dave Ripley</a>, François Schroeter, Allen Hazen, and my current and former graduate students, Kai, Timo, Lian, John, Sakinah and Adam who have helped us sort out some of our thinking about these issues.</p>
Presentations
https://consequently.org/presentation/
Mon, 01 Jan 0001 00:00:00 UTChttps://consequently.org/presentation/What's So Special About Logic? Practices, Rules and Definitions
https://consequently.org/presentation/2019/whats-so-special-about-logic-logicmelb/
Thu, 31 Oct 2019 00:00:00 UTChttps://consequently.org/presentation/2019/whats-so-special-about-logic-logicmelb/<p><em>Abstract</em>: Over the last century or so, the discipline of logic has grown and transformed into a powerful set of tools and techniques that find their use in fields as far apart as philosophy, mathematics, computer science, electrical engineering and linguistics. Is there anything distinctive about logic and its results, or is it just another kind of abstract mathematics, or another kind of empirical scientific theory? In this talk I’ll explain why the distinctive subject matter of logical theory means that the tools of logic (<em>proofs</em> and <em>models</em>) can play a special role in our thought and in our talk. This explanation will turn crucially on our practices of assertion and denial, and how it can constrain those practices by using rules and definitions.</p>
<ul>
<li><p>The talk is an presentation at <a href="https://philevents.org/event/show/76846">Melbourne Logic Day 2019</a>.</p></li>
<li><p>The <a href="https://consequently.org/slides/whats-so-special-about-logic-logicmelb.pdf">slides for the talk are available here</a>.</p></li>
</ul>
Assertions, Denials, Questions, Answers, and the Common Ground
https://consequently.org/presentation/2019/assertion-denial-qa-common-ground-arche/
Sun, 29 Sep 2019 00:00:00 UTChttps://consequently.org/presentation/2019/assertion-denial-qa-common-ground-arche/<p><em>Abstract</em>: In this talk, I examine some of the interconnections between norms governing assertion, denial, questions and answers, and the common ground of a discourse. When we pay attention to the structure of norms governing polar (yes/no) questions, we can clarify the distinction between strong and weak denials, together with the parallel distinction between strong and weak assertion, and the way that these speech acts interact with the common ground.</p>
<p>With those connections established, I respond to two criticisms of the program sketched out in my 2005 paper “Multiple Conclusions”. First, that understanding the upshot of a valid sequent <em>X</em> ⊢ <em>Y</em> as enjoining us to not assert each member of <em>X</em> and deny each member of <em>Y</em> is altogether too weak to explain the inferential force of logical validity. Deriving <em>X</em> ⊢ <em>A</em> should tell us, after all, something about justifying <em>A</em> on the basis of <em>X</em>, rather than merely prohibiting <em>A</em>’s denial. Where is the force to actually conclude the conclusion of a proof? A second, related criticism is that the format of multiple conclusion sequents seems unsatisfactory, in that it has no place for distinguishing a single conclusion, and proofs, after all, seem to be proofs of individual claims.</p>
<p>I will argue that both of these concerns can be assuaged if we pay closer attention to the norms connecting assertions and denials along with <em>justification requests</em> – questions aiming at eliciting reasons for assertions or denials. Once we understand the connection between justification requests, definitionsand the common ground, we will see not only that the these two concerns can be met. A derivation of a sequent <em>X</em> ⊢ <em>A</em>,<em>Y</em> gives us an answer to a justification request “why <em>A</em>?” in any available context where each member of <em>X</em> has been ruled in and each member of <em>Y</em> has been ruled out, and a derivation of a sequent <em>X</em>,<em>B</em> ⊢ <em>Y</em>, similarly gives us an answer to the justification request “why not <em>B</em>?” in any such context. The picture that results utilises the full multiple premise, multiple conclusion sequent calculus of classical logic, and does due justice to the idea that a proof (or a refutation) proves (or refutes) <em>one thing</em> relative to background assumptions or premises. In addition, when we consider the connection between justification requests and the norms governing <em>definitions</em>, we can see more clearly what could be involved in taking the connective/quantifier rules of a logical system to <em>define</em> the concepts they introduce.</p>
<ul>
<li><p>The talk is a presentation at the Metaphysics and Logic Group seminar at Arché at the University of St Andrews.</p></li>
<li><p>The <a href="https://consequently.org/slides/assertion-denial-qa-common-ground-slides-arche.pdf">slides for the talk are available here</a>, and the <a href="https://consequently.org/handouts/assertion-denial-qa-common-ground-handout-arche.pdf">handout is here</a>.</p></li>
</ul>
Collection Frames for Substructural Logics
https://consequently.org/presentation/2019/collection-frames-lancog-lisbon/
Tue, 24 Sep 2019 00:00:00 UTChttps://consequently.org/presentation/2019/collection-frames-lancog-lisbon/<p><em>Abstract</em>: In this talk I present a new frame semantics for positive substructural and relevant propositional logics. This frame semantics is both a <em>generalisation</em> of Routley–Meyer ternary frames and a <em>simplification</em> of them. The key innovation is the use of a single accessibility relation to relate collections of points to points. Different logics are modelled by varying the kinds of collections featuring in the relation: for example, they can be sets, multisets, lists or trees. In this talk I will focus on multiset frames, which are sound and complete for the logic RW+ (positive multiplicative and additive linear logic with distribution for the additive connectives, or equivalently, the relevant logic R+ without contraction).</p>
<p>This is joint work with Shawn Standefer.</p>
<ul>
<li><p>The talk is a presentation at the <a href="http://cful.letras.ulisboa.pt/events/workshop-on-substructural-logics/">LanCog Workshop on Substructural Logics</a> at the Facultate de Letras at the University of Lisbon.</p></li>
<li><p>The <a href="https://consequently.org/slides/collection-frames-talk-lancog-lisbon.pdf">slides for the talk are available here</a>.</p></li>
</ul>
Classes
https://consequently.org/class/
Mon, 01 Jan 0001 00:00:00 UTChttps://consequently.org/class/PHIL40013: Uncertainty, Vagueness and Disagreement
https://consequently.org/class/2019/phil40013/
Wed, 24 Jul 2019 00:00:00 UTChttps://consequently.org/class/2019/phil40013/<p><strong><span class="caps">PHIL40013</span>: Uncertainty, Vagueness and Disagreement</strong> is a <a href="http://unimelb.edu.au">University of Melbourne</a> honours seminar subject for fourth-year students. Our aim in the Honours program is to introduce students to current work in research in philosophy of logic and language.</p>
<p>In 2019, we’re covering the connections between speech acts, epistemology and normative theory.</p>
<ol>
<li><strong>Introduction and overview, background</strong></li>
<li><strong>Speech acts: what are they?</strong>
<ul>
<li>J. L. Austin, <em>How to Do things with Words</em>, Clarendon Press,
Oxford, 1962. [<strong><em>Read Lecture 9</em></strong>]</li>
<li>H. P. Grice, “Logic and Conversation,” pages 41–58 in <em>Syntax and
Semantics</em>: <em>Speech Acts</em>, edited by P. Cole and J. L. Morgan,
Academic Press, New York, 1975.</li>
<li>Sarah E. Murray and William B. Starr, “<a href="http://dx.doi.org/10.1093/oso/9780198738831.003.0009">Force and Conversational States</a>,” pages 202–236 in <em>New Work on Speech Acts</em>, edited by Daniel Fogal, Daniel Harris and Matthew Moss, Oxford University Press, 2018. [<strong><em>Read Sections 9.1 and 9.2</em></strong>]</li>
<li>Nuel Belnap “<a href="http://dx.doi.org/10.1007/BF00368389">Declaratives are not Enough</a>”, <em>Philosophical Studies</em> 59:1 (1990) 1–30.</li>
<li>Mark Lance and Rebecca Kukla “<a href="http://dx.doi.org/10.1086/669565">Leave the Gun; Take the Cannoli! The Pragmatic Topography of Second-Person Calls</a>” <em>Ethics</em> 123:3 (2013) 456–478.</li>
<li>Mark Lance and Rebecca Kukla <em>Yo! and Lo! The Pragmatic Topography of the Space of Reasons,</em> Harvard University Press, 2009. [<strong><em>Read Chapter 1</em></strong>]</li>
<li>Craige Roberts “<a href="http://dx.doi.org/10.1093/oso/9780198738831.001.0001">Speech Acts in Discourse Context</a>”, pages 317–359 in <em>New Work on Speech Acts</em>, edited by Daniel Fogal, Daniel Harris and Matthew Moss, Oxford University Press, 2018.</li>
</ul></li>
<li><strong>Assertion</strong>
<ul>
<li>John Macfarlane, “<a href="http://dx.doi.org/10.1093/acprof:oso/9780199573004.001.0001">What is Assertion?</a>” pages 79–96 in <em>Assertion</em>:
<em>New Philosophical Essays</em>, edited by Jessica Brown and Herman
Cappelen, Oxford University Press, 2011.</li>
<li>Ishani Maitra, “<a href="http://dx.doi.org/10.1093/acprof:oso/9780199573004.001.0001">Assertion, Norms, and Games</a>” pages 277–296 in
<em>Assertion</em>: <em>New Philosophical Essays</em>, edited by Jessica Brown and
Herman Cappelen, Oxford University Press, 2011.</li>
<li>Jennifer Lackey, “<a href="http://dx.doi.org/10.1111/j.1468-0068.2007.00664.x">Norms of Assertion</a>,” <em>Noûs</em> 41:4 (2007) 594–626.</li>
<li>Rachel Mckinnon, <em>The Norms of Assertion</em>: <em>Truth, Lies, and Warrant,</em> Palgrave, 2015.</li>
<li>Peter Pagin, “<a href="http://plato.stanford.edu/archives/spr2015/entries/assertion/">Assertion</a>”, <em>The Stanford Encyclopedia of Philosophy,</em> 2015.</li>
</ul></li>
<li><strong>Common Ground and Accommodation</strong>
<ul>
<li>Robert Stalnaker, “<a href="http://dx.doi.org/10.1023/A:1020867916902">Common Ground</a>,” <em>Linguistics and Philosophy</em> 25:5–6 (2002) 701–721.</li>
<li>Mandy Simons, “<a href="http://dx.doi.org/10.1023/A:1023004203043">Presupposition and Accommodation: Understanding the Stalnakerian Picture</a>,” <em>Philosophical Studies</em> 112:3 (2003) 251–278.</li>
<li>Craige Roberts, “<a href="https://onlinelibrary-wiley-com/doi/pdf/10.1002/9781118398593.ch22">Accommodation in a Language Game</a>”, pages 345–366 in <em>A Companion to David Lewis</em>, edited by Barry Loewer and Jonathan Schaffer, John Wiley & Sons, Ltd., 2015.</li>
<li>David Lewis, “<a href="http://dx.doi.org/10.1007/BF00258436">Scorekeeping in a Language Game</a>”, <em>Journal of Philosophical Logic</em> 8:1 (1979) 339–359.</li>
<li>Paal Antonsen, “<a href="http://dx.doi.org/10.1093/analys/anx145">Scorekeeping</a>”, <em>Analysis</em> 78:4 (2018) 589–595.</li>
</ul></li>
<li><strong>Cooperation, Convention and Norms</strong>
<ul>
<li>Sarah E. Murray and William B. Starr, “<a href="http://dx.doi.org/10.1093/oso/9780198738831.003.0009">Force and Conversational States</a>,” pages 202–236 in <em>New Work on Speech Acts</em>, edited by Daniel Fogal, Daniel Harris and Matthew Moss, Oxford University Press, 2018. [<strong><em>Read Sections 9.3 to 9.5</em></strong>]</li>
<li>Cristina Bicchieri, <em>The Grammar of Society</em>: <em>the nature and dynamics of social norms</em>, Cambridge University Press, 2006. [<strong><em>Read Chapter 1</em></strong>]</li>
<li>Cristina Bicchieri, <a href="http://dx.doi.org/10.1093/acprof:oso/9780190622046.001.0001"><em>Norms in the Wild</em>: <em>how to diagnose, measure, and change social norms</em></a>, Oxford University Press, 2017.</li>
</ul></li>
<li><strong>Stereotypes and Generics</strong>
<ul>
<li>Sarah-Jane Leslie, “<a href="http://dx.doi.org/10.1111/j.1520-8583.2007.00138.x">Generics and the Structure of the Mind</a>,” <em>Philosophical Perspectives</em> 21:1 (2007) 375–403.</li>
<li>Sally Haslanger, “<a href="http://dx.doi.org/10.1007/978-90-481-3783-1_11">Ideology, Generics, and Common Ground</a>,” pages 179–207 in <em>Feminist Metaphysics</em>: <em>Explorations in the Ontology of Sex, Gender and the Self</em>, edited by Charlotte Witt, Springer, Dordrecht, 2011.</li>
<li>Rachel Katharine Sterken, “<a href="http://dx.doi.org/10.1111/phc3.12431">The Meaning of Generics</a>” <em>Philosophy Compass,</em> 12:8 (2017) e12431.</li>
<li>Jennifer Saul, “<a href="http://dx.doi.org/10.1080/0020174x.2017.1285995">Are Generics Especially Pernicious?</a>” <em>Inquiry,</em> advance access (2019), 1–18.</li>
</ul></li>
<li><strong>Authority and Epistemic Territory</strong>
<ul>
<li>Jennifer Nagel, “<a href="http://dx.doi.org/10.1017/epi.2015.4">The Social Value of Reasoning in Epistemic
Justification</a>,” <em>Episteme</em> 12:2 (2015) 297–308.</li>
<li>John Heritage, “<a href="http://dx.doi.org/10.1080/08351813.2012.646684">Epistemics in Action: Action Formation and Territories of Knowledge</a>,” <em>Research on Language and Social Interaction</em> 45:1 (2012) 1–29.</li>
<li>Akio Kamio, <em>Territory of Information,</em> John Benjamins, 1997.</li>
<li>Hugo Mercier and Dan Sperber, “<a href="http://dx.doi.org/10.1017/s0140525x10000968">Why do Humans Reason? Arguments for an argumentative theory</a>,” <em>Behavioral and Brain Sciences</em> 34:2 (2011) 57–74.</li>
</ul></li>
<li><strong>Illocutionary Silencing</strong>
<ul>
<li>Rae Langton, “<a href="https://www-jstor-org/stable/2265469">Speech Acts and Unspeakable Acts</a>,” <em>Philosophy</em> & <em>Public Affairs</em> 22:4 (1993) 293–330.</li>
<li>Ishani Maitra, “<a href="https://www-jstor-org/stable/27822050">Silencing Speech</a>,” <em>Canadian Journal of Philosophy</em> 39:2 (2009) 309–338.</li>
<li>Alessandra Tanesini, “<a href="http://aristoteliansupp.oxfordjournals.org/content/90/1/71">“Calm Down, Dear”: Intellectual Arrogance,
Silencing and Ignorance</a>,” <em>Aristotelian Society Supplementary Volume</em> 90:1 (2016) 71–92.</li>
<li>Alexander Bird, “<a href="https://doi-org/10.1111/1468-0114.00137">Illocutionary Silencing</a>,” <em>Pacific Philosophical Quarterly</em> 83:1 (2002) 1–15.</li>
<li>Mari Mikkola, “<a href="http://dx.doi.org/10.1111/j.1468-0114.2011.01404.x">Illocution, Silencing and the Act of Refusal</a>,” <em>Pacific Philosophical Quarterly</em> 92:3 (2011) 415–437.</li>
<li>Kristie Dotson, “<a href="http://dx.doi.org/10.1111/j.1527-2001.2011.01177.x">Tracking Epistemic Violence, Tracking Practices of Silencing</a>,” <em>Hypatia</em> 26:2 (2011) 236–257.</li>
</ul></li>
<li><strong>Gaslighting</strong>
<ul>
<li>Kate Abramson, “<a href="http://dx.doi.org/10.1111/phpe.12046">Turning up the Lights on Gaslighting</a>,” <em>Philosophical Perspectives</em> 28:1 (2014) 1–30.</li>
<li>Kate Manne, <a href="http://dx.doi.org/10.1093/oso/9780190604981.001.0001"><em>Down Girl</em>: <em>the logic of misogyny</em></a>, Oxford
Univeristy Press, 2018. [<strong><em>Read Chapter 1</em></strong>]</li>
<li>Andrew D. Spear, “<a href="http://dx.doi.org/10.1007/s11245-018-9611-z">Gaslighting, Confabulation, and Epistemic
Innocence</a>,” <em>Topoi</em> early access (2018).</li>
<li>Cynthia A. Stark, “<a href="http://dx.doi.org/10.1093/monist/onz007">Gaslighting, Misogyny, and Psychological
Oppression</a>,” <em>The Monist</em> 102:2 (2019) 221–235.</li>
</ul></li>
</ol>
<p>For further information, contact me. To participate, check <a href="https://handbook.unimelb.edu.au/view/2019/PHIL40013">the handbook</a>.</p>
PHIL20030: Meaning, Possibility and Paradox
https://consequently.org/class/2019/phil20030/
Wed, 24 Jul 2019 00:00:00 UTChttps://consequently.org/class/2019/phil20030/
<p><strong><span class="caps">PHIL20030</span>: Meaning, Possibility and Paradox</strong> is a <a href="http://unimelb.edu.au">University of Melbourne</a> undergraduate subject introducing logic to philosophy students. It’s taught by <a href="http://consequently.org">Greg Restall</a> and <a href="https://shawn-standefer.github.io">Shawn Standefer</a>.</p>
<p>This year, we have completely revised our curriculum. Now the subject introduces the proof theory and model theory of propositional, modal and predicate logic–in that order. We’re writing an introductory text <em>Logical Methods</em>, which we’re trialling with this class, as well as producing explanatory videos to use along with the text.</p>
<p>Here’s the outline of the subject.</p>
<h3 id="preliminaries">Preliminaries</h3>
<ul>
<li>Introduction
<ul>
<li>Arguments and Trees</li>
<li>Sentences and Formulas</li>
</ul></li>
</ul>
<h3 id="propositional-logic">Propositional Logic</h3>
<ul>
<li>Connectives: and & if
<ul>
<li>Conjunction</li>
<li>Conditional</li>
<li>Biconditional</li>
</ul></li>
<li>More connectives: not & or
<ul>
<li>Negation and falsum</li>
<li>Disjunction</li>
<li>Our System of Proofs</li>
</ul></li>
<li>Facts about proofs & provability
<ul>
<li>Facts about provability</li>
<li>Normalisation</li>
<li>The Subformula Property</li>
<li>Consequences of Normalisation</li>
</ul></li>
<li>Models & counterexamples
<ul>
<li>Models and truth tables</li>
<li>Counterexamples and validity</li>
<li>Model-theoretic validity</li>
</ul></li>
<li>Soundness & completeness
<ul>
<li>Soundness</li>
<li>Completeness</li>
<li>Proofs first or models first?</li>
<li>Heyting algebras</li>
</ul></li>
</ul>
<h3 id="modal-logic">Modal Logic</h3>
<ul>
<li>Necessity & possibility
<ul>
<li>Possible worlds models</li>
<li>Validity</li>
<li>Strict conditionals and ambiguities</li>
<li>Propositions</li>
<li>Another notion of necessity</li>
<li>Equivalence relations and epistemic logic</li>
</ul></li>
<li>Actuality & two-dimensional logic
<ul>
<li>Actuality models and double indexing</li>
<li>Validity</li>
<li>Fixity and diagonal propositions</li>
<li>Real world validity</li>
</ul></li>
<li>Natural deduction for modal logics
<ul>
<li>Natural deduction for S4</li>
<li>Natural deduction for S5</li>
<li>Features of S5</li>
</ul></li>
</ul>
<h3 id="predicate-logic">Predicate Logic</h3>
<ul>
<li>Quantifiers
<ul>
<li>Syntax</li>
<li>Natural deduction for CQ</li>
<li>What is provable?</li>
<li>Generality and eliminating detours</li>
</ul></li>
<li>Models for first-order logic
<ul>
<li>Models and assignments of values</li>
<li>Substitution</li>
<li>Counterexamples and validity</li>
<li>Compactness and what this means</li>
</ul></li>
</ul>
<p>One novelty in our approach to the subject is the balance between proof theory and model theory. We introduce propositional logic by way of Gentzen/Prawitz-style natural deduction—for intuitionistic logic—and along the way, each time we introduce the rules for a connective, we show that they are in harmony. So, it’s not too hard to show that proofs in the whole system can be normalised and we get the subformula property for normal proofs. (So, we can gesture in the direction of provability being <em>analytic</em> in a strong sense, since a normal proof literally <em>analyses</em> the premises and conclusion into components and connects them using the fundamental rules governing the concepts involved.)</p>
<p>Once that’s done, we then introduce Boolean valuations (and truth tables), and we can show that the proof system is sound but not complete for validity defined as the absence of a Boolean counterexample. Approaching things this way means we have an interesting discussion about soundness and completeness, and about intuitionistic and classical logic, and whether we should be happy with the gap between proofs and models or not, and if not, whether we should close that gap by adding to our proof system (that way lies <em>classical</em> natural deduction), or whether we should close the gap by enriching our class of models to serve as counterexamples (here we sketch Heyting algebras, as generalisations of Boolean valuations, but we point to Kripke models, too). There’s also scope for a discussion of whether we should understand logic in a proof-first way or a model-first way (or both, or neither), and how proofs and models relate to however it is that words and concepts get their meanings.</p>
<p>With that done, we’re halfway through the subject. Having arrived at Boolean valuations, it’s a short hop, skip and jump to Carnap’s models for modality, and their generalisation, universal models for the modal logic S5. So, we look at these models for possibility and necessity, and show how these possible worlds models can be used to analyse modality, strict conditionality, and similar notions.</p>
<p>Then with models like these we can be of service to our colleagues by introducing double-indexing and two-dimensional modal logic, and the analysis of fixedly diagonal propositions, and the relationship between analyticity, necessity and <em>a priority</em>.</p>
<p>With these model-theoretic considerations in hand, we turn to the question of what it might be to <em>derive</em> a modal claim, and we turn to the natural deduction rules for modals, which introduce constraints on assumptions. One way to prove that \(A\) is necessary, after all, is to prove \(A\) from claims of the form \(\Box B\), for those claims hold not only <em>here</em>, but also in any alternate circumstances, too. So, we get natural deduction systems for S4 and S5 rather straightforwardly.</p>
<p>Proving something more <em>general</em> than \(A\) by proving \(A\) from premises satisfying certain conditions sounds familiar if you’ve dealt with <em>quantifiers</em> before. How to you show that <em>everything</em> is an \(F\)? By proving that \(Fa\) when we have assumed <em>nothing about \(a\)</em>. Then our proof applies <em>no matter what \(a\) is</em>. So, we can generalise the conditions for modal proof to proofs with <em>quantifiers</em> too. So, we introduce the logic of first-order quantifiers with natural deduction first, and once we’ve done that, we turn back to models at last.</p>
<p>So, the introduction to logic has a rhythm, taking us from proofs to models of propositional logic, through models and then proofs for modal logic, and then to proofs and models for predicate logic. Along the way we look at issues in the philosophy of logic and the applications of logic to different issues in philosophy.</p>
<p>Although this curriculum and the course material is all ours, we are indebted to our colleagues for many discussions concerning the pedagogy of logic. I’ll single out two here. Allen Hazen talked to GR for many years about the pedagogical virtues of introducing modal logic before predicate logic to philosophy students. And <a href="http://davewripley.rocks">Dave Ripley</a> has, for the last couple of years, introduced logic using intuitionistic natural deduction and classical truth tables, making a virtue out of the soundness and <em>in</em>completeness of the pairing between the proof theory and the model theory. Neither Allen nor Dave would teach things how we have, but we’ve valued talking over the pedagogy with them over the years.</p>
<p>If you’d like to compare your mastery of logic, in comparison to what our students are learning, you can try your own hand at our <a href="https://consequently.org/resources/PHIL20030-2019-class-tasks-1-6.pdf">in-class tasks for weeks 1 to 6</a>.</p>
Assertions, Denials, Questions, Answers, and the Common Ground
https://consequently.org/presentation/2019/assertion-denial-qa-common-ground-express/
Thu, 13 Jun 2019 00:00:00 UTChttps://consequently.org/presentation/2019/assertion-denial-qa-common-ground-express/<p><em>Abstract</em>: In this talk, I examine some of the interconnections between norms governing assertion, denial, questions and answers, and the common ground of a discourse. When we pay attention to the structure of norms governing polar (yes/no) questions, we can clarify the distinction between strong and weak denials, together with the parallel distinction between strong and weak assertion, and the way that these speech acts interact with the common ground.</p>
<p>With those connections established, I respond to two criticisms of the program sketched out in my 2005 paper “Multiple Conclusions”. First, that understanding the upshot of a valid sequent <em>X</em> ⊢ <em>Y</em> as enjoining us to not assert each member of <em>X</em> and deny each member of <em>Y</em> is altogether too weak to explain the inferential force of logical validity. Deriving <em>X</em> ⊢ <em>A</em> should tell us, after all, something about justifying <em>A</em> on the basis of <em>X</em>, rather than merely prohibiting <em>A</em>’s denial. Where is the force to actually conclude the conclusion of a proof? A second, related criticism is that the format of multiple conclusion sequents seems unsatisfactory, in that it has no place for distinguishing a single conclusion, and proofs, after all, seem to be proofs of individual claims.</p>
<p>I will argue that both of these concerns can be assuaged if we pay closer attention to the norms connecting assertions and denials along with <em>justification requests</em> — questions aiming at eliciting reasons for assertions or denials. Once we understand the connection between justification requests, definitionsand the common ground, we will see not only that the these two concerns can be met. A derivation of a sequent <em>X</em> ⊢ <em>A</em>,<em>Y</em> gives us an answer to a justification request “why <em>A</em>?” in any available context where each member of <em>X</em> has been ruled in and each member of <em>Y</em> has been ruled out, and a derivation of a sequent <em>X</em>,<em>B</em> ⊢ <em>Y</em>, similarly gives us an answer to the justification request “why not <em>B</em>?” in any such context. The picture that results utilises the full multiple premise, multiple conclusion sequent calculus of classical logic, and does due justice to the idea that a proof (or a refutation) proves (or refutes) <em>one thing</em> relative to background assumptions or premises. In addition, when we consider the connection between justification requests and the norms governing <em>definitions</em>, we can see more clearly what could be involved in taking the connective/quantifier rules of a logical system to <em>define</em> the concepts they introduce.</p>
<ul>
<li><p>The talk is an invited address at the <a href="https://inferentialexpressivism.com/workshop/">Workshop on Bilateral Approches to Meaning</a>, at the University of Amsterdam.</p></li>
<li><p>The <a href="https://consequently.org/slides/assertion-denial-qa-common-ground-slides-express.pdf">slides for the talk are available here</a>, and the <a href="https://consequently.org/handouts/assertion-denial-qa-common-ground-handout-express.pdf">handout is here</a>.</p></li>
</ul>
Assertions, Denials, Questions, Answers, and the Common Ground
https://consequently.org/presentation/2019/assertion-denial-qa-common-ground-mcmp/
Thu, 13 Jun 2019 00:00:00 UTChttps://consequently.org/presentation/2019/assertion-denial-qa-common-ground-mcmp/<p><em>Abstract</em>: In this talk, I examine interconnections between norms governing assertion, denial, questions and answers, and the common ground of a discourse. When we pay attention to the structure of norms governing polar (yes/no) questions, we can clarify the distinction between strong and weak denials, together with the parallel distinction between strong and weak assertion, and the way that these speech acts interact with the common ground.</p>
<p>With those connections established, I respond to two criticisms of the program sketched out in my 2005 paper “Multiple Conclusions”. First, that understanding the upshot of a valid sequent <em>X</em> ⊢ <em>Y</em> as enjoining us to not assert each member of <em>X</em> and deny each member of <em>Y</em> is altogether too weak to explain the inferential force of logical validity. Deriving <em>X</em> ⊢ <em>A</em> should tell us, after all, something about justifying <em>A</em> on the basis of <em>X</em>, rather than merely prohibiting <em>A</em>’s denial. Where is the force to actually conclude the conclusion of a proof? A second, related criticism is that the format of multiple conclusion sequents seems unsatisfactory, in that it has no place for distinguishing a single conclusion, and proofs, after all, seem to be proofs of individual claims.</p>
<p>I will argue that both of these concerns can be assuaged if we pay closer attention to the norms connecting assertions and denials along with <em>justification requests</em> — questions aiming at eliciting reasons for assertions or denials. Once we understand the connection between justification requests, definitionsand the common ground, we will see not only that the these two concerns can be met. A derivation of a sequent <em>X</em> ⊢ <em>A</em>,<em>Y</em> gives us an answer to a justification request “why <em>A</em>?” in any available context where each member of <em>X</em> has been ruled in and each member of <em>Y</em> has been ruled out, and a derivation of a sequent <em>X</em>,<em>B</em> ⊢ <em>Y</em>, similarly gives us an answer to the justification request “why not <em>B</em>?” in any such context. The picture that results utilises the full multiple premise, multiple conclusion sequent calculus of classical logic, and does due justice to the idea that a proof (or a refutation) proves (or refutes) <em>one thing</em> relative to background assumptions or premises. In addition, when we consider the connection between justification requests and the norms governing <em>definitions</em>, we can see more clearly what could be involved in taking the connective/quantifier rules of a logical system to <em>define</em> the concepts they introduce.</p>
<ul>
<li><p>The talk is a <a href="https://www.mcmp.philosophie.uni-muenchen.de/events_this-_week/restall_20190618/index.html">Seminar at the Munich Centre for Mathematical Philosophy</a>.</p></li>
<li><p>The <a href="https://consequently.org/slides/assertion-denial-qa-common-ground-slides-mcmp.pdf">slides for the talk are available here</a>, and the <a href="https://consequently.org/handouts/assertion-denial-qa-common-ground-handout-mcmp.pdf">handout is here</a>.</p></li>
</ul>
Assertions, Denials, Questions, Answers, and the Common Ground
https://consequently.org/presentation/2019/assertion-denial-qa-common-ground-logicmelb/
Thu, 06 Jun 2019 00:00:00 UTChttps://consequently.org/presentation/2019/assertion-denial-qa-common-ground-logicmelb/<p><em>Abstract</em>: In this talk, I examine some of the interconnections between norms governing assertion, denial, questions and answers, and the common ground of a discourse. When we pay attention to the structure of norms governing polar (yes/no) questions, we can clarify the distinction between strong and weak denials, together with the parallel distinction between strong and weak assertion, and the way that these speech acts interact with the common ground.</p>
<p>With those connections established, I respond to two criticisms of the program sketched out in my 2005 paper “Multiple Conclusions”. First, that understanding the upshot of a valid sequent <em>X</em> ⊢ <em>Y</em> as enjoining us to not assert each member of <em>X</em> and deny each member of <em>Y</em> is altogether too weak to explain the inferential force of logical validity. Deriving <em>X</em> ⊢ <em>A</em> should tell us, after all, something about justifying <em>A</em> on the basis of <em>X</em>, rather than merely prohibiting <em>A</em>’s denial. Where is the force to actually conclude the conclusion of a proof? A second, related criticism is that the format of multiple conclusion sequents seems unsatisfactory, in that it has no place for distinguishing a single conclusion, and proofs, after all, seem to be proofs of individual claims.</p>
<p>I will argue that both of these concerns can be assuaged if we pay closer attention to the norms connecting assertions and denials along with <em>justification requests</em> — questions aiming at eliciting reasons for assertions or denials. Once we understand the connection between justification requests, definitionsand the common ground, we will see not only that the these two concerns can be met. A derivation of a sequent <em>X</em> ⊢ <em>A</em>,<em>Y</em> gives us an answer to a justification request “why <em>A</em>?” in any available context where each member of <em>X</em> has been ruled in and each member of <em>Y</em> has been ruled out, and a derivation of a sequent <em>X</em>,<em>B</em> ⊢ <em>Y</em>, similarly gives us an answer to the justification request “why not <em>B</em>?” in any such context. The picture that results utilises the full multiple premise, multiple conclusion sequent calculus of classical logic, and does due justice to the idea that a proof (or a refutation) proves (or refutes) <em>one thing</em> relative to background assumptions or premises. In addition, when we consider the connection between justification requests and the norms governing <em>definitions</em>, we can see more clearly what could be involved in taking the connective/quantifier rules of a logical system to <em>define</em> the concepts they introduce.</p>
<ul>
<li><p>The talk is a <a href="https://philevents.org/event/show/73102">Melbourne Logic Seminar</a>.</p></li>
<li><p>The <a href="https://consequently.org/slides/assertion-denial-qa-common-ground-slides-logicmelb.pdf">slides for the talk are available here</a>.</p></li>
</ul>
Writings
https://consequently.org/writing/
Mon, 01 Jan 0001 00:00:00 UTChttps://consequently.org/writing/Proofs and Models in Naive Property Theory: A Response to Hartry Field's “Properties, Propositions and Conditionals”
https://consequently.org/writing/proofs-and-models-in-npt/
Tue, 02 Apr 2019 00:00:00 UTChttps://consequently.org/writing/proofs-and-models-in-npt/<p>In our response Field’s “Properties, Propositions and Conditionals”, we explore the methodology of Field’s program. We begin by contrasting it with a proof-theoretic approach and then commenting on some of the particular choices made in the development of Field’s theory. Then, we look at issues of property identity in connection with different notions of equivalence. We close with some comments relating our discussion to Field’s response to Restall’s “<a href="https://consequently.org/writing/stp/">What are we to accept, and what are we to reject, when saving truth from paradox?</a>”.</p>
Isomorphisms in a Category of Proofs
https://consequently.org/presentation/2019/isomorphisms-pts3/
Thu, 07 Mar 2019 00:00:00 UTChttps://consequently.org/presentation/2019/isomorphisms-pts3/<p><em>Abstract</em>: In this talk, I show how a category of classical proofs can give rise to three different hyperintensional notions of sameness of content. One of these notions is very fine-grained, going so far as to distinguish \(p\) and \(p\land p\), while identifying other distinct pairs of formulas, such as \(p\land q\) and \(q\land p\); \(p\) and \(\neg\neg p\); or \(\neg(p\land q)\) and \(\neg p\lor\neg q\). Another relation is more coarsely grained, and gives the same account of identity of content as equivalence in Angell’s logic of analytic containment. A third notion of sameness of content is defined, which is intermediate between Angell’s and Parry’s logics of analytic containment. Along the way, we show how purely classical proof theory gives resources to define hyperintensional distinctions thought to be the domain of properly non-classical logics.</p>
<ul>
<li>This is a talk at the <a href="http://ls.informatik.uni-tuebingen.de/PTS3/overview.html">Third Tübingen Conference on Proof-Theoretic Semantics</a>, 27–30 March 2019.</li>
<li>The slides are <a href="https://consequently.org/slides/isomorphisms-talk-tubingen-2019.pdf">available here</a>, while a handout <a href="https://consequently.org/handouts/isomorphisms-handout-tubingen-2019.pdf">is here</a>.</li>
</ul>
Collection Frames for Substructural Logics
https://consequently.org/presentation/2019/collection-frames-logicmelb/
Thu, 07 Mar 2019 00:00:00 UTChttps://consequently.org/presentation/2019/collection-frames-logicmelb/<p><em>Abstract</em>: In this talk I present a new frame semantics for positive substructural and relevant propositional logics. This frame semantics is both a <em>generalisation</em> of Routley–Meyer ternary frames and a <em>simplification</em> of them. The key innovation is the use of a single accessibility relation to relate collections of points to points. Different logics are modelled by varying the kinds of collections featuring in the relation: for example, they can be sets, multisets, lists or trees. In this talk I will focus on multiset frames, which are sound and complete for the logic RW+ (positive multiplicative and additive linear logic with distribution for the additive connectives, or equivalently, the relevant logic R+ without contraction).</p>
<p>This is joint work with Shawn Standefer.</p>
<ul>
<li><p>The talk is a <a href="https://philevents.org/event/show/69618">Melbourne Logic Seminar</a>.</p></li>
<li><p>The <a href="https://consequently.org/slides/collection-frames-talk-logicmelb.pdf">slides for the talk are available here</a>.</p></li>
</ul>
PHIL30043: The Power and Limits of Logic
https://consequently.org/class/2019/phil30043/
Sat, 02 Mar 2019 00:00:00 UTChttps://consequently.org/class/2019/phil30043/
<p><strong><span class="caps">PHIL30043</span>: The Power and Limits of Logic</strong> is a <a href="https://handbook.unimelb.edu.au/view/2019/PHIL30043">University of Melbourne undergraduate subject</a>. It covers the metatheory of classical first order predicate logic, beginning at the <em>Soundness</em> and <em>Completeness</em> Theorems (proved not once but <em>twice</em>, first for a tableaux proof system for predicate logic, then a Hilbert proof system), through the <em>Deduction Theorem</em>, <em>Compactness</em>, <em>Cantor’s Theorem</em>, the <em>Downward Löwenheim–Skolem Theorem</em>, <em>Recursive Functions</em>, <em>Register Machines</em>, <em>Representability</em> and ending up at <em>Gödel’s Incompleteness Theorems</em> and <em>Löb’s Theorem</em>.</p>
<figure>
<img src="https://consequently.org/images/godel.jpg" alt="Kurt Godel, seated">
<figcaption>Kurt Gödel, seated</figcaption>
</figure>
<p>The subject is taught to University of Melbourne undergraduate students (for Arts students as a part of the Philosophy major, for non-Arts students, as a breadth subject). Details for enrolment are <a href="https://handbook.unimelb.edu.au/view/2018/PHIL30043">here</a>. I make use of video lectures I have made <a href="http://vimeo.com/album/2262409">freely available on Vimeo</a>.</p>
<h3 id="outline">Outline</h3>
<p>The course is divided into four major sections and a short prelude. Here is a list of all of the videos, in case you’d like to follow along with the content.</p>
<h4 id="prelude">Prelude</h4>
<ul>
<li><a href="http://vimeo.com/album/2262409/video/59401942">Logical Equivalence</a></li>
<li><a href="http://vimeo.com/album/2262409/video/59403292">Disjunctive Normal Form</a></li>
<li><a href="http://vimeo.com/album/2262409/video/59403535">Why DNF Works</a></li>
<li><a href="http://vimeo.com/album/2262409/video/59463569">Prenex Normal Form</a></li>
<li><a href="http://vimeo.com/album/2262409/video/59466141">Models for Predicate Logic</a></li>
<li><a href="http://vimeo.com/album/2262409/video/59880539">Trees for Predicate Logic</a></li>
</ul>
<h4 id="completeness">Completeness</h4>
<ul>
<li><a href="http://vimeo.com/album/2262409/video/59883806">Introducing Soundness and Completeness</a></li>
<li><a href="http://vimeo.com/album/2262409/video/60249309">Soundness for Tree Proofs</a></li>
<li><a href="http://vimeo.com/album/2262409/video/60250515">Completeness for Tree Proofs</a></li>
<li><a href="http://vimeo.com/album/2262409/video/61677028">Hilbert Proofs for Propositional Logic</a></li>
<li><a href="http://vimeo.com/album/2262409/video/61685762">Conditional Proof</a></li>
<li><a href="http://vimeo.com/album/2262409/video/62221512">Hilbert Proofs for Predicate Logic</a></li>
<li><a href="http://vimeo.com/album/2262409/video/103720089">Theories</a></li>
<li><a href="http://vimeo.com/album/2262409/video/103757399">Soundness and Completeness for Hilbert Proofs for Predicate Logic</a></li>
</ul>
<h4 id="compactness">Compactness</h4>
<ul>
<li><a href="http://vimeo.com/album/2262409/video/63454250">Counting Sets</a></li>
<li><a href="http://vimeo.com/album/2262409/video/63454732">Diagonalisation</a></li>
<li><a href="http://vimeo.com/album/2262409/video/63454732">Compactness</a></li>
<li><a href="http://vimeo.com/album/2262409/video/63455121">Non-Standard Models</a></li>
<li><a href="http://vimeo.com/album/2262409/video/63462354">Inexpressibility of Finitude</a></li>
<li><a href="http://vimeo.com/album/2262409/video/63462519">Downward Löwenheim–Skolem Theorem</a></li>
</ul>
<h4 id="computability">Computability</h4>
<ul>
<li><a href="http://vimeo.com/album/2262409/video/64162062">Functions</a></li>
<li><a href="http://vimeo.com/album/2262409/video/64167354">Register Machines</a></li>
<li><a href="http://vimeo.com/album/2262409/video/64207986">Recursive Functions</a></li>
<li><a href="http://vimeo.com/album/2262409/video/64435763">Register Machine computable functions are Recursive</a></li>
<li><a href="http://vimeo.com/album/2262409/video/64604717">The Uncomputable</a></li>
</ul>
<h4 id="undecidability-and-incompleteness">Undecidability and Incompleteness</h4>
<ul>
<li><a href="http://vimeo.com/album/2262409/video/65382456">Deductively Defined Theories</a></li>
<li><a href="http://vimeo.com/album/2262409/video/65392670">The Finite Model Property</a></li>
<li><a href="http://vimeo.com/album/2262409/video/65393543">Completeness</a></li>
<li><a href="http://vimeo.com/album/2262409/video/65440901">Introducing Robinson’s Arithmetic</a></li>
<li><a href="http://vimeo.com/album/2262409/video/65442289">Induction and Peano Arithmetic</a></li>
<li><a href="http://vimeo.com/album/2262409/video/65443650">Representing Functions and Sets</a></li>
<li><a href="http://vimeo.com/album/2262409/video/65483655">Gödel Numbering and Diagonalisation</a></li>
<li><a href="http://vimeo.com/album/2262409/video/65497886">Q (and any consistent extension of Q) is undecidable, and incomplete if it’s deductively defined</a></li>
<li><a href="http://vimeo.com/album/2262409/video/65498016">First Order Predicate Logic is Undecidable</a></li>
<li><a href="http://vimeo.com/album/2262409/video/65501745">True Arithmetic is not Deductively Defined</a></li>
<li><a href="http://vimeo.com/album/2262409/video/65505372">If Con(PA) then PA doesn’t prove Con(PA)</a></li>
</ul>
UNIB10002: Logic, Language and Information
https://consequently.org/class/2019/unib10002/
Sat, 02 Mar 2019 00:00:00 UTChttps://consequently.org/class/2019/unib10002/<p><strong><span class="caps">UNIB10002</span>: Logic, Language and Information</strong> is a <a href="http://unimelb.edu.au">University of Melbourne</a> undergraduate breadth subject, introducing logic and its applications to students from a wide range of disciplines in the Arts, Sciences and Engineering. I coordinate this subject with my colleague Dr. Jen Davoren, with help from Prof. Lesley Stirling (Linguistics), Dr. Peter Schachte (Computer Science) and Dr. Daniel Murfet (Mathematics).</p>
<p>The subject is taught to University of Melbourne undergraduate students. Details for enrolment are <a href="https://handbook.unimelb.edu.au/view/2019/UNIB10002">here</a>.</p>
Generality and Existence I: Quantification and Free Logic
https://consequently.org/writing/generality-and-existence-1/
Fri, 01 Mar 2019 00:00:00 UTChttps://consequently.org/writing/generality-and-existence-1/<p>In this paper, I motivate a cut free sequent calculus for classical logic with first order quantification, allowing for singular terms free of existential import. Along the way, I motivate a criterion for rules designed to answer Prior’s question about what distinguishes rules for logical concepts, like ‘conjunction’ from apparently similar rules for putative concepts like ‘tonk’, and I show that the rules for the quantifiers—and the existence predicate—satisfy that condition.</p>
Generality and Existence 2: Modality and Quantifiers
https://consequently.org/presentation/2019/generality-and-existence-2-apa/
Tue, 05 Feb 2019 00:00:00 UTChttps://consequently.org/presentation/2019/generality-and-existence-2-apa/<p><em>Abstract</em>: In this talk, I motivate and define a cut free sequent calculus for first order modal predicate logics, allowing for singular terms free of existential import. I show that the <em>cut</em> rule is admissible in the cut-free calculus, and explore the relationship between contingent ‘world-bound’ quantifiers and possibilist ‘world-undbound’ quantifiers in the system.</p>
<ul>
<li><p>This is a talk for the Association for Symbolic Logic at the Central Division meeting of the American Philosophical Association, at Denver, Colorado.</p></li>
<li><p>The <a href="https://consequently.org/slides/generality-and-existence-2-slides-apa-screen.pdf">slides for the talk are available here</a>, and a version formatted for printing, as a handout, is <a href="https://consequently.org/slides/generality-and-existence-2-slides-apa-print.pdf">available here</a>.</p></li>
</ul>
Summer Reading 2018-2019
https://consequently.org/news/2019/summer-reading-2018-2019/
Sun, 27 Jan 2019 20:49:05 +1100https://consequently.org/news/2019/summer-reading-2018-2019/<p>This summer break, I set aside some time to turn off my devices, unplug from the internet, and read some honest-to-goodness <em>books</em>. Some I received from friends and family as Christmas or Birthday gifts (thanks, Sharon, Zac, Neil!), and some I had accumulated on my “to-read” pile waiting for just the right time. Here are some short reviews of my summer reading pile, in case you’d like to follow along.</p>
<p></p>
<p><blockquote class="twitter-tweet" data-lang="en"><p lang="en" dir="ltr">Christmas and New Year reading (and reference). <a href="https://t.co/LKLFIbQKPM">pic.twitter.com/LKLFIbQKPM</a></p>— Greg Restall (@consequently) <a href="https://twitter.com/consequently/status/1078484355981414400?ref_src=twsrc%5Etfw">December 28, 2018</a></blockquote> <script async src="https://platform.twitter.com/widgets.js" charset="utf-8"></script></p>
<hr />
<p>Haruki Murakami’s <a href="https://www.amazon.com/What-Talk-About-When-Running/dp/0307389839/consequentlyorg"><em>What I Talk About When I Talk About Running</em></a> is a delightful little book. It’s an enjoyable and personable mixture of <em>memoir</em> and <em>runners’ journal</em>. I’ve taken up running as a serious exercise practice in the last few years, and Murakami’s writing about his serious practice of long-distance running, and how he fits that in to the life of a writer was challenging and inspiring.</p>
<p>After reading it, I thought I could take my running practice more seriously, and I surprised myself by managing my first sub 5 minute-per-kilometre 10K run in the next week. Reading <em>What I Talk About When I Talk About Running</em> will remain with me for some time.</p>
<hr />
<p>Rowan Williams, the former Archbishop of Canterbury, is well known to be a reflective thinker, whose theological writing seriously engages with a range of theological traditions, but which also comes from a sustained contemplative practice. I don’t find Williams’ writing <em>easy</em>, but it’s always been rewarding when I’ve made the time to slow down and digest it. Williams’ new book <a href="https://www.amazon.com/Christ-Heart-Creation-Rowan-Williams/dp/1472945549/consequentlyorg"><em>Christ the Heart of Creation</em></a> is an attempt to revisit the classical doctrine of the incarnation in a new way: by focussing relentlessly on the idea that there is no competition between divine and creaturely action. According to Williams, too often we conceive of God as just another agent like any agent–except perhaps rather <em>Bigger</em>. (The metaphor is strained, but the relationship between a creature and God is more akin to the relationship between a fictional character and its author than between one character and another. Hermione stands to Harry in rather a different way than Hermione does to J. K. Rowling.) The way the Creator acts in creation is categorically distinct from the way a creature acts in creation. Williams examines different vocabulary used to give an account of the incarnation–from Augustine, the Chalcedonian Creed and Byzantine theologians Maximus the Confessor and John of Damascus, through Aquinas and Calvin to Barth and Bonhoeffer, with a sprinkling of Kierkegaard and Wittgenstein along the way, and always with care to the creature/creation distinction firmly on focus.</p>
<p>The result is a sympathetic recasting of traditional doctrines in a manner that breathes life into what may have seemed obsolete vocabulary. For Williams, incarnational vocabulary is a natural expression of a community attempting to articulate what they have encountered God doing in and through the human life of Jesus. The icing on the cake for me was Williams’ discussion of Paul’s “Body of Christ” language, which is, on this view, <em>much</em> more than a metaphor. This was a valuable read, well worth the time to digest slowly.</p>
<hr />
<p><a href="https://www.amazon.com/Zen-Doctrine-No-Mind/dp/0877281823/consequentlyorg"><em>The Zen Doctrine of No-Mind</em></a>, by D. T. Suzuki, is an exposition of the teaching of the Zen master Hui-neng (638–713). This book is an introduction to a debate in the early development of Zen Buddhism, a debate about sudden enlightenment and the doctrine of no-mind. I’d read some elementary expositions of Zen Buddhism before, but it was good to tackle a more extended work by the master D. T. Suzuki.</p>
<hr />
<p><a href="https://www.amazon.com/Return-Prodigal-Son-Story-Homecoming/dp/0385473079/consequentlyorg"><em>The Return of the Prodigal Son</em>: <em>A Story of Homecoming</em></a>, is a little book featuring reflections by Henri Nouwen, on a famous <a href="https://en.wikipedia.org/wiki/The_Return_of_the_Prodigal_Son_(Rembrandt)">painting by Rembrandt</a>. The painting depicting the return of the prodigal son, from Jesus’ parable (<a href="http://bible.oremus.org/?ql=415579440">Luke 15:11-32</a>). Nouwen reflects on the painting as he undergoes a significant turn in his life, departing his life as an academic in the US to live as a chaplain at Daybreak, a L’Arche community in Toronto.</p>
<p>The book is a thoughtful meditation on the painting, systematically taking three distinct perspectives, first identifying with the returning younger son, then identifying with the older son, and – at the end – reflecting on what it could mean to identify with the father in the parable.</p>
<hr />
<p><a href="https://www.amazon.com/MaddAddam-Trilogy-Margaret-Atwood/dp/0307455483/consequently"><em>MaddAddam</em></a>, by Margaret Atwood is the third novel and the conclusion of the dystopian (post-apocalyptic) <em>Oryx and Crake</em> trilogy. I’d read the <a href="https://www.amazon.com/gp/product/0385721676/consequentlyorg">first (<em>Oryx and Crake</em>)</a> and <a href="https://www.amazon.com/gp/product/0307455475/consequentlyorg">second (<em>The Year of the Flood</em>)</a> books of the trilogy years ago, and this had been sitting on my shelf for a couple of years. Now, with this summer, I finally had time to read it.</p>
<p>The books of the trilogy are set in and around the “waterless flood”, which swept away most of humanity in a genetically engineered disaster. There is a two-track narrative in <em>MaddAddam</em>, with one thread set before the flood, and the other, in its aftermath. In this book we learn more of Zeb and Adam, half-brothers who play very different roles in the world leading up to the flood and its immediate aftermath, and we learn more of the Crakers, the genetically engineered placid human-variants who Crake designed to replace us in the wake of the apocalypse. Atwood is perceptive when it comes to the different social roles religions can play in a world undergoing radical change. While Adam’s community of God’s Gardeners (think of a sect of environmentally-minded Quakers and you won’t go far wrong) are the central focus in <em>The Year of the Flood</em> (Book 2), in <em>MaddAddam</em> we hear from Adam and Zeb’s father, “The Rev”, who established the corporate friendly Church of PetrOleum: “My friends, as we all know, ‘oleum’ is the Latin word for oil. And indeed, oil is holy throughout the Bible! What else is used for the anointing of priests and prophets and kings? Oil!” As with <em>The Handmaid’s Tale</em>, religion can be co-opted into repression or exploitation, as much as it might be a force for liberation or conservation.</p>
<hr />
<p>Richard Prum’s <a href="https://www.amazon.com/Evolution-Beauty-Darwins-Forgotten-Theory/dp/0385537212/consequentlyorg"><em>The Evolution of Beauty</em></a> is a colourful account of the evolutionary dynamics of mate choice and the debate between adaptationists and non-adaptationists. What I enjoyed most in the book was the many examples of the variety of behaviours in the animal world–particularly in different bird species, but also in primates–and the insight into the distinct dynamics for selection and how different behaviours arise as a result of how mate selection takes place. There are many striking examples of different mating behaviour between bower birds on the one hand (where the selection of mates is basically up to the female bird–the males perform in their bowers and the females choose from among the males) and ducks (where the males choose and mate with females). The evolutionary dynamics are very different in each case, resulting in not only an incredible variety of different behaviours (in bower collecting, mating displays, plumage colouration, etc.), but also in the differences between species in which forced copulation occurs (common in ducks, for example) and those in which it is rare or nonexsitent (bower birds).</p>
<p>Without reading into the secondary literature, I can’t say much about the debate between adaptationists and non-adaptationists (as far as I can tell this turns on different ways “fitness” can be understood, and this turns out to be a pretty subtle matter), so I’m not going to judge on whether Prum is right about the side of the debate he lands on – but I <em>do</em> think that the book is very valuable as an introduction to the many and varied dynamics of mate selection and evolution among animal life, and the consequences that this might have for the evolution of the variety of behaviours among our primate cousins–including us. This was a delightful read.</p>
<hr />
<p>The last book in my pile was <em>not</em> like the others. Gozo Shioda’s <a href="https://www.amazon.com/Aikido-Complete-Techniques-Gozo-Shioda/dp/1568364857/consequentlyorg"><em>Aikido</em>: <em>The Complete Basic Techniques</em></a> is not the kind of book you read from cover to cover. It’s a reference book, that you dip in and out of as required. I’ve referred to it repeatedly to help me remember and understand techniques I’m learning in my Aikodo classes. It’s one of the definitive Yoshinkan Aikido texts, and in my couple of years of practice, I’m reaching the stage where I’ve begun to learn enough of the <em>very</em> basic things that I am beginning to get hints of where the practice goes from here. I’m finding that having written words and pictures does help me reflect on and remember what I’m learning in class, so I’ll be referring to this a great deal in the years ahead.</p>New Work for a (Formal) Theory of Grounds
https://consequently.org/presentation/2018/new-work-for-a-theory-of-grounds-logicmelb/
Fri, 07 Dec 2018 00:00:00 UTChttps://consequently.org/presentation/2018/new-work-for-a-theory-of-grounds-logicmelb/<p><em>Abstract</em>: In this talk, I provide two different models for a theory of grounds meeting the following desiderata:\(\def\yright{\succ}\)</p>
<ol>
<li><em>Grammar</em>: There are objects, which we call <em>grounds</em>, which can be grounds <em>for</em> propositions or grounds <em>against</em> propositions.</li>
<li><em>Derivation</em>: A derivation of a sequent \(X\yright A,Y\) gives us a systematic way to construct a ground <em>for</em> \(A\) out of grounds for each member of \(X\) and grounds against each member of \(Y\), and a derivation of a sequent \(X,A\yright Y\) gives us a systematic way to construct a ground <em>against</em> \(A\) out of grounds for each member of \(X\) and grounds against each member of \(Y\). So, a derivation of \(\yright A\) gives us a way to construct a ground for \(A\), and a derivation of \(A\yright\) gives us a way to construct a ground against \(A\).</li>
<li><em>Interpretation</em>: This theory can be interpreted in an <em>epistemic</em> sense, where grounds are our means to access the truth or falsity of a proposition, or a <em>metaphysical</em> sense, where grounds show how a proposition is made true by the world.</li>
<li><em>Grasp</em>: Grounds are the kinds of things we can <em>possess</em>.</li>
<li><em>Hyperintensionality</em>: Not every ground is a ground for every tautology. A ground for \(A\) need not also be a ground for each logical consequence of \(A\).</li>
<li><em>Structure</em>: A ground for \(A\to B\) can be seen as a function from grounds for \(A\) to grounds for \(B\). A ground for \(A\land B\) can be seen as consisting of a ground for \(A\) and a ground for \(B\). A ground against \(A\lor B\) can be seen as consisting of a ground against \(A\) and a ground against \(B\). A ground for \(\neg A\) can be obtained from a ground against \(A\), and a ground against \(\neg A\) can be obtained from a ground for \(A\).</li>
</ol>
<p>The result is a model of grounds with significant similarities to the BHK interpretation of constructive logic, but for the classical sequent calculus.</p>
<ul>
<li><p>This is a talk for the <a href="http://blogs.unimelb.edu.au/logic/logic-seminar/">Melbourne Logic Seminar</a>.</p></li>
<li><p>The <a href="https://consequently.org/slides/new-work-for-a-theory-of-grounds-logicmelb.pdf">slides of the talk are available here</a>.</p></li>
</ul>
Truth and Stereotypes
https://consequently.org/presentation/2018/truth-and-stereotypes/
Sun, 21 Oct 2018 00:00:00 UTChttps://consequently.org/presentation/2018/truth-and-stereotypes/<p><em>Abstract</em>: Our thoughts and our conversations are filled with generalisations. From everyday trivialities such as <em>birds fly</em> or <em>trams are crowded</em> to contested claims such as <em>women are oppressed</em> or <em>Muslims are peace-loving</em>, we think and communicate using generalisations and stereotypes. This way of understanding the world is useful and pervasive, but at the same time, it has significant limitations.</p>
<p>In this lecture, I will explain some of the surprising features of these generalisations. Then I’ll apply some of the tools developed by philosophers of language over the last decades, in order to understand why generalisations and stereotypes are so pervasive; why they can behave so strangely and can sometimes lead us astray; and finally, to learn how we can use generalisations and stereotypes productively in our thinking and our communication.</p>
<ul>
<li>This is a <a href="https://events.unimelb.edu.au/events/11429-truth-and-stereotypes">free public lecture at the University of Melbourne</a>, held at 7pm in the Kathleen Fitzpatrick Lecture Theatre (Arts West). Although it’s free, it’s a good idea to <a href="http://alumni.online.unimelb.edu.au/GRestall">book tickets</a>.</li>
<li>The slides for the talk are <a href="https://consequently.org/slides/truth-and-stereotypes.pdf">available here</a>.</li>
</ul>
Philosophy in Public
https://consequently.org/news/2018/philosophy-in-public/
Sun, 28 Oct 2018 13:34:27 +1100https://consequently.org/news/2018/philosophy-in-public/<p>Last Wednesday, I went down to the studios at <a href="http://about.abc.net.au/press-releases/abc-opens-its-new-southbank-centre/">ABC Southbank</a>, to be interviewed by Libbi Gorr for ABC Radio Melbourne’s <a href="https://www.abc.net.au/radio/melbourne/programs/sundays/">Sunday program</a>. As I made my way through the building, and settled into the little studio, I thought I heard a familiar voice, faintly in the distance. Libbi explained that this was Kevin Rudd (the former Prime Minister), who was being interviewed in the next room. Unlike the former PM, I wasn’t doing the rounds of media because I had a book to promote. But I was doing promotion in my own small way. The <a href="http://newsroom.melbourne.edu/about">University of Melbourne’s Media Office</a> does a good job at getting the word out about public lectures, and the description for the lecture I’m giving on <a href="https://consequently.org/presentation/2018/truth-and-stereotypes/">Tuesday night</a> apparently appealed to Libbi Gorr and her producer, and they thought it would be fun to interview me for the Sunday program, so on Tuesday midday, I get an email from the Media Office asking if I’d be up for an interview in the studio with Libbi, talking about Truth and Stereotypes.</p>
<p>So, that’s why I found myself in the studio having a fun 20 minute conversation with Libbi about stereotypes, thoughts, language and communication, and the possibility of objectivity and agreement (or disagreement) when we’re all situated in different places and have different perspectives. It didn’t go in the directions I expected. But I wasn’t trying to stick to any particular talking points. The aim was to have a fruitful conversation, and to engage the audience with some interesting questions, and to spark interest in the topics I’ll be covering in my public lecture. The interview was edited down to 17 minutes, and <a href="https://www.abc.net.au/radio/melbourne/programs/sundays/greg-restall/10432666">the result is here</a>. If it gets people interested in thinking in a different way about things, and curious about what we do when we approach issues of language and meaning as philosophers, I’ll count that as a win.</p>
<p>So now, I’ve got to finish my preparation for <a href="https://consequently.org/presentation/2018/truth-and-stereotypes/">Tuesday’s lecture</a>.</p>
With help from Hugo, GitHub, Netlify, Working Copy and Shortcuts, I might update this website more frequently
https://consequently.org/news/2018/with-help-from-hugo-github-netlify-working-copy-and-shortcuts-i-might-update-this-website-more-frequently/
Sun, 21 Oct 2018 16:39:00 +1100https://consequently.org/news/2018/with-help-from-hugo-github-netlify-working-copy-and-shortcuts-i-might-update-this-website-more-frequently/<p>If you’ve been following my <a href="https://consequently.org/presentation/">travels</a>, you’ll get some sense that this has been a busy year. I’ve done lots of writing on my <a href="https://consequently.org/writing/ptrm">book</a>, and I’ve managed to give lots of talks, both in the US and in Argentina, as well as at home. I haven’t posted here for nearly a year–writing elsewhere has been a higher priority.</p>
<p>However, this weekend, I’ve made a few changes to the website which means that I might post here a little more often. The site is produced by <a href="http://gohugo.io">Hugo</a>, a really sweet static site generator. Until yesterday, if I wanted to update my site, what I did was</p>
<ol>
<li>Write files on whatever device I was using–most probably my Mac, but maybe my iPad–and push them to my my <a href="https://github.com/consequently/consequently-hugo">Git repository</a>, which contains the source for the whole website.</li>
<li>Then, on my Mac, sync up the repository.</li>
<li>Run hugo to update the generated files.</li>
<li>Sync the result up to GitHub.</li>
</ol>
<p>That worked fine, but I needed to do steps 2–4 on my Mac, and I don’t always have my Mac with me. Sometimes I prefer to write on my (smaller, less fiddly an distracting) iPad, and sometimes I only have my phone with me, and it’d be nice to update files on the website without having to run through my Mac to do that. I use <a href="http://workingcopyapp.com">Working Copy</a> on my iPhone and iPad to keep local copies of my website files (as well as the papers and book I’m currently working on) so it’s as easy as anything to edit these files wherever I have one of these devices on hand.</p>
<p>Here’s where <a href="http://netlify.com">Netlify</a> comes in. It’s a continuous integration service, that does step 2-4 in the cloud, without me having to be at my Mac. It’s <a href="https://gohugo.io/hosting-and-deployment/hosting-on-netlify/">very easy to wire up Netlify and Github</a> so that whenever I add a new file (or edit a file) in the source to my website, a little daemon spins up on the Netlify servers, runs hugo on the files, and syncs the result up to my website. It means that now I can edit files from any device connected to the internet, and the site is nicely generated, without me having to either edit in a web form (ugh!) or deal with a database driven website that either needs software maintenance or is prone to spam and server injection nastiness, or goes down at a drop of a hat. The site is still statically generated HTML, and I have control over how it is made. It’s a lovely solution.</p>
<p>So, over the weekend I’ve set things up, flipped the switches, and if you’re reading this, you’re reading the first entry written on my iPad and served up through the Netlify CI service.</p>
<p>The next step is to write some little <a href="https://support.apple.com/en-us/HT208309">Shortcuts</a> which make the job of creating new entries in the <a href="https://consequently.org/news/">News</a>, <a href="https://consequently.org/writing/">Writing</a>, <a href="https://consequently.org/class/">Class</a> and <a href="https://consequently.org/presentation/">Presentation</a> categories, with the datestamps and other boilerplate set automatically, even quicker, so there’s less friction in making new entries. I’ve done the first draft of the “News” shortcut already, and if you can see this entry, it means it’s worked.</p>
<p>As always, this is a work in progress, and probably things broke as I shifted things around. If you notice anything broken, please let me know. Thanks!</p>
Accommodation, Inference, Generics and Pejoratives
https://consequently.org/presentation/2018/accommodation-melb-workshop/
Wed, 10 Oct 2018 00:00:00 UTChttps://consequently.org/presentation/2018/accommodation-melb-workshop/<p><em>Abstract</em>: In this talk, I aim to give an account of norms governing our uses of <em>generic judgements</em> (like “kangaroos have long tails”, “birds lay eggs”, or “logic talks are boring”), norms governing <em>inference</em>, and the relationship <em>between</em> generics and inference. This connection goes some way to explain why generics exhibit some very strange behaviour: Why is it, for example, that “birds lay eggs” seems true, while “birds are female” seems false, despite the fact that only female birds lay eggs?</p>
<p>Given the connection between generics and inference, I’ll go on to consider how inference relates to the process of <em>accommodation</em>, which plays a significant role in how we manage dialogue and conversation. This, in turn, helps shed some light on some different ways expressions can involve <em>pejorative force</em>, and can inform options for how our vocabulary and our concepts can be revised or reformed.</p>
<ul>
<li>This is a talk for a workshiop on Social Ontology at the University of Melbourne.</li>
<li>The <a href="https://consequently.org/slides/accommodation-melb-workshop.pdf">slides for the talk are available here</a>, and the <a href="https://consequently.org/handouts/accommodation-melb-workshop-handout.pdf">handout is here</a>.</li>
</ul>
Accommodation, Inference, Generics and Pejoratives
https://consequently.org/presentation/2018/accommodation-uq/
Thu, 04 Oct 2018 00:00:00 UTChttps://consequently.org/presentation/2018/accommodation-uq/<p><em>Abstract</em>: In this talk, I aim to give an account of norms governing our uses of <em>generic judgements</em> (like “kangaroos have long tails”, “birds lay eggs”, or “logic talks are boring”), norms governing <em>inference</em>, and the relationship <em>between</em> generics and inference. This connection goes some way to explain why generics exhibit some very strange behaviour: Why is it, for example, that “birds lay eggs” seems true, while “birds are female” seems false, despite the fact that only female birds lay eggs?</p>
<p>Given the connection between generics and inference, I’ll go on to consider how inference relates to the process of <em>accommodation</em>, which plays a significant role in how we manage dialogue and conversation. This, in turn, helps shed some light on some different ways expressions can involve <em>pejorative force</em>, and can inform options for how our vocabulary and our concepts can be revised or reformed.</p>
<ul>
<li>This is a <a href="https://hapi.uq.edu.au/event/session/3538">talk for the University of Queensland Philosophy Seminar Series</a> (3pm-5pm, Fridays).</li>
<li>The <a href="https://consequently.org/slides/accommodation-uq.pdf">slides for the talk are available here</a>, and the <a href="https://consequently.org/handouts/accommodation-uq-handout.pdf">handout is here</a>.</li>
</ul>
Negation on the Australian Plan
https://consequently.org/writing/nap/
Tue, 18 Sep 2018 00:00:00 UTChttps://consequently.org/writing/nap/<p>We present and defend the Australian Plan semantics for negation. This is a comprehensive account, suitable for a variety of different logics. It is based on two ideas. The first is that negation is an exclusion-expressing device: we utter negations to express incompatibilities. The second is that, because incompat<em>ibility</em> is modal, negation is a modal operator as well. It can, then, be modelled as a quantifier over points in frames, restricted by accessibility relations representing compatibilities and incompatibilities between such points. We defuse a number of objections to this Plan, raised by supporters of the American Plan for negation, in which negation is handled via a many-valued semantics. We show that the Australian Plan has substantial advantages over the American Plan.</p>
Defining Rules, Proofs and Counterexamples
https://consequently.org/presentation/2018/defining-rules-proofs-and-counterexamples-ba-logic-vii/
Thu, 26 Jul 2018 00:00:00 UTChttps://consequently.org/presentation/2018/defining-rules-proofs-and-counterexamples-ba-logic-vii/<p><em>Abstract</em>: In this talk, I will present an account of <em>defining rules</em>, with the aim of explaining these rules they play a central role in analytic proofs. Along the way, I’ll explain how Kreisel’s <em>squeezing argument</em> helps us understand the connection between an informal notion of validity and the notions formalised in our accounts of proofs and models, and the relationship between proof-theoretic and model- theoretic analyses of logical consequence.</p>
<ul>
<li><p>This is a talk for the <a href="http://ba-logic.com/workshops/7th-workshop/">VII Workshop on Philosophical Logic</a>.</p></li>
<li><p>The <a href="https://consequently.org/slides/defining-rules-proofs-and-counterexamples-slides.pdf">slides for the talk are available here</a>, and the <a href="https://consequently.org/handouts/defining-rules-proofs-and-counterexamples-handout.pdf">handout is here</a>.</p></li>
</ul>
Proof Theory, Rules and Meaning — an introduction
https://consequently.org/presentation/2018/proof-theory-rules-and-meaning/
Mon, 30 Jul 2018 00:00:00 UTChttps://consequently.org/presentation/2018/proof-theory-rules-and-meaning/<p><em>Abstract</em>: I introduce the key themes from my book-in-progress, <a href="https://consequently.org/writing/ptrm/">Proof Theory, Rules and Meaning</a>.</p>
<ul>
<li><p>This is a talk for the <a href="http://ba-logic.com/workshops/symposium-restall/">symposium</a> on the manuscript held at the Argentinean Society of Philosophical Analysis (SADAF) in Buenos Aires, in July 2018.</p></li>
<li><p>The <a href="https://consequently.org/slides/proof-theory-rules-and-meaning-intro-ba.pdf">slides for the talk are available here</a>.</p></li>
</ul>
PHIL30043: The Power and Limits of Logic
https://consequently.org/class/2018/phil30043/
Mon, 16 Jul 2018 00:00:00 UTChttps://consequently.org/class/2018/phil30043/
<p><strong><span class="caps">PHIL30043</span>: The Power and Limits of Logic</strong> is a <a href="https://handbook.unimelb.edu.au/view/2018/PHIL30043">University of Melbourne undergraduate subject</a>. It covers the metatheory of classical first order predicate logic, beginning at the <em>Soundness</em> and <em>Completeness</em> Theorems (proved not once but <em>twice</em>, first for a tableaux proof system for predicate logic, then a Hilbert proof system), through the <em>Deduction Theorem</em>, <em>Compactness</em>, <em>Cantor’s Theorem</em>, the <em>Downward Löwenheim–Skolem Theorem</em>, <em>Recursive Functions</em>, <em>Register Machines</em>, <em>Representability</em> and ending up at <em>Gödel’s Incompleteness Theorems</em> and <em>Löb’s Theorem</em>.</p>
<figure>
<img src="https://consequently.org/images/godel.jpg" alt="Kurt Godel, seated">
<figcaption>Kurt Gödel, seated</figcaption>
</figure>
<p>The subject is taught to University of Melbourne undergraduate students (for Arts students as a part of the Philosophy major, for non-Arts students, as a breadth subject). Details for enrolment are <a href="https://handbook.unimelb.edu.au/view/2018/PHIL30043">here</a>. I make use of video lectures I have made <a href="http://vimeo.com/album/2262409">freely available on Vimeo</a>.</p>
<h3 id="outline">Outline</h3>
<p>The course is divided into four major sections and a short prelude. Here is a list of all of the videos, in case you’d like to follow along with the content.</p>
<h4 id="prelude">Prelude</h4>
<ul>
<li><a href="http://vimeo.com/album/2262409/video/59401942">Logical Equivalence</a></li>
<li><a href="http://vimeo.com/album/2262409/video/59403292">Disjunctive Normal Form</a></li>
<li><a href="http://vimeo.com/album/2262409/video/59403535">Why DNF Works</a></li>
<li><a href="http://vimeo.com/album/2262409/video/59463569">Prenex Normal Form</a></li>
<li><a href="http://vimeo.com/album/2262409/video/59466141">Models for Predicate Logic</a></li>
<li><a href="http://vimeo.com/album/2262409/video/59880539">Trees for Predicate Logic</a></li>
</ul>
<h4 id="completeness">Completeness</h4>
<ul>
<li><a href="http://vimeo.com/album/2262409/video/59883806">Introducing Soundness and Completeness</a></li>
<li><a href="http://vimeo.com/album/2262409/video/60249309">Soundness for Tree Proofs</a></li>
<li><a href="http://vimeo.com/album/2262409/video/60250515">Completeness for Tree Proofs</a></li>
<li><a href="http://vimeo.com/album/2262409/video/61677028">Hilbert Proofs for Propositional Logic</a></li>
<li><a href="http://vimeo.com/album/2262409/video/61685762">Conditional Proof</a></li>
<li><a href="http://vimeo.com/album/2262409/video/62221512">Hilbert Proofs for Predicate Logic</a></li>
<li><a href="http://vimeo.com/album/2262409/video/103720089">Theories</a></li>
<li><a href="http://vimeo.com/album/2262409/video/103757399">Soundness and Completeness for Hilbert Proofs for Predicate Logic</a></li>
</ul>
<h4 id="compactness">Compactness</h4>
<ul>
<li><a href="http://vimeo.com/album/2262409/video/63454250">Counting Sets</a></li>
<li><a href="http://vimeo.com/album/2262409/video/63454732">Diagonalisation</a></li>
<li><a href="http://vimeo.com/album/2262409/video/63454732">Compactness</a></li>
<li><a href="http://vimeo.com/album/2262409/video/63455121">Non-Standard Models</a></li>
<li><a href="http://vimeo.com/album/2262409/video/63462354">Inexpressibility of Finitude</a></li>
<li><a href="http://vimeo.com/album/2262409/video/63462519">Downward Löwenheim–Skolem Theorem</a></li>
</ul>
<h4 id="computability">Computability</h4>
<ul>
<li><a href="http://vimeo.com/album/2262409/video/64162062">Functions</a></li>
<li><a href="http://vimeo.com/album/2262409/video/64167354">Register Machines</a></li>
<li><a href="http://vimeo.com/album/2262409/video/64207986">Recursive Functions</a></li>
<li><a href="http://vimeo.com/album/2262409/video/64435763">Register Machine computable functions are Recursive</a></li>
<li><a href="http://vimeo.com/album/2262409/video/64604717">The Uncomputable</a></li>
</ul>
<h4 id="undecidability-and-incompleteness">Undecidability and Incompleteness</h4>
<ul>
<li><a href="http://vimeo.com/album/2262409/video/65382456">Deductively Defined Theories</a></li>
<li><a href="http://vimeo.com/album/2262409/video/65392670">The Finite Model Property</a></li>
<li><a href="http://vimeo.com/album/2262409/video/65393543">Completeness</a></li>
<li><a href="http://vimeo.com/album/2262409/video/65440901">Introducing Robinson’s Arithmetic</a></li>
<li><a href="http://vimeo.com/album/2262409/video/65442289">Induction and Peano Arithmetic</a></li>
<li><a href="http://vimeo.com/album/2262409/video/65443650">Representing Functions and Sets</a></li>
<li><a href="http://vimeo.com/album/2262409/video/65483655">Gödel Numbering and Diagonalisation</a></li>
<li><a href="http://vimeo.com/album/2262409/video/65497886">Q (and any consistent extension of Q) is undecidable, and incomplete if it’s deductively defined</a></li>
<li><a href="http://vimeo.com/album/2262409/video/65498016">First Order Predicate Logic is Undecidable</a></li>
<li><a href="http://vimeo.com/album/2262409/video/65501745">True Arithmetic is not Deductively Defined</a></li>
<li><a href="http://vimeo.com/album/2262409/video/65505372">If Con(PA) then PA doesn’t prove Con(PA)</a></li>
</ul>
PHIL20030: Meaning, Possibility and Paradox
https://consequently.org/class/2018/phil20030/
Mon, 16 Jul 2018 00:00:00 UTChttps://consequently.org/class/2018/phil20030/
<p><strong><span class="caps">PHIL20030</span>: Meaning, Possibility and Paradox</strong> is a <a href="http://unimelb.edu.au">University of Melbourne</a> undergraduate subject. The idea that the meaning of a sentence depends on the meanings of its parts is fundamental to the way we understand logic, language and the mind. In this subject, we look at the different ways that this idea has been applied in logic throughout the 20th Century and into the present day.</p>
<p>In the first part of the subject, our focus is on the concepts of necessity and possibility, and the way that ‘possible worlds semantics’ has been used in theories of meaning. We will focus on the logic of necessity and possibility (modal logic), times (temporal logic), conditionality and dependence (counterfactuals), and the notions of analyticity and a priority so important to much of philosophy.</p>
<p>In the second part of the subject, we examine closely the assumption that every statement we make is either true or false but not both. We will examine the paradoxes of truth (like the so-called ‘liar paradox’) and vagueness (the ‘sorites paradox’), and we will investigate different ways attempts at resolving these paradoxes by going beyond our traditional views of truth (using ‘many valued logics’) or by defending the traditional perspective.</p>
<p>The subject serves as an introduction to ways that logic is applied in the study of language, epistemology and metaphysics, so it is useful to those who already know some philosophy and would like to see how logic relates to those issues. It is also useful to those who already know some logic and would like to learn new logical techniques and see how these techniques can be applied.</p>
<p>The subject is offered to University of Melbourne undergraduate students (for Arts students as a part of the Philosophy major, for non-Arts students, as a breadth subject). Details for enrolment are <a href="https://handbook.unimelb.edu.au/view/2018/PHIL20030">here</a>.</p>
<figure>
<img src="https://consequently.org/images/peter-rozsa-small.png" alt="Rosza Peter">
<figcaption>The writing down of a formula is an expression of our joy that we can answer all these questions by means of one argument. — Rózsa Péter, Playing with Infinity</figcaption>
</figure>
<p>I make use of video lectures I have made <a href="http://vimeo.com/album/2470375">freely available on Vimeo</a>. If you’re interested in this sort of thing, I hope they’re useful. Of course, I appreciate any constructive feedback you might have.</p>
<h3 id="outline">Outline</h3>
<p>The course is divided into four major sections and a short prelude. Here is a list of all of the videos, in case you’d like to follow along with the content.</p>
<h4 id="classical-logic">Classical Logic</h4>
<ul>
<li><a href="https://vimeo.com/album/2470375/video/71195118">On Logic and Philosophy</a></li>
<li><a href="https://vimeo.com/album/2470375/video/71196826">Classical Logic—Models</a></li>
<li><a href="https://vimeo.com/album/2470375/video/71200032">Classical Logic—Tree Proofs</a></li>
</ul>
<h4 id="meaning-sense-reference">Meaning, Sense, Reference</h4>
<ul>
<li><a href="https://vimeo.com/album/2470375/video/71206884">Reference and Compositionality</a></li>
<li><a href="https://vimeo.com/album/2470375/video/71226471">Sense and Reference</a></li>
</ul>
<h4 id="basic-modal-logic">Basic Modal Logic</h4>
<ul>
<li><a href="https://vimeo.com/album/2470375/video/71556216">Introducing Possibility an Necessity</a></li>
<li><a href="https://vimeo.com/album/2470375/video/71558401">Models for Basic Modal Logic</a></li>
<li><a href="https://vimeo.com/album/2470375/video/71558696">Tree Proofs for Basic Modal Logic</a></li>
<li><a href="https://vimeo.com/album/2470375/video/71560394">Soundness and Completeness for Basic Modal Logic</a></li>
</ul>
<h4 id="normal-modal-logics">Normal Modal Logics</h4>
<ul>
<li><a href="https://vimeo.com/album/2470375/video/72135540">What Are Possible Worlds?</a></li>
<li><a href="https://vimeo.com/album/2470375/video/72137443">Conditions on Accessibility Relations</a></li>
<li><a href="https://vimeo.com/album/2470375/video/72137856">Equivalence Relations, Universal Relations and S5</a></li>
<li><a href="https://vimeo.com/album/2470375/video/72139085">Tree Proofs for Normal Modal Logic</a></li>
<li><a href="https://vimeo.com/album/2470375/video/72140275">Applying Modal Logics</a></li>
</ul>
<h4 id="double-indexing">Double Indexing</h4>
<ul>
<li><a href="https://vimeo.com/album/2470375/video/72140275">Temporal Logic</a></li>
<li><a href="https://vimeo.com/album/2470375/video/72143616">Actuality and the Present</a></li>
<li><a href="https://vimeo.com/album/2470375/video/72266887">Two Dimensional Modal Logic</a></li>
</ul>
<h4 id="conditionality">Conditionality</h4>
<ul>
<li><a href="https://vimeo.com/album/2470375/video/74494229">Strict Conditionals</a></li>
<li><a href="https://vimeo.com/album/2470375/video/74498276"><em>Ceteris Paribus</em> Conditionals</a></li>
<li><a href="https://vimeo.com/album/2470375/video/74504639">Similarity</a></li>
</ul>
<h4 id="three-values">Three Values</h4>
<ul>
<li><a href="https://vimeo.com/album/2470375/video/74628150">More than Two Truth Values</a></li>
<li><a href="https://vimeo.com/album/2470375/video/74636384">K3</a></li>
<li><a href="https://vimeo.com/album/2470375/video/74680756">Ł3</a></li>
<li><a href="https://vimeo.com/album/2470375/video/74680954">LP</a></li>
<li><a href="https://vimeo.com/album/2470375/video/74682689">RM3</a></li>
</ul>
<h4 id="four-values">Four Values</h4>
<ul>
<li><a href="https://vimeo.com/album/2470375/video/74685077">FDE: Relational Evaluations</a></li>
<li><a href="https://vimeo.com/album/2470375/video/74685986">FDE: Tree Proofs</a></li>
<li><a href="https://vimeo.com/album/2470375/video/74695340">FDE: Routley Evaluations</a></li>
</ul>
<h4 id="paradoxes">Paradoxes</h4>
<ul>
<li><a href="https://vimeo.com/album/2470375/video/76045884">Truth and the Liar Paradox</a></li>
<li><a href="https://vimeo.com/album/2470375/video/76049193">Fixed Point Construction</a></li>
<li><a href="https://vimeo.com/album/2470375/video/76055233">Curry’s Paradox</a></li>
<li><a href="https://vimeo.com/album/2470375/video/76057722">The Sorites Paradox</a></li>
<li><a href="https://vimeo.com/album/2470375/video/76061452">Fuzzy Logic</a></li>
<li><a href="https://vimeo.com/album/2470375/video/76066245">Supervaluationism</a></li>
<li><a href="https://vimeo.com/album/2470375/video/76070423">Epistemicism</a></li>
</ul>
<h4 id="what-to-do-with-so-many-logical-systems">What to do with so many logical systems</h4>
<ul>
<li><a href="https://vimeo.com/album/2470375/video/76070953">Logical Monism and Pluralism</a></li>
</ul>
What Proofs are For
https://consequently.org/presentation/2018/what-proofs-are-for-melbourne-glasgow/
Thu, 07 Jun 2018 00:00:00 UTChttps://consequently.org/presentation/2018/what-proofs-are-for-melbourne-glasgow/<p><em>Abstract</em>: In this short talk, I present a new account of the nature of proof, with the aim of explaining how proof could actually play the role in reasoning that it does, and answering some long-standing puzzles about the nature of proof. Along the way, I’ll explain how Kreisel’s Squeezing argument helps us understand the connection between an informal notion of of validity and the notions formalised in our accounts of proofs and models, and the relationship between proof-theoretic and model-theoretic analyses of logical consequence.</p>
<ul>
<li><p>This is a talk for the <a href="https://philevents.org/event/show/41790">Melbourne–Glasgow Formal Philosophy Workshop</a>.</p></li>
<li><p>The <a href="https://consequently.org/slides/what-proofs-are-for-melbourne-glasgow-slides.pdf">slides for the talk are available here</a>, and the <a href="https://consequently.org/handouts/what-proofs-are-for-melbourne-glasgow-handout.pdf">handout is here</a>.</p></li>
</ul>
Isomorphisms in a Category of Proofs
https://consequently.org/presentation/2018/mit-sllerg/
Fri, 05 Jan 2018 00:00:00 UTChttps://consequently.org/presentation/2018/mit-sllerg/<p><em>Abstract</em>: In this talk, I show how a category of formulas and classical proofs can give rise to three different hyperintensional notions of sameness of content. One of these notions is very fine-grained, going so far as to distinguish \(p\) and \(p\land p\), while identifying other distinct pairs of formulas, such as \(p\land q\) and \(q\land p\); \(p\) and \(\neg\neg p\); or \(\neg(p\land q)\) and \(\neg p\lor\neg q\). Another relation is more coarsely grained, and gives the same account of identity of content as equivalence in Angell’s logic of analytic containment. A third notion of sameness of content is defined, which is intermediate between Angell’s and Parry’s logics of analytic containment. Along the way we show how purely classical proof theory gives resources to define hyperintensional distinctions thought to be the domain of properly non-classical logics.</p>
<ul>
<li>This is a talk for the MIT SLLERG Group.</li>
<li>The <a href="https://consequently.org/slides/isomorphisms-talk-mit-2018.pdf">slides can be downloaded here</a>, but the <a href="https://consequently.org/handouts/isomorphisms-handout-mit-2018.pdf">handout</a> (4 pages) is best for printing out and reading, so it’s probably better that you <a href="https://consequently.org/handouts/isomorphisms-handout-mit-2018.pdf">download and print that</a>.</li>
</ul>
Accommodation, Inference, Generics and Pejoratives
https://consequently.org/presentation/2018/mit-wip/
Fri, 05 Jan 2018 00:00:00 UTChttps://consequently.org/presentation/2018/mit-wip/<p><em>Abstract</em>: In this talk, I aim to give an account of norms governing our uses of <em>generic judgements</em> (like “kangaroos have long tails”, “birds lay eggs”, or “logic talks are boring”), norms governing <em>inference</em>, and the relationship <em>between</em> generics and inference. This connection goes some way to explain why generics exhibit some very strange behaviour: Why is it, for example, that “birds lay eggs” seems true, while “birds are female” seems false, despite the fact that only female birds lay eggs?</p>
<p>Given the connection between generics and inference, I’ll go on to consider how inference relates to the process of <em>accommodation</em>, which plays a significant role in how we manage dialogue and conversation. This, in turn, helps shed some light on some different ways expressions can involve <em>pejorative force</em>, and can inform options for how our vocabulary and our concepts can be revised or reformed.</p>
<ul>
<li>This is a talk for the MIT Philosophy Work in Progress series (1pm-2pm, Thursdays).</li>
<li>The <a href="https://consequently.org/slides/accommodation-mit.pdf">slides for the talk are available here</a>, and the <a href="https://consequently.org/handouts/accommodation-mit-handout.pdf">handout is here</a>.</li>
</ul>
Accommodation, Inference, Generics and Pejoratives
https://consequently.org/presentation/2018/uconn-brown-bag/
Fri, 05 Jan 2018 00:00:00 UTChttps://consequently.org/presentation/2018/uconn-brown-bag/<p><em>Abstract</em>: In this talk, I aim to give an account of norms governing our uses of <em>generic judgements</em> (like “kangaroos have long tails”, “birds lay eggs”, or “logic talks are boring”), norms governing <em>inference</em>, and the relationship <em>between</em> generics and inference. This connection goes some way to explain why generics exhibit some very strange behaviour: Why is it, for example, that “birds lay eggs” seems true, while “birds are female” seems false, despite the fact that only female birds lay eggs?</p>
<p>Given the connection between generics and inference, I’ll go on to consider how inference relates to the process of <em>accommodation</em>, which plays a significant role in how we manage dialogue and conversation. This, in turn, helps shed some light on some different ways expressions can involve <em>pejorative force</em>, and can inform options for how our vocabulary and our concepts can be revised or reformed.</p>
<ul>
<li>This is a talk for the <a href="http://events.uconn.edu/event/60881/2018-04-18">University of Connecticut Philosophy Brown Bag</a>.</li>
<li>The <a href="https://consequently.org/slides/accommodation-uconn.pdf">slides for the talk are available here</a>, and the <a href="https://consequently.org/handouts/accommodation-uconn-handout.pdf">handout is here</a>.</li>
</ul>
Accommodation, Inference, Generics and Pejoratives
https://consequently.org/presentation/2018/pitt-philosophy-colloquium/
Fri, 05 Jan 2018 00:00:00 UTChttps://consequently.org/presentation/2018/pitt-philosophy-colloquium/<p><em>Abstract</em>: In this talk, I aim to give an account of norms governing our uses of <em>generic judgements</em> (like “kangaroos have long tails”, “birds lay eggs”, or “logic talks are boring”), norms governing <em>inference</em>, and the relationship <em>between</em> generics and inference. This connection goes some way to explain why generics exhibit some very strange behaviour: Why is it, for example, that “birds lay eggs” seems true, while “birds are female” seems false, despite the fact that only female birds lay eggs?</p>
<p>Given the connection between generics and inference, I’ll go on to consider how inference relates to the process of <em>accommodation</em>, which plays a significant role in how we manage dialogue and conversation. This, in turn, helps shed some light on some different ways expressions can involve <em>pejorative force</em>, and can inform options for how our vocabulary and our concepts can be revised or reformed.</p>
<ul>
<li>This is a talk for the <a href="http://www.philosophy.pitt.edu/event/greg-restall-u-melbourne-talk">University of Pittsburgh Philosophy Colloquium</a>.</li>
<li>The <a href="https://consequently.org/slides/accommodation-pitt.pdf">slides for the talk are available here</a>, and the <a href="https://consequently.org/handouts/accommodation-pitt-handout.pdf">handout is here</a>.</li>
</ul>
Isomorphisms in a Category of Proofs
https://consequently.org/presentation/2018/cmu-pure-and-applied-logic/
Fri, 05 Jan 2018 00:00:00 UTChttps://consequently.org/presentation/2018/cmu-pure-and-applied-logic/<p><em>Abstract</em>: In this talk, I show how a category of formulas and classical proofs can give rise to three different hyperintensional notions of sameness of content. One of these notions is very fine-grained, going so far as to distinguish \(p\) and \(p\land p\), while identifying other distinct pairs of formulas, such as \(p\land q\) and \(q\land p\); \(p\) and \(\neg\neg p\); or \(\neg(p\land q)\) and \(\neg p\lor\neg q\). Another relation is more coarsely grained, and gives the same account of identity of content as equivalence in Angell’s logic of analytic containment. A third notion of sameness of content is defined, which is intermediate between Angell’s and Parry’s logics of analytic containment. Along the way we show how purely classical proof theory gives resources to define hyperintensional distinctions thought to be the domain of properly non-classical logics.</p>
<ul>
<li>This is a <a href="https://calendar.google.com/calendar/event?eid=NG4zNDZkbXA5OTRqNzEwcDVpdTZhcHZjbm8gMDFsMXQ2c2I1dGJhcWk2NmJnOGIxOWszN29AZw&ctz=America/New_York">talk for the CMU Pure and Applied Logic Seminar Series</a>.</li>
<li>The <a href="https://consequently.org/slides/isomorphisms-talk-cmu-2018.pdf">slides can be downloaded here</a>, but the <a href="https://consequently.org/handouts/isomorphisms-handout-cmu-2018.pdf">handout</a> (4 pages) is best for printing out and reading, so it’s probably better that you <a href="https://consequently.org/handouts/isomorphisms-handout-cmu-2018.pdf">download and print that</a>.</li>
</ul>
Isomorphisms in a Category of Proofs
https://consequently.org/presentation/2018/cuny-gc-logic-and-metaphysics/
Fri, 05 Jan 2018 00:00:00 UTChttps://consequently.org/presentation/2018/cuny-gc-logic-and-metaphysics/<p><em>Abstract</em>: In this talk, I show how a category of classical proofs can give rise to three different hyperintensional notions of sameness of content. One of these notions is very fine-grained, going so far as to distinguish \(p\) and \(p\land p\), while identifying other distinct pairs of formulas, such as \(p\land q\) and \(q\land p\); \(p\) and \(\neg\neg p\); or \(\neg(p\land q)\) and \(\neg p\lor\neg q\). Another relation is more coarsely grained, and gives the same account of identity of content as equivalence in Angell’s logic of analytic containment. A third notion of sameness of content is defined, which is intermediate between Angell’s and Parry’s logics of analytic containment. Along the way we show how purely classical proof theory gives resources to define hyperintensional distinctions thought to be the domain of properly non-classical logics.</p>
<ul>
<li><p>This is a talk for the <a href="https://logic.commons.gc.cuny.edu">CUNY Graduate Center Logic and Metaphysics Seminar</a>.</p></li>
<li><p>The <a href="https://consequently.org/slides/isomorphisms-talk-cuny-2018.pdf">slides can be downloaded here</a>, but the <a href="https://consequently.org/handouts/isomorphisms-handout-cuny-2018.pdf">handout</a> (4 pages) is best for printing out and reading, so it’s probably better that you <a href="https://consequently.org/handouts/isomorphisms-handout-cuny-2018.pdf">download and print that</a>.</p></li>
</ul>
What Proofs are For
https://consequently.org/presentation/2018/what-proofs-are-for-nyu/
Fri, 05 Jan 2018 00:00:00 UTChttps://consequently.org/presentation/2018/what-proofs-are-for-nyu/<p><em>Abstract</em>: In this short talk, I present a new account of the nature of proof, with the aim of explaining how proof could actually play the role in reasoning that it does, and answering some long-standing puzzles about the nature of proof. Along the way, I’ll explain how Kreisel’s Squeezing argument helps us understand the connection between an informal notion of of validity and the notions formalised in our accounts of proofs and models, and the relationship between proof-theoretic and model-theoretic analyses of logical consequence.</p>
<ul>
<li><p>This is a talk for the NYU Philosophy Department Brown Bag Series.</p></li>
<li><p>The <a href="https://consequently.org/slides/what-proofs-are-for-nyu-slides.pdf">slides for the talk are available here</a>, and the <a href="https://consequently.org/handouts/what-proofs-are-for-nyu-handout.pdf">handout is here</a>.</p></li>
</ul>
Accommodation, Inference, Generics and Pejoratives
https://consequently.org/presentation/2018/cuny-gc-colloquium/
Fri, 05 Jan 2018 00:00:00 UTChttps://consequently.org/presentation/2018/cuny-gc-colloquium/<p><em>Abstract</em>: In this talk, I aim to give an account of norms governing our uses of <em>generic judgements</em> (like “kangaroos have long tails”, “birds lay eggs”, or “logic talks are boring”), norms governing <em>inference</em>, and the relationship <em>between</em> generics and inference. This connection goes some way to explain why generics exhibit some very strange behaviour: Why is it, for example, that “birds lay eggs” seems true, while “birds are female” seems false, despite the fact that only female birds lay eggs?</p>
<p>Given the connection between generics and inference, I’ll go on to consider how inference relates to the process of <em>accommodation</em>, which plays a significant role in how we manage dialogue and conversation. This, in turn, helps shed some light on some different ways expressions can involve <em>pejorative force</em>, and can inform options for how our vocabulary and our concepts can be revised or reformed.</p>
<ul>
<li><p>This is a talk for the <a href="https://philosophy.commons.gc.cuny.edu/spring-2018-colloquium-schedule/">CUNY Graduate Center Philosophy Colloquium</a>.</p></li>
<li><p>The <a href="https://consequently.org/slides/accommodation-cuny-2018.pdf">slides for the talk are available here</a>, and the <a href="https://consequently.org/handouts/accommodation-cuny-handout-2018.pdf">handout is here</a>.</p></li>
</ul>
Accommodation, Inference, Generics and Pejoratives
https://consequently.org/presentation/2018/unimelb-accommodation/
Tue, 13 Feb 2018 00:00:00 UTChttps://consequently.org/presentation/2018/unimelb-accommodation/<p><em>Abstract</em>: In this talk, I aim to give an account of norms governing our uses of <em>generic judgements</em> (like “kangaroos have long tails”, “birds lay eggs”, or “logic talks are boring”), norms governing <em>inference</em>, and the relationship <em>between</em> generics and inference. This connection goes some way to explain why generics exhibit some very strange behaviour: Why is it, for example, that “birds lay eggs” seems true, while “birds are female” seems false, despite the fact that only female birds lay eggs?</p>
<p>Given the connection between generics and inference, I’ll go on to consider how inference relates to the process of <em>accommodation</em>, which plays a significant role in how we manage dialogue and conversation. This, in turn, helps shed some light on some different ways expressions can involve <em>pejorative force</em>, and can inform options for how our vocabulary and our concepts can be revised or reformed.</p>
<ul>
<li><p>This is a talk for the <em><a href="https://philevents.org/event/show/42298">University of Melbourne Thursday Philosophy Seminar</a></em>.</p></li>
<li><p>The <a href="https://consequently.org/slides/accommodation-unimelb-2018.pdf">slides for the talk are available here</a>, and the <a href="https://consequently.org/handouts/accommodation-unimelb-handout-2018.pdf">handout is here</a>.</p></li>
</ul>
Truth Tellers in Bradwardine's Theory of Truth
https://consequently.org/writing/bradwardine-truth-tellers/
Wed, 21 Mar 2018 00:00:00 UTChttps://consequently.org/writing/bradwardine-truth-tellers/<p>Stephen Read’s work on Bradwardine’s theory of truth is some of the most exciting work on truth and insolubilia in recent years. Read brings together modern tools of formal logic and Bradwardine’s theory of signification to show that medieval distinctions can give great insight into the behaviour of semantic concepts such as truth. In a number of papers, I have developed a model theory for Bradwardine’s account of truth. This model theory has distinctive features: it serves up models in which every declarative object (any object signifying <em>anything</em>) signifies its own truth. This leads to a puzzle: there are good arguments to the effect that if anything is a truth-teller, it is <em>false</em>. This is a puzzle. What distinguishes <em>paradoxical</em> truth-tellers from <em>benign</em> truth tellers? It is my task in this paper to explain this distinction, and to clarify the behaviour of truth-tellers, given Bradwardine’s account of signification.</p>
Isomorphisms in a Category of Propositions and Proofs
https://consequently.org/presentation/2018/logicmelb-isomorphisms/
Tue, 13 Feb 2018 00:00:00 UTChttps://consequently.org/presentation/2018/logicmelb-isomorphisms/<p><em>Abstract</em>: In this talk, I show how a category of propositions and classical proofs can give rise to three different hyperintensional notions of sameness of content. One of these notions is very fine-grained, going so far as to distinguish \(p\) and \(p\land p\), while identifying other distinct pairs of formulas, such as \(p\land q\) and \(q\land p\); \(p\) and \(\neg\neg p\); or \(\neg(p\land q)\) and \(\neg p\lor\neg q\). Another relation is more coarsely grained, and gives the same account of identity of content as equivalence in Angell’s logic of analytic containment. A third notion of sameness of content is defined, which is intermediate between Angell’s and Parry’s logics of analytic containment. Along the way we show how purely classical proof theory gives resources to define hyperintensional distinctions thought to be the domain of properly non-classical logics.</p>
<ul>
<li><p>This is a talk for the <a href="blogs.unimelb.edu.au/logic/logic-seminar/">Melbourne Logic Seminar</a>.</p></li>
<li><p>The <a href="https://consequently.org/slides/isomorphisms-talk-unimelb-2018.pdf">slides of the talk are available here</a>, and the <a href="https://consequently.org/handouts/isomorphisms-handout-unimelb-2018.pdf">handout is here</a>.</p></li>
</ul>
Substructural Logics
https://consequently.org/writing/slintro/
Wed, 21 Feb 2018 00:00:00 UTChttps://consequently.org/writing/slintro/<p><i>Substructural logics</i> are non-classical logics <i>weaker</i> than classical logic, notable for the absence of <i>structural rules</i> present in classical logic. These logics are motivated by considerations from philosophy (relevant logics), linguistics (the Lambek calculus) and computing (linear logic). In addition, techniques from substructural logics are useful in the study of traditional logics such as classical and intuitionistic logic. This article provides an overview of the field of substructural logic.</p>
Community (the twelfth of twelve things I love about philosophical logic)
https://consequently.org/news/2017/twelve-things-12-community/
Sat, 30 Dec 2017 17:12:57 +1100https://consequently.org/news/2017/twelve-things-12-community/<p>I love the way I’ve met so many different people through working in logic, that I’ve made good friends, good colleagues, good teachers and mentors. I’ve been part of an enterprise that’s larger than any one person. I have been shaped by that community, and have had the opportunity to made some small mark on it myself.</p>
<p>Logic, like any other academic discipline, has a history. The activities of <em>doing</em> logic — of <em>studying</em>, <em>researching</em> and <em>teaching</em> — are spread out through time. Those activities are also, equally, spread out in space. Logic is done in many different places, in many different contexts, by many different individuals, and research teams. As I’ve already pointed out, those activities are shaped by different disciplinary connections (into philosophy, mathematics, computer science, linguistics, engineering, etc.), but they are also shaped by the emphases of different research groups and traditions. Research, these days, is dominated not so much by a small number of iconic logicians, but by research groups with distinctive research programmes.</p>
<p>Here are some examples: think of the difference between Amsterdam-style modal logic, on the one hand, and exact truthmaking semantics on the other, concerning approaches to intensionality and hyperintensionality, or for examples on the proof theoretical side of the street, the different traditions of Higher Order Type Theory and of Linear Logic and Ludics as frameworks for understanding proof, computation and meaning. The differences between these traditions are not simply matters of differences between individual researchers and their emphases — though of course, there are significant founding figures for each tradition I mention — the driving forces in each of these active research programmes is at the level of the <em>team</em> or beyond. Each approach brings with it a (larger or smaller) loose formation of researchers who work on problems in their fields: they get together at conferences and workshops, co-author papers, apply for research grants, supervise graduate students, all the while, maintaining and developing the tradition. Research that leaves a mark is not so much the activity of the brilliant sole researcher, it occurs at a larger scale.</p>
<p>Recognising this fact brings important questions to the fore: given that research at this scale is a community enterprise, how does that community function? Who is included? Who is excluded? How are people trained and shaped? What kinds of conversations are possible? What approaches are encouraged? My little corner of philosophical logic is only beginning to explicitly address some of these issues. <a href="https://gillianrussell.net">Gill Russell</a> and worked to get a decent gender balance in our <a href="http://consequently.org/writing/new-waves-in-philosophical-logic/">edited collection</a>. We partly succeeded on that front. We fail, mightily, on including participants from outside Europe, America and Australia. Further, the group of authors is overwhelmingly white. We could have done better. There is scope for the community to be more representative of thew wider community around us. Lasting change will require more than just good will and effort from individuals: it will involve broader social change, so that the oppressed and excluded get their due, and all to have the opportunities currently afforded to those who have the easiest access to higher education. That social change won’t come easy. However, those of us with the institutional capital to be able to shape and support research groups nonetheless have the opportunity to leave the discipline better than we found it, with a wider spectrum of voices included, with all people treated well, and a broader family of concerns taken seriously. We can run conferences where people are treated well; we can mentor and support our students, both women and men; we can encourage the work of those whose voices are routinely excluded, and so, build up a community that is resilient and flourishing.</p>
<p>As for me, I’ve been fortunate, more fortunate than I can readily discern. Not only have I been shaped by encouraging and supportive teachers and mentors throughout my own research career, but unlike many of my female colleagues, I’ve not been harassed or endangered. No-one has attempted to take advantage of me, or pass my work off as theirs. Overwhelmingly, people in my field have taken me seriously, even when I was a blundering student, attempting to find my way in the wider academic world. The reception I’ve had in the wider academic world is the kind of community I want for those coming after me.</p>
<p><em>Community</em> is the twelfth of <a href="http://consequently.org/news/2017/twelve-things-i-love/">twelve things that I love about philosophical logic</a>.</p>
Proof Identity, Aboutness and Meaning
https://consequently.org/presentation/2017/proof-identity-aboutness-and-meaning/
Mon, 06 Nov 2017 00:00:00 UTChttps://consequently.org/presentation/2017/proof-identity-aboutness-and-meaning/<p><em>Abstract</em>: This talk is a comparison of how different approaches to hyperintensionality, aboutness and subject matter treat (classically) logically equivalent statements. I compare and contrast two different notions of subject matter that might be thought to be representational or truth first – <em><a href="https://www.amazon.com/Aboutness-Carl-G-Hempel-Lecture/dp/0691144958/consequentlyorg">Aboutness</a></em> (Princeton University Press, 2014), and truthmakers conceived of as situations, as discussed in my “<a href="http://consequently.org/writing/ten/">Truthmakers, Entailment and Necessity</a>.” I contrast this with the kind of inferentialist account of hyperintensionality arising out of the <em>proof invariants</em> I have explored <a href="http://consequently.org/writing/proof-terms-for-classical-derivations/">in recent work</a>.</p>
<p>This is a talk presented at the <a href="https://www.gla.ac.uk/schools/humanities/research/philosophyresearch/researchprojects/thewholetruth/formalphilosophy/">Glasgow-Melbourne Formal Philosophy Workshop</a>.</p>
<ul>
<li>The <a href="http://consequently.org/slides/proof-identity-aboutness-and-meaning.pdf">slides are available here</a>.</li>
</ul>
Negation on the Australian Plan
https://consequently.org/presentation/2017/negation-on-the-australian-plan/
Wed, 23 Aug 2017 00:00:00 UTChttps://consequently.org/presentation/2017/negation-on-the-australian-plan/<p><em>Abstract</em>: In this talk, I explain the difference between <em>Australian Plan</em> semantics for negation – which treat negation as a kind of negative modality – and semantics based on the <em>American Plan</em>, which conceive of negation in terms of independent truth and falsity conditions. I will update the presentation of the Australian Plan (introduced in the 1970s in early days of the ternary relational semantics for relevant logics), in the light of more recent developments in logic, and defend this updated plan in the face of some recent criticisms due to <a href="http://www.michaelde.com">Michael De</a> and <a href="https://sites.google.com/site/hitoshiomori/home">Hitoshi Omori</a>, in their paper “<a href="http://dx.doi.org/10.1007/s10992-017-9427-0">There is More to Negation than Modality</a>.” Along the way, I hope to draw out some insights into what we might want out of a representational semantics for a language with a consequence relation.</p>
<p>This talk is based on joint work with <a href="http://www.uva.nl/en/profile/b/e/f.berto/f.berto.html">Professor Franz Berto</a>, from the University of Amsterdam.</p>
<p>This is a talk presented at the <a href="http://blogs.unimelb.edu.au/logic/logic-seminar/">Melbourne Logic Seminar</a>.</p>
<ul>
<li>The <a href="https://consequently.org/slides/negation-on-the-australian-plan-logicmelb.pdf">slides are available here</a>.</li>
</ul>
Learning and Teaching (the eleventh of twelve things I love about philosophical logic)
https://consequently.org/news/2017/twelve-things-11-learning-and-teaching/
Tue, 19 Sep 2017 22:47:48 +1100https://consequently.org/news/2017/twelve-things-11-learning-and-teaching/<p>Working in philosophical logic, I love the opportunity to <em>learn</em> from so many people through history, and not only to <em>learn</em>, but to pass on a tradition, and to have the opportunity to extend the tradition, and to refine it a little, in passing it on. It’s been a delight to learn from some <a href="http://consequently.org/writing/logicians/">great figures</a>, the historical figures through their writing, and my contemporaries in person, both as <em>face-to-face teachers</em> (while a student, I learned logic from Sheila Oates-Williams, Neil Williams, Rod Girle, Ian Hinckfuss, and Graham Priest), but the learning doesn’t stop when you finish your degree. I’ve learned much from colleagues (Bob Meyer, Richard Sylvan, John Slaney, Allen Hazen, Graham Priest (again), Zach Weber, Dave Ripley, Shawn Standefer), whose work I admire, and who generously share of their time at whiteboards, in seminars, and in many many conversations. I have also learned a great deal from all of my <a href="http://consequently.org/writing/logicians/">graduate students</a>, who have sent me in directions I never expected to head. If learning logic is (in part) <a href="http://consequently.org/news/2017/twelve-things-05-recognition/">gaining facility with the concepts you have</a>, as well as <a href="http://consequently.org/news/2017/twelve-things-06-expansion/">acquiring new concepts</a>, then working <em>with others</em> is a very good way to learn. The kinds of knowledge you acquire is not merely <em>knowing that</em>, but it (at least in part) skills to be learned, and they’re learned by practice, and sometimes skilled practice is best acquired when guided by others — explicitly, when the teacher knows she is <em>teaching</em> — or implicitly, when we observe an expert displaying expertise, and we can use their practice to scaffold our own, and learn by imitation. I’ve learned so much from my teachers, not only in consciously building on their ideas, but in learning how to <em>be</em> a logician by starting in their footsteps.</p>
<p>One way to develop the tradition is to <a href="http://consequently.org/class/">teach</a>, and a significant part of my job at the <a href="http://unimelb.edu.au">University of Melbourne</a> is to teach, and a lot of my time is spent teaching philosophical logic. Putting together a course is a good way of sorting out your ideas, and in philosophical logic, where the concepts very clearly and precisely build on prior ideas, it is a real intellectual challenge to see how you can teach a course in 12 weeks that, say, <a href="http://consequently.org/class/2017/PHIL30043">introduces Gödel’s incompleteness theorems</a> and everything you need to understand them. This is a challenge, and designing the curriculum in such a way to carry undergraduate students from the basics of predicate logic, through soundness and completeness, into Peano arithmetic, recursive functions, diagonalisation, and into Gödel’s proofs — and to do it in some way that there is hope that the students will survive the journey with their curiosity and interest intact! — forces you to come to grips with the concepts in a way that a cursory understanding won’t suffice. I can truly say that I’ve come to understand things much more deeply when I’ve had the opportunity to <em>teach</em> them.</p>
<p>That’s why I’m enjoying <a href="http://consequently.org/writing/ptp/">writing my new book</a>. Officially, it is a research monograph and not a textbook, but one of the ways I’ve been describing it (to myself, and to others, who ask me what I’m writing on) is that it’s trying to explain to people attracted to normative pragmatic theories of meaning what they can do with recent work in logic (in proof theory, in particular), and to explain to logicians what philosophy they should have to understand why proof theory works so well. Yes, the core of it is a particular <em>argument</em> for a way of understanding the distinctive nature of logic, but that argument is buttressed by a lot of <em>showing</em> as well as <em>saying</em>. You’ve got to <em>learn some logic</em> to understand why it is the kind of thing it is, and to get a real sense of what it can <em>do</em> (and what it can’t). To do that, is to <em>teach</em>, as well as to <em>argue</em>, and that is just how I like it.</p>
<p><em>Learning and Teaching</em> is the eleventh of <a href="http://consequently.org/news/2017/twelve-things-i-love/">twelve things that I love about philosophical logic</a>.</p>