# Southern Summer Logic Day

# 2022

With the purpose of celebrating the UNESCO World Logic Day, the Australasian Association for Logic will host a **Southern Summer Logic Day**. The event will take place on Zoom (contact Guillermo Badia at g.badia@uq.edu.au for the Zoom link). There will be one keynote presentation by Max Cresswell . Max is Emeritus Professor at Victoria University of Wellington and a world-renowned modal logician. The date and time will be Thursday, 13 January 2022 at 23:00:00 (UTC). In addition to the keynote, there will be four invited talks. The speakers will be John N. Crossley (Emeritus Professor, Monash University), Isabella McAllister (PhD student, University of Auckland), Gillian Russell (Professor, Australian Catholic University) and Lavinia Picollo (Assistant Professor/Lecturer, National University of Singapore/University College London).

**Timetable **** (in **AEDT**): **

** **

Max Cresswell (Keynote): 10AM - 11:10AM

Gillian Russell: 11:25AM - 12:30PM

Lunch break

Isabella McAllister: 1:30PM - 2:30PM

Lavinia Picollo : 2:45 PM- 3:45PM

John N. Crossley: 4PM - 5 PM

**ORGANIZERS**

Guillermo Badia (University of Queensland, Australia)

Nick J J Smith (University of Sydney, Australia)

Shawn Standefer (National Taiwan University, Taiwan)

Zach Weber (University of Otago, New Zealand)

Max Cresswell (Victoria University of Wellington)

# WHY DID W. V. O. QUINE HATE RUTH BARCAN MARCUS?

# The Curious Relation between Ideology and Logic

[Supplementary Handout; Timeline; Becker-Title Page; Oscar Becker's *Zur Logik der Modalitäten*; Quine on politics]

It is known that Willard van Orman Quine had an antipathy to modal logic in general and to modal predicate logic in particular. While that dispute is known to modal logicians it has always seemed to many of us that there must be more to the story than that. Apart from Quine and Marcus I will mention another American logician, William Tuthill Parry. Both Quine and Parry were in Germany in the 1930s. Among the Continental logicians I will mention Oskar Becker and Rudolf Carnap, and talk about the connection between political ideology in Germany at that time, and the differing philosophical ideologies (essentially metaphysics vs logical positivism). I will then look at how these differences affected attitudes to modal logic.

I will then move to the political situation in the United States in the 1950s and and mention the communist views of Parry and the socialist background of Ruth Barcan.

Finally I will point out how all these factors affect attitudes to quantified modal logic in a way in which from Quine's perspective Marcus ticked all the wrong boxes.

This talk will be about logic but **will not be a technical talk** and should be **accessible to anyone with an interest in the topic**.

Hume’s Law is the thesis that you *can’t get an ought from an is* or, less snappily, that descriptive premises never entail normative conclusions. The thesis is deeply controversial in both logic and metaethics. This talk will look at some famous attempted counterexamples to the law and then at a method for proving it as an instance of a more general theorem, which has several other philosophically interesting—though less controversial—barriers to entailment as instances as well. For example, that you can't get general conclusions from particular premises, or conclusions about the future from premises that are only about the past.

So called “impossible worlds” have soared in popularity over the past couple of decades due to their usefulness in analyzing various hyperintentional phenomena, counterlogicals and their ilk, as well as other interesting topics. In recent years, some authors writing about these have developed a habit of describing some logic or another as being the “correct” logic at a world and of making modal claims about the correctness of logics. However, such talk occurs without examination of what it means for a logic to be correct at a world. Additionally, worlds at which classical logic is "correct" are often given a privileged status over those at which some other logic is correct. In my talk I explore in (non-technical) detail how to understand these claims by developing an account of how worlds can be governed by different logics. I then illustrate how this particular treatment of worlds can be used to analyze a range of philosophical questions.

Arithmetical pluralism is the view that every consistent arithmetical theory is true (of some objects) and, therefore, as legitimate as any other, at least from a theoretical standpoint. Pluralist views have recently attracted much interest but have also been the subject of significant criticism, most saliently from Putnam (1979) and Koellner (2009). These critics argue that, due to the possibility of arithmetizing the syntax of arithmetical languages, one cannot coherently be a pluralist about arithmetical truth while holding that claims about consistency are matters of fact. In response, Warren (2015) argued that Putnam's and Koellner's argument relies on a misunderstanding, and that it is in fact coherent to maintain a pluralist conception of arithmetical truth while supposing that consistency is a matter of fact. In this paper we argue that it is not. We put forward a modified version of Putnam's and Koellner's argument that isn't subject to Warren's criticisms. This is joint work with Dan Waxman.

John N. Crossley (Monash University)

# WHAT IS MATHEMATICAL LOGIC?

[Audio 1974 Reminiscence of logicians; transcript 1974 Reminiscence of logicians; Alan Robinson's interview (Part 1, Part 2); Crossleyfest 14 June- 15 June 2022]

*What is mathematical logic?*, the book, was published fifty years ago. It was a first in many ways, not least it was an Australian production.

What has changed since then and what has remained the same?

In this presentation I shall give an account of the Melbourne lectures that gave birth to the book, then go on to the 1974 Monash conference and subsequent developments.

A caveat: The interests of the groups I have worked with have primarily been very mathematical --- little, if any, modal or other such logic.

What has been special about my career is the people I have met, so my concern is more with what they said than what I have said or have to say.

In the seventies the four branches of Mathematical Logic were Model Theory, Proof Theory, Recursive Function Theory and Set Theory.

Over the succeeding years Computer Science has grown and has both influenced and been influenced by formal logic. Some `new' areas, dependent on theory, are Program Verification, Theorem Proving and Denotational Semantics.

Of course there is also Logic Programming. So the question becomes: `What is mathematical logic now?'

There will be unashamed name dropping: Steve Kleene, Dana Scott, Alan Robinson, Jean-Yves Girard, to name but four.

Finally I shall briefly talk about the Philosophy of Mathematics: certainly Constructivism, but also mathematics as a human endeavour.