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Conference Report: SOTFOM III, 21-23 September 2015

The 3rd Symposium on the Foundations of Mathematics was held in the Lecture Hall of the KGRC, in Vienna, from the 21st to the 23rd of September 2015.

The purpose of the conference was to bring together scholars who, in the last years, have contributed to the ongoing debate on the foundations of set theory, in particular  on such topics as the universe/multiverse dichotomy, new axioms of set theory and their ontological and epistemological features, different forms of justification for the acceptance of new axioms, competing foundations and, finally, the Hyperuniverse Programme (HP), which is currently investigated at the KGRC by S. Friedman and collaborators.

The conference was opened by Tatiana Arrigoni’s talk, which aimed to assess the current status of the HP, as recently developed by Friedman, Antos, Honzik and Ternullo. Arrigoni acknowledged that much work has been done within the programme in the direction of connecting multiverse axioms to the concept of set, but she also pointed out that further work is needed to make a full case for the `intrinsicness’ of the programme’s maximality principles. She also encouraged further work on the issue of why the programme believes that intrinsically justified axioms are particularly valuable for the fruitful (and correct) development of set theory.

In his talk, Giorgio Venturi explained how forcing may lend support to a realist conception of set theory, by using what he calls trans-universe realism, whose plausibility, in turn, is grounded on some recent mathematical results due to Hamkins. Pushing this interpretation of forcing even further, Venturi suggested that the notion of arbitrary set, which is an integral part of what he sees as a feature of a realist attitude in set theory (Bernays’ quasi-combinatorialism), may find a sharper formulation in that of generic set, as used in forcing.

Finally, in the last talk in the morning of Day 1, Dan Waxman assessed the argument that the independence phenomenon in set theory leads one to viewing some set-theoretic statements as indeterminate. The specific argument assessed by Waxman takes determinacy to arise either from the `world’ or from our `practice’. Now, if one accepts what Waxman defines, respectively, a metaphysical (1) and a cognitive (2) constraints on our theories, whereby, respectively, (1) objects are not ineliminable in our best account of mathematics and (2) we cannot attribute non-mechanical powers to our minds, then there will, of necessity, be indeterminate statements in set theory.

In the afternoon, Matteo Viale reviewed some of the reasons why forcing axioms have proved to be `successful’ in set theory. Among others, he pointed to the following two: (1) they are equivalent to key, well-established principles, such as the Axiom of Choice, and (2) they lead to absoluteness results within the set-generic multiverse.

In the last talk of Day 1, Øystein Linnebo presented his well-known modal version of the axioms of set theory using plural quantification, showing how it fits the requirements of a potentialist conception which originates from Cantor’s work (which famously identifies proper classes such as the ordinals as inconsistent, qua incompletable, multiplicities). In Linnebo’s account, this means, in particular, that (1) not all objects in V are given immediately (rather, they are produced gradually) and (2) that truths are `created’ as the hierarchy gradually unfolds.

On Day 2, Mary Leng reviewed Penelope Maddy’s recent `Defending the New Axioms’ book, where Maddy advocates a form of realism labelled `thin’ realism or `arealism’. In particular, Leng described how, by this conception, the old dispute about the existence of mathematical objects is irrelevant, while it is still relevant for it, and it still makes sense to ask, whether CH, e.g., is true or false. She then took a step further, by pointing out that arealism might, in fact, be compatible with the view that there is no fact of the matter about whether CH is true or false.

Afterwards, Neil Barton showed that the HP may be compatible with several pictures of the universe of sets and, in particular, with that arising from an `absolutist’ conception of V. The bulk of Barton’s strategy consists in showing that not only forcing extensions of V can be coded into models definable in V itself, as already shown by Hamkins, but, in general, that this, using V-logic, applies to all outer models of the Morse-Kelley axioms (which, in turn, best express the absolutist viewpoint). V-logic is a basic ingredient to express HP’s maximality principles and, thus, Barton’s project may open the way to an `absolutist’ construal of the HP.
The rest of Day 2 was spent making a trip in the Wienerwald. After having lunch in the rural Mostalm, Dr Peter Telec kindly offered to lead a relaxing walk through the beautiful Viennese woods.

IMG_20150922_133159

Day 3 opened with Geoffrey Hellman’s talk detailing a height-potentialist conception of V. Hellman showed us how his account, relying on a modal version of Zermelo’s second-order ZFC, is adequate to express some crucial intuitions behind set theory, including the \emph{set/class} distinction as proposed by Zermelo, as well as the indefinite extendability of the universe. Moreover, he showed how his account could also more naturally justify second-order reflection, which would take us beyond the inaccessibles and would help justify all small large cardinals.
Talking after Hellman, Sam Sanders showed that, using non-standard analysis, one can successfully respond to Voevodsky’s recently questioning the adequacy of ZFC as a foundation of mathematics, insofar as the latter cannot be `computational’. This presupposition led Voevodsky to reject ZFC as a foundation and advocate HoTT (Homotopy Type Theory) as a plausible alternative. As shown by Sanders, `computational’, here, does not mean `implemented by a computer’, but rather `constructive’ in the sense of Per-Löf’s intuitionistic type-theoretic system.
Subsequently, Emil Weydert explored the intiriguing topic of how the HP could be used to produce an axiom induction framework. The basic ingredient is given by formalising `multiverse reasoning’ in terms of non-monotonic reasoning, whereby the addition of new hypotheses (i.e., new axioms) leads to finding differring conclusions. Weydert’s project also envisages taking into account other parameters which are relevant to selecting new axioms.
In his talk, Douglas Blue started with a definition of maximality in set theory as the demand that a candidate axiom maximise the interpretative power of a theory T. But he showed us the interesting case of the axiom (\star), which satisfies the aforementioned definition (that is, as shown by Woodin, it maximises the theory of H(\omega_2) as far as \Pi_2-sentences are concerned), but is in contrast with a more intuitive version of maximality, one entailing that the power-set operation adds novel structure: if we adopt (\star), then we have that H(\omega_1) is bi-interpretable with H(\omega_2) and, thus, (\star) fails to satisfy the second version of maximality.

Our last speaker was Sy Friedman, who described different notions of `new axiom’ and justifications thereof. Friedman reviewed the maximality principles which have been investigated within the HP and, arguably, related to the concept of set (and, thus, intrinsically justified). Now, one further criterion to judge the value of an axiom is to see whether it is useful. However, here Friedman departs from the standard interpretation of this, by suggesting that the most useful set-theoretic axioms should be those which are also useful for non-set-theoretic mathematics. Finally, he formulated the conjecture that the intrinsically justified higher-order principles of HP will prove useful to find first-order axioms which are useful for non-set-theoretic mathematics: such axioms will then have to be considered true axioms of set theory.

The conference had several outcomes. First, we believe it helped understand some of the underlying assumptions in the HP, and also the theoretical challenges it has to face up to, and the different ways such challenges can be met (Arrigoni, Weydert, Barton).

The potentialist conception was reviewed in depth (Linnebo, Hellman), and its main advantages in light of the clear foundational purposes of set theory fully described.

A description of the multiverse and its utility for set theory was carried out in several talks, and the pressing issues of truth and ontology relating to it, as arising from pluralism (Waxman) or in relation to realism (Venturi), were also examined.

Naturalism was evoked in some talks (Leng, Venturi, Arrigoni). From these talks and the ensuing discussion, it seems reasonable to assert that it is still unclear whether naturalism can properly ground set-theoretic work in a fully satisfactory way, especially if one shifts to a multiversist conception.

New set-theoretic axioms, arising from the need for `maximality’ principles, were the subject of several talks (Barton, Friedman, Blue, Viale), all of which, in our opinion, helped dispel some confusion relating to the notion of maximality, but, at the same time, also clearly highlighted how poorly understood the notion still is. The debate on what form maximality is more acceptable is still open, but it seems that the HP may have good prospects to break new grounds.

Finally, Sanders’ talk hinted at how the issue of what foundational theory is preferable, among those available, might be solved in a way alternative to those usually discussed, that is, by looking into such features as that of `computability’.

In recognition of the joint effort of the organisers and speakers, a proposal for the proceedings of the conference, also including some of the papers discussed at previous SOTFOMs, will be submitted to Synthese.

A selection of slides for the talks is available here: Weydert, Venturi, Arrigoni, Hellman, Linnebo, Friedman, Sanders, VialeBarton,  Waxman and Warren.

We already look forward to SotFoM IV!

*CHANGES* and FINAL CFR: SoTFoM III and The Hyperuniverse Programme, Vienna, 21-23 September 2015.

*CHANGES* and FINAL CFR: SoTFoM III and The Hyperuniverse Programme, Vienna, 21-23 September 2015.

The organisers are delighted to announce the programme for the upcoming conference on `The Hyperuniverse Programme’, part of the Symposia on the Foundations of Mathematics series. The Hyperuniverse Programme was launched in 2012, and is currently pursued within a Templeton-funded research project at the Kurt Gödel Research Center in Vienna. It aims to identify and philosophically motivate the adoption of new set-theoretic axioms.The programme intersects several topics in the philosophy of set theory and of mathematics, such as the nature of mathematical (and set-theoretic) truth, the universe/multiverse dichotomy, the alternative conceptions of the set-theoretic multiverse, the conceptual and epistemological status of new axioms and their alternative justificatory frameworks.The aim of SotFoM III and The Hyperuniverse Programme Joint Conference is to bring together scholars who, over the last years, have contributed mathematically and philosophically to the ongoing work and debate on the foundations and the philosophy of set theory, in particular, to the understanding and the elucidation of the aforementioned topics. The three-day conference, taking place September 21-23 at the KGRC in Vienna, will feature invited and contributed speakers.

Programme:
Day 1 – 21 September 2015
1000-1005 Introductory remarks
1005-1135 Tatiana Arrigoni: TBC
1135-1150 Coffee Break
1150-1250 Giorgio Venturi: `Forcing, Multiverse and Realism’
1250-1500 Lunch
1500-1600 Daniel Waxman and Jared Warren: `Is there a good argument for mathematical pluralism?’
1600-1615 Coffee Break
1615-1715 Matteo Viale: `Category forcings and generic absoluteness: Explaining the success of strong forcing axioms.’
1715-1730 Coffee break
1730-1900 Øystein Linnebo: `Potentialism about set theory.’

Day 2 – 22 September 2015

0900-1030 Mary Leng: `On “Defending The Axioms”.’
1030-1045 Coffee Break
1045-1215 Neil Barton: `How the hyperuniverse behaves.’
1230 Trip to Mostalm for social lunch.

Day 3 – 23 September

1000 -1005 Introductory remarks
1005-1135 Geoffrey Hellman: `A height-potentialist multiverse view of set theory.’
1135-1150 Coffee Break
1150-1250 Sam Sanders: `Non-standard analysis as a computational foundation.’
1250-1500 Lunch
1500-1600 Emil Weydert: `A multiverse axiom induction framework.’
1600-1615 Coffee Break
1615-1715 Douglas Blue: `Forcing axioms and maximality as the demand for interpretability.’
1715-1730 Coffee break
1730-1900 Sy-David Friedman: `What are axioms of set theory?’

To register, please send an e-mail to sotfom [at] gmail [dot] com with SOTFOM III REGISTRATION as the subject header.

For more information contact one of:

Carolin Antos: carolin.antos-kuby [at] univie [dot] ac [dot] at

Claudio Ternullo: claudio [dot] ternullo [at] univie [dot] ac [dot] at

John Wigglesworth: jmwigglesworth [at] gmail [dot] com

Neil Barton: barton [dot] n [dot] a [at] gmail [dot] com

Or visit https://sotfom.wordpress.com/

CFR and Programme: SoTFoM III and The Hyperuniverse Programme.

The organisers are delighted to announce the programme for the upcoming conference on `The Hyperuniverse Programme’, part of the Symposia on the Foundations of Mathematics series. The Hyperuniverse Programme was launched in 2012, and is currently pursued within a Templeton-funded research project at the Kurt Gödel Research Center in Vienna. It aims to identify and philosophically motivate the adoption of new set-theoretic axioms.The programme intersects several topics in the philosophy of set theory and of mathematics, such as the nature of mathematical (and set-theoretic) truth, the universe/multiverse dichotomy, the alternative conceptions of the set-theoretic multiverse, the conceptual and epistemological status of new axioms and their alternative justificatory frameworks.The aim of SotFoM III and The Hyperuniverse Programme Joint Conference is to bring together scholars who, over the last years, have contributed mathematically and philosophically to the ongoing work and debate on the foundations and the philosophy of set theory, in particular, to the understanding and the elucidation of the aforementioned topics. The three-day conference, taking place September 21-23 at the KGRC in Vienna, will feature invited and contributed speakers.

Programme:
Day 1 – 21 September 2015
1000 -1005 Introductory remarks
1005-1135 Tatiana Arrigoni: TBC
1135-1150 Coffee Break
1150-1250 Giorgio Venturi: `Forcing, Multiverse and Realism’
1250-1500 Lunch
1500-1600 Daniel Waxman and Jared Warren: `Is there a good argument for mathematical pluralism?’
1600-1615 Coffee Break
1615-1715 Matteo Viale: `Category forcings and generic absoluteness: Explaining the success of strong forcing axioms.’
1715-1730 Coffee break
1730-1900 Øystein Linnebo: `Potentialism about set theory.’

Day 2 – 22 September 2015

0900-1030 Mary Leng: TBC
1030-1045 Coffee Break
1045-1215 Hugh Woodin: TBC
1230 Trip to Mostalm for social lunch.

Day 3 – 23 September

1000 -1005 Introductory remarks
1005-1135 Geoffrey Hellman: `A Height-Potentialist Multiverse View of Set Theory.’
1135-1150 Coffee Break
1150-1250 Sam Sanders: `Non-standard analysis as a computational foundation.’
1250-1500 Lunch
1500-1600 Emil Weydert: `A multiverse axiom induction framework.’
1600-1615 Coffee Break
1615-1715 Douglas Blue: `Forcing axioms and maximality as the demand for interpretability.’
1715-1730 Coffee break
1730-1900 Peter Koellner: `On the Multiverse Conception of Set.’

To register, please send an e-mail to sotfom [at] gmail [dot] com with SOTFOM III REGISTRATION as the subject header.

For more information contact one of:

Carolin Antos: carolin.antos-kuby [at] univie [dot] ac [dot] at

Claudio Ternullo: claudio [dot] ternullo [at] univie [dot] ac [dot] at

John Wigglesworth: jmwigglesworth [at] gmail [dot] com

Neil Barton: barton [dot] n [dot] a [at] gmail [dot] com

Or visit https://sotfom.wordpress.com/

SOTFOM_poster_print

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

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

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

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

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

Invited Speakers

T. Arrigoni (Bruno Kessler Foundation)
G. Hellman (Minnesota)
P. Koellner (Harvard)
M. Leng (York)
Ø. Linnebo (Oslo)
W.H. Woodin (Harvard)

+

I. Jané (Barcelona) [TBC]

Call for papers
We invite (especially young) scholars to send their abstracts (of 1’500 words or fewer), addressing one of the following topical strands:

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

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

https://easychair.org/conferences/?conf=sotfom3hyp

If there is a paper to back up the abstract (say containing details of proofs, if any) they can be sent to sotfom [at] gmail [dot] com.

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

Key Dates:
Submission deadline: 15 June 2015 (there will *not* be a deadline extension)
Notification of acceptance: 15 July 2015

For further information, please contact:

sotfom [at] gmail [dot] com

or alternatively one of:

C. Antos
N. Barton
C. Ternullo
J. Wigglesworth

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

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

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

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

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

Invited Speakers

T. Arrigoni (Bruno Kessler Foundation)
G. Hellman (Minnesota)
P. Koellner (Harvard)
M. Leng (York)
Ø. Linnebo (Oslo)
W.H. Woodin (Harvard)

+

I. Jané (Barcelona) [TBC]

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

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

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

https://easychair.org/conferences/?conf=sotfom3hyp

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

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

For further information, please contact:

sotfom [at] gmail [dot] com

or alternatively one of:

C. Antos
N. Barton
C. Ternullo
J. Wigglesworth

Report: Second Symposium on the Foundations of Mathematics

The Second Symposium on the Foundations of Mathematics was held at Senate House, University of London, from the 12-14 January 2015. The event was successfully advertised through the organising team’s network of contacts, including online mailing lists and blogs, local, national and international philosophy department mailing lists, and the Symposium’s dedicated website. Extensive advertising for the event resulted in approximately 40 participants. The event focused on different approaches to the foundations of mathematics, and built on themes discussed at the First Symposium on the Foundations of Mathematics, held in July 2014 at the Kurt Gödel Research Center, University of Vienna. Talks on the first day, by James Ladyman (University of Bristol), David Corfield (University of Kent), and Dimitris Tsementzis (Princeton University) focused on category-theoretic approaches to the foundations of mathematics. There was particular emphasis on cutting edge research in Homotopy Type Theory, an emerging foundations programme that has been hailed as a strong alternative to traditional set-theoretic foundations. One of the main questions that arose from these talks was how it would be possible to compare category-theoretic and set-theoretic approaches as competing programmes in the foundations of mathematics. This question was directly addressed by Toby Meadows (University of Aberdeen), who gave the last talk of the day, and discussed a general framework for comparing different foundational programmes.

Dr. Meadows’s talk led naturally into the second day of the conference, which focused primarily on recent work on set-theoretic foundations. Sy-David Friedman (University of Vienna) discussed his current project, the hyper-universe programme, which aims to find and justify new set-theoretic axioms in order to reduce the incompleteness of ZFC set theory (Zermelo-Fraenkel set theory with the Axiom of Choice).  Shivaram Lingamneni (Stanford University/University of California, Berkeley) discussed the possibility of resolving the Continuum Hypothesis, a very natural set-theoretic statement that cannot be resolved by the ZFC axioms.  Sam Sanders (University of Ghent / Munich Center for Mathematical Philosophy) gave a presentation arguing that predicativism, a limitative approach to arithmetic, justifies different resources dependent upon the acceptance of infinitesimals (a controversial but useful kind of mathematical object). Finally, the day was rounded off by Victoria Gitman (City University of New York) who explored different kinds of Choice principle (a natural mathematical principle) in the context of class theory, thus informing the debate concerning a philosophically and mathematically fascinating kind of entity linked to the very inception of foundations.

Because of the outstanding quality of the contributed papers, the organisers accepted an additional paper from Benedict Eastaugh (Bristol), who presented the last talk on the morning of the third day.  In this presentation, Benedict’s research on reverse mathematics was applied to the problem of discovering new set-existence principles.

On all three days, there was ample time for lively and informal discussion at the organised coffee breaks, lunches and dinners. We were fortunate to have delegates from across the UK, Europe and the US to bring international perspectives on all of the topics discussed in the presentations. We anticipate that these informal discussions will lead to the development of research networks where these issues can be discussed in further detail.  Given the high quality of all of the presentations, we plan to arrange for a proceedings volume to collect together a selection of papers based on the talks given at all of the Symposia on the Foundations of Mathematics.

The most important conclusion to be drawn from the conference is that there is still a lot of work to be done in the foundations of mathematics.  From the set-theoretic perspective, the search for new axioms, and how to justify them, is well under way. On the category-theoretic/homotopy type theory side, more work is needed to enable philosophers to understand and apply the methods used in these areas.  And further work is needed to develop a framework within which we can compare these two approaches (and any others) in the foundations of mathematics.

We hope to tackle these projects in further instalments of the Symposia on the Foundations of Mathematics.  Based on the success of this conference in London, there are plans for two more Symposia.  The next event will take place in Vienna, at the Kurt Gödel Research Center, in August/September 2015.  And there are plans for a subsequent event to take place in Bristol during the Summer 2016. There has been an enthusiastic response to the idea of further events to continue these discussions.

SotFom2

Final Programme for SoTFoM II

Here is the Final Programme for SoTFoM II:

12th January. Location: Room 349, Senate House.

09:30-10:00 Coffee/Announcements
10:00-11:30 James Ladyman-‘What Kind of Foundation for Mathematics Is Homotopy Type Theory?’
11:30-12:00 Coffee
12:00-13:15 David Corfield -`Homotopy Type Theory: A New Foundational Language.’
14:45-16.00 Dimitris Tsementzis -`On Structuralist Foundations of Mathematics.’
16.00-16.30 Coffee
16.30-18:00 Toby Meadows-` What are foundations good for and how can we compare them?’

13th January. Location: Room 349, Senate House.
09:30-10:00 Coffee/Announcements
10:00-11:30 Sy-David Friedman-` The three sources of set-theoretic truth.’
11:30-12:00 Coffee
12:00-13:15 Sam Sanders -`On The Contingency of Predicativism.’
13:15-14:45 Lunch
14:45-16.00 Shivaram Lingamneni -`Can We Resolve the Continuum Hypothesis?’
16.00-16.30 Coffee
16.30-18:00 Victoria Gitman-` Kelley-Morse Set Theory and Choice Principles for Classes.’

14 January, Location: Room G22, Senate House.

11:30-13:30 Benedict Eastaugh-`Set Existence Principles in Reverse

The organisers are very grateful to the following organisations for their support of the conference: The Mind Association, The British Society for the Philosophy of Science, The British Logic Colloquium, The Aristotelian Society, The Institute of Philosophy, and Birkbeck College.

CFR: SoTFoM, SYMPOSIUM II `COMPETING FOUNDATIONS?’; INSTITUTE OF PHILOSOPHY, LONDON, 12-13 January 2015.

CFR: SoTFoM, SYMPOSIUM II `COMPETING FOUNDATIONS?’; INSTITUTE OF PHILOSOPHY, LONDON, 12-13 January 2015.

The organisers are delighted to announce a provisional programme and call for registration for the upcoming Symposium in the Foundations of Mathematics, to be held at the Institute of Philosophy in London on 12-13th January 2015. There will be an additional (free) affiliated talk by Benedict Eastaugh at the Institute on the 14th January.

Sponsors: The Mind Association, British Logic Colloquium, Aristotelian Society, British Society for the Philosophy of Science, and Birkbeck College.

Keynote speakers: James Ladyman, Victoria Gitman, Sy-David Friedman, Toby Meadows.

Contributed speakers: David Corfield, Sam Sanders, Dimitris Tsementzis, Shivaram Lingamneni.

Registration: Registration is £10 for students and £20 otherwise. Those wishing to register should send an e-mail to sotfom [at] gmail [dot] com with the subject line `SOTFOM II REGISTRATION’ with their name and fee payable.

Further information can be found on sotfom [dot] wordpress [dot] com, or by e-mailing one of the organisers:

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

Provisional Programme:

12th January.
09:30-10:00     Coffee/Announcements
10:00-11:30     James Ladyman – TBA
11:30-12:00     Coffee
12:00-13:15     David Corfield – `Homotopy Type Theory: A New Foundational Language.’
13:15-14:45     Lunch (Own arrangements)
14:45-16.00     Dimitris Tsementzis – `On Structuralist Foundations of Mathematics.’
16.00-16.30     Coffee
16.30-18:00     Toby Meadows – TBA

13th January.
09:30-10:00     Coffee/Announcements
10:00-11:30     Sy-David Friedman – TBA
11:30-12:00     Coffee
12:00-13:15     Sam Sanders – `On The Contingency of Predicativism.’
13:15-14:45     Lunch (Own arrangements)
14:45-16.00     Shivaram Lingamneni – `Can We Resolve the Continuum Hypothesis?’
16.00-16.30     Coffee
16.30-18:00     Victoria Gitman – TBA

FINAL CFP and *EXTENDED DEADLINE*: SoTFoM II `Competing Foundations?’, 12-13 January 2015, London.

FINAL CFP and *EXTENDED DEADLINE*: SoTFoM II `Competing Foundations?’, 12-13 January 2015, London.

The focus of this conference is on different approaches to the foundations of mathematics. The interaction between set-theoretic and category-theoretic foundations has had significant philosophical impact, and represents a shift in attitudes towards the philosophy of mathematics. This conference will bring together leading scholars in these areas to showcase contemporary philosophical research on different approaches to the foundations of mathematics. To accomplish this, the conference has the following general aims and objectives. First, to bring to a wider philosophical audience the different approaches that one can take to the foundations of mathematics. Second, to elucidate the pressing issues of meaning and truth that turn on these different approaches. And third, to address philosophical questions concerning the need for a foundation of mathematics, and whether or not either of these approaches can provide the necessary foundation.

Date and Venue: 12-13 January 2015 – Birkbeck College, University of London.

Confirmed Speakers: Sy David Friedman (Kurt Goedel Research Center, Vienna), Victoria Gitman (CUNY), James Ladyman (Bristol), Toby Meadows (Aberdeen).

Call for Papers: We welcome submissions from scholars (in particular, young scholars, i.e. early career researchers or post-graduate students) on any area of the foundations of mathematics (broadly construed). While we welcome submissions from all areas concerned with foundations, particularly desired are submissions that address the role of and compare different foundational approaches. Applicants should prepare an extended abstract (maximum 1,500 words) for blind review, and send it to sotfom [at] gmail [dot] com, with subject `SOTFOM II Submission’.

Submission Deadline: 31 October 2014

Notification of Acceptance: Late November 2014

Scientific Committee: Philip Welch (University of Bristol), Sy-David Friedman (Kurt Goedel Research Center), Ian Rumfitt (University of Birmigham), Carolin Antos-Kuby (Kurt Goedel Research Center), John Wigglesworth (London School of Economics), Claudio Ternullo (Kurt Goedel Research Center), Neil Barton (Birkbeck College), Chris Scambler (Birkbeck College), Jonathan Payne (Institute of Philosophy), Andrea Sereni (Universita  Vita-Salute S. Raffaele), Giorgio Venturi (CLE, Universidade Estadual de Campinas)

Organisers: Sy-David Friedman (Kurt Goedel Research Center), John Wigglesworth (London School of Economics), Claudio Ternullo (Kurt Goedel Research Center), Neil Barton (Birkbeck College), Carolin Antos-Kuby (Kurt Goedel Research Center)

Conference Website: sotfom [dot] wordpress [dot] com

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

The conference is generously supported by the Mind Association, British Logic Colloquium, and Birkbeck College.