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Konkurs w projekcie SONATA BIS „Logiczne i epistemologiczne kryteria istotności w podstawach matematyki”

mstarczewska

Open Call for a fully funded PhD position (4 years) within the framework of the grant SONATA BIS 2022/46/E/HS1/00452, financed by National Science Center (Narodowe Centrum Nauki), Poland

Host institution: the Faculty of Philosophy, University of Warsaw, Poland

Project title: Logical and epistemological criteria of salience in the foundations of mathematics.

Our main research objective is to analyse the distinction between natural (or salient) and artificial (or ad hoc) theories in the foundations of mathematics. Intuitively, natural theories have a foundational idea behind them or derive from a normal mathematical practice. Examples of such theories include Peano Arithmetic, Second Order Arithmetic (and its various finite fragments, such as the Big Five), Zermelo-Fraenkel set theory, Kelley Morse theory of classes. Artificial theories occur mostly as counterexamples to some intuitively plausible claims and often originate by applications of various fixed-point techniques. 

Our project has a more philosophical and more mathematical component. In terms of the latter, we shall investigate the categoricity-like notions of tightness and solidity. The main goal here is to check whether the condition of minimal solidity filters out an interesting subclass of natural theories. We study the relations of both notions to the notion of internal categoricity, as introduced by Vaananen and estimate their applicability to the philosophical debates surrounding the notion of internal categoricity. 

Secondly, we scrutinize the intuitive view that natural theories shall admit language-independent characterizations. We study the possibility of characterizing various axiomatic theories of semantical notions (truth, definability, satisfaction) based on biconditionals in a coordinate-free way via different universal properties. 

On the more philosophical side, we aim at elucidating the notion of epistemic stability. A theory V is said to be epistemically stable if there is a coherent rationale for accepting V that does not oblige a theorist to accept any sentences which are unprovable in V. The examples of theories that are conjectured to be epistemically stable, include the Primitive Recursive Arithmetic (motivated by Hilbert’s finitism), Peano Arithmetic (motivated by Isaacsons first-orderism), Ramified Analysis up to Gamma_0 (motivated by predicativism) and Second Order Arithmetic (motivated by Dedekind’s categoricity statement). 

For further information about the project, see the project’s description on .
https://sites.google.com/uw.edu.pl/lelyk

Principal investigator: Mateusz Łełyk, PhD, Faculty of Philosophy, University of Warsaw, Poland.

Requirements:

We are looking for a PhD candidate who satisfies the following conditions:

  • Master’s degree in a field relevant to the project (preferably in mathematical or philosophical logic or set theory. In particular, familiarity with axiomatic theories of truth counts as a plus.) In case of candidates without the Master’s degree, a signed letter from their supervisor is required, stating that the graduation will take place before the deadline specified by the Doctoral School (this deadline has not been published yet; last year it was September 18).  
  • Good speaking and writing command of English
  • Strong interest in logic.
  • Strong motivation for scientific work.
  • Very good problem-solving skills.
  • Good social and organizational skills.

Tasks will include:

  • Preparation within the contract period of a PhD thesis on a topic related to the project.
  • Regular presentation of intermediate research results at workshops and conferences.
  • Publication of results in journals and/or conference proceedings.
  • Participation in the Doctoral School PhD training program. 
  • Participation in the organization of research activities and events related to the research project, such as conferences, workshops and joint publications.

We offer:

  • Very interesting open research problems (of both philosophical and formal nature).
  • Membership in an internationally active and vibrant research team.
  • Budget for conference travel and research visits. 
  • Attractive remuneration.

Employment conditions:

  • The candidate’s primary responsibility will be to conduct research and write a PhD thesis.
  • The position starts on October 1st, 2023 and lasts for a maximum of four years. 
  • Important:  After successful recruitment, the candidate will have to obtain the status of a PhD student at the University of Warsaw according to standing procedures. For details, visit https://szkolydoktorskie.uw.edu.pl/en/.
  • Total remuneration: PLN 7371 gross during the first and second year of PhD-studies; PLN 8653 gross per month during the third and the fourth year of PhD studies. The remuneration has two components:
    • Doctoral school scholarship in the amount of PLN 2371.70 monthly for the first two years of studies (before the mid-term evaluation) and PLN 3653.70 in the next two years after the mid-term evaluation. Supplement for people with disabilities: PLN 711.51.  From this amount mandatory medical insurance contribution is subtracted (around 11%). The scholarship amount is regulated by the Ministry of Science and Higher Education and may be subject to change. Note: If you already hold a PhD degree, you will not be eligible for this part of remuneration.  
    • NCN project scholarship, which amounts to PLN 5000 monthly for 4 years.
  • In the project there is also a budget for conference and research travel. 
  • The candidate will have a right to use a number of campus facilities, such as the sports facilities and the library.

Required documents

  1. Cover letter including motivation for doing PhD research within the proposed research project.
  2. Current curriculum vitae, including a description of prior research experience,  previous education, professional information (previous employment), language proficiency, grants/honours, a list of publications and conference presentations (if applicable). 
  3. Scan of the Master’s degree diploma or the supervisor’s statement of the planned acquisition of the diploma graduation before the deadline specified by the Doctoral School. A list of grades (transcript) obtained for your Master (or equivalent) programme.
  4. At least two reference contacts (with e-mails).
  5. A writing sample, such as a project paper or a chapter of a master’s thesis, of up to 10,000 words maximum.
  6. Consent for  the  processing  of  personal  data  for  the  purposes  of  the  recruitment  process.

How to apply

  • In order to apply, please send the message to mlelyk@uw.edu.pl ​​attaching the required documents in pdf format.

A short list will be made based on the candidates’ applications. Shortlisted candidates might be invited for an interview (possibly, in a remote form).  

Timetable and deadlines

  • 12 May 2023 – deadline for submission applications.
  • 15-19 May – interviews with the candidates.
  • Mid-May – the applicants are informed about the result. 
  • Starting Mid-May – the successful candidate prepares the application to a chosen Doctoral School at the University of Warsaw. Important: the proposed dissertation project has to be consulted with the Principal Investigator of the Maestro grant.
  • Submitting the application to the Doctoral School. The deadline for submitting the application has not been published yet (last year it was June 28).
  • 1 October 2023 – The applicant starts the PhD project.

Contact

  • If you have questions, ​please contact us at mlelyk@uw.edu.pl. 
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