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Postdoctoral position (1y) on "The implicit commitment of mathematical theories through intensional notions", Pisa (Italy)

The Scuola Normale Superiore of Pisa announces a selection, based on work 
to date and interview, for a research contract as part of the research 
project ?The implicit commitment of mathematical theories through 
intensional notions?.

https://en.sns.it/bando/research-contract-part-research-project-?-implicit-commitment-mathematical-theories-through

The research project focuses on themes at the crossroads of proof-theory, 
philosophical logic, and philosophy of mathematics. According to the 
implicit commitment thesis, once accepting a mathematical formal system, 
one is implicitly committed to additional resources not immediately 
available in it. Semantic and intensional notions have been used to reach 
a significant deductive strength starting with basic combinatorial 
assumptions. Clear examples are basic arithmetical theories enriched with 
axioms for truth or necessity. Yet, the role that these notions play in 
the justification process is far from being clear. Why semantic and 
intensional notions are epistemically better than mathematical ones? The 
standard answer is that the "logical" principles governing them are simple 
and corroborated by firm philosophical intuitions. But the notion of 
simplicity employed in this context is in need of clarification, and it is 
well- known that philosophical intuitions may be misleading if they are 
not made fully explicit. The main aim of this project concerns developing 
strategies for justifying, through minimal intensional resources, the 
existence and properties of mathematical axioms. Roughly speaking, the 
idea is that of viewing intensional `logical' axioms as bridging a gap 
between epistemically accessible mathematical theories and higher-order 
mathematics.

Scientific supervisor: Prof. Mario Piazza (mario.piazza@sns.it)
Duration of the contract: 1 year
Estimated starting date: September 2018
Gross remuneration, inclusive of all taxes: ? 23.787,00
Requisites

Applications are invited from candidates who have completed a PhD in 
Philosophy, Logic or Mathematics. Candidates who have completed the 
aforementioned degrees abroad may also apply, if said degrees are 
recognized as equivalent to Italian degrees.
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