As far the physical world is concerned, the standard realist attitude which conceives of objects as existing independently of our representations of them might be (prima facie) plausible: if things go well, we represent physical objects in the way we do because they are so-and-so. In contrast, as we want to argue, in the mathematical world the situation is reversed: if things go well, mathematical objects are so-and-so because we represent them as we do. This does not mean that mathematics could not be objective: mathematical representations might be subject to constraints that impose objectivity on what they constitute. If this is right, in order to understand the nature of mathematical objects we should first understand how mathematical representations work. In the words of Kreisel’s famous dictum: “the problem is not the existence of mathematical objects but the objectivity of mathematical statements” (Dummett 1978, p. xxxviii). The problem we tackle concerns the philosophical question of clarifying the role of representations in mathematical reasoning and proofs and the way they contribute to mathematical ontology and understanding. This is a fresh inquiry concerning a classical problem in philosophy of mathematics connecting understanding to proofs and to the way the ontology of mathematic is conceived. But our starting point is neither classical proof theory nor classical metaphysics. We are rather looking at the problem by opening the door to the practical turn in science. In our perspective the question is then neither to find a topic-neutral formalization of mathematical reasoning, nor to offer a new argument for the existence of mathematical objects. We rather wonder how appropriate domains of mathematical (abstract) objects are constituted, by appealing to different sorts of representations, and how appropriate reasoning on them are licensed. Accordingly, we plan to analyse: (i) in which sense in mathematical practice relevant stipulations determine objects by appealing to appropriate representations; (ii) in what sense inferential rigor conceived in a contentual (informal) perspective can depend on these stipulations; (iii) in what sense it is possible to characterize nevertheless (by interlinking philosophical studies with scientific investigations) informal provability by formal means, which allows using logic and mathematics as a tool for epistemology. We also contrast our approach with classical foundational approaches of mathematics and logic, like classical Platonism and Nominalism, which both share an “existential attitude” facing mathematical objects (they both take as crucial the question whether they exist or do not exist, though giving opposite answers) and consider mathematical reasoning as topic-invariant.

The PRIMOFOOD project aims to innovate in modelling the effect of food prices on household purchasing behaviour. It is in line with axis 1.5 of the AAPG2019 "Food and Food Systems". The proposed innovations will allow for a better assessment of the effectiveness and distributive effects of nutritional taxation policies. The identification of price effects can be based either on the econometric analysis of existing market data or on the analysis of experimental data generated in lab. Econometric methods may have limited internal validity, while experimental methods have questionable external validity. Our project therefore proposes to address the respective weaknesses of these two methods and, beyond that, to exploit their complementarities. WP1 will develop innovative experimental analyses of price effects. First, using innovative protocols, we will analyze the effect of large price changes, similar to the levels used in micro-simulations of pricing policies, but much larger than the changes observed in market data. The objective is to identify possible salience and reference price effects, which can induce non-linearities and discontinuities in consumer reactions to prices. We will also test the potential complementarities between pricing policies and nutritional labelling of the NutriScore type. We will also study the effects of social norm, cognitive load, and the existence of opportunity costs. WP2 will develop a structural econometric model of quality and quantity demand under multiple constraints. Beyond the usual budget constraint, the model will include a nutritional intake constraint, with possible extension to multiple linear constraints. The objective is to reflect that the choices of some households are constrained by the need to ensure a minimum of energy intake, or for some potentially addictive goods (alcohol and sugar). This econometric modelling work poses various theoretical and practical challenges. The empirical work will use Kantar WorldPanel scanner data on the consumption of non-alcoholic drinks by French households, and will aim in particular to identify the existence of effects of sugar habituation. WP3 will aim to show the possibility of evaluating the ex-ante evaluation of pricing policies by a micro-simulation of taxation policies based on a model that integrates the outcomes of the two work packages. We will first cross-validate the experimental and econometric methods, comparing the econometric approach with the data generated in the experiments. This will allow us to identify opportunities to improve the specifications of the econometric model, an improvement that will be implemented by a Bayesian method. Finally, we will carry out micro-simulations based on the case of the taxation of sweetened drinks, which has been in place in France since 2012. This will allow us to better characterize the effectiveness of this tax, as well as its distributive and welfare impacts on the various socio-economic segments of the population. PRIMOFOOD provides methodological contributions to the scientific communities and to important public policy issues. The team includes researchers covering the spectrum of issues addressed, from fundamental methodological issues to public policy expertise. The project proposes an international approach, with the ambition of replicating part of the work on American data, with a view to comparing food systems. Finally, the project will produce tools to better understand the links between the long-term dynamics of price changes and the sustainability of food systems.

In a fairly short time, virtual globes have become a key medium for the visualization of global change, promoted by scientific, political and NGO interests alike. Taking this as a starting point, SPHEROGRAPHIA proposes to reflect on the unequal geo-digitization of the world in terms of spatial justice through a two-pronged study: First, concerning the creation of such globes, to unravel the socio-technical processes that participate in the cartographic story relating to the Anthropocene and to reveal the disparity of their data; and secondly, concerning the effects of such devices, in order to decipher their performativity on both the imaginary and the political commitments of those who promote or feed them. The aim is to question these global environmental images in order to shed light on their uncertainties and the 'blank spaces' that they manipulate explicitly or implicitly. The ambition is also to study how, in the era of post-sovereign cartography, transnational coalitions are taking place in an attempt to make specific regions visible on these globes. The example of the Guiana Shield will serve as a case study. The scientific challenges are methodological (designing a method and a tool for visualizing data deserts), theoretical (integrating the informational dimension into work on spatial and environmental justice) and epistemological (rethinking critical approaches to cartography). The originality of the project is to use a subject that has not yet been fully articulated (virtual globes) in order to address the issue of informational equity of territories by combining a multi-scalar approach (spatial analysis, discourse analysis, geo-visualization, participatory observation, art/science creation) associating geography and geomatics, but also history, semiotics, and both the plastic and digital arts.

In order to contribute to the analysis of the internationalization trends in higher education in a long-term perspective, the GlobalYouth Project aims to analyze individual admission records of 200,000 residents who were students at the Cité Internationale Universitaire de Paris (CIUP) in the 20th Century and to build a historical database. The data collected will first measure how the CIUP contributed to the making of a "global youth", what an experience inside an international campus meant for students and what was the French strategy for international students. At the same time, the GlobalYouth Project aims to build an international scientific team interested in the history of international academic motilities, in order to candidate to an European call for projects.