Subtropical philosophy: homological ontology in characteristic one

This PhD thesis seeks to answer the question of how the ancient philosophical problem of the ccontinuous and the discrete can be approached in a unified manner by assuming the validity of the 'generic matrix' developed (since 2008) by F. Laruelle as a new 'onto-vectorical' paradigm of thought. The problem is treated from four different angles: first, Laruelle's solution is presented through his 'quantizing' gesturality of thought. Second, this paradigm is subjected (contrary to A. Badiou's 'set-theoretic' approach [1988, 2006, 2018]) to a 'categorial' reinterpretation and 'tropical dequantization' (subsequent to a model of V. P. Maslov, V. N. Kolokoltsov et G. L. Litvinov). This gives rise to a 'semi-philosophical' solution for the initial problem called 'tropical philosophy'. Third, an analytic prolongation of Laruelle's 'quantum-oriented theory' leads to a 'non-commutative ontology' drawing further conclusions with regard to coherence considerations and the emergence of time in a non-commutative 'space of lived experience'. The fourth and final proposition consists in a 'topos-oriented' approach (after the models of A. Connes [2017] and O. Caramello [2018]). The concept of topos (dating back to A. Grothendieck [1972]) is conceived as a 'category-concept', which embraces continuous and discontinuous structures by the idea of a path toward the truth. Instead of being interested in only one particular and static space of thought, 'subtropical philosophy' being developed as a complex 'lift' of 'tropical philosophy' explains Laruelle's 'non-philosophical Chôra' as a topos or a parameter space that governs the spectral variability (implied by the relative point of view on philosophy) in the 'worldly foreground'. At the same time, it establishes a 'homological bridge' for an imaginary and indirect transfer between multiple philosophical worlds in the 'universal background', along with a new commutative but variable ontology 'in characteristic one' (1 +1 = 1).