Here is a presentation of my thesis project, use the internal links to move across the three subpages: Philosophy First Thesis Concept, Mathematics First Thesis Concept and Appendix of the Thesis.
Abstract
I begin giving arguments for two ground assumptions: first that possible worlds, to some extent, are real and second, that possible worlds share the same structure as mathematical models. One must then conclude that mathematical constructions, like ultraproducts, on possible worlds must be possible worlds and hence real to the same extent as possible worlds are. I then analyse the structure of some ultraproducts and conclude with the existence of bizarre possible worlds. The choice whether this argument shall be considered as an indirect proof against the two assumptions or some concrete results on the nature of possible worlds will be faced, though essentially the choice remains to the reader.
Structure
The available material is divided in the Philosophy First Thesis Concept and Mathematics First Thesis Concept. The former contains more details on the broad structure of the argument and the assumptions, the latter concerns particular ultraproduct structures. Once the mathematical results are fixed, I will proceed by philosophically analysing the consequences of treating those structures as possible worlds.
More bureaucratic details, sources, references and names of possible supervisors are available in the Appendix of the Thesis.
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