There are two main assumptions that are required for my argument, here I give a more precise statement of both and present the content that will be part of the thesis.
Structuralism
I follow from the Tarskian definition of truth the necessity of considering possible worlds as mathematical models. This argument will be expanded in Structuralism, this page contains the references to the essay(s) in Philosophy of Logic regarding the same theme but also further considerations that will be part of the thesis only. In Horsten, L. (2010), Having an Interpretation I expended the discourse in relation to the debate on fixing reference, the model theoretic argument and the interpretation of our language. I also uploaded a list of references I will consult when writing this section of the thesis.
Abstract
The Tarskian definition of logical consequence requires us to consider models within the same formal system of any proposition that we want to prove true. I then expose how the Tarskian Truth definition applied to any sort of empirical sentence requires an analysis of the formal system of possible worlds, considered as structures. I proceed by analysing the form of structuralism required for the theory to work and its implications.
To read further on the topic, visit:
- Structuralism
- The Silent Assumption in Tarskian Semantics
- Horsten, L. (2010), Having an Interpretation
Modal Realism
For this section I will mainly refer to SEP section 6, I plan to only expose the Lewis’ argument and show compatibility with Structuralism. I plan to start working on this section later on.
Live updates on this part are to be found here: Overleaf: Modal Realism.
On Ultraproducts
This section will be dedicated to why I believe that ultraproducts of possible worlds must be considered possible worlds as well. I will then analyse the single ultraproducts constructed in Mathematics First Thesis Concept and show what philosophical consequence they imply. I will work on this last part of the philosophy thesis as soon as I have some results in the mathematics thesis, this will be therefore the very last part I will begin.
Live updates on this part are to be found here: Overleaf: Ultraproducts.