A naturalistic justification of the Generic Introduction Multiverse - PowerPoint PPT Presentation

A justification of the GM H M. de Ceglie A naturalistic justification of the Generic Introduction Multiverse with a core Background The main argument Conclusions Matteo de Ceglie decegliematteo@gmail.com Paris Lodron Universität Salzburg PhD in Logic X - Prague 2 nd May 2018

Structure of the Presentation A justification of the GM H M. de Ceglie 1 Introduction Introduction Background The main argument 2 Background Conclusions 3 The main argument 4 Conclusions

Structure of the Presentation A justification of the GM H M. de Ceglie 1 Introduction Introduction Background The main argument 2 Background Conclusions 3 The main argument 4 Conclusions

Structure of the Presentation A justification of the GM H M. de Ceglie 1 Introduction Introduction Background The main argument 2 Background Conclusions 3 The main argument 4 Conclusions

Structure of the Presentation A justification of the GM H M. de Ceglie 1 Introduction Introduction Background The main argument 2 Background Conclusions 3 The main argument 4 Conclusions

Structure of the Presentation A justification of the GM H M. de Ceglie 1 Introduction Introduction Background The main argument 2 Background Conclusions 3 The main argument 4 Conclusions

Introduction outline A justification of the GM H M. de Ceglie Introduction Background Pluralism, Anti-Pluralism and Naturalism The main argument The reasons of the emergence of the multiverse: Conclusions Independent propositions; Alternative set theories. A brief sketch of the main argument

Introduction outline A justification of the GM H M. de Ceglie Introduction Background Pluralism, Anti-Pluralism and Naturalism The main argument The reasons of the emergence of the multiverse: Conclusions Independent propositions; Alternative set theories. A brief sketch of the main argument

Introduction outline A justification of the GM H M. de Ceglie Introduction Background Pluralism, Anti-Pluralism and Naturalism The main argument The reasons of the emergence of the multiverse: Conclusions Independent propositions; Alternative set theories. A brief sketch of the main argument

Introduction outline A justification of the GM H M. de Ceglie Introduction Background Pluralism, Anti-Pluralism and Naturalism The main argument The reasons of the emergence of the multiverse: Conclusions Independent propositions; Alternative set theories. A brief sketch of the main argument

Introduction outline A justification of the GM H M. de Ceglie Introduction Background Pluralism, Anti-Pluralism and Naturalism The main argument The reasons of the emergence of the multiverse: Conclusions Independent propositions; Alternative set theories. A brief sketch of the main argument

Pluralism, Anti-Pluralism and Naturalism A justification of the GM H M. de Ceglie Naturalism Introduction Mathematical practice should be considered the final judge for Background The main questions in philosophy of mathematics. argument Conclusions Anti-Pluralism There is only one set theoretic universe. Pluralism There are various set theoretic universes.

Pluralism, Anti-Pluralism and Naturalism A justification of the GM H M. de Ceglie Naturalism Introduction Mathematical practice should be considered the final judge for Background The main questions in philosophy of mathematics. argument Conclusions Anti-Pluralism There is only one set theoretic universe. Pluralism There are various set theoretic universes.

Pluralism, Anti-Pluralism and Naturalism A justification of the GM H M. de Ceglie Naturalism Introduction Mathematical practice should be considered the final judge for Background The main questions in philosophy of mathematics. argument Conclusions Anti-Pluralism There is only one set theoretic universe. Pluralism There are various set theoretic universes.

A brief Sketch of the argument A justification of the GM H M. de Ceglie Introduction Background The multiverse is just as good, when dealing with actual The main mathematical practice, as the single universe; argument Moreover, in the multiverse is possible to prove more Conclusions things than in the single universe; Thus, from a naturalistic point of view, the multiverse should be preferred over the single universe.

A brief Sketch of the argument A justification of the GM H M. de Ceglie Introduction Background The multiverse is just as good, when dealing with actual The main mathematical practice, as the single universe; argument Moreover, in the multiverse is possible to prove more Conclusions things than in the single universe; Thus, from a naturalistic point of view, the multiverse should be preferred over the single universe.

A brief Sketch of the argument A justification of the GM H M. de Ceglie Introduction Background The multiverse is just as good, when dealing with actual The main mathematical practice, as the single universe; argument Moreover, in the multiverse is possible to prove more Conclusions things than in the single universe; Thus, from a naturalistic point of view, the multiverse should be preferred over the single universe.

Structure of the Presentation A justification of the GM H M. de Ceglie 1 Introduction Introduction Background The main argument 2 Background Conclusions 3 The main argument 4 Conclusions

Background outline A justification of the GM H M. de Ceglie Introduction Background The main The Multiverse conceptions in set theory argument The broad multiverse; Conclusions The Generic Multiverse with a core ( GM H ) The naturalistic approach

Background outline A justification of the GM H M. de Ceglie Introduction Background The main The Multiverse conceptions in set theory argument The broad multiverse; Conclusions The Generic Multiverse with a core ( GM H ) The naturalistic approach

Background outline A justification of the GM H M. de Ceglie Introduction Background The main The Multiverse conceptions in set theory argument The broad multiverse; Conclusions The Generic Multiverse with a core ( GM H ) The naturalistic approach

Background outline A justification of the GM H M. de Ceglie Introduction Background The main The Multiverse conceptions in set theory argument The broad multiverse; Conclusions The Generic Multiverse with a core ( GM H ) The naturalistic approach

Multiverse conceptions in set theory A justification of the GM H The broad multiverse M. de Ceglie All the possible universes are part of the multiverse, with no Introduction hierarchy nor criterion to sort them. Background The main argument The generic multiverses Conclusions In this kind of multiverses we differentiate between universes using a strong logic (an idea owed to Woodin, from now on GM Ω ) or supposing the existence of a core (an idea owed to Steel, that is the GM H ). The hyperverse A multiverse of multiverses.

Multiverse conceptions in set theory A justification of the GM H The broad multiverse M. de Ceglie All the possible universes are part of the multiverse, with no Introduction hierarchy nor criterion to sort them. Background The main argument The generic multiverses Conclusions In this kind of multiverses we differentiate between universes using a strong logic (an idea owed to Woodin, from now on GM Ω ) or supposing the existence of a core (an idea owed to Steel, that is the GM H ). The hyperverse A multiverse of multiverses.

Multiverse conceptions in set theory A justification of the GM H The broad multiverse M. de Ceglie All the possible universes are part of the multiverse, with no Introduction hierarchy nor criterion to sort them. Background The main argument The generic multiverses Conclusions In this kind of multiverses we differentiate between universes using a strong logic (an idea owed to Woodin, from now on GM Ω ) or supposing the existence of a core (an idea owed to Steel, that is the GM H ). The hyperverse A multiverse of multiverses.

The Generic Multiverse with a core ( GM H ) A justification of the GM H M. de Ceglie Introduction Definition of the core Background The main The core of the multiverse is the argument collection of all the statements that Conclusions are true in every universe of the multiverse. We can then consider every universe of the generic multiverse and extension of its core.

The naturalistic approach A justification of the GM H The problem M. de Ceglie Which is best for mathematical practice? The Single Universe Introduction framework or the Multiverse?. Background The main argument UNIFY Conclusions Our framework should be foundational . MAXIMIZE The framework theory should be as powerful as possible, not restricting in any way the development of the foundations of mathematics (the framework theory should be the most Generous Arena for mathematics).

The naturalistic approach A justification of the GM H The problem M. de Ceglie Which is best for mathematical practice? The Single Universe Introduction framework or the Multiverse?. Background The main argument UNIFY Conclusions Our framework should be foundational . MAXIMIZE The framework theory should be as powerful as possible, not restricting in any way the development of the foundations of mathematics (the framework theory should be the most Generous Arena for mathematics).