Timeline for Set-theoretical multiverses and their representation as functors? Why *the* multiverse?
Current License: CC BY-SA 4.0
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| Jul 31, 2018 at 11:28 | comment | added | Joel David Hamkins | ...That work in turn seems to have highlighted certain philosophical issues about the nature of potentialism, focusing attention on the inevitability/divergence of potentiality. I discuss this much further in the last section of my paper jdh.hamkins.org/…. | |
| Jul 31, 2018 at 11:27 | comment | added | Joel David Hamkins | @FWE That kind of interaction seems to have been a recurring feature with some of my work, such as my recent work on potentialism (for example, see the diagram at the top of my notes for this talk: jdh.hamkins.org/…). The main potentialist idea originates classically and is philosophical; Linnebo made a turn toward mathematics by introducing the modal account, and this has now been much more developed mathematically, for we determined the precise modal commitments of various potentialist conceptions. | |
| Jul 31, 2018 at 10:41 | comment | added | FWE | Thank you very much for explaining some of the background and different approaches to these ideas! You once wrote (if I understand well) that you favour settings where mathematical developments are driven by philosophical questions and the mathematical insights in turn lead to new philosophical insights and questions - could you recommend a reference where you explain more about this interaction between philosophical and mathematical developments - in this context or more generally? | |
| Jul 31, 2018 at 10:06 | vote | accept | FWE | ||
| Jul 31, 2018 at 3:46 | comment | added | Morteza Azad | Next, comes a question that long baffled me but I am not sure what the best way of formulating it would be. It is inspired by your cosmic quote about multiverse (from the MO post linked in the OP) and the homogenity situation that could be observed in the Cosmic Microwave Background. Q: Fixing a particular multiverse, and viewing it as a large graph of nodes and edges, how homogeneous is it in the model-theoretic or any other sense? Does every part of this big picture looks like any other part or one's viewpoint matters? | |
| Jul 31, 2018 at 3:42 | comment | added | Joel David Hamkins | Oh yes, I cite their paper in my paper on arithmetic potentialism and the universal algorithm jdh.hamkins.org/…. | |
| Jul 31, 2018 at 3:37 | comment | added | Morteza Azad | (+1) Comprehensive answer, Joel! First, let me draw your attention to a related paper of Saveliev and Shapirovsky titled "On modal logics of model-theoretic relations" in which they investigated the modal logic of the multiverse of relational structures connected with substructure relation. | |
| Jul 31, 2018 at 3:08 | history | edited | Joel David Hamkins | CC BY-SA 4.0 |
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| Jul 31, 2018 at 3:05 | comment | added | Joel David Hamkins | Oh dear, Kameryn. It seems one can never truly leave New York, and I shall leave a large-cardinal part of my heart here. So let us continue to call it the New York approach. | |
| Jul 31, 2018 at 3:02 | history | edited | Joel David Hamkins | CC BY-SA 4.0 |
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| Jul 31, 2018 at 2:42 | comment | added | Julia Williams | Is it still the New York approach? Or should we now call it the Oxford approach? | |
| Jul 31, 2018 at 2:34 | history | answered | Joel David Hamkins | CC BY-SA 4.0 |