Not signed in (Sign In)

Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

  • Sign in using OpenID

Discussion Tag Cloud

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

Welcome to nForum
If you want to take part in these discussions either sign in now (if you have an account), apply for one now (if you don't).

nLab > Latest Changes: necessity and possibility

Bottom of Page

201 to 209 of 209

  1. <
  2. 1
  3. 2
  4. 3
  5. >
    • CommentRowNumber201.
    • CommentAuthorzskoda
    • CommentTimeDec 29th 2022
    • (edited Dec 29th 2022)

    191

    Aristotle’s actuality and potentiality

    Late Ivan Supek (Croatian theoretical physicist, writer and a bit of philosopher and political activist), who was a student of Heisenberg, often emphasized that because of this aspect of Aristotle’s picture of the world, Aristotle’s point of view would better suit quantum world than Platon’s which is otherwise more dominant in traditional scientific Weltanschauung. I listened to one lecture of him as a student dedicated to this topic, at a Croatian Academy of Sciences workshop related to Ruđer Bošković (whose theory of forces influenced Bohr according to Bohr himself).

    • CommentRowNumber202.
    • CommentAuthorUrs
    • CommentTimeDec 29th 2022

    If there is any reference, I’d be interested in having a look.

    • CommentRowNumber203.
    • CommentAuthorzskoda
    • CommentTimeDec 29th 2022
    • (edited Dec 29th 2022)

    He definitely wrote something about that idea but I believe in Croatian only. Maybe with some effort some summary can be found in English somewhere.

    • CommentRowNumber204.
    • CommentAuthorDavid_Corfield
    • CommentTimeMar 11th 2023

    With the expected arrival of directed HoTT next week, what can we say of how the analogue of our possible worlds story should go?

    So we have in the ordinary case the adjoint triple generating the necessity and possibility (co)monads:

    (∃ W⊣W *⊣∀ W):H /W⟶∃ w:W⟵W *⟶∀ w:WH. (\exists_W \dashv W^\ast \dashv \forall_W) \;\colon\; \mathbf{H}_{/W} \stackrel{\stackrel{\forall_{w \colon W}}{\longrightarrow}}{\stackrel{\stackrel{W^\ast}{\longleftarrow}}{\underset{\exists_{w\colon W}}{\longrightarrow}}} \mathbf{H} \,.

    Presumably in the directed case we have similar maps between a slice of some (∞,2)(\infty, 2)-topos and itself.

    Let’s keep things simple. So a classic example of the undirected case sees a set of worlds, WW, and then WW-dependent propositions. We also might consider WW-dependent sets and look at sections or the total space.

    In the directed case, we might take WW to be a poset of worlds. A WW-dependent proposition is presumably an upper set. Then adjoints to base change, W *W^{\ast}, are the limit and colimit over WW, I take it. And we might consider presheaves of (∞,1)(\infty, 1)-categories over WW.

    This set-up then generates 2-(co)monads which resemble necessity and possibility, and so on right up to dependence on an (∞,1)(\infty, 1)-category or a morphism between two such. I take it there wouldn’t be anything new here, but considering things modally might be interesting.

    • CommentRowNumber205.
    • CommentAuthorUrs
    • CommentTimeJul 28th 2023

    added pointer to

    for the observation that S5 Kripke semantics is given by base change adjoint triples.

    diff, v53, current

    • CommentRowNumber206.
    • CommentAuthorUrs
    • CommentTimeJul 28th 2023

    have touched wording, typesetting, and hyperlinking in the section Via S4 modal logic, in the hope of streamlining a little more

    diff, v54, current

    • CommentRowNumber207.
    • CommentAuthorUrs
    • CommentTimeAug 4th 2023

    have made more explicit (here) how to read the argument that “potential data is possibility-modal data” namely as: “potential data is data whose possibility entails its actuality, consistently”.

    diff, v57, current

    • CommentRowNumber208.
    • CommentAuthorUrs
    • CommentTimeAug 4th 2023

    added (here) quotes from Aristotle matched to this formalization of “potentiality”.

    diff, v58, current

    • CommentRowNumber209.
    • CommentAuthorUrs
    • CommentTimeAug 6th 2023
    • (edited Aug 6th 2023)

    added (here) the (co)joins to the table of (co)units of the (co)modalities in quantum modal logic

    diff, v59, current

201 to 209 of 209

  1. <
  2. 1
  3. 2
  4. 3
  5. >