What is a reflexive relation?
  • frank
    16k
    This is a quote from Noonan's book on Kripke. I've looked for info on reflexive relations, but none of it seems to be relevant. Anyone able to explain this quote?


    "Kripke introduces the idea of a model structure, a triple < G, K, R >, where G is an element of K, K is a set and R is a reflexive relation on K. Intuitively, he says, we may think of G as the actual world, K as a set of possible worlds, and R as a relation of relative possibility. This brought back into the philosophical mainstream the Leibnizian language according to which necessity is truth in all possible worlds and possibility is truth in some."
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  • fdrake
    6.7k
    ↪frank


    When the accessibility relation is reflexive, it means that a world is always accessible from itself. This means what is actual in it is possible in it.
    fdrake Options
  • frank
    16k
    ↪fdrake
    Still confused. What is R exactly?
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  • fdrake
    6.7k
    ↪frank


    The accessibility relation. It tells you what pairs of worlds are connected to each other, and in what directions. So if we had two worlds A,B and a relation on them R which consisted of pairs (A,B), (A,A), (B,B) and (B,A), reading (x,y) as 'y is accessible from x', this would then mean B is accessible from A, (A,B), A is accessible from B (B,A), A is accessible from A (A,A) and B is accessible from B (B,B). Prosaically, B 'is a possible world' for A, A 'is a possible world' for B, A is a possible world for itself and B is a possible world for itself.
    fdrake Options
  • frank
    16k
    ↪fdrake
    So R is like a set of rules? And there is both an a priori and a posteriori aspect to my knowledge of those rules?

    For instance, there was a time when many people thought it was impossible to go to the moon. They learned a posteriori that they were wrong about R.
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  • fdrake
    6.7k
    ↪frank


    The rules are just the set of pairs. They model different types of modality. EG if you wanted to model sequential counterfactuals and non-time symmetry, you might want a sequence of worlds where you can't access previous ones (making the relation anti-symmetric or an order like <). The sense of possibility you want to capture is modelled by the set of pairs you throw into the accessibility relation.
    fdrake Options
  • frank
    16k
    ↪fdrake
    Ok, thanks!
    frank Options
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