Relational Logic
  • Rayan
    26
    So, I am learning a bit of Relational Logic and there is something about the definition of a quantified sentence that I don't quite get. So, it says this: ‘‘A universally quantified sentence is used to assert that all objects have a certain property. For example, the following expression is a universally quantified sentence asserting that, if p holds of an object, then q holds of that object and itself.’’

    (∀x.(p(x) ⇒ q(x,x)))
    ;
    Well, I don't quite get what is meant by ‘‘then q holds of that object and itself.’’
    Rayan Options
  • MetaphysicsNow
    311
    ↪Rayan
    Under relational logic there will be some relations that are are reflexive and some that are not. In this case, q is a reflexive relation. Think of the relation "as tall as". I am as tall as myself, so "as tall as" is reflexive since it holds between me and myself. It also holds between me and anyone else as tall as me. However, "smaller than" is not a relation that holds between me and myself, even though it holds between me and anyone smaller than me.

    Does that help, or am I missing your point?
    MetaphysicsNow Options
  • Rayan
    26
    Yes, it does help, thank you!
    Rayan Options
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