Let X() be a consistent probability assignment (function from statement to probability number).
What does it mean for this function to be “consistent”? What kinds of statements do you allow?
Let Y() be a probability assignment …
What’s X(Y is consistent)?
If “probability assignment” is a mapping from statements (or Goedel numbers) to the real interval [0,1], it’s not a given that Y, being a “probability assignment”, is definable, so that you can refer to it in the statement “Y is consistent” above.
What does it mean for this function to be “consistent”? What kinds of statements do you allow?
If “probability assignment” is a mapping from statements (or Goedel numbers) to the real interval [0,1], it’s not a given that Y, being a “probability assignment”, is definable, so that you can refer to it in the statement “Y is consistent” above.