Posted: Apr 05, 2011 6:14 pm
In all honesty, I wouldn't look at it that way.
I'm quite happy to let Alvin have an intuition that S5 can describe the universe. I'm quite happy to let him have an intuition that there is a possible world where it's possible that a necessary being exists - I would read this as a statement of intent about what his metaphysics are trying to capture with the formalism of "possible" and "necessary", that any statement that we lack information to decide can be represented by a member of the set of possible worlds.
Of course, he can't reach his conclusion from that, so I don't need to discuss his intuitions at all.
The thing I object to is the "intuition" that "necessary" and "in all possible worlds" need to be conflated, despite them having different formal definitions - which amounts to an assumption that not only is S5 sufficiently powerful to describe some feature of the universe (I concede that sounds ok), but that it can accomodate his desire for the meaning of "possible world" within a single equivalence class. This is a formal statement with no actual meaning regarding reality, tinkering with it is a backhanded trick that makes the proof work and is totally unjustifiable, it changes the meanings of "possible world" quite clearly against his intuition of what they should mean (some state of affairs that we can't rule out, or similar).
ETA: An attempt to explain this in a non-technical way:
Basically, we have two statements:
1) The possible worlds of Plantinga's metaphysics represent states of affairs (ways the world could be) that we do not have information to rule out - i.e. they are possibilities relative to our knowledge. (We might "intuitively" say that this is a fair enough concept and thus he can have an "intuition" that it's possible that a necessary being exists.)
2) That necessary means "in every possible world" rather than "in every possible world seen under the accessibility relation". (Which is a technical statement we define into our logic, a simple matter of choice)
You can have one, but not both. Encoding the second into our logic simply changes what sets of possible worlds we can choose, thus changing the meaning of "possible world" away from what it's supposed to mean.
I'm quite happy to let Alvin have an intuition that S5 can describe the universe. I'm quite happy to let him have an intuition that there is a possible world where it's possible that a necessary being exists - I would read this as a statement of intent about what his metaphysics are trying to capture with the formalism of "possible" and "necessary", that any statement that we lack information to decide can be represented by a member of the set of possible worlds.
Of course, he can't reach his conclusion from that, so I don't need to discuss his intuitions at all.
The thing I object to is the "intuition" that "necessary" and "in all possible worlds" need to be conflated, despite them having different formal definitions - which amounts to an assumption that not only is S5 sufficiently powerful to describe some feature of the universe (I concede that sounds ok), but that it can accomodate his desire for the meaning of "possible world" within a single equivalence class. This is a formal statement with no actual meaning regarding reality, tinkering with it is a backhanded trick that makes the proof work and is totally unjustifiable, it changes the meanings of "possible world" quite clearly against his intuition of what they should mean (some state of affairs that we can't rule out, or similar).
ETA: An attempt to explain this in a non-technical way:
Basically, we have two statements:
1) The possible worlds of Plantinga's metaphysics represent states of affairs (ways the world could be) that we do not have information to rule out - i.e. they are possibilities relative to our knowledge. (We might "intuitively" say that this is a fair enough concept and thus he can have an "intuition" that it's possible that a necessary being exists.)
2) That necessary means "in every possible world" rather than "in every possible world seen under the accessibility relation". (Which is a technical statement we define into our logic, a simple matter of choice)
You can have one, but not both. Encoding the second into our logic simply changes what sets of possible worlds we can choose, thus changing the meaning of "possible world" away from what it's supposed to mean.