### Relational Space

Leibniz has an argument against absolute space that employs the Principle of Sufficient Reason. Of course, PSR is false. So, the argument is no good. However, some philosophers have come to accept a new principle, the Principle of Necessary Reason. This principle may be formulated as follows (though it is not so formulated by its defenders):

For every contingently true proposition, P, there is true proposition N which is neither identical to P nor a part of P such that if N were not to obtain, then P would not obtain.

I believe that we can make a new argument against absolute space based on this principle. Let u be the universe and let O be a property that something has when it has all the geometric features that the universe in fact has. Finally, let R be the property that the universe in fact has in virtue of being oriented in space the way that it in fact is and let L be a the property that the universe would have if it were oriented in a mirror reverse way. Now consider the following proposition:

(Ou and Ru) or ~(Ou and Lu)

If space is absolute, then this is a contingently true proposition. But if that is a contingently true proposition, then by PNR, there must be a proposition, N such that if N were not to obtain, then it would not be the case that (Ou and Ru) or ~(Ou and Lu). That is, if N were not to obtain, then it would be the case that ~(Ou and Ru) and (Ou and Lu). But there is no such proposition. So, space is not absolute.

I take it that the weakest part of this argument is the principle PNR.

For every contingently true proposition, P, there is true proposition N which is neither identical to P nor a part of P such that if N were not to obtain, then P would not obtain.

I believe that we can make a new argument against absolute space based on this principle. Let u be the universe and let O be a property that something has when it has all the geometric features that the universe in fact has. Finally, let R be the property that the universe in fact has in virtue of being oriented in space the way that it in fact is and let L be a the property that the universe would have if it were oriented in a mirror reverse way. Now consider the following proposition:

(Ou and Ru) or ~(Ou and Lu)

If space is absolute, then this is a contingently true proposition. But if that is a contingently true proposition, then by PNR, there must be a proposition, N such that if N were not to obtain, then it would not be the case that (Ou and Ru) or ~(Ou and Lu). That is, if N were not to obtain, then it would be the case that ~(Ou and Ru) and (Ou and Lu). But there is no such proposition. So, space is not absolute.

I take it that the weakest part of this argument is the principle PNR.

## 6 Comments:

Isn't PNR subject to the 'conjunction of all contingent propositions is itself contingent' objection?

No

Oh because the proposition that satisfies the condition w.r.t. the conjunction of all contingent truths for PNR is allowed to be necessary?

yes

I know that it's been awhile since this was posted. However, it seems to me that, as formulated, PNR should be obvious. For consider an arbitrary contingently true proposition P. Now consider the proposition, P or N, that is the result of disjoining P with some necessary truth N. P or N is a true proposition which is neither identical to P nor a part of P such that if it were not to obtain, P would not obtain. So, for every contingently true proposition P, there is a true proposition N which is neither identical to P nor a part of P such that if N were not to obtain, then P would not obtain; that is, PNR is true, and pretty obviously so.

This is exactly what Andrew and I talked about. I suggested interpreting the conditional in PNR as a subjunctive interpreted over the class of possible and impossible worlds. I also made some other suggestions, but I can't remember waht they are now.

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