## Michael Lynch’s _Truth as One and Many_ on Domain Logical Pluralism

February 26, 2018

~1500 words, ~1200 w/o footnotes

Recently I was looking through Lynch’s book on truth, Truth as One and Many. I was interested in its chapter-long discussion of domain-specific logical pluralism. There he writes about the natural idea that different logics should apply in different domains: say, intuitionism in moral or mathematical domains, but classical logic when talking about physical objects.

I wanted to see what he thought about what we ought to do in the case of sentences mixed across domains. For example, a disjunction might have its first disjunct from one domain and one logic but its second from another. (The logics might disagree about how to handle $\lor$, after all.)

Here’s his idea (and, what this whole post is about):

Modest
where a compound proposition or inference contains propositions from distinct domains, the default governing logic is that of the compound or inference’s weakest member. (100)

## Elga’s Highly Restricted Principle of Indifference

July 24, 2010

In the Sleeping Beauty paper, Elga tells us that “Since being in [Tails and Monday] is subjectively just like being in [Tails and Tuesday], and since exactly the same propositions are true whether you are in [Tails and Monday] or [Tails and Tuesday], even a highly restricted principle of indifference yields that you ought then to have equal credence in each”.

Recall that the unrestricted Principle of Indifference says that when your evidence doesn’t give you any more reason to believe one proposition rather than another, you should assign credence to the possibilities equally.

The more restricted principle Elga seems to be endorsing here is this:

Highly Restricted POI: If some collection of situations are subjectively identical and exactly the same uncentered propositions are true at them, one ought to divide one’s credences among them.