## Sunday, June 27, 2010

### Presentism and induction

Start with this rough principle:

1. If a hypothesis that is both simpler and weaker can cover the same data, we should prefer it to an alternate hypothesis that is both more complex and stronger.
For instance, if our data is that all observed emeralds are green, we should prefer the hypothesis that all emeralds are green to the stronger and more complex hypothesis that all emeralds-or-diamonds are green (where x is an emerald-or-diamond iff x is an emerald or diamond). On the other hand, often we should prefer a stronger but simpler hypothesis to a weaker but more complex one.

Now suppose we acquire this data:

1. Every time a star was observed to be formed, that was in a nebula.
And now consider two hypotheses:
1. Every time a star was formed, that was in a nebula.
2. Every time a star was, is or will be formed, that was, is or will be (respectively) in a nebula.
Hypothesis (3) is simpler and weaker than hypothesis (4). So (3) should be preferred to (4). That's a problem, since we want to do induction to the future! Now consider another hypothesis:
1. Every time a star is (tenseless) formed, that is (tenseless) in a nebula.
If eternalism is true, the temporally unrestricted quantifier in (5) is simpler than the temporally restricted quantifier in (3), and so (at least if B-theory holds, but maybe even if not) (5) is simpler than (3). On the other hand, if presentism is true, the quantifier in (5) requires a complex presentist analysis (e.g., using quantification over haecceities or a conjunction of past, present and future quantifiers), and (3) will be simpler than (5). So if presentism holds, then by (1), we should prefer (3) to (5). But if eternalism holds, there is a case to be made for preferring (5) to (3) due to its simplicity, despite the greater strength.

#### 1 comment:

enigMan said...

When a Presentist quantifies over times, as in your hypotheses (under Presentism), the simpler hypothesis is as it is under Eternalism, for pretty much the same reasons. And the Presentist scientist will want to quantify over times, much as nominalistic mathematicians will want to quantify over numbers. The Presentist will believe that what she is doing could be translated into some more explicit Presentist talk (cf. mathematical nominalism). But surely such a translation would take simple hypotheses to simple hypotheses, in the relevant sense (it would not turn talk of emeralds into talk of gemstones), for all that it would give us a more complicated expression.