Gustavo Lacerda

According to the "received view" in formal philosophy of science, we need a notion of nomic (law-like) necessity in order to formulate scientific laws.

For example:
"all lions that ever drowned in the North Atlantic were female"
forall x ( (lion(x) /\ drowned-in-NA(x)) -> female(x) )

is not considered a law because it's a contingent fact,

while
"all bodies with mass have a gravitational attraction to the sun"
forall x ( ( body(x) /\ has-mass(x) -> has-grav-attraction-to-the-sun(x) )

is.

There is a sense in which the latter statement is necessary: if we learn that X is a body with mass, we say that X *must* have a gravitational attraction to the sun. While you could still say the word "must" when drawing a conclusion from the first sentence, you would be less likely to.

I would say that this is because the first sentence is only quantifying over actual lions in actual observed situations, whereas the second quantifies over all possible bodies, giving it the generality required for being a scientific law.

The necessity expressed by the "must" can be formalized by adding the so-called "nomic" modality (nomos(gr.) = law). There are many things that are nomically necessary that are not logically necessary: in fact, scientific laws are never logically necessary. Any statement that is logically necessary is unfalsifiable, and thus fails to be "scientific", at least in Popper's view.

Determinism can be seen as the view in which all true statements are necessarily true (different modes of "necessary" corresponding to different brands of determinism). While determinism is an irrefutable view, one should not simply discard the nomic modality: there exists an important difference between the two kinds of sentences exemplified above, even if it's only a cognitive difference: the second sentence allows us to draw conclusions about all potential massy bodies (or future situations involving massy bodies), while the first does not allow us to draw conclusions about all possible lions (or future lions).

My thesis has been about formalizing scientific reasoning. I think my formalization is safe, even though it doesn't use a nomic modality, because my laws always quantify over all possible situations.

So for example, (IMPLIES (PRED1 x) (PRED2 x)) should be interpreted as saying that all potential objects (are these the same as Zalta & Fitelson's abstract objects?) satisfying PRED1 will satisfy PRED2. You could put a nomic necessity box in front of this statement if you like, but I don't think it adds anything.

My system already distinguishes laws (tagged "LAW TH" for some theory TH) from contigent statements (boundary-conditions, tagged "BC"). While laws in the corpus (a corpus is log of what has been seen before: the idea is that it represents the scientist's experience) can get reused, boundary conditions should not (although they are still true, as long as names are kept unique), except when the same condition remains across problems. Better idea: we could have libraries of boundary-conditions, for reuse in problems that share the same BC's. Each library contains statements a set of BC's, and you could possibly use several libraries simulatenously (e.g. one library has information about the sun's radiation, one has information about the Itaipu Dam).

So while statements like (IMPLIES (UCM B1 B2 (UCM-PERIOD B1 B2)) (= (acc B1) (/ (^ (vel B1) 2) (distance B1 B2))))) should get reused, statements like (= (height wall) (* 3 m)) should not, unless there exists only one wall in the universe, whose height is 3 meters. A statement like (= (height wall78942396) (* 3 m)) seems perfectly fine, however, as long as there is some name management (generating large random numbers seems like a fine solution).