Logic: Is it a science?

Necessarily, you join our facebook group.

Seth Kurtenbach here.  The above link is a claim that can be formalized with modal logic.  Modal logic is a branch of logic that deals with necessity and possibility qualifiers on truth.  Depending on how one specifies the type of necessity and possibility, one can formalize arguments from many domains that cannot otherwise be precisely represented with regular old classical logic.  Classical logic is strictly extensional, because it was developed to explore the foundations of mathematics.  It is complicated why this is so, but trust me, it is.  An intensional logic is one that does not guarantee the substitution of identities.  For example, suppose the number of planets = 8.  Furthermore, suppose, reasonably, that 8 = 8.  In regular extensional logic, one can substitute these equivalencies, due to transitivity.  However, suppose one wants to say that necessarily, 8 = 8.  Now, one cannot validly make the substitution.  It is not necessary that the number of planets = 8.  It is possible that the number of planets = 9.  This is an example of intensionality disrupting the logic.  In the last half of the 20th century much work has gone into exploring the various types of modal logic and their rules of inference.

During the recent XKCD hubbub about all Wikipedia roads leading to philosophy, I encountered a Wikipedia page about the formal sciences.  The page indicates that these sciences are different from most other sciences insofar as the formal sciences are a priori, while the other sciences are a posteriori.  That is, the formal sciences are not empirical, but instead amass knowledge based on definitions and axioms.

Among the so-called formal sciences is logic and its various subfields.  I do work in modal logic, and so it would seem that if Wikipedia is correct, then I am a sort of scientist.  But, I have never thought of my work as being a type of science.  I usually consider logic to be a subfield of analytic philosophy, and I consider analytic philosophy to be distinct from science.  In that same vein, I am not sure any of the so-called formal sciences are actually sciences, because my impression is that all science is primarily empirical.

I would like to know what others think about these so-called formal sciences, specifically about logic.  Am I a formal scientist, or is that a misnomer?