UC San Diego

"Form" is one of the first concerns of philosophy, though its centrality to philosophy has somewhat faded. However, in the last few decades it has reemerged as a central idea in a particular area of philosophy -- the demarcation of "logicality." I show that it should be of concern more broadly. As invariance, the underlying principle used to characterize logical formality, is not itself essentially logical, important questions arise. Can invariance be used to characterize other formal theories? Can it furthermore form the basis of a contemporary, general theory of formality? I develop and advocate for just such a general theory of formality (GTOF). This GTOF is based on a notion of invariance which is completely generalized -- it consists simply of the stability of features under functional mappings in a given domain. Different domains and functional mappings give rise, then, to different types of formality. In advocating the view, I show that the GTOF has promise for an acceptable combination of adequacy -- it does minimal damage to intuitions about formality -- and usefulness. I first show that the GTOF rules geometrical theories to be formal. This is followed by an examination of standard first order logic, which illuminates the possibility that a close correlation between syntactic and semantic formalities may be distinctive of formal languages. This is bolstered by an examination of a number of programming languages and methods. Finally, some deeper consequences of the GTOF are examined and its association to other philosophical theories is explored. The general theory of formality I develop is a promising candidate to fill a gap in existing theory. Not only does it do justice to some of our deepest intuitions about formality, but it sheds light on important relationships between formal systems that have not been previously recognized