Any act of measurement presupposes a high degree of uniformity in the subject of measurement such that the measurement itself can be legitimately generalized and thus meaningfully compared to others of its kind. This assumption of generalizable uniformity is rarely made explicit, but it significantly informs the logical and operational characteristics of both the measurement itself and the theoretical systems in which the measurement is embedded.

This need for uniformity of subject matter constitutes a kind of pragmatic / operational a priori, which has both formal and methodological aspects. This research project will initially focus on the formal aspects of spatial measurement, with the primary intention of unifying some of the existing works that are relevant to the subject. This will be accomplished by building upon the formal and philosophical connections between mereotopology – which provides the logical foundations of extensional / spatial reasoning – with that of contemporary measurement theory. The uniformities in question will make themselves apparent in the group theoretical structural invariances of the relevant systems of transformations linking spatial structures with the linear functions of extensive modes of measurement.

This will entail some formal work of its own. In particular, issues from computer science of algorithmic and descriptive complexity will come into play as expressions of the operational practicalities of the measurement process, over and above the purely mathematical aspects. In addition, modal logics will be useful in characterizing the relational aspects of contexts of comparison in which meaningful measurements can take place.

This research straddles the divide between technology and science and promises to provide insight into the metrical activities of both.

Contemporary developments in algebra and Category Theory have shown that there is a deep connection between spatial reasoning – particularly in the form of the topological relations of open sets – and the foundations of logic. On the other hand, Whitehead's theory of extension, a primary component in his general metaphysical scheme, was itself a development from the logical and algebraic foundations of spatial reasoning. Indeed, Whitehead's extensa are basically open topological sets in a point-free geometry.

The same trends that led to Whitehead's work were themselves formative in the origination of Category Theory. In both instances, techniques were being evolved for studying general systems of spatial relations, and in both instances these developments were taking place from within an algebraic perspective which emphasized the stability of structural relations across various kinds of transformation.

This suggests that the issues here might run well beyond their connections with logic, and into the foundations of metaphysics proper. Logic is the normative study of the characters of good reasoning while metaphysics is the normative study of the characters of the real. Clearly in order for logic to fulfill its normative function, then the nature of good reasoning must exemplify a robust relationship with reality. Spatial reasoning may well be the bridge that establishes that relationship.

It is already evident from the literature that Whitehead's work on extension is foundational for a significant body of research in computer science relating to artificial intelligence and spatial reasoning. What is now called for is a detailed development of the connections between Whitehead's work, Category Theory, and the continuities amongst these with the metaphysical structure of the world.

The works of Alfred North Whitehead are an extraordinarily rich trove of ideas that comprise a systematic whole, an approach not only to philosophy but to all of life and thought. Yet despite the staggering volume of secondary literature on Whitehead's work, there is a relative paucity¹ of genuinely synoptic approaches to Whitehead's work that attempt to synthesize and integrate the various parts into a real totality. This leads to an unfortunate fragmentation of developments and research relating to the field to which Whitehead contributed.

Thus, alternative scientific approaches to cosmology operate in a vacuum with respect to their philosophical foundations, a vacuum that is readily filled by Whitehead's philosophy of nature and discussions on the logic of measurement.² Moreover, Whitehead's work in the philosophy of science has been all but ignored. Meanwhile, workers in the artificial intelligence of spatial reasoning cite Whitehead's work on extension as foundational for their discipline. Yet Whitehead scholars are generally unaware of this work, while logicians are befogged as to the reasons behind Whitehead's contributions.

In conjunction with the above mentioned research projects, this work is aimed at bringing Whitehead's work as a systematic whole into clearer focus.

¹ There are certainly exceptions to this rule, for example Michel Weber's Whitehead's Pancreativism, ontos verlag, 2006.
² See Whitehead and the Measurement Problem of Cosmology, Gary Herstein, ontos verlag, 2006.

View one of my published works on Whitehead