Mereologists have often considered points as ‘unmereological’ entities. Most clearly this attitude shows up in the rivalry between mereological and non-mereological theories of space. On one hand, there are mereological theories of space that attempt to eschew points; on the other hand, there are topological or geometrical theories that take points as the basic building blocks of space. Adherents of mereological theories of space tend to regard points as non-basic entities to be reconstructed in honest mereological terms of spatial regions in some way or other. A similar point can be made for mereological and nonmereological theories of time.
1 Bennett, B.; Düntsch, I., (2007), “Axioms, Algebras and Topology”, in Aiello, M.; Pratt-Hartmann, I. E.; van Bentham, J. F. A. K. (eds.), Handbook of Spatial Logic, Springer, 99-159.
2 Biacino, L.; Gerla, G., (1996), “Connection Structures: Grzegorczyk’s and Whitehead’s Definitions of Point”, Notre Dame Journal of Formal Logic 47: 441-449.
3 Clarke, B. L., (1985), “Individuals and Points”, Notre Dame Journal of Formal Logic 26: 61-75.
4 Forrest, P., (1996), “From Ontology to Topology in the Theory of Regions”, The Monist 79(1): 34-50.
5 De, Laguna, T., (1922), “Point, Line, and Surface, as Sets of Solids”, Journal of Philosophy 19: 449-461.
6 Gerla, G., (1995), “Pointless Geometries”, in Buekenhout, F. (ed.), Handbook of Incidence Geometry, Amsterdam: Elsevier.
7 Gierz, G.; Hofmann, K. H.; Keimel, K.; Lawson, J. D.; Mislove, M.; Scott, D. S., (2003), Continuous Domains and Lattices, Cambridge: Cambridge University Press.
8 Heath, T. L. (ed.), 1956, Euclid. The Thirteen Books of the Elements, Second Edition, New York: Dover Publications.
9 Hilbert, D., (1899) (2001), Foundations of Geometry, Chicago and LaSalle: Open Court.
10 Hilbert, D., (1935), Gesammelte mathematische Abbhandlungen III, darin (von Otto Blumenthal), Lebensgeschichte, 403: Springer.
11 Johnstone, P. T., (1984), “The Point of Pointless Topology”, Bulletin (New Series) of the American Mathematical Society 8: 4-54.
12 Mac, Lane, S.; Moerdijk, I., (1992), Sheaves in Geometry and Logic, A First Introduction to Topos Theory, New York: Springer.
13 Mormann, T., (1998), “Continuous Lattices and Whiteheadian Theory of Space”, Logic and Logical Philosophy 6: 45-54.
14 Ridder, L., (2002), Mereologie. Ein Beitrag zur Ontologie und Erkenntnistheorie, Frankfurt/Main: Vittorio Klostermann.
15 Roeper, P., (1997), “Region-Based Topology”, Journal of Philosophical Logic 26: 251-409.
16 Russell, B., (1914) (1995), Our Knowledge of the External World as Field for Research in Scientific Philosophy, London: Routledge.
17 Stone, M. H., (1936), “The Theory of Representations for Boolean Algebras”, Transactions American Mathematical Society 40: 37-111.
18 Tarski, A., (1956), “Foundations of the Geometry of Solids”, in Tarski, A., Logic, Semantics, and Metamathematics, Oxford: Clarendon Press.
19 Whitehead, A. N., (1929), Process and Reality: An Essay in Cosmology, New York: Macmillan.
20 Vickers, S., (1989), Topology via Logic, Cambridge: Cambridge University Press.