atomless

Or is everything made up of atomless “gunk” (in the terminology of Lewis 1970)?

Wild Dreams Of Reality, 3 2009

An interesting question, discussed at some length in the late 1960's (Yoes 1967, Eberle 1968, Schuldenfrei 1969) and taken up more recently by Simons (1987: 44f) and Engel and Yoes (1996), is whether there are atomless analogues of (33).

Wild Dreams Of Reality, 3 2009

In an atomless mereology, by contrast, the choice of the base would depend each time on the level of “granularity” set by the relevant specification of

Wild Dreams Of Reality, 3 2009

However, it is plausible to suppose that (P. 9) should hold at least with respect to the domain of spatio-temporal regions, regardless of whether these are construed as atomless gunk or as aggregates of spatio-temporal atoms.

Wild Dreams Of Reality, 3 2009

Accordingly, an atomless mereology AX admits only models of infinite cardinality.

Wild Dreams Of Reality, 3 2009

For instance, it can be held that there are atoms, though not everything need have a complete atomic decomposition, or it can be held that there is atomless gunk, though not everything need be gunky.

Wild Dreams Of Reality, 3 2009

(A world containing such wonders as Borges's Aleph, where parthood is not antisymmetric, might by contrast be finite and yet atomless.)

Wild Dreams Of Reality, 3 2009

Is there any predicate that can play the role of ˜A™ in an atomless mereology?

Wild Dreams Of Reality, 3 2009

An example of such a model, establishing the consistency of the atomless versions of most mereological theories considered in this survey, is provided by the regular open sets of a Euclidean space, with ˜P™ interpreted as set-inclusion (Tarski 1935).

Wild Dreams Of Reality, 3 2009

Unless this be conceded, we have the first and second rules of our Philosophy violated, as an atomless Aether is opposed to that simplicity of conception, which is an essential requirement of all hypotheses, and is moreover contrary to that presumptive evidence gathered from observation and experiment, which teaches us that all matter is atomic.

Aether and Gravitation William George Hooper