|Similarity: conformity of one or more - but not all - properties of two or more objects.|
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Problem of Qualities/Querweltein congruence/Field: Solution: sameness of distance ratios.
Def Equality/Temperature equality/Field: x = y "x is between y and y".
Def Equally divided region/Equal split/Divided evenly/Distance equality/Field: (all distances within the region equal to: R: is a space-time-region all of whose points lie on a single line, and that for each point x of R of strictly st-between (spatio-temporally) two points of R is, its points y and z are of R so that a) st-between is just a point of strictly R y and z, and this is x and - b) xy P-Cong xz - ((s), thus avoiding any arbitrary (linear) units - E.g. - "less" points in the corresponding interval or "the same number of" - in mixed products - then: "... the mixed product ... is less than the mixed product ..." - distance equality in every area of its own: scalar/Spatio-temporal.
Realism, Mathematics and Modality Oxford New York 1989
Truth and the Absence of Fact Oxford New York 2001
Science without numbers Princeton New Jersey 1980