How this calculator works
Represent a predicate by the subset of objects for which it is true. If all subsets count equally, requiring two chosen objects to be present leaves the other n - 2 memberships free. Every distinct pair therefore shares the same number of predicates. The model illustrates why meaningful similarity requires choices about which properties matter. It assumes all subsets are available and weights them equally.
Formula
All predicates = 2^n. True of both chosen objects = 2^(n-2). True of exactly one = 2 × 2^(n-2).
Worked example
For three objects there are eight subsets. Objects 1 and 2 occur together in {1, 2} and {1, 2, 3}, so they share two predicates. Every other distinct pair also shares two.
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Frequently asked questions
Does this say all real objects look alike?
No. It concerns a particular unweighted count over all predicates. Everyday similarity selects or weights a much smaller set of properties.
Why must the two objects differ?
A single object belongs to half of all subsets. A pair of distinct objects belongs together to one quarter, so the counts differ.
Why stop at eight objects?
The table doubles with every added object. Eight objects already produce 256 predicates, enough to inspect the pattern.