[3][8] The more common view is that the similarity between two things is determined by other facts, for example, by the properties they share, by their qualitative distance or by the existence of certain transformations between them.
The numerical conception holds that the degree of similarity between objects is determined by the number of properties they have in common.
For example, "[i]f the properties of peas in a pod were just greenness, roundness and yuckiness ... then their degree of similarity would be three".
[11][12] Quantitative properties, like temperature or mass, which occur in degrees, pose another problem for the numerical conception.
The problem of quantitative properties is better handled by the metric conception of similarity, which posits that there are certain dimensions of similarity concerning different respects, e.g. color, shape or weight, which constitute the axes of one unified metric space.
[3] Any such factor would seem to be artificial,[13] as can be seen, for example, when considering possible responses to the following case: "[l]et one person resemble you more closely, overall, than someone else does.
[3] A weaker version of respective resemblance is possible for quantitative properties, like mass or temperature, which involve a degree.
This type of respective resemblance and its impact on overall similarity gets further complicated for multi-dimensional quantities, like colors or shapes.
[16][17] For example, consider two children with the same bicycles engaged in a race while their mother is watching.
[18] A well-known counterexample comes from Max Black, who describes a symmetrical universe consisting of only two spheres with the same features.
[21][22] The realist solution posits an underlying universal that is instantiated by both objects and thus grounds their similarity.
[22][3] Counterfactuals are sentences that express what would have been true under different circumstances, for example, "[i]f Richard Nixon had pushed the button, there would have been a nuclear war".
The most well-known approach, due to Robert Stalnaker and David Lewis, proposes to analyze counterfactuals in terms of similarity between possible worlds.
[25] A "system of weights" in the form of a set of criteria is to guide us in assessing the degree of similarity between possible worlds.
[7] For example, avoiding widespread violations of the laws of nature ("big miracles") is considered an important factor for similarity while proximity in particular facts has little impact.
[28] The traditional account, originally suggested by Plato, explains depiction in terms of mimesis or similarity.
In this regard, pictures are different from linguistic signs, which are arbitrarily related to their referents for most part.
[28][30] Defenders of resemblance-theories try to avoid these counter-examples by moving to more sophisticated formulations involving other concepts beside resemblance.
[32] Arguments from analogy have the following form: a is similar to b and a has feature F, therefore b probably also has feature F.[31][33] Using this scheme, it is possible to infer from the similarity between rats (a) and humans (b) and from the fact that birth control pills affect the brain development (F) of rats that they may also affect the brain development of humans.
[34] Arguments from analogy are defeasible: they make their conclusion rationally compelling but do not ensure its truth.
Different games share various features with each other, like being amusing, involving winning and losing, depending on skill or luck, etc.
[39] These considerations threaten to render traditional attempts of discovering analytic definitions futile, such as for concepts like proposition, name, number, proof or language.