In philosophy, similarity or resemblance is a relation between objects that constitutes how much these objects are alike. Similarity comes in degrees: e.g. oranges are more similar to apples than to the moon. It is traditionally seen as an internal relation and analyzed in terms of shared properties: two things are similar because they have a property in common. The more properties they share, the more similar they are. They resemble each other exactly if they share all their properties. So an orange is similar to the moon because they both share the property of being round, but it is even more similar to an apple because additionally, they both share various other properties, like the property of being a fruit. On a formal level, similarity is usually considered to be a relation that is reflexive (everything resembles itself), symmetric (if a is similar to b then b is similar to a) and non-transitive (a need not resemble c despite a resembling b and b resembling c). Similarity comes in two forms: respective similarity, which is relative to one respect or feature, and overall similarity, which expresses the degree of resemblance between two objects all things considered. There is no general consensus whether similarity is an objective, mind-independent feature of reality, and, if so, whether it is a fundamental feature or reducible to other features. Resemblance is central to human cognition since it provides the basis for the categorization of entities into kinds and for various other cognitive processes like analogical reasoning. Similarity has played a central role in various philosophical theories, e.g. as a solution to the problem of universals through resemblance nominalism or in the analysis of counterfactuals in terms of similarity between possible worlds.
Conceptions of similarity
Conceptions of similarity give an account of similarity and its degrees on a metaphysical level. The simplest view, though not very popular, sees resemblance as a fundamental aspect of reality that cannot be reduced to other aspects. 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. These conceptions analyze resemblance in terms of other aspects instead of treating it as a fundamental relation.
Numerical
The numerical conception holds that the degree of similarity between objects is determined by the number of properties they have in common. On the most basic version of this view, the degree of similarity is identical to this number. 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". Two things need to share at least one property to be considered similar. They resemble each other exactly if they have all their properties in common. This is also known as qualitative identity or indiscernibility. For the numerical conception of similarity to work, it is important that only properties relevant to resemblance are taken into account, sometimes referred to as sparse properties in contrast to abundant properties. Quantitative properties, like temperature or mass, which occur in degrees, pose another problem for the numerical conception. The reason for this is that e.g. a body with 40 °C resembles another body with 41 °C even though the two bodies do not have their temperature in common.