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Reference
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.
Respective and overall similarity
Judgments of similarity come in two forms: referring to respective similarity, which is relative to one respect or feature, or to overall similarity, which expresses the degree of resemblance between two objects all things considered. For example, a basketball resembles the sun with respect to its round shape but they are not very similar overall. It is usually assumed that overall similarity depends on respective similarity, e.g. that an orange is overall similar to an apple because they are similar in respect to size, shape, color, etc.
This means that two objects cannot differ in overall similarity without differing in respective similarity. But there is no general agreement whether overall similarity can be fully analyzed by aggregating similarity in all respects. If this was true then it should be possible to keep the degree of similarity between the apple and the orange constant despite a change to the size of the apple by making up for it through a change in color, for example. But that this is possible, i.e. that increasing the similarity in another respect can make up for the lack of similarity in one respect, has been denied by some philosophers.[9]
One special form of respective resemblance is perfect respective resemblance, which is given when two objects share exactly the same property, like being an electron or being made entirely of iron. A weaker version of respective resemblance is possible for quantitative properties, like mass or temperature, which involve a degree. Close degrees resemble each other without constituting shared properties. In this way, a pack of rice weighing 1000 grams resembles a honey melon weighing 1010 grams in respect to mass but not in virtue of sharing property. This type of respective resemblance and its impact on overall similarity gets further complicated for multi-dimensional quantities, like colors or shapes.[3]
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.[3][10] 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.[5][11] 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.
Metric
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.[13][3] This can be visualized in analogy to three-dimensional physical space, the axes of which are usually labeled with x, y and z.[8] In both the qualitative and the physical metric space, the total distance is determined by the relative distances within each axis. The metric space thus constitutes a manner of aggregating various respective degrees of similarity into one overall degree of similarity.[9][8] The corresponding function is sometimes referred to as a similarity measure. One problem with this outlook is that it is questionable whether the different respects are commensurable with each other in the sense that an increase in one type can make up for a lack in another type.[9] Even if this should be allowed, there is still the question of how to determine the factor of correlation between degrees of different respects.[3] Any such factor would seem to be artificial,[8] 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. And let him become a bit less like you in respect of his weight by gaining a little. Now answer these questions: How much warmer or cooler should he become to restore the original overall comparison? How much more similar in respect of his height?"[9] This problem does not arise for physical distance, which involves commensurable dimensions and which can be kept constant, for example, by moving the right amount north or south, after having moved a certain distance to the west.[9][8] Another objection to the metric conception of similarity comes from empirical research suggesting that similarity judgments do not obey the axioms of metric space. For example, people are more likely to accept that "North Korea is similar to China" than that "China is similar to North Korea", thereby denying the axiom of symmetry.[12][3]
https://en.wikipedia.org/wiki/Similarity_(philosophy)
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