Intra-categorical analogy draws on the relationship between individuals belonging to the same category. For a definition of the concept of category, the categorization process of individuals; the organization of categories in classifications and the corresponding forms of syllogistic reasoning, S. Categorization and Nomination.
1. From identity to intra-categorical analogy and circumstantial analogy
1.1 Individual identity
An individual is identical to itself (not similar nor resembling); it is not “more or less” identical to itself. This self-evidence establishes the principle of identity “A = A”.
1.2 Identity of indiscernibles
Two different individuals perfectly identical, for example products taken out of the same industrial production chain, are materially identical, that is perceptually indistinguishable. All that can be said of one can be said of the other; their descriptions coincide, they share all their properties, essential (categorical) or accidental.
Discernibility depends on the observer, the layman does not see any difference, and believes that “it’s all the same”, whereas the specialist will make crucial distinctions.
1.3 Intra-categorical analogy
Intra-categorical analogy is the relationship between the members of a category C. All members share, by definition, the characteristics defining the category. The phrase “another C” refers to another member of the same class C. Two beings belonging to the same category are identical for this category; a whale and a rat are identical from the point of view of the category “— be a mammal”. This categorical identity is a partial identity, compatible with major differences; two beings of the same category are said to be analogous or similar. They are comparable in respect of their other non-categorical properties. Chicken eggs are all similar as eggs; an egg is identical to another egg; it is comparable to all other eggs in terms of freshness, size, color, etc. S. Comparison.
1.4 Circumstantial analogy
An individual a possessing the features (x, y, z, t), is similar to all individuals who have any of those features, whether it be an essential or accidental feature.
The descriptors of two objects define the point of view under which they are equivalent; two beings are similar if their descriptions overlap, contain a common part, which may or may not include all or some of their essential features. In other words, this common part generates a category, which may or may not make sense. One might speak of circumstantial analogy. Alice and a snake are identical from the standpoint of the category “— is a long-necked egg eater”, S. Definition.
2. Intra-categorical analogy as induction or deduction
Intra-categorical analogy can be reconstructed as an induction or a deduction:
2.1 As an induction
O is similar to P
P has the properties w, x, y, m
O has the properties w, x, y
So O probably has also property m.
From an overall judgment of analogy between two beings, based on the shared features w, x, y … we conclude that if one has the property m then the other most probably also possesses m. In other words, analogy is pushed towards identity.
2.2 As a deduction
O is similar to P
P has the property m
Conclusion: O probably has the property m.
O is similar to P. This means that they share a common set of features, and therefore belong to the category C defined by those features. In conclusion, as members of the same category C, O and P probably share other properties, among them m. This means that the predicate « — is like” is to be interpreted as a weaker form of « — is the same as”; analogy is seen as a weakened identity.
Deduction and induction are considered valid forms of reasoning. The purpose of the discussion about the possibility of reducing analogy to deduction or induction is to determine whether or not analogy is also valid as a form of reasoning. Reasoning by analogy is sometimes used to prove the existence of God, the ideological stakes of this issue are therefore high.
These formulations of the argument by analogy in the form of a dialectical syllogism are rather sterile because they do not emphasize the warranting operations, that contain all the interesting problems. The formulation of the conclusion not as a secure finding but as the product of a heuristic rule of thumb, however, is of great value. The conclusion should be written not as something “probable”, that is a kind of belief, but as a suggestion to do something:
It might be interesting to test P for property m.
It might be interesting to see whether O and P share other properties.
3. Arguments based on intra-categorical analogy
— Categories as a whole are structured according to their respective definition; two individuals belong to the same category if they have the same definition.
— Categories may be gradual, S. Rule of Justice.
4. Refutation of categorical analogy
In one or other aspect, everything is like everything else, and analogies can be more or less “far-fetched”. Any rejected categorical analogy will be dubbed fallacious and denounced as a confusion, an amalgam (Doury 2003, 2006).
Intra-categorical analogy can be refuted by showing that the category created from those two beings is not based on essential features, but on some accidental property; in general, the generated class is deemed irrelevant. The nonsensical analogy “Chinese ~ Butterfly”, ironically discussed by Musil, illustrates the perils of circumstantial analogy, based on the arbitrary choice of a non-essential feature, here the “lemon yellow” color.
There are lemon yellow butterflies; there are also lemon yellow Chinese people. So, in a sense, butterflies can be defined as miniature winged Chinese people. Butterflies and Chinese people are symbolic of sensual pleasure. Here we can see for the first time a glimmer of a possible match, never considered before, between the great period of the moth fauna and Chinese civilization. The fact that butterflies have wings and not the Chinese people is only a superficial phenomenon. […] Butterflies did not invent powder: precisely because the Chinese have done it before them. The suicidal predilection for the lights of some nocturnal species is still an artifact of the past, which is difficult to explain in view of the daylight understanding of this morphological relationship between butterflies and China.
Robert Musil, [Spirit and Experience],  
The analogy relationship has difficulties with transitivity, S. Relation. Intra-categorical analogy is transitive: if A and B on the one hand, B and C on the other hand, are said to be similar because they possess the same essential features, A is thus similar to C. Circumstantial analogy is not transitive: nothing proves that if, on the one hand, the descriptions of A and B have common parts, and, on the other hand, the description of B and C have common parts, then the description of A and C will also have also common parts. Khallaf invokes a traditional analogy to criticize the concatenation of analogies:
A man is walking on the beach trying to find similar shells; once he finds a shell similar to the original, he throws away the original shell and goes on to find a seashell which resembles the second, and so on. When she has found the tenth shell, she should not be surprised to see that it is totally different from the first in the series. (Khallâf , p. 89)
 Quoted in Jacques Bouveresse, Prodiges et vertiges de l’analogie [Prodigies and Dizziness of Analogy]. Paris: Raisons d’Agir, 1999. P. 21-22.