Achinstein's formal analogy between swans and line segments — mapping 'has the same color as' to 'is congruent with' on the basis of shared reflexivity, symmetry, and transitivity — satisfies rule (5) but clearly establishes nothing about swans or line segments.
Rule (5)(a criterion that the analogy succeeds in meeting)
A specific criterion or standard (the fifth one in whatever list is being discussed) that the analogy is being tested against to see if it's logically valid.
Symmetry(one of the three shared logical properties between the two comparisons)
A logical property meaning if A relates to B in some way, then B relates to A the same way—like if swan A is the same color as swan B, then swan B is the same color as swan A.
congruent(Kant, Prolegomena 4:286)
Capable of being superimposed or made to coincide exactly; used contrastively with incongruent counterparts which share all relational properties but cannot be superimposed.
A relationship between two domains that are interpretations of the same formal theory, linked to common mathematical structure; includes nomic isomorphism as a special case and extends, on Bartha's definition, to any two features occupying corresponding positions in formally analogous theories
reflexivity(Relational models in modal logic)
A property of a relation R on W such that every state w stands in relation R to itself; corresponds to the Veracity axiom in epistemic logic (what is known is true)
transitivity(Applied to the temporal relation 'earlier than' on a set of worlds W)
A property of a relation R such that if wRv and vRu, then wRu
Argumentation theorists also make use of tools such as speech act theory (Bermejo-Luque 2012), argumentation schemes and dialogue types (Macagno et al. 2017; Walton and Hyra 2018) to distinguish different types of analogical argument. Arguments by analogy are also discussed in the vast literature on scientific models and model-based reasoning, following the lead of Hesse (1966). Bailer-Jones (2002) draws a helpful distinction between analogies and models. ” In brief, models are tools for predic