Equivalence: How Can Different Things Still Count as the Same?

Equivalence does not mean that two objects have no differences. It means their differences do not affect a judgement under a stated question. Two keys may differ in shape and wear yet both open the same lock. For the question “Can it open this door?”, they can be treated as equivalent. If the question is which key will last longer, that equivalence may disappear.

This differs from similarity. Similarity allows degrees of resemblance; equivalence requires a stable rule that places objects in the same class. Nor is it identity. Identity says we are dealing with the very same object, while equivalence accepts that the objects differ and treats selected differences as irrelevant for the present purpose.

Equivalence makes classification, substitution and reasoning possible. Without it, every object with a different detail would have to be handled separately. Applied too broadly, however, it erases differences that genuinely change the outcome. Whenever we say two things are “the same”, the useful follow-up is: the same with respect to what? When the rule changes, the boundary of equivalence must be checked again.