The nonequivalence of behavioral and mathematical equivalence.
Stop saying "equivalent" unless you can prove the three behavioral properties.
01Research in Context
What this study did
Demello et al. (1992) wrote a theory paper. They looked at how behavior analysts talk about stimulus equivalence.
The authors compared behavioral equivalence with math equivalence. They said the two ideas are not the same.
They urged researchers to use clearer words and tighter tests.
What they found
The team found that loose math talk hides real behavioral processes.
They warned that calling two things "equivalent" does not make them the same in behavior.
How this fits with other research
Belisle et al. (2020) extends the warning. They built a new physics-like model that gives equivalence real measures like mass and volume.
Marin et al. (2024) also extends the critique. They ask if lab-perfect equivalence holds in noisy everyday life.
Fields et al. (1991) came just before the critique. It used equivalence-generalization links that the 1992 paper later challenged.
Why it matters
When you write goals or train staff, say exactly what you mean. Do not claim "equivalence" unless you show reflexivity, symmetry, and transitivity in your data. Clear words lead to clear teaching and cleaner data.
Want CEUs on This Topic?
The ABA Clubhouse has 60+ free CEUs — live every Wednesday. Ethics, supervision & clinical topics.
Join Free →Check your program sheets: replace vague "same" with tested reflexivity, symmetry, and transitivity probes.
02At a glance
03Original abstract
Sidman and his colleagues derived behavioral tests for stimulus equivalence from the axiom in logic and mathematics that defines a relation of equivalence. The analogy has generated abundant research in which match-to-sample methods have been used almost exclusively to study interesting and complex stimulus control phenomena. It has also stimulated considerable discussion regarding interpretation of the analogy and speculation as to its validity and generality. This article reexamines the Sidman stimulus equivalence analogy in the context of a broader consideration of the mathematical axiom than was included in the original presentation of the analogy and some of the data that have accumulated in the interim. We propose that (a) mathematical and behavioral examples of equivalence relations differ substantially, (b) terminology is being used in ways that can lead to erroneous conclusions about the nature of the stimulus control that develops in stimulus equivalence experiments, and (c) complete analyses of equivalence and other types of stimulus-stimulus relations require more than a simple invocation of the analogy. Implications of our analysis for resolving current issues and prompting new research are discussed.
Journal of the experimental analysis of behavior, 1992 · doi:10.1901/jeab.1992.57-227