The mainstream philosophical approach to inference, which insists on sentence-like representations and a linguistic capability, excludes non-human animals as possible agents capable of making inferences. However, an abundance of studies show that many animal species exhibit behaviors that seem to rely on some kind of reasoning. My focus here are the transitive inference tasks, which most species solve quite successfully. These findings put pressure on the mainstream views, and still lack a convincing explanation. I introduce the concept of affective representations, (...) which satisfy the semantic and structural requirements for participating in inferences. I also argue for a broader conception of inference, and show how we can apply this view to explain the results of the transitive inference studies. Finally, I suggest it is more useful to think of flexibility of thought in terms of a continuous range, rather than a dichotomy of flexible vs. inflexible. (shrink)