All fish can swim. No fish can walk. So nothing that can walk, swims.

Let's evaluate the logical arguments using set theory rules:
1. Premise 1: "All fish can swim." This means the set of Fish is a subset of the set of entities that can Swim ($\text{Fish}\subseteq \text{Swim}$).
2. Premise 2: "No fish can walk." This means the set of Fish and the set of entities that can Walk are disjoint ($\text{Fish}\cap \text{Walk}=\varnothing$).
3. Inference: "So nothing that can walk, swims." This claims that the set of entities that can Walk and the set of entities that can Swim are entirely disjoint ($\text{Walk}\cap \text{Swim}=\varnothing$).

However, while we know that no fish can walk, there could be other creatures (like frogs or humans) that can both walk and swim. The premises do not eliminate the possibility of an overlap between the set of things that can walk and things that can swim outside of the fish category. Therefore, concluding definitively that nothing that can walk swims is invalid.

Thus, the inference is false.