Putnam’s views on issues of metaphysics and language have actually evolved extensively over time, and his main arguments for realism about natural kinds, which I’ll present here, do not accurately represent his views now, or for that matter, any time since about 1980. “Internal realism,” his current (last I checked) ontology, is extremely nuanced, and I’m not going to talk about it right here. Instead, the opponent whose arguments for natural kinds realism is, specifically, the Putnam of the 1970s. Putnam, in my opinion, deserves great respect for being one of the few philosophers to be completely forthright about changing his mind; he freely admits that his metaphysics has changed dramatically and that, in his opinion, his earlier incarnation was simply wrong.
Why investigate views whose own author has repudiated? The fact is, most of the philosophical community doesn’t agree with Putnam about his own earlier theories. I’d estimate that, currently, the hardcore scientific realist Putnam of the 1970s has more adherents than the internal realist of the 1980s and beyond.