"So reductionism is wrong - a thing can be more than the sum of it's parts (since "thing" includes action)."

The problem with this statement is that you don't define what you mean by sum. I for one cannot imagine what the term 'fingers + palm + thumb' is supposed to mean. Apparently by sum you don't mean arithmetic sum, but something different. Perhaps by 'sum' you mean something like 'put those ingredients into a beaker, shake it a little and then see what you get'.

And of course, if you defined 'sum', you'll need to define 'more' (and 'less') in this context. Perhaps you'll see that it's about the language and how we use it. We overload many words to mean different things and too often we use the special meaning of a word in a context where it doesn't belong.