In microeconomics : is this the contradiction in the atomicity of firms ? Let $p$ be the market demand. It is a function of the market production $Q$. Let $q_i$ be the production of firm $i$.

Reading Steve Keen (in Debunking Economics, chapter II) quoting George Stigler, I think the first wants to deduce the following contradiction in the atomicity of firms.

Using the chain rule, we get : $\frac{dp}{dq_i}= \frac{dp}{dQ} \frac{dQ}{dq_i}$.

The firm $i$ is price-taker, so the market price is the same whatever its production and so $\frac{dp}{dq_i}=0$.

The demand $p$ is a (strictly) decreasing function of $Q$ (supposing the law of demand is true). Thus $\frac{dp}{dQ} &lt; 0$

The other firms than firm $i$ are not supposed to react to a change in production of firm $i$, so that $\frac{dQ}{dq_i}=1$.

We get : $0 &lt; 0$. Is that the contradiction that Steve Keen means (or another way of expressing it) ?

Thank you so very much !
A price-taking firm takes prices as given, but that does not mean that the firm cannot influence prices; it just means that the firm ignores its own impact on prices.  

Now the question is how sensible it is to assume that firms take prices as given. The usual view is that it is a reasonable assumption when the impact of a firm on prices is small enough that profit-maximizing behavior for given prices does not differ much from profit-maximization under actual prices. This is usually the case if there are many firms that are small relative to the market. There are various ways to make this precise. One can also work with models with a continuum of firms in which a single firm hs literally no impact on prices. 

As a side remark, Steve Keen's book reveals a strange mixture of incompetence and dishonesty. Keen is ignorant of basic calculus. Keen, sometimes with coauthors, has come up with a nonsensical theory of the firm. Here is a note by Paulin Anglin pointing out several of the many problems. One of these problems is acknowledged here. Later, Keen (and Standish) wrote a survey of Keen's history of criticising the theory of the firm in which they did not acknowledge Anglin's criticism. I recommend reading books from people with higher scholarly standards than Keen.