The term "positive law" is opposed to "natural law" (the set of universal and unchangeable rules which derive from the human nature itself, from God or from reasoning). Positive law is the set of rules governing a particular country at a particular time. Positive law originates from an authority who has been empowered to do so, such as Congress.

For example, the right to live is a "natural law" right, because it is inherent in every human being, it is a right every human being has just because of being human. This right may also be part of positive law ONLY IF it is included in a country's body of law by, say, the enactment of a statute or the decision of a judge. So, in a "positivist view", you have the right to live (and not to be killed) only because it is granted in the Constitution, or in a statute or a judge's decision.

In a Common Law country, positive law includes both statutes and judicial precedents (mainly). But Argentina is a Civil Law country, and is therefore governed by statutory law ONLY (with sove few exceptions). That is, a jugde has the obligation to apply statutory law (or "written law") when deciding a case, but he/she does not rely on judicial precedents. Judicial precedents are persuasive, but NOT mandatory in Argentina.

The appellant in you translation is arguing that the judge decided based on something vague (a "vague argument") instead of applying the positive law, that is, the written law, statutory law.

"Normas positivas" does not mean "mandatory rules" because, although they are mandatory, the emphasis is on the "written" or "statutory" nature of the law.
It does NOT mean "substantive" either, because it has nothing to do with them being accurate, or detailed.

You can check this page below for a more detailed explanation on Hans Kelsen (the Theory of Pure Law) and positivism:
http://www.xrefer.com/entry.jsp?xrefid=552595