Talmudic is the adjective from 'Talmud', the great collection of Jewish law and argument. In its plain sense it just means 'belonging to or found in the Talmud': Talmudic law, a Talmudic scholar, a Talmudic story, the Talmudic period. Used this way it is neutral and descriptive, the ordinary word for anyone writing about Judaism. But it also has a second life outside religion, and this is where you will most often meet it in newspapers. Because the Talmud is famous for very fine, very careful, very long argument — splitting a question into smaller and smaller pieces, weighing rare cases, never letting a difficulty go — people describe any reasoning like that as Talmudic. 'The contract was written with Talmudic care.' 'They fell into a Talmudic argument about what counts as a sandwich.' In this second use the tone shifts with the speaker. It can be admiring, meaning deeply learned and rigorous. It can also be a gentle dig, meaning far too clever and detailed for something that does not deserve it. Listen to the sentence around it to know which is meant. Usually capitalised, since it comes from a name.