Argumentation is an essential part of Judaism. We see this in the Mishnah and Talmud, in every student’s education in a kollel, yeshiva or Jewish religious school. Arguments are aimed at reasoning and conclusions, not ad homenim (aimed at a person)
In a typical deductive argument, premises guarantee the truth of the conclusion: Sure, that’s pretty hard to do in religion, in general. So we usually see a combination of deductive argumentation, with some amount of inductive argument (one in which logic provides reasons for supporting the conclusion’s probable truth.)
In rabbinical Judaism, our premises are not secular atheism, or Christian texts, or Muslim, Hindu or Buddhist texts.
Our premises start with the Torah (five books of Moses) and Tanakh (Hebrew Bible), and read them through the evolving tradition of our oral law – including the Mishnah, Tosefta, Midrash, the two Talmuds and the responsa literature.
Responsa (Hebrew: She’elot u-Teshuvot, שאלות ותשובות , questions and answers”) comprise the body of written decisions given by poskim (“deciders of Jewish law”)
A good overview of this topic may be found in History of responsa in Judaism (Wikipedia) and in Responsa in the Conservative/Masorti Jewish movement.
The image below is really good; it shows the sources we use.
One note – it does imply primacy to a late medieval code of Jewish law, the Shulkhan Arukh. But the idea of it’s primacy is a post-1700’s belief, and not quite traditional. For more on that see The Shulchan Aruch in perspective