In this paper I consider the historical background of Hebrew Orthodoxy finally formed in Belarusian lands. Further, I try to explicate the Judaic logic (i.e. the logic used by Talmudists for inferring Judaic laws from the Pentateuch). The only logical connective of that logic is the Judaic conjunction 'and' which is not idempotent or commutative, but it is associative. I propose Austin's style of semantics for Judaic logic and explicate also the inference rules used by Talmudists. I show that the Judaic logic is characterized by non-well-foundedness.