Behavioral predictions about reasoning have usually contrasted two accounts, Mental Logic and Mental Models. Neuroimaging techniques have been providing new measures that transcend this debate. We tested a hypothesis from Goel and Dolan (2003) that predicts neural activity predominantly in a left parietal-frontal system when participants reason with arbitrary (non-meaningful) materials. In an event-related fMRI investigation, we employed propositional syllogisms, the majority of which involved conditional reasoning. While investigating conditional reasoning generally, we ultimately focused on the neural activity linked to the two valid conditional forms--Modus Ponens (If p then q; p//q) and Modus Tollens (If p then q; not-q//not-p). Consistent with Goel and Dolan (2003), we found a left lateralized parietal frontal network for both inference forms with increasing activation when reasoning becomes more challenging by way of Modus Tollens. These findings show that the previous findings with more complex Aristotlean syllogisms are robust and cast doubt upon accounts of reasoning that accord primary inferential processes uniquely to either the right hemisphere or to language areas.