We can understand language at the rate of several hundred words per minute even though, doing so involves establishing referential and causal coherence, generating expectations and making predictions. This suggests that we can (and do) draw a wide range of inferences very rapidly, automatically and without conscious effort -- as though they are a reflexive response of our cognitive apparatus. In view of this such reasoning may be described as reflexive (Shastri 1991). As an example reflexive reasoning consider the inference 'John owns a car' upon hearing 'John bought a Rolls-Royce'. We can make this inference effortlessly even though it requires multiple steps of inference using background knowledge such as Rolls-Royce is a car and if z buys y then owns y. Not all reasoning is, and as complexity theory tells us, cannot be, reflexive. We contrast reflexive reasoning with reflective reasoning -- reasoning that requires reflection, conscious deliberation, and at times, the use of external props such as paper and pencil (e.g., solving logic puzzles, doing cryptarithmetie, or planning a vacation).