I view cognitive linguistics as defined by the commitment to characterize the full range of linguistic generalizations while being faithful to empirical discoveries about the nature of the mind/brain. The Invariance Hypothesis is a proposed general principle intended to characterize a broad range or regularities in both our conceptual and linguistic systems. Given that all metaphorical mappings are partial, the Invariance Hypothesis claims that the portion of the source domain structure that is mapped preserves cognitive topology (though, of course, not all the cognitive topology of the source domain need be mapped). Since the cognitive topology of image schemas determines their inference patterns, the Invariance Hypothesis claims that imagistic reasoning patterns are mapped onto abstract reasoning patterns via metaphorical mappings. It entails that at least some (and perhaps all) abstract reasoning is a metaphorical version of image-based reasoning. The data covered by the Invariance Hypothesis includes the metaphorical understanding of time, states, events, actions, purposes, means, causes, modalities, linear scales, and categories. Because the source domains of these metaphorical concepts are structured by image schemas, the Invariance Hypothesis suggests that reasoning involving these concepts is fundamentally image-based. This includes the subject matter of Boolean, scalar, modal, temporal, and causal reasoning. These cases cover such a large range of abstract reasoning that the question naturally arises as to whether all abstract human reasoning is a metaphorical version of imagistic reasoning. I see this as a major question for future research in cognitive linguistics. (George Lakoff)