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Lines of Thought addresses how we are able to think about abstract possibilities: How can we think about math, despite the immateriality of numbers, sets, and other mathematical entities? How are we able to think about what might have happened if history had taken a different turn? Questions like these turn up in nearly every part of cognitive science, and they are central to our human position of having only limited knowledge concerning what is or might be true. Because we cannot experience hypothetical or future events or abstract concepts, we cannot use our ordinary sense of perception or memory to think about these subjects, so what underlies our ability to make these assumptions? Lance Rips explores people's beliefs about possibilities as they arise in the context of basic concepts, including numbers, causality, and reasons. He argues that beliefs about these concepts cannot be meaningfully reduced to perceptual information, remembered instances, or probabilities. He also claims that analogies to cognitive perception models are equally unhelpful in understanding what makes thinking of possibilities possible. Instead, he makes the case that our abilities here depend on the intrinsic hardwiring of the human mind. Lines of Thought provides an overview and a point of view on research in higher-level cognitive science, integrating theories from psychology, philosophy, and linguistics. The book is written in an accessible style that will provide students with essential background for their own thoughts about this domain.