Numerical thinking

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We are at a point where sufficient data is readily available to derive almost any analysis from first principles. Such a procedure is necessary, least all argumentation is reduced to appeals to authority of analysis and mathematical models. However doing so requires moving beyond classical logic and reasoning to include statistics, uncertainty and appreciation of orders of magnitude; neither of which is commonly associated, nor indeed taught, with critical thinking. In the following paper I introduce numerical thinking -- a new pillar of critical thinking -- by arguing that 1) there is a category of cognitive bias that turns mathematics against intuition; that 2) it takes active effort for rationally to trump intuition; that 3) neither peer-review nor The Economist editorial board are sufficient guard against these fallacies; therefore 4) any mathematical model dealing with unconstrained (real-world) phenomena should be treated with suspicion; that 5) classical logic and reasoning are ill-suited to the task; therefore 6) critical thinking needs to be augmented to 7) include tools to critique mathematical models; and 8) offer insight into systematic (and system-wide) cognitive bias underpinning our reasoning.

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