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A heuristic argument is an argument that reasons from the value of a method or principle that has been shown by experimental (especially trial-and-error) investigation to be a useful aid in learning, discovery and problem-solving. A widely used and important example of a heuristic argument is Occam's Razor.
It is a speculative, non-rigorous argument, that relies on an analogy or in intuition, that allows to achieve a result or approximation to be checked after with more rigor, otherwise the results are of doubt. It is used as a hypothesis or conjecture in an investigation. It can also be used as a mnemonic.
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