To identify which procedures are examples of Descartes’s rules for scientific reasoning, let’s briefly summarize what his method entails. Descartes emphasized a systematic approach to knowledge, focusing on doubt, analysis, and logical reasoning. The following procedures align with his principles:
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Keeping a detailed record of the procedure and results of a scientific experiment - This aligns with Descartes's emphasis on systematic observation and documentation in scientific inquiry.
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Conducting an experiment to confirm the effects of gravity on Earth - This also fits within Descartes's methodology, as he advocated for empirical testing to validate hypotheses.
The following options do not align with Descartes's principles:
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Accepting all of Descartes’s theories as truth - Descartes's approach encourages skepticism and questioning rather than uncritical acceptance of any theory.
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Answering a math problem using mental mathematics - While logical reasoning is important, using mental mathematics does not exemplify Descartes’s formal procedures for scientific reasoning.
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Solving an expression in steps using the order of operations - This is a mathematical procedure and doesn’t directly relate to Descartes’s broader rules of scientific reasoning.
So, the valid examples that correspond to Descartes's rules for scientific reasoning are:
- Keeping a detailed record of the procedure and results of a scientific experiment
- Conducting an experiment to confirm the effects of gravity on Earth