LessonsReason, Sound Inference and Classifications of KnowledgeQuiz

Some critics conceded the usefulness of mathematics while expressing doubts about metaphysical demonstration because metaphysical thinkers disagreed so widely.

The objection contains two steps: (1) substantial disagreement exists; (2) therefore sound reasoning cannot produce knowledge in that field.

The second conclusion does not follow from the first without further argument. Divergence may also reflect false premises, omitted conditions or faulty inferences. A disputed conclusion is not thereby proof that valid inference as such is impossible.

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Mathematics and Metaphysics: Different Claims

Reason, Sound Inference and Classifications of Knowledge

Some critics conceded the usefulness of mathematics while expressing doubts about metaphysical demonstration because metaphysical thinkers disagreed so widely.

The objection contains two steps: (1) substantial disagreement exists; (2) therefore sound reasoning cannot produce knowledge in that field.

The second conclusion does not follow from the first without further argument. Divergence may also reflect false premises, omitted conditions or faulty inferences. A disputed conclusion is not thereby proof that valid inference as such is impossible.