First principles cannot be denied…

There are certain fundamental axioms of thought by which thought is possible. For we cannot build a house of knowledge unless there is a foundation on which to erect it. Aquinas calls these foundational principles of knowing first principles.

First principles are necessary constituents of all knowledge, but they do not supply any content of knowledge.

Since first principles are self-evident, there is a sense in which it is absurd to attempt a direct proof or demonstration of them. Since some people deny their validity, however, there is an indirect sense in which some attempt to prove them. This is done by showing that first principles cannot actually be denied without absurdity. Aristotle lists several arguments of this kind in defense of the first principle of noncontradiction:

  1. To deny it would deprive words of their fixed meaning and render speech useless.
  2. Reality of essences must be abandoned. There would be becoming without anything that becomes, flying without a bird, accidents without substance.
  3. There would be no distinction between things. All would be one.
  4. It would mean the destruction of truth, for truth and falsity would be the same.
  5. It would destroy all thought, even opinion, for its affirmation would be its negation.
  6. Desire and preference would be useless, for there would be no difference between good and evil.
  7. Everything would be equally true and false at the same time. No opinion would be more wrong than any other, even in degree.
  8. It would make impossible all becoming, change, or motion, for all this implies a transition from one state to another, but all states would be the same, if contradiction is not true.

— Norman Geisler, from Thomas Aquinas: An Evangelical Appraisal, p. 71, 72, 78

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