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The Longmire Argument for the Ground of Logical Necessity

The Longmire Argument for the Ground of Logical Necessity

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Abstract

This paper presents the Longmire Argument, which contends that the laws of thought—universal, necessary, and self-evident principles of logic—require a metaphysical ground. Utilizing the principle of sufficient reason (PSR), the argument demonstrates that the laws of thought cannot be self-caused, grounded in mental or material processes, or explained by infinite regress. Instead, the laws of thought require an uncaused, self-existent, necessary, intelligent, and personal being. This being, traditionally identified with God, is shown to possess omnipotence and omniscience to ensure the universal applicability and immutability of logical principles.

Introduction

The laws of thought are foundational to rational inquiry. As self-evident and necessarily true principles, they provide the framework for all logical reasoning and intelligible discourse. These include:

  • The law of identity (A is A).
  • The law of non-contradiction (A cannot be both A and not-A at the same time).
  • The law of excluded middle (A is either A or not-A).

Despite their evident truth, the metaphysical basis for the laws of thought remains underexplored. Are these principles simply brute facts? Do they emerge from physical reality or human cognition? Or do they point to a transcendent ground? The Longmire Argument seeks to answer these questions by rigorously applying the PSR and analyzing competing explanations.

The Full Longmire Argument

  1. The laws of thought are necessarily true and self-evident. Their necessity and universality demand explanation beyond contingent processes.
  2. Nothing can be self-caused (principle of sufficient reason). The PSR asserts that all entities or truths must have an explanation, either in themselves (necessary) or in something else (contingent). The laws of thought cannot be self-caused, as this would violate the PSR.
  3. Therefore, the laws of thought require a ground beyond themselves.
  4. This ground cannot be:
    • Mental operations: Minds presuppose the laws of thought to operate rationally. Using mental operations to explain the laws is circular.
    • Material reality: Matter depends on logical structures for its intelligibility. Logical laws cannot emerge from what presupposes them.
    • Infinite regress: An infinite chain of explanations violates the PSR by failing to provide a sufficient ground.
  5. Therefore, the ground must be an uncaused cause.
  6. This uncaused cause must be:
    • Self-existent: To avoid infinite regress, it must exist necessarily and in itself.
    • Necessary: It must ground the necessity of logical truths, which cannot depend on contingent factors.
    • Intelligent: The intelligibility of the laws implies a rational source.
    • Personal: Rational agency and intentionality, essential for logic, point to a personal being.
  7. Only a necessary being can serve as an uncaused cause. Contingent entities cannot ground necessary truths. Only a necessary being provides a sufficient explanation.
  8. Therefore, the laws of thought require a necessary being as their ground.
  9. This necessary being must be omnipotent and omniscient. Omnipotence ensures the laws of thought are universally binding. Omniscience guarantees their consistent application across all possible worlds.

Conclusion

The Longmire Argument demonstrates that the laws of thought—self-evident, necessary, and universal—require a metaphysical ground. Competing explanations, such as materialism, brute facts, or infinite regress, fail to account for their necessity, universality, and intelligibility. The argument concludes that the only sufficient ground is a necessary, self-existent, intelligent, and personal being with omnipotence and omniscience. This being, traditionally identified as God, provides the ultimate foundation for the rational and logical structure of reality.

References

  • Aquinas, Thomas. Summa Theologica. Translated by the Fathers of the English Dominican Province, 1920.
  • Craig, William Lane. Reasonable Faith: Christian Truth and Apologetics. Crossway, 2008.
  • Leibniz, Gottfried Wilhelm. Monadology. Translated by Nicholas Rescher, University of Pittsburgh Press, 1991.
  • Plantinga, Alvin. Warrant and Proper Function. Oxford University Press, 1993.
  • Pruss, Alexander R. The Principle of Sufficient Reason: A Reassessment. Cambridge University Press, 2006.
  • Swinburne, Richard. The Existence of God. Clarendon Press, 2004.
  • Oppy, Graham. Philosophical Perspectives on Infinity. Cambridge University Press, 2006.
The Longmire Argument - Syllogism

The Longmire Argument - Syllogism

1. The laws of thought are universal, necessary, intelligible to persons, and require a metaphysical ground.

2. This ground cannot be mental operations (circular), material reality (contingent), or an infinite regress (violates the principle of sufficient reason).

3. Therefore, the laws of thought require a self-existent, necessary, intelligent, and personal being as their ground.

Conclusion: Only a necessary being (God) can account for the universal applicability, necessity, and intelligibility of the laws of thought to persons.

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