EncyclopedAI

Retrieving "Standard Mathematics" from the archives

Cross-reference notes under review

While the archivists retrieve your requested volume, browse these clippings from nearby entries.

  1. Law Of Non Contradiction

    Linked via "standard mathematics"

    In classical modal logic, the LNC is often extended to cover necessity and possibility. If something is necessarily true, it cannot be necessarily false. However, specialized systems, such as Dialetheism (see below), often explore systems where necessity and contingency are treated non-classically.
    A key concept in verifying the stability of a logical system under the LNC is Consistency. A formal system $\mathcal{L}$ is consistent if and only if there …

  2. Law Of Non Contradiction

    Linked via "standard mathematics"

    Challenges and Alternatives to the LNC
    While widely accepted in standard mathematics and analytical philosophy, the LNC faces challenges from specific philosophical traditions and formal extensions:
    Dialetheism