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The modal syllogism

The modal syllogism. Paul Thom. A. B. C. The first figure. Barbara LLL. Barbara LXL. Celarent LLL. Celarent LXL. Darii LLL. Darii LXL. Ferio LLL. Ferio LXL. A. B. C. The second figure. Cesare LLL. Cesare LXL. Camestres LLL. Camestres XLL. Festino LLL. Festino LXL.

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The modal syllogism

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  1. The modal syllogism Paul Thom

  2. A B C The first figure Barbara LLL Barbara LXL Celarent LLL Celarent LXL Darii LLL Darii LXL Ferio LLL Ferio LXL

  3. A B C The second figure Cesare LLL Cesare LXL Camestres LLL Camestres XLL Festino LLL Festino LXL Baroco LLL

  4. A B C The third figure Darapti LLL Darapti LXL Felapton LLL Darapti XLL Disamis LLL Felapton LXL Datisi LLL Disamis XLL Bocardo LLL Datisi LXL Ferison LLL Ferison LXL

  5. Direct Reduction of the second figure to the first A B C Problem: Under what condition can this transformation be made?

  6. Indirect reduction of the second figure to the first A B C ~ ~ Problem: Under what condition can this transformation be made? ~(ALaB) = AMoB; ~(ALeB) = AMiB; ~(ALiB) = AMeB; ~(ALoB) = AMaB

  7. MML XML MXL XXL MLL LML XLL MMX XMX MXX LMX MLX MMM MXM Valid XMM LXL LLL XXX XLX LXX LLX LMM MLM XXM LXM XLM LLM First figure L / M / X syllogisms

  8. Lo La Le Le Reduction of Baroco LLL by exposition A La B Lo C D Problem: Under what condition can this transformation be made?

  9. Axiom 1. Axiom 2. Axiom 3. Axiom 4. Axiom 5. Axiom 6. Definition 1. A concept κ is per se iff Definition 2. κ is a primary essence iff Axiom 7. Axiom 8. Semantic base

  10. Truth conditions for necessity propositions ALaB is true iff ALeB is true iff ALiB is true iff ALoB is true iff

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