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Logic as a Tool by Valentin Goranko

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Chapter 3Understanding First-order Logic

Propositional logic can only formalize some patterns of reasoning, but it cannot grasp the logical structure or the truth behavior of very simple sentences such as:

  • c03-math-001 is greater than 5;”
  • there exists c03-math-002 such that c03-math-003;”
  • for every real number c03-math-004, if c03-math-005 is greater than 0 then there exists a real number c03-math-006 such that c03-math-007 is less than 0 and c03-math-008 equals c03-math-009;” or, for a non-mathematical example;
  • every man loves a woman.”

Indeed, note that an expression such as “c03-math-010 is greater than ...

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