Logic as a Tool

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:

• “ is greater than 5;”
• “there exists such that ;”
• “for every real number , if is greater than 0 then there exists a real number such that is less than 0 and equals ;” or, for a non-mathematical example;
• “every man loves a woman.”

Indeed, note that an expression such as “ is greater than ...