Homework 11 - All humans are mortal*Socrates is human...

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If something is true of every individual, then it is certainly true of any particular individual you might choose. This is the pattern of inference captured by the rule for eliminating universal quantifiers, universal elimination or E, which we represent as follows: DEFINITION: Universal Elimination In case you are wondering just what φ[τ/υ] means, you might want to quickly reread the section on the formal syntax of predicate logic—but we also give you a quick reminder right here: φ[τ/υ] is a substitution instance of ( υ)φ, obtained by substituting the term τ for each occurrence of υ in φ. Since you are already fairly familiar with derivations, why don't we just jump right in to an example. Let's consider our original predicate argument:
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Unformatted text preview: * All humans are mortal. *Socrates is human. * Socrates is mortal. ∴ We agreed on the symbolization of this argument in our definition-style demonstration of its validity, so we can begin our first predicate derivation: It is pretty obvious here that there is not much we could do at this point with the second premise, so we use ∀ E right away. The only choice we need to make in applying this rule is what term we wish to use for the substitution instance, that is, the constant or variable we want to be our instantiating term. Seeing as anything other than s won't be of much help, s it will be: Not so difficult, is it? We are actually only one step away from completing the derivation—all we need to do is apply →E, and we are done:...
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