by Brian Bosse, Copyright July 24, 2008, all rights reserved. 48 views
Existential Generalization: "Brian is mortal" leads to "Something is mortal." In other words, M(B) leads to ∃x(M(x)). Let's now present the abstract rule -
φζ leads to ∃α(φα) where α is a variable, ζ is symbolic term, φα and φζ are symbolic formulas, and φζ comes from φα by proper substitution of ζ for α.
"Brian is mortal" translates to M(B). Now our rule is that φζ leads to ∃α(φα). In this case, φζ stands for M(B). α stands for 'x', φα stands for M(x). Since ζ is a proper substitution for α in φα, then we are allowed to conclude to ∃α(φα) , which is ∃x(M(x)).
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