LPL 2.5 lecture - Consider the following invalid argument...

Info icon This preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
Nonconsequence Not only can we prove that an argument is valid (that is that its conclusion is a logical consequence of its premises), but we can also prove that an argument is invalid (that its conclusion is not a logical consequence of its premises). Demonstrating logical consequence requires that we give either an informal proof on paper or a formal proof in Fitch showing that from a given set of premises we can derive the desired conclusion. Demonstrating logical nonconsequence requires that we give a counterexample to the given argument. This can be done either informally or formally. The informal method for demonstrating nonconsequence is to describe in English a situation in which all the premises of an argument are true while the conclusion remains false. These sorts of proofs will mirror our informal proofs of logical consequence.
Image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Consider the following invalid argument: All actors who win academy awards are famous. Harrison Ford has never won an academy award. Harrison Ford is not famous How might we demonstrate informally that the conclusion of this argument is not a consequence of the given premises? The formal method for demonstrating logical nonconsequence is to build a counterexample world, using Tarski’s World, in which the premises of the argument are true while the conclusion is false. Consider this invalid argument expressed in the block’s language of Tarski’s World. How might we build a formal counterexample? Adjoins(a, b) SameCol(b, c) FrontOf(c, b) FrontOf(c, a) Another demonstration of nonconsequence: Exercise 2.21...
View Full Document

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern