May_20 [Compatibility Mode] - Wednesday May 20 So Today...

Info icon This preview shows pages 1–6. Sign up to view the full content.

View Full Document Right Arrow Icon
Wednesday, May 20 So. Today, we'll talk about - - We'll probably do a little more Natural Deduction - 9.6 Rules of Replacement - 9.7, 9.8 More Natural Deduction - 9.9 Proof of Invalidity - 9.10 inconsistency - 9.11, 9.12 Indirect Proof of Validity and Short Truth Table - Introduction to Inductive Arguments
Image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
9.6 Rules of Replacement In addition to the Rules of Inference, there are 10 Rules of Replacement. Some comments about Rules of Replacement: - You can only apply Rules of Inference to whole lines – for example, you can only do Addition to a whole line, you can't do it to just part of a line. Rules of Replacement, on the other hand, can be applied to part of a line. - Also, because both sides of a Rule of Replacement are logically equivalent, you can go back and forth between both sides of a Rule of Replacement as needed. You can never go from the conclusion of a Rule of Inference to its premises. - It is easy to forget that Simplification and Addition are Rules of Inference
Image of page 2
9.7, 9.8 More Natural Deduction Like I said last Friday, you have to do Rules of Inference exactly as written. Rules of Inference comprise a precise system that is relatively complete but that also contains a minimum number of rules (more or less), and including (p v q); ~q; therefore p in addition to Disjunctive Syllogism would clutter things up. I will probably try and trip you up on this on a test at some point – be wary.
Image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
9.9 Proof of Invalidity So, you know how to prove validity with Natural Deduction. However, you may have wondered at some point or another how to prove invalidity – if we don't have a way to prove invalidity, we'll just end up adding lines to our proofs until we give up. What we can do is ASSUME THE CONCLUSION TO BE FALSE. This is how proofs are normally done. An argument is shown invalid if there is at least one row of its truth table that has all true premises and a false conclusion. We can assume the conclusion is false, and then see if we can get the premises all to be true while keeping the truth values of all the letters we're using constant. (And I should throw an example in here).
Image of page 4
9.10 Inconsistency A deductive argument that is not valid, is invalid. So, if we're attempting to prove invalidity by assuming the conclusion false and the premises true, and we cannot do so, the argument is valid.
Image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 6
This is the end of the preview. Sign up to access the rest of the 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