methods of deduction
DESCRIPTION
logicTRANSCRIPT
![Page 1: Methods of Deduction](https://reader035.vdocuments.net/reader035/viewer/2022062308/55cf8ee6550346703b96cd5c/html5/thumbnails/1.jpg)
Methods of Deduction
Presented by: Vaericke Kingad
![Page 2: Methods of Deduction](https://reader035.vdocuments.net/reader035/viewer/2022062308/55cf8ee6550346703b96cd5c/html5/thumbnails/2.jpg)
Section 6
Expanding the Rules of Inference:Replacement RulesThe nine elementary valid argument forms with which we have been working are powerful tools of inference, but they are not powerful enough. There are very many valid truth-functional arguments whose validity cannot be proved using only the nine rules thus far developed. We need to expand the set of rules, to increase the power of our logical toolbox.
![Page 3: Methods of Deduction](https://reader035.vdocuments.net/reader035/viewer/2022062308/55cf8ee6550346703b96cd5c/html5/thumbnails/3.jpg)
• We need rules that identify legitimate replacements precisely.• Such rules are available to us. Recall that the only compound
statements that concern us here are truth-functional compound statements, and in a truth-functional compound statement, if we replace any component by another statement having the same truth value, the truth value of the compound statement remains unchanged.
• Therefore we may accept as an additional principle of inference what may be called the general rule of replacement—a rule that permits us to infer from any statement the result of replacing any component of that statement by any other statement that is logically equivalent to the component replaced.
![Page 4: Methods of Deduction](https://reader035.vdocuments.net/reader035/viewer/2022062308/55cf8ee6550346703b96cd5c/html5/thumbnails/4.jpg)
Definition of Terms
• Rule of replacement• A rule that permits us to infer from any
statement the result of replacing any component of that statement by any other statement that is logically equivalent to the component replaced.
![Page 5: Methods of Deduction](https://reader035.vdocuments.net/reader035/viewer/2022062308/55cf8ee6550346703b96cd5c/html5/thumbnails/5.jpg)
![Page 6: Methods of Deduction](https://reader035.vdocuments.net/reader035/viewer/2022062308/55cf8ee6550346703b96cd5c/html5/thumbnails/6.jpg)
![Page 7: Methods of Deduction](https://reader035.vdocuments.net/reader035/viewer/2022062308/55cf8ee6550346703b96cd5c/html5/thumbnails/7.jpg)
![Page 8: Methods of Deduction](https://reader035.vdocuments.net/reader035/viewer/2022062308/55cf8ee6550346703b96cd5c/html5/thumbnails/8.jpg)
![Page 9: Methods of Deduction](https://reader035.vdocuments.net/reader035/viewer/2022062308/55cf8ee6550346703b96cd5c/html5/thumbnails/9.jpg)
![Page 10: Methods of Deduction](https://reader035.vdocuments.net/reader035/viewer/2022062308/55cf8ee6550346703b96cd5c/html5/thumbnails/10.jpg)
![Page 11: Methods of Deduction](https://reader035.vdocuments.net/reader035/viewer/2022062308/55cf8ee6550346703b96cd5c/html5/thumbnails/11.jpg)
![Page 12: Methods of Deduction](https://reader035.vdocuments.net/reader035/viewer/2022062308/55cf8ee6550346703b96cd5c/html5/thumbnails/12.jpg)
![Page 13: Methods of Deduction](https://reader035.vdocuments.net/reader035/viewer/2022062308/55cf8ee6550346703b96cd5c/html5/thumbnails/13.jpg)
![Page 14: Methods of Deduction](https://reader035.vdocuments.net/reader035/viewer/2022062308/55cf8ee6550346703b96cd5c/html5/thumbnails/14.jpg)
![Page 15: Methods of Deduction](https://reader035.vdocuments.net/reader035/viewer/2022062308/55cf8ee6550346703b96cd5c/html5/thumbnails/15.jpg)
![Page 16: Methods of Deduction](https://reader035.vdocuments.net/reader035/viewer/2022062308/55cf8ee6550346703b96cd5c/html5/thumbnails/16.jpg)
![Page 17: Methods of Deduction](https://reader035.vdocuments.net/reader035/viewer/2022062308/55cf8ee6550346703b96cd5c/html5/thumbnails/17.jpg)
Transposition
![Page 18: Methods of Deduction](https://reader035.vdocuments.net/reader035/viewer/2022062308/55cf8ee6550346703b96cd5c/html5/thumbnails/18.jpg)
Material Implication
![Page 19: Methods of Deduction](https://reader035.vdocuments.net/reader035/viewer/2022062308/55cf8ee6550346703b96cd5c/html5/thumbnails/19.jpg)
![Page 20: Methods of Deduction](https://reader035.vdocuments.net/reader035/viewer/2022062308/55cf8ee6550346703b96cd5c/html5/thumbnails/20.jpg)
Compromise
![Page 21: Methods of Deduction](https://reader035.vdocuments.net/reader035/viewer/2022062308/55cf8ee6550346703b96cd5c/html5/thumbnails/21.jpg)
![Page 22: Methods of Deduction](https://reader035.vdocuments.net/reader035/viewer/2022062308/55cf8ee6550346703b96cd5c/html5/thumbnails/22.jpg)
![Page 23: Methods of Deduction](https://reader035.vdocuments.net/reader035/viewer/2022062308/55cf8ee6550346703b96cd5c/html5/thumbnails/23.jpg)
Application
2, Trans
3, D.N.
1,4, H.S.
![Page 24: Methods of Deduction](https://reader035.vdocuments.net/reader035/viewer/2022062308/55cf8ee6550346703b96cd5c/html5/thumbnails/24.jpg)
![Page 25: Methods of Deduction](https://reader035.vdocuments.net/reader035/viewer/2022062308/55cf8ee6550346703b96cd5c/html5/thumbnails/25.jpg)
![Page 26: Methods of Deduction](https://reader035.vdocuments.net/reader035/viewer/2022062308/55cf8ee6550346703b96cd5c/html5/thumbnails/26.jpg)
![Page 27: Methods of Deduction](https://reader035.vdocuments.net/reader035/viewer/2022062308/55cf8ee6550346703b96cd5c/html5/thumbnails/27.jpg)
![Page 28: Methods of Deduction](https://reader035.vdocuments.net/reader035/viewer/2022062308/55cf8ee6550346703b96cd5c/html5/thumbnails/28.jpg)
![Page 29: Methods of Deduction](https://reader035.vdocuments.net/reader035/viewer/2022062308/55cf8ee6550346703b96cd5c/html5/thumbnails/29.jpg)
![Page 30: Methods of Deduction](https://reader035.vdocuments.net/reader035/viewer/2022062308/55cf8ee6550346703b96cd5c/html5/thumbnails/30.jpg)
![Page 31: Methods of Deduction](https://reader035.vdocuments.net/reader035/viewer/2022062308/55cf8ee6550346703b96cd5c/html5/thumbnails/31.jpg)
![Page 32: Methods of Deduction](https://reader035.vdocuments.net/reader035/viewer/2022062308/55cf8ee6550346703b96cd5c/html5/thumbnails/32.jpg)
![Page 33: Methods of Deduction](https://reader035.vdocuments.net/reader035/viewer/2022062308/55cf8ee6550346703b96cd5c/html5/thumbnails/33.jpg)
![Page 34: Methods of Deduction](https://reader035.vdocuments.net/reader035/viewer/2022062308/55cf8ee6550346703b96cd5c/html5/thumbnails/34.jpg)
![Page 35: Methods of Deduction](https://reader035.vdocuments.net/reader035/viewer/2022062308/55cf8ee6550346703b96cd5c/html5/thumbnails/35.jpg)
![Page 36: Methods of Deduction](https://reader035.vdocuments.net/reader035/viewer/2022062308/55cf8ee6550346703b96cd5c/html5/thumbnails/36.jpg)