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Logic I Notes, Week 4, Class 09/06

by: Amanda Notetaker

Logic I Notes, Week 4, Class 09/06 PHL 1100

Marketplace > Appalachian State University > Philosophy > PHL 1100 > Logic I Notes Week 4 Class 09 06
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These notes contain: Homework #5 answers Notes about Exam 1 Statement forms and Statements Replacement routines Argument forms and Arguments Homework #6
Logic I
Dr. Patrick Rardin
Class Notes
logic, Rardin, Amanda, Horsley, Homework, statement, replacement, forms, Argument
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This 6 page Class Notes was uploaded by Amanda Notetaker on Wednesday September 7, 2016. The Class Notes belongs to PHL 1100 at Appalachian State University taught by Dr. Patrick Rardin in Fall 2016. Since its upload, it has received 7 views. For similar materials see Logic I in Philosophy at Appalachian State University.

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Date Created: 09/07/16
Logic I Week 4 09/06 Homework #5 Answers Pg 308 A­11. F A­12. F B­11. (~A כ ~B) ∙ C B­12. A כ B B­13. B כ A B­14. C כ (A ∙ B) B­16. (B ᵛ C)כ A B­17. B ᵛ C B­18. A כ (B ᵛ C) B­19. ~B ᵛ A Notes about the exam next week (09/15) The test questions will be straightforward, not comma crazy like the textbook. Memorize the four main truth tables. These will help you do the calculations that we worked on  last Thursday. You do NOT need to memorize all of the calculations we did last week. Just the  four main truth tables. Statement and Argument Forms Statement – a logical symbolization that only uses statement letters (uppercase letters) Statement form – a logical symbolization that only uses statement variables (lowercase letters),  used to formulate statements Specific form – 1 statement letter substituted for each different statement variable (1:1) and only simple statements are used. Ex.) Statement: Aכ (~A ᵛ T)         Specific Forכ:(~p ᵛ q) Replacement routines (RR)– The substitutions that occur to turn a statement form into a  statement. Logic I Week 4 09/06 Types: 1 for 1, 1 for many, NOT many for 1 Examples Statement Form Logical Symbolization Replacement Other Notes Routine  Statement Example # Substitution s i. p כ (~p ᵛ q) 1. A  כ (~A ᵛ T) A for p Statement from Form i.  T for q (and Form ii. and Form iii) Form i. is the specific form of this statement. RR 1:1 2. (A ∙ T)כ [~(A∙ T) ᵛ (C ∙ T)] A ∙ T for p Statement from Form i.  C ∙ T for q RR 1:M 3. A  כ (~A ᵛ A) A for p Statement from Form i. A for q RR 1:1 4. ~A  כ (A ᵛ ~B) ~A for p NOT statement from Form ~B for q i. If it followed the form, it  would look like this: ~A כ (~~A ᵛ ~B) ii. p כ q 1. A  כ (~A ᵛ T) A for p RR 1:1 and 1:M ~A ᵛ T for q iii. p 1. A  כ (~A ᵛ T) A  כ (~A ᵛ T)  RR 1:M for p Argument form – Two or more statement forms put together to express an argument. Includes at  least one premise and a conclusion, and only written with statement variables. Example Argument form: Arguments with only 1 premise p כ q Premise 1 Conditional cannot come from this form; it p Premise 2 Antecedent of Conditional cannot be simplified. It also cannot get more complicated, except by q Conclusion Consequent of Conditional substituting compound statements for the statement variables. Logic I Week 4 09/06 Argument: If Al is happy then Betty is happyPremise 1 p כ q Al is happy. Premise 2 p Betty is happy. Conclusion q Practice Questions from Textbook Done in Class Pg 313 – For each letter in Group A, write any numbers from Group B that correspond to  argument forms which could have created that argument. State which number is the specific  form, if applicable. a. 3. (specific) b. 6. (specific) c. 4. (specific) m. 3.  24. HOMEWORK # 6 DUE 09/08: PG 313 A f., h., i., Read 8.6, 8.7, 8.8 NOTE: EXAM 1 NEXT THURSDAY, 09/15 I WILL POST A STUDY GUIDE NO LATER THAN SUNDAY, 09/11. Logic I Week 4 09/06 Homework #5 Answers Pg 308 A-11. F A-12. F B-11. (~A כ ~B) · C B-12. A כ B B-13. B כ A B-14. C כ (A · B) B-16. (B ᵛ C)כ A B-17. B ᵛ C B-18. A כ (B ᵛ C) B-19. ~B ᵛ A Notes about the exam next week (09/15) The test questions will be straightforward, not comma crazy like the textbook. Memorize the four main truth tables. These will help you do the calculations that we worked on last Thursday. You do NOT need to memorize all of the calculations we did last week. Just the four main truth tables. Statement and Argument Forms Statement – a logical symbolization that only uses statement letters (uppercase letters) Statement form – a logical symbolization that only uses statement variables (lowercase letters), used to formulate statements Specific form – 1 statement letter substituted for each different statement variable (1:1) and only simple statements are used. Ex.) Statement: A כ (~A ᵛ T) Specific Form: p כ(~p ᵛ q) Replacement routines(RR)– The substitutions that occur to turn a statement form into a statement. Types: 1 for 1, 1 for many, NOT many for 1 Logic I Week 4 09/06 Examples Statement Form Logical Symbolization Replacement Other Notes Routine Statement Substitutions Example # i. p כ(~p ᵛ q) 1. A כ (~A ᵛ T) A for p Statement from Form i. T for q (and Form ii. and Form iii) Form i. is the specific form of this statement. RR 1:1 2. (A · T)כ [~(A· T) ᵛ (C · T)] A · T for p Statement from Form i. C · T for q RR 1:M 3. A כ (~A ᵛ A) A for p Statement from Form i. A for q RR 1:1 4. ~A כ(A ᵛ ~B) ~A for p NOT statement from Form ~B for q i. If it followed the form, it would look like this: ~A כ (~~A ᵛ ~B) ii. p כq 1. A כ (~A ᵛ T) A for p RR 1:1 and 1:M ~A ᵛ T for q iii. p 1. A כ (~A ᵛ T) A כ (~A ᵛ T) RR 1:M for p Argument form – Two or more statement forms put together to express an argument. Includes at least one premise and a conclusion, and only written with statement variables. Example Argument form: Arguments with only 1 premise cannot p כq Premise 1 Conditional come from this form; it cannot be p Premise 2 Antecedent of Conditional simplified. It also cannot get more complicated, except by substituting q Conclusion Consequent of Conditional compound statements for the statement variables. Argument: If Al is happy then Betty is happy.Premise 1 pכ q Al is happy. Premise 2 p Betty is happy. Conclusion q Logic I Week 4 09/06 Practice Questions from Textbook Done in Class Pg 313 – For each letter in Group A, write any numbers from Group B that correspond to argument forms which could have created that argument. State which number is the specific form, if applicable. a. 3. (specific) b. 6. (specific) c. 4. (specific) m. 3. 24. HOMEWORK # 6 DUE 09/08: PG 313 A f., h., i., Read 8.6, 8.7, 8.8 NOTE: EXAM 1 NEXT THURSDAY, 09/15 I WILL POST A STUDY GUIDE NO LATER THAN SUNDAY, 09/11.


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