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# PHI 120 Ch.3 In Class Notes 2/1-2/22 PHI 120

Marketplace > University of Kentucky > PHI 120 > PHI 120 Ch 3 In Class Notes 2 1 2 22
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Exactly one, translations, Demorgans Law, etc.
COURSE
Introductory Logic
PROF.
Daniel B. Cole
TYPE
Class Notes
PAGES
5
WORDS
CONCEPTS
philosophy, logic, PHI120
KARMA
25 ?

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This 5 page Class Notes was uploaded by Maddi Caudill on Wednesday February 24, 2016. The Class Notes belongs to PHI 120 at University of Kentucky taught by Daniel B. Cole in Spring 2016. Since its upload, it has received 77 views.

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Date Created: 02/24/16
Class Notes 2/1/16-2/22/16 DeMorgans Law -(A ^ B) <--> -A v -B   The "not" negates the "and" symbol ( ^ ) and makes it an "or" ( v ) "Not both"     • When "if" starts a sentence, translation goes from left to right   • "If" always signals the antecedent is coming   • Whatever comes right after the if, goes on the left hand side of the arrow   • When "if" is in the middle,  switch the left and right (order things appear in)   • "only if" means something different than "if"   Ex.) Ardbeg and Bobo Howl if Coco Howls      C --->  (A ^ B)   "but" "furthermore" " ^ "   Ex.) I am driving… but… you all have to pay   "only if"      only if __ --> __ "if"                if __ __ --> "unless"      -->    (can put claims in any order as long you put a "not" before the ﬁrst thing)   Ex.) I am driving to apple bees… unless you all pay for your meals        -D --> P    or     -P --> D        *they mean the same thing!*     IMPORTANT: Atomics are only affected by ONE connective   • If more than 2 atomics, then you need ( , ) 's that group those atomics     "At most one" = "not both"   "exactly one" = "at least one, but not both"   "neither" --> negation of "or" ( v )     Counter-Example: all true premises and a false conclusion • Means the argument is not valid (valid = if the premises are true, the conclusion must be true) • If the premises are all true, then its impossible to have a false conclusion     Translations Practice   Albus is hungry = A   Clare is playful = C   Guppy is sleepy = G   Liam is pretty = L   1. Clare isn't playful unless Guppy is sleepy        --C --> G C --> G -G --> -C   1. Liam is pretty and Clare is playful, if and only if Albus is hungry.   (L ^ C) <--> A     Pg. 66-74   Counterexample: a set of truth values that makes the premises all true and the conclusion false     Pg. 75-78   *WILL BE ON FINAL!!!*   Contradictions: a sentence that is always false (impossible to be true) E.g.    A ^ -A   (A and "not" A cannot be possible) • For "and" ( ^ ) both have to be true   Tautology: a sentence that is always true E.g.    A v -A    (Is or is not) • For "or" ( v ) to be false, both components have to be false   Special Cases to always remember:   --> F when T --> F    v F when F v F   ^ T when T ^ T                                                                                                                          Valid or Invalid   All true premises                           true conclusion                      ??? Actually don’t know   All true premises                           false conclusion                      invalid (counter example)   At least one false premise           true conclusion                               don’t know   At least one false premise           false conclusion                                don’t know     Ex.) all true premises and true conclusion ---> valid or invalid?   Premise:             Albus is a cat                             ____________ Conclusion:        Guppy is a cat       *What you are looking for in a truth table is for a counterexample, because THAT is the thing that determines whether or not the entire argument is valid or invalid *     Good indicators of ( , ) 's & [ , ]'s   =   punctuation           1. If Albus and Claire play,  then Guppy doesn't sleep; unless Liam bites.    - [ (A ^ C) --> -G  ] --> L         1. Liam bites unless Claire plays   -L --> C         1. Only if Albus plays does Guppy sleep; or Claire plays.    ( G --> A ) v C       *switch the order of things with "only if"*           1. If Albus plays, then Guppy sleeps = Albus plays only if Guppy sleeps    *equivalent*   If ______ --->     ---> only if ____                                1. It is not the case that Albus and Claire play, then Guppy doesn’t sleep; unless Liam bites   -{-[(A ^ C) --> -G] --> L}           1. Of Albus and Claire playing, exactly one occurs.   (A v C) ^ -(A ^ C) OR (A ^ -C) v (-A ^ C)                         1. Albus plays and Liam bites if and only if neither Claire plays nor Guppy sleeps.   (A ^ L) <--> -(C v G)         1. Albus and Claire don’t play, but Guppy sleeps.   (-A ^ -C) ^ G        Things to look for: 1. Punctuation 2. Subject/verb relations 3. Connectives, groupings ( if…..then, either/neither…….or)

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