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Symbolic Logic

by: Alexis Kreusch

Symbolic Logic PHL

Marketplace > Wright State University > PHL > Symbolic Logic
Alexis Kreusch

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About this Document

Intro into using symbols to start the process to check validity on deductive arguments
Critical Thinking
Jacob N. Bauer
Class Notes
Crtical, thinking, philosophy, Symbolic, logic, Jacob, Bauer
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This 3 page Class Notes was uploaded by Alexis Kreusch on Thursday October 13, 2016. The Class Notes belongs to PHL at Wright State University taught by Jacob N. Bauer in Fall 2016. Since its upload, it has received 4 views.


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Date Created: 10/13/16
10­13­16 Symbolic Logic  Another system to check validity for deductive arguments o This is used for the claim statements that are too hard to translate and diagram  Symbols: o ~ means not o & means and o v means or o → means If…then  Each variable used (P/Q/R/etc.) represent a claim as a whole o Ex.  P could mean something as simple as “This is an apple”  Q could mean “He is at school”  How to diagram o The most simple is when there is only one term such as P      P  T F  However, for every term added the amount of Trues (T) and False (F) is doubled  o Or you can use the formula r=2^n   r is the rows of Ts and Fs needed  n is the number of terms used in the statement  the highest usually given in an introduction course is three terms or eight  rows  The reason this happens is to show every possible combination of Trues  and False for the terms  Two terms would look like this     P   Q             T   T T   F F   T F   F  It is easier to know where to put the Ts and Fs if you alternate like so with doubling the  amount to alternate in the first row (in this case 2) then the second row (switching back  and forth) o This can be shown when we use three terms   P   Q   R T   T   T T   T   F T   F   T T   F   F  F   T   T F   T   F F   F   T F   F   F  Notice the new first row has four true then four false doubling the amount together in the  second row How to use each of the symbols mentioned at the beginning  ~ flips the clams (Flip Ts and Fs) o Represented by ~P (put ~ in front of the flipped term) o Meaning not P o Original                               Flipped  P ~P T F F T  Conjunction & means and o Only true if both terms are true (T) o Start by diagramming P and Q as we would without the and to tell when it is True  or False   Ex. P & Q  P   Q   P & Q T   T      T                 Only one with 2 Ts so true T   F      F F   T      F F   F      F  Disjunction v means or  o Two ways that or is defined  Inclusive or means “and/or”   You can call me Alexis or Lexi (Either one or both)  The one that is used for these diagrams  Exclusive or means “one or the other, but not both”  The paper can be red or blue, not both  Only False if both terms are False  P v Q  P   Q      P v Q T    T       T T    F       T F    T       T F    F        F                 Only one False because both P and Q were  Conditional → means If…then st nd o Only False if the 1  part (term) is True and the 2  part (term) is False  P→Q  P   Q     P→Q T   T       T T   F       F          Only one false because P is True and Q is False F   T       T F   F       T     Parentheses are used just like in math to show the order of operation o Start in the parenthesis and then work out  Tables must show every combination  Tables contain columns for all parts of complex expressions o Here is an example of a complex expression and how to graph it out o ~P & (B→P) o P   B   ~P    (B→P)   ~P & (B→P) T   T    F          T               F T   F    F          T               F F   T    T          F               F F   F    T          T               T    You would start like any other with the regular terms   Then you would do the ~ term  Followed by anything in parenthesis using the Ts and Fs found for the terms individually  Then the rest of the terms as a whole using everything found before 


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