Background:  While SL cannot demonstrate the validity or inv…

Background:  While SL cannot demonstrate the validity or invalidity of categorical arguments, we can use our deduction system.  The fix requires changing the unit of analysis: shifting the atomic units of our language from full statements to parts of statements — namely, subjects and predicates.  When we say something like “Max is a dog,” we identify a subject (max) and assign that subject a predicate (is a dog, or belongs to the class “Dogs”).  So, another way of representing “Max is a dog” is with the formal expression: ISDOG{max}.  Notice, that “ISDOG” is capable of taking any number of subjects — all subjects that are, in fact, dogs.  So, if our UD (“universe of discourse”) contains exactly 3 dogs, our predicate ISDOG could be represented by a set like: {max, rover, sparky}.  In that case, ISDOG{max}, ISDOG{rover}, and ISDOG{sparky} would be TRUE, and all other ISDOG{x} would be FALSE. Notice also, that a subject paired with a definite (“bound”) Predicate ALWAYS EXPRESSES A STATEMENT — ALWAYS EXPRESSES SOMETHING THAT IS EITHER TRUE OR FALSE.  In that way, every Predicate{subject} assignment is like an atomic sentence letter in SL.  So, let’s take the argument that gives SL fits: “Socrates is a man, and all men are mortal. Therefore, Socrates is mortal.”  Using our new Predicate Logic, we can represent this argument as:  1. ISMAN{Socrates} 2. ALLx: ISMAN{x} -> ISMORTAL{x} __________ 3. ISMORTAL{Socrates} By changing the unit of analysis from FULL STATEMENTS to PARTS OF STATEMENTS. we are thus able to represent this obviously valid argument using our formal, logical notation.  To prove the argument valid, we need add only 1 simple rule to our Natural Deduction system: Universal Elimination: if ALL A’s are B’s (for all x, Ax -> Bx), then if x is an A (Ax), x must also be a B (Bx).    TASK:  1. Translate the following NL argument into our new Predicate Logic (5 pts) 2. Demonstrate the validity of that argument using our Natural Deduction system (10 pts)   “Everything here is either a cat or dog. Spots is not a dog, so Spots must be a cat.”  

1. Translate the following natural language argument into st…

1. Translate the following natural language argument into standard syllogistic form (i.e., with statements like “All A’s are B’s, etc.” with clear and consistent assignment of letters to classes) 2. State whether the argument is valid (i.e., if it conforms to a “perfect” syllogism) or invalid (i.e., if it does not)   “It never rains on a sunny day in San Diego, and every San Diego July 4th is beautifully sunny. You can’t deny: rain never ruins a San Diego Independence Day!”

  The Van Euler diagram above demonstrates the validity of t…

  The Van Euler diagram above demonstrates the validity of the following argument:    “All interstate crimes are under the jurisdiction of the federal government, and all instances are arbitrage are interstate crimes. It follows, then, that all instances of arbitrage are under the jurisdiction of the federal government.”