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Lecture 2

PHIL 2020 Lecture 2: PHIL 2020 Unit 4 Lecture 2

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PHIL 2020
Sean Meslar

PHIL 2020 Unit 4: Lecture 2 Major operators Finally lets define a Major Operator as the operator that operates on the highest, or two highest level statements in the proposition. Example: (A B); (A v (B C)); (((((((A v B) v C) v D) v E) v F) v G) v H); ~ (S v T) ~ (~~~~~~~A) Thus, the major operator should be the one for which there is only one open paren to its left and only one to its right (or the operator that is not operated on any others). Operators and truthfunctionality All of our operators are truthfunctional. This means that the truth of a complex proposition is a result of performing a function corresponding to the complex propositions major operator. Some examples should make this clear. The and operator is truth functional, because the truth of the claim Socrates is a man and a mortal is a function of the truth of the claims Socrates is a man and Socrates is mortal. What is an example of an operator that is not truth functional? o Because Consider: You have class today because today is Wednesday. The water froze because I told it to. We can (partially) translate both as saying P because Q. Assuming that all the simple statements above are true, we can see that the truth of the complex statement varies: the first example is true, but the second is false. Thus, because is not a truth functional operator. Why should we try avoid using nontruthfunctional operators in our formal logical system? Because that would require us to look at the content of such propositions, which would negate the advantages afforded by studying formal logic. So, what would be the best way to translate P because Q into our formal system? P Q, because both statements are asserted, albeit with an additional causal claim that we cant accommodate. Basic Translations Today is either a weekday, or it is Saturday or Sunday. o (W v (A v U)) You should not come to class if and only if I dont tell you not to come to class. o (Y ~I) If you like chocolate or vanilla icecream, then you like chocolate icecream, and you like vanilla icecream. o ((C v V) (C V)) Advanced Translations I eat dairy, but I dont eat meat. o (D ~M) You can have dessert only if you eat your vegetables. o (D V)
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