CSC165 Lecture Weeks 1 and 2

This is my first post for CSC165, so just a quick housekeeping note. This used to be a physics blog for physics class, but from this point forward all posts will be dedicated to CSC165.

Learning about mathematical expression and reasoning or logic is pretty much the same as learning a new language. Instead of learning new words we are leaning new symbols such as ∀ for universal quantification and ∃ for existential quantification. Instead of learning grammar, we are learning new, more precise ways to interpret the English language. Surprisingly, I am actually really enjoying this course, which is odd since I hated those years where I was forced to learn French.

The first week’s topic was very intuitive for me. Universal quantifiers like ‘all’ and ‘every’ can only be proven by looking at every element in the set, and can be disproven by one counter example. Existential quantifies like ‘some’ and ‘there exists’ can be proven by one example and disproven only by looking at all the elements of a set. I think this duality is really elegant and really makes sense in everyday English.

On the other hand, the topic from the past two weeks that I have found most interesting is the vacuous truth and it seems very counter intuitive. It’s pretty weird to think that a statement such as, ‘If the sun does not rise, then pigs will fly’, is true. In everyday English, this whole sentence is absurd. None of these things will ever happen, so it would seem as if this sentence where completely false. Although, once I think about it, the fact that this statement is true starts to make a lot more sense. If P, then Q implications can only be proven false if there is an example where P is true but Q is false. In the case of the statement above, P is never true, so this statement can never be proven false, and is therefore true. I really like how precisely this the rules for implication are defined. It definitely trips me up sometimes, but I do often find everyday English to be too loose and ambiguous, so maybe that’s why I’m liking this course.