First of all, I would like to sincerely thank the people who prepared and placed this course on coursera. Not too many logic courses out there.
As for the course itself, it is basically a read only course. There are numerous graded assignments that exploit web-based tools and it all works fine. The lack of video lectures may be a little intimidating, but the reading material's quality makes up for this. What bothered me slightly though, is not enough formality in definitions and stated claims. I had tendency to get lost in the meaning of numerous abstract objects such as constants, literals, constant functions, terms, relations, sentences, free and non-free variables, contingency, validity, satisfiability, soundness, completeness, compactness....
What I learned from the course:
- Lookin at logic systems as systems of manipulating strings of literals according to pre-defined semantics. We started with proposition logic, went on to relational logic and Herbrand logic.
- Formal proof system such as the Fitch system and resolution.
Some things I have hoped to learn but did not:
- How did logic evolve throughout history and how did we arrive at the picture that is seen today?
- What are the main branches of modern logic and what are - in general - logic researchers preoccupied with?
- Since logic, as it was presented, boils down to performing semantical operations on a predefined scheme of literals, isn't there a general way to formalize this? It seems there should be a general notion of language consisting of an alphabet, syntax, semantics and a set of inference rules.
- Does mathematics boil down to manipulating strings of literals according to some rules? If so, can we have many valid mathematics based on different axioms and different semantical rules? For instance, what would be the consequence of dropping the axiom of choice?
- What are the implications of Gödel incompleteness theorems for math and for science in general? Do the imply that the Riemann hypothesis could be undecidable?
To summarize, this course was an entertaining adventure, but I completed it with seemingly more questions regarding logic the prior to starting the course. But maybe that is not so bad?