Logic [part ed: Benjamin Martin]
@benjamin.martin Sure, Benjamin, I’d be glad to do chapter 1 or 2–or both. (And thanks for saying nice things about my book.)
Regarding toy syllogistic examples. As you saw in my first chapter, I trot those out immediately, as soon as I start talking about validity. It’s pretty easy, at an early stage, to give students a sense that form is what matters in deductive logic, and even to show how one can identify a formally fallacious argument (by adducing a counterexample). What’s hard–and maybe impossibly hard given constraints on word-count–is showing how to prove that certain forms are valid. For that, you need a method (truth tables, proofs, etc.), and it just takes a lot of words to lay the groundwork necessary to even get to the method. Switching to syllogistic logic is no help there, if the goal is to get to the Venn diagram test. My Chapter 3 covers Aristotelian logic, and it comes in at over 18,000 words. A lot of that could be cut, but not enough to get down to 3,000, I don’t think.
I’m sorry that I’m just making trouble here, pointing out problems without offering solutions. Just kind of thinking out loud, brainstorming. I need to do some more thinking (not out loud) about how to address these challenges.
Thanks, Matt. Let’s keep it to one chapter for the moment. Have a think about which you’d prefer to write, and then put your name down on the Section spreadsheet (link at the top of this page).
You aren’t making trouble at all. I agree that if the role of ch. v were to provide an account of how to prove (in)validity within a particular system, then this would be too much to ask in 3,000 words. However, I conceived of the chapter just providing a brief explanation of how validity within formal logic is associated with the form of arguments. This wouldn’t seem to require providing a decision procedure to do so within a particular logic. If my description of ch. 5 suggests otherwise, I’ll change this on the Section outline.
@benjamin.martin I guess I was thinking that the place for a brief explanation of the role of form in determining validity was in ch. 2’s “outline of the means through which we evaluate arguments.” But I suppose you could introduce validity as the standard in ch. 2, give a brief gloss of what that means (premises guarantee conclusion; if they’re true, conclusion has to be), but then delay a discussion of the role of form until later in ch. 5.
But I’ll leave that, for now, for you and somebody else to sort out. I’ll put myself down for ch. 1.
Thanks to everyone who provided their feedback on the outline for this part! It is now closed for comments. We will start looking for chapter authors very soon, and if you’re interested, just add your name to the spreadsheet at the top of the page.
It’s been a very busy past couple of months, but I’m glad to see things are going well underway! I had some remarks about the part outline I saw back when it first came out. I’m sorry if these are out-dated, but for some highly uncomfortable reason, I do not have permission to view any of the google docs…
So here are my thoughts:
Do you intend to provide any details in the historical development of the subject? Will there be mentions of Aristotle, Boole, Frege, Russell, and Gödel?
Also, I think that it is very important to emphasize the significance that Boolean algebra, as a formal logic system, has had on computer science! It would be very neat to have a little box somewhere on logic gates and how these operations underlie the functioning of all modern computers!
Finally, it would be worth considering to include a discussion of the significance of formal logic in the foundations of mathematics leading up to incompleteness.
As soon as I get access to the actual outline I will revise the above points. Sorry for the inconvenience.
Hi Sebastian–pinging @zoe and @apurva here because though the chapter outline is now closed for comment I don’t know if the intention was to close from viewing at all. I do see now that only a few people are invited to view that doc, and I am not sure if that is what was supposed to happen.
EDIT later: I discovered that the chapter outline is also on the spreadsheet that is a sign-up form for volunteering to write chapters: https://docs.google.com/spreadsheets/d/1n44S8YwSiV5m17c8CmY7J-WSN_zur0LAFVpYKFnZx4I/edit#gid=2047143349
So you can see the outline and the chapter descriptions there! Perhaps, then, the original document that was open for comment doesn’t need to be available for all to read because the outline is also on the spreadsheet. But in that case, maybe we take that document that is not open for reading off the forum! Or open it for all to view, at least.
Thanks, @clhendricksbc. We’d like to keep the outlines public, for anyone with the link to view, and I’ve looked at the permissions on the document to make sure that this is the case.
@sebastian-higherlearning, you should be able to view the outline. If you still have trouble accessing the file, please let me know. Thanks for leaving your comments here in the forum. Since we won’t actively be checking the document for new comments, it would be best to leave your feedback in this thread.
@sebastian.higherlearning Hi Sebastian. Thanks for posting.
Firstly, I hope the access problems you were having have now been sorted.
Secondly, thanks for your suggestions. The Open Textbook is intended for a first-year introductory audience, and so I’m concerned that both discussions of the relationship of formal logic to computer science and the foundations of mathematics would be lost on the audience. The last section of the Logic Part is aimed at explaining the role that form plays within modern logic. I think this would certainly provide an opportunity to explain the special status of the logical constants, and their applicability to machines. However, each section only has ~2500 words to play with.
Do let us know what you think after having a read of the outline.
@rzach Thanks for putting together those resources. Nice to see them all in one place and so clearly distinguished.