Formal Logic

[Deception]

What are some good books and essays on Formal Logic? I've read a couple of Gharam Priests' works (one was an introduction to logic), but I am not sure where to go from here. I don't have any professors that would be able to guide me in this study, so I ask for help here. The price of these books really add up so I don't want to go out and purchase reading material which is poor in quality or for some reason an inadvisable read.

[jesternl]

Godel, Escher, Bach; an Eternal Golden Braid, by Douglas Hofstadter.
Not exactly light reading, but tremendously entertaining.

[Zag]

Ummm, yeah. Maybe not the right choice if you're just learning the subject. Once you're comfortable with the basics, and the intermediate, and a little of the advanced stuff, then head for the Hofstadter. Meanwhile, I did a quick Google of formal logic and saw a couple online tutorials. I don't know what level you're looking for, though.

[Deception]

[Zag]

Well, they must, but perhaps only as textbooks in Formal Logic classes.

[jesternl]

I found Hofstadter is doable, but don't try to take it all in at once. He does try and ease you into most subjects

[Deception]

Alright, I'll check out the Hofstadter book. Thanks to both of you!

[extro...*]

You should first clarify what you want, i.e. what you mean by "formal logic". Formal is a relative term, and Hofstadter's work, to me, is at the low end of it. Some say Hofstadter isn't light reading, on the other hand it's the lightest treatment of the subject it covers, I think (well, it covers a lot, but speaking of the logic portions).

[Zag]

The problem with Hofstadter is that he spends a lot of time on breaking formal logic -- showing that it can not be both complete and consistent. (He also covers some interesting aspects of infinity, which is totally worth reading but isn't really logic.) If you're looking to cover basic logic, i.e. syllogisms, DeMorgan's Theorum, formal proofs, etc. then his stuff dumps you in the deep end but doesn't teach any basic strokes. It's not that a bright person can't understand his stuff without the formal basics -- you can -- but you won't be any closer to understanding a more applied version of formal logic than you were before you started reading it.

For instance, one part that I remember from reading it, some decade and a half ago, is how he shows that the formality of logic can't be used to declare the rules of logic -- you need basic assumptions. He starts with the classic syllogism:

A. All men are mortal. (More formally, if X is a man, then X is mortal.)
B. Socrates is a man.
ergo Socrates is mortal.

His antagonist, however, then says, "I'll accept A and B, but I don't accept the conclusion."
To which the protagonist replies, "Surely you can see that if A is true and B is true, then the conclusion must also be true."
Antagonist: I'll accept that statement. Let's write it down. I'll give the conclusion a letter to make it easy to refer to

A. All men are mortal. (More formally, if X is a man, then X is mortal.)
B. Socrates is a man.
C. If A is true and B is true, then Z is true
Z?. Socrates is mortal.

Protagonist: Now you have to see that Z must be true
Antagonist: No, I accept A and B and C all as true, but I don't accept Z.
Protagonist: Surely you see that if A, B, and C are all true, Z must be true.
Antagonist: OK, I accept that. I'll even write it down

A. All men are mortal. (More formally, if X is a man, then X is mortal.)
B. Socrates is a man.
C. If A is true and B is true, then Z is true
D. If A and B and C are all true, then Z is true
Z?. Socrates is mortal.

But I still don't accept Z.

He continues in this vein, including allowing an infinite number of terms following that pattern (declaring the infinite number of terms with a single line), but points out that once you declare them within the syntax of the logic system, the conclusion can just be pushed out further. Then an infinite number of the infinite steps (aleph 0, aleph 1, etc.) but those can be declared, as well, so they won't get you any closer.

My point is that while it is interesting reading, it isn't really intended to teach logic, but instead to teach the flaws and limitations of logic and other mathematical systems. Interesting and valuable to learn, but perhaps not what you were hoping to learn.

----------------

Somebody who has read the book more recently than the late 1980's, critique my memory for me.

[Deception]

Extro, I suppose I wasn't too specific, I was looking to read some logical philosophy. That is to say discussion about the principles, flaws, and/or an attempt to discover.

Zag, I think you quoted the story: "What the Tortoise said to Achilles". It's a famous one and I've certainly heard of it. If I'm not mistaken, it is a perfect example of why contemporary logic assumes that if the premise is true, so is the conclusion (this has its own flaws, however).

While it may be true that Hofstadter did write that, I do believe he wasn't the creator. A quick wikipedia search tells me that Lewis Carroll did, and several other sources seem to agree.

I will be very intrigued to read Hofstadter if he wants to "break formal logic", as that is always interesting to read in my opinion. Either way, it seems to be a classic work, so I wouldn't want to avoid it much.

[Deception]

I really enjoyed the Hofstadter book and recommend to all my willing friends. Thanks again for the suggestion.

Now that I have a little more time to read and a little more money to spend - any other suggestions?

For reference, that book was right down my alley. As in, it was 100% what I was looking for and I fell in love with it a few pages in. Only problem is that it seems to be very unique and I struggle to find books similar to it. Or at least, books with the same acclaim. I see tons of logical philosophy books and am reminded of the philosopher I once spoke to who told me that there are a lot of useless logic books out there. I'm worried about diving into useless material.

Thanks again.

[Chuck]

I like Raymond Smullyan's stuff, but only the easy and entertaining parts.

[Deception]

I just did a googlebooks preview for Smullyan's Alice puzzles, but it looks like the preview stops right in the middle of the hardest puzzle so far. The previous ones didn't take more than a minute or two each.

I'm going to go to my local bookstore tomorrow and look at that one and the sherlock holmes chess puzzle book.

Are these types of books what he's all about? Hopefully it gets harder than the googlebooks preview but he seems interesting, even if it's not exactly philosophy.

[Scurra]

No, neither the Alice book nor the Chess books really get into the philosophy of these sort of puzzles; the Alice book is aimed at early teens I think, and the chess puzzles are, well, chess puzzles. I would expect someone with experience to race through most of the Alice puzzles (although there are still some neat twists on old ideas.)

I seem to remember it's books like Forever Undecided and Satan and Infinity that get more into the nitty-gritty of formal logical philosophy and Godel etc.
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New definitions: COFFEE - someone who is coughed upon}

[Chuck]

Smullyan's 5000 B.C. and Other Philosophical Fantasies is more philosophical.

[Lepton]

https://www.coursera.org/#course/intrologic
Free online university course in logic. Coursera is pretty great.

[LordKinbote]

While we're at it, there is a free logic and discrete mathematics class starting up soon at [url="http://www.udacity.com]Udacity[/url]. It was supposed to start today, but has been delayed for some reason.

Udacity classes are the best actual online learning classes I've seen thus far. They're not just "Here are a bunch of video lectures and unchecked assignments."

[Nsof]

The Mind's I by Douglas R. Hofstadter and Daniel C. Dennett.
I red it a long while ago. Very much in line with GEB and same excellent writing style.
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Will sell this place for beer

[extropalopakettle]

Smullyan has some definite hard-core logic texts. 3 on my bookshelf:

Theory of Formal Systems (1961)
Gödel's Incompleteness Theroems (1992)
Recursion Theory for Metamathematics (1993)