Teach Yourself Logic: A Study Guide [pdf]
logicmatters.net
Teach Yourself Logic: A Study Guide [pdf]
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Re: Teach Yourself Logic: A Study Guide [pdf]
#2I'd like to recommend Logic 2010[1], a application with which you can do logic exercises to learn the natural deduction system from *"Logic: Techniques of Formal Reasoning" by Kalish, Montague, and Mar.[2]
The program is officially only for MacOS and Windows, but with a little work it's possible to get it running on Linux, as it's just Java.
The exercises are fun, and the program will not only check your work to make sure it's right, but also point out where and sometimes why it's wrong.
[1] - https://logiclx.humnet.ucla.edu/Logic/Download
[2] - https://www.amazon.com/Logic-Techniques-Reasoning-Donald-Kal...
Re: Teach Yourself Logic: A Study Guide [pdf]
#3I've been working my way through Kleene's "Mathmatical Logic". It's a great read so far, touching on the details and proofs in some detail. I'm looking forward to the chapters on completeness and the like. I was mostly inspired to get his book because of the Kleene star, who knows why.
Also, though very different, I just got GEB for Christmas, so I guess I'll be reading that finally now too.
Re: Teach Yourself Logic: A Study Guide [pdf]
#4Re: Teach Yourself Logic: A Study Guide [pdf]
#5I'd like to recommend Logic 2010[1], a application with which you can do logic exercises to learn the natural deduction system from *"Logic: Techniques of Formal Reasoning" by Kalish, Montague, and Mar.[2] The program is officially only for MacOS and Windows, but with a little work it's possible to get it running on Linux, as it's just Java. The exercises are fun, and the program will not only check your work to make…
I'm assuming that program is more approachable than something like Coq or others? I used ACL2 a bit in college, and could imagine people being frustrated trying to learn it on their own.
Re: Teach Yourself Logic: A Study Guide [pdf]
#62017: https://news.ycombinator.com/item?id=15114139 2015: https://news.ycombinator.com/item?id=10819702
Off topic: I'm honestly kinda surprised this kind of comment isn't built into HN by this point. There's often so many good comments from old articles we rely on adventurous users to dig up.
Re: Teach Yourself Logic: A Study Guide [pdf]
#7Fyi, there are many correspondences between logic and type theory / functional programming. I have found that as a programmer, many ideas are more accessible to me in type theory as opposed to logic. Languages like Haskell are great for exploring these relationships.
This is also known as computational trinitarianism - https://ncatlab.org/nlab/show/computational+trinitarianism
Robert Harper, the computer scientist that coined "computational trinitarianism," has a series of lectures on the foundations of type theory including some commentary on these correspondences - https://youtu.be/9SnefrwBIDc.
Re: Teach Yourself Logic: A Study Guide [pdf]
#8I'd like to recommend Logic 2010[1], a application with which you can do logic exercises to learn the natural deduction system from *"Logic: Techniques of Formal Reasoning" by Kalish, Montague, and Mar.[2] The program is officially only for MacOS and Windows, but with a little work it's possible to get it running on Linux, as it's just Java. The exercises are fun, and the program will not only check your work to make…
I'm assuming that program is more approachable than something like Coq or others? I used ACL2 a bit in college, and could imagine people being frustrated trying to learn it on their own.
It's infinitely more approachable than Coq/PVS or whatever other theorem prover since it was designed for teaching and not a research tool or potential application to actually verifying properties of complex systems.
Re: Teach Yourself Logic: A Study Guide [pdf]
#9I'd like to recommend Logic 2010[1], a application with which you can do logic exercises to learn the natural deduction system from *"Logic: Techniques of Formal Reasoning" by Kalish, Montague, and Mar.[2] The program is officially only for MacOS and Windows, but with a little work it's possible to get it running on Linux, as it's just Java. The exercises are fun, and the program will not only check your work to make…
Oh man, brings back memories. I used an earlier version of this program as a philosophy undergrad at UCLA in the early 2000s. I LOVED doing the homework in my logic classes!
Re: Teach Yourself Logic: A Study Guide [pdf]
#10This guide covers many different topics and specialties related to logic so it may help to introduce a taxonomy so we don't get intimidated by the breadth of Dr. Smith's scholarship. Let's break it down into 5 topics:
1. Using a well-known and widely accepted system of logic to produce proofs and solve problems. A working man's logic is propositional logic (AND, OR, NOT, and the material conditional) plus first-order predicate logic (quantifiers "there exits" and "for all" over bound variables), natural deduction, and ZFC set theory.
2. "non-standard" logic systems which are somehow "better" or "more expressive:" 2nd order logics, modal logics, many-valued logics, etc.
3. Meta-mathematical investigations into the properties of different formal logic systems: model theory, proof theory, forcing, consistency, completeness, etc.
4. The philosophy of logic: Semantics, sense/reference, truth, nominalism/realism, theory of descriptions, etc.
5. Logic and computability: lambda calculus, recursive functions, turing machines, complexity classes, etc. This is somewhat tangential to logic proper but there are connections and Dr. Smith has a section on it so it's worth enumerating.
While everyone will need to know (1) as a working man's logic, the other topics are more or less independent and can be approached independently.
For people just starting out and finding this study guide pretty overwhelming, let me re-emphasize two of Dr. Smith's suggestions for starting points: Smullyan's First Order Logic and Halmos's Naive Set Theory. These two books will get you to the same depth of understanding that 95% of working mathematicians need or apply in their day-to-day work, and it's a fact that 95% of modern mathematical theories are built on (formalized within) ZFC set theory and first order logic.
https://en.wikipedia.org/wiki/Naive_Set_Theory_(book)
http://store.doverpublications.com/0486683702.html
I also suggest the online game The Incredible Proof Machine. It's extremely helpful to have a computer formally check your proofs when you're just starting out in logic because it's incredibly easy to "cheat" and skip steps or use rules that "make sense" but aren't part of the formal system your using. TIPM lets you do that without learning any specialized syntax.