
Teach Yourself Logic 2017: A Study Guide [pdf] - adamnemecek
http://www.logicmatters.net/resources/pdfs/TeachYourselfLogic2017.pdf
======
imh
I've been reading through this
([https://www.cs.cmu.edu/~fp/courses/15317-f00/handouts/logic....](https://www.cs.cmu.edu/~fp/courses/15317-f00/handouts/logic.pdf)),
and have found it way more useful and fun. I expect it's much closer to what
the HN crowd would be interested in.

~~~
dvt
At the risk of getting downvoted, I'm just going to say that I really hate
this book. First of all, it moves way, way, _way_ too fast. I glossed over it,
and chapter 3 is already the Curry-Howard isomorphism? That took us a semester
of λ-calculus to come to grips with. These are _big_ results.

Second of all, it just seems like a mish-mash of like three or four different
classes put into one: computability, type theory, first order logic -- all
these can be their own concentrations.

Third, it uses type-theoretic terminology ("elimination" and [->e] instead of,
e.g., modus ponens [MP]).

Finally, imo that notation really sucks (the top-to-bottom branching is really
jarring), I've only seen it used in Type Theory and λ-calculus books.

Some books I suggest: this one from the University of Toronto[1] or this one
from one of my favorite classes I took at UCLA[2]. If curious, you can see
some problem sets on my website[3].

[1]
[http://euclid.trentu.ca/math/sb/pcml/pcml-16.pdf](http://euclid.trentu.ca/math/sb/pcml/pcml-16.pdf)

[2]
[http://www.math.ucla.edu/~dam/135.07w/135notes.pdf](http://www.math.ucla.edu/~dam/135.07w/135notes.pdf)

[3] [https://dvt.name/logic](https://dvt.name/logic)

~~~
tom_mellior
I have no dog in this race, but...

> the top-to-bottom branching is really jarring

What do you mean? From what I've seen from skimming the first few chapters, it
uses 100% standard natural deduction proof trees. How would you present the
proofs?

(The "linear format" is indeed ugly, but it doesn't seem to be meant for human
consumption.)

> I've only seen it used in Type Theory and λ-calculus books

That's the point of the Curry-Howard isomorphism: It's all the same thing. It
makes sense to use the same notation.

~~~
dvt
> I've seen from skimming the first few chapters, it uses 100% standard
> natural deduction proof trees. How would you present the proofs?

You're totally right. I just really don't like proof trees, nor do I think
they're clear when first starting out studying logic.

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fizixer
Just a heads up, this pdf is not a logic tutorial or textbook, but an
annotated bibliography.

That said, if you got stuck on material implication (practically a topic
discussed on the first or second day of logic study), as I did, and eventually
were able to understand it, I'd love to know how. (Notice, only if you got
stuck first, not if you never had problem understanding it).

~~~
ihm
You can think of "A => B" as stating "there is a way of transforming proofs of
A into proofs of B". If "A" is false, then there are no proofs of "A", and
thus there is trivially a way of transforming proofs of "A" of "B" (since you
will never be confronted with a proof of "A"). So a false statement implies
anything.

If "B" is true, then there is some proof p of "B". Now here is a way of
transforming a proof of "A" into a proof of "B": given a proof q of "A", just
return that one proof p. So anything implies a true statement.

~~~
dvt
This _is_ actually the best way to understand it. But without some background
(Proof Theory 101, The Deductive Theorem, Metalogic 101), I'm sure this sounds
like gibberish :)

NB: Although you muddy the waters a bit. "A => B" is _literally_ "A proves B".
And to see why an inconsistent set implies anything at all, we just need to
look at the Principle of Explosion[1] -- which is probably less contentious
than material implication.

[1]
[https://en.wikipedia.org/wiki/Principle_of_explosion](https://en.wikipedia.org/wiki/Principle_of_explosion)

~~~
dvt
Small clarification (I wrote my parent post super late last night). Via the
Deduction Theorem, we have:

    
    
       ⊢ A -> B => A ⊢ B
    

That's what I mean by "A proves B"

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schuke
I loved Paul Tomassi's _Logic_. If like me you find all the symbols
intimidating and fear that you're not mathematically-minded, try it. It's like
the iPhone for learning logic. Everything is clearly explained and explained
to an extremely accessible degree. It's such a shame that the author died very
early, I'll never see it updated or revised.

[https://www.amazon.co.uk/Logic-Paul-
Tomassi/dp/0415166969/re...](https://www.amazon.co.uk/Logic-Paul-
Tomassi/dp/0415166969/ref=sr_1_1?ie=UTF8&qid=1503904811&sr=8-1&keywords=tomassi+logic)

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Red_Tarsius
If you're looking for an introduction to classical logic, I highly recommend
Peter Kreeft's _Socratic Logic_. I'm reading it right now.

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solomatov
They don't mention dependent types at all which is unfortunate. IMO, it's the
most promising subfield of logic now.

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greppy
Unrelated; but does anyone have resources like these for other related
subjects?

