
Teach Yourself Logic: A Study Guide [pdf] - furcyd
https://www.logicmatters.net/resources/pdfs/TeachYourselfLogic2017.pdf
======
BucketSort
Fyi, 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](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](https://youtu.be/9SnefrwBIDc).

~~~
_emacsomancer_
> many ideas are more accessible to me in type theory as opposed to logic

But how do you understand type theory without some basic understanding of
logic?

~~~
BucketSort
It's possible, but I guess I should have specified "logic outside the standard
curriculum of computer science studies." For example, I think understanding
bits of modal logic through how monads behave is much more fruitful for a CS
person. Also, I want to further add here that the correspondence between
proofs and programs is known as the Curry–Howard correspondence. This is the
more general term under which these relationships between type theory and
logic are discussed. The term "computational trinitarianism" also adds a
further correspondence to categories. ( As shown in my link above ).

~~~
BucketSort
Also, "Curry–Howard–Lambek correspondence" is the real name for "computational
trinitarianism." I like the latter better because I don't like naming
mathematical things after people, which have no bearing on the actual meaning.

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pmoriarty
I'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](https://logiclx.humnet.ucla.edu/Logic/Download)

[2] - [https://www.amazon.com/Logic-Techniques-Reasoning-Donald-
Kal...](https://www.amazon.com/Logic-Techniques-Reasoning-Donald-
Kalish/dp/0195155041)

~~~
nixpulvis
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.

~~~
pvarangot
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.

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edoo
Studying logic taught me one of the more important distinctions in life is
identifying when things are always true vs sometimes true. We are taught to
often group things that are mostly true into the always true category. This is
effectively lossy compression that can introduce serious error into your line
of reasoning.

~~~
nurettin
That doesn't make sense to me as in real life most of our reasoning comes from
syllogisms for practical reasons. And if something is consistently
demonstrated to be true, chances are it will continue to be so, so we take our
chances with that. It isn't lossy anything, it is life.

~~~
claudiawerner
As a side note, it's always kind of funny to see hackers/computer types try
and frame discussions in terms of things which are familiar to them, and these
comments are often highly upvoted because of the explanation. In this
instance, "lossy compression". But few people ever seem to question whether
the domain of such categorisations is at all applicable to real human
situations, and even if it's possible to make such categorisations. Is the
method of the natural sciences or mathematics applicable identically to the
social sciences? Often hackers assume this to be the case.

I think there's also an element that hackers want to feel as though using the
concepts they've developed which are very powerful in computer science should
therefore be key to understanding the world as a whole. It's partially being
eager to apply one's knowledge and partly hubris and unwillingness to defer to
philosophy, sociology or critical theory which they view as less rigorous (and
therefore bad).

~~~
elefanten
Is this phenomenon uniquely pronounced among hackers/computer types in your
experience? In a sense, it kind of sounds like your comment could be
summarized as "people often try to apply already-available concepts and
reasoning to new problems areas". But it's uniquely funny when hackers do it.

On the flip side, how many philosophy, sociology and critical theory types
reach for concepts from biology and physics? And how well do you think they
grasp and employ those concept compared to specialists in those fields?

I think any specialist who believes their specialty will necessarily magically
generalize is presuming too much.

FWIW, as a formerly deeply-invested philosophy/critical theory type for over a
decade... I have to say I had to begrudgingly admit that math/hard science are
unequivocally more rigorous than the soft ones. Each is suited to it's
purpose, but it doesn't help to pretend that Zizek is as rigorous as Knuth.

~~~
claudiawerner
I think that philosophy offers much more general mental models and
abstractions than computer science, which isn't to say they're better or
worse, but applicable differently. To that end, I also feel as though many of
the concepts hackers use to describe the world are actually more concrete
instances of the ones philosophers might use. There's also a difference
between analogy (what I have seen philosophers use more often) and trying to
fit the world to the model (what I have seen hackers do more often). I also
think it's one thing for a philosopher to talk about quantum mechanics
(perhaps not understanding mathematical intricacies or even the ideas
themselves) and another thing for a physicist to do the same with a
philosophical concept. I think the physicist will have more success than the
philosopher, just because the philosophical case can be made more abstractly
in most circumstances.

My issue is not the application of the concept, but the apparent lack of
consideration for if the concept is valid for the domain to begin with, and
secondly if so, to what extent it models the world or ought to model the
world. Are the levels of abstraction matched? Is it better to think about this
with dialectical logic? Do the concepts use represent any particular
ideologies? What sort of instrumental reason do they employ? The complete
disregard for these is what makes them "funny" to me. When I saw the mention
of lossy compression, I (maybe unjustifiably) cracked a smile. It's not just a
mismatch in ways of thinking, it's a total mismatch in the content of the
concepts.

So I would say it is more pronounced among hackers, and I feel that there is a
strong current (perhaps also due to the very industry-orientedness of the
field) to eschew what philosophy has to offer. This isn't only in explaining
the world, but also questions of how the world should be (several other
commenters over the years here have noted the general want to ignore issues of
ethics in computer science). Maybe I just think it's funny because I see it
very often and I only see it on Hacker News and Reddit, usually leading with
"This <complex real-world sociological phenomenon> can be thought of as a...",
which is a trend I've seen in some branches of philosophy itself which tries
to excise the "mystical" content of "bygone" theories using new techniques,
which significantly weakens the original idea's applicability in favor of
putting it into a dogmatic (perhaps ideology-laden) analytical framework.

And on the last point on rigor, I agree, though I do want to salvage some
dignity in my view of the world when I say that rigor as formalised through
equations has its uses in some views of the world, and descriptions of
ideology, power, the state, metaphysics etc. have their uses in other parts.
There's also a difference between an argument (which I think must be rigorous)
and a critique (to which I don't consider the concept of rigor to apply to in
many cases, if we want to retain the normative force of them).

~~~
323454
The phenomenon of people pulling in and trying to explain problems from
outside their specialty occurs in every discipline and is a part of normal
scientific work. Usually the overwhelming majority of these attempts fail, but
they are useful nonetheless because in failing they help to define the limits
of the specialty. Ironically, you're complaint that they do this witout
considering "if the concept is valid for the domain" is unanswerable until an
attempt is made and its claims critiqued.

That aside, you raised good questions. I think would be useful if you turned
your list of critical questions into a template for criticising instances of
analogous reasoning anywhere. It would help greatly in evaluating these
attempts.

------
nixpulvis
I'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.

------
khrm
A much shorter guide by the same author in 2 pages instead of 90:
[https://www.logicmatters.net/tyl/shorter-
tyl/](https://www.logicmatters.net/tyl/shorter-tyl/)

------
dang
2017:
[https://news.ycombinator.com/item?id=15114139](https://news.ycombinator.com/item?id=15114139)

2015:
[https://news.ycombinator.com/item?id=10819702](https://news.ycombinator.com/item?id=10819702)

~~~
nixpulvis
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.

~~~
barry-cotter
It is. Ctrl + F “past” and you’ll see it between hide and web up top.

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topynate
I've been following this guide for several months. It's made some excellent
recommendations so far. Prospective type theorists, students of linear logic,
etc. will have to venture beyond the reading list, but having a good grasp of
the modern fundamentals of logic has made a big difference to me in how well I
can follow texts like HoTT.

------
jesuslop
And for leisure, www.logicomix.com (a surprising graphical novel bio-"pic" of
Russell and some episodes of the foundations saga).

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olooney
This 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)](https://en.wikipedia.org/wiki/Naive_Set_Theory_\(book\))

[http://store.doverpublications.com/0486683702.html](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.

[http://incredible.pm/](http://incredible.pm/)

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alphakilo
On pages 43-44, the author mentions a member of my school's faculty G.
Toualakis. The criticisms are valid and his textbook is convoluted. I
appreciate the recognition on unnecessary formalism and complexity.

For a 1000 level logic course that Software Engineers, Computer Engineers and
Computer Science must take, it is extreme.

Overall, interesting to see!

~~~
bsznjyewgd
The author is refering to a different Tourlakis text than the one used in the
1000 level logic course for compsci students.

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james_s_tayler
This is a pretty epic map.

Does anyone know of any others for other domains of knowledge??

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bostonvaulter2
Is there an ePub version of the guide available anywhere?

