Logic - 2017-10-17

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shredalert

11:07

@user21820 up to you, really. You could pin another post that just lists the errors with their corrections. Saves you having to repin the whole post.

@user21820 apologies for the late reply, I wasn't at home.

4 hours later…

user21820

15:35

@shredalert No problem at all. I suppose the better solution next time is to post it somewhere else that I can edit, rather than in a chat message. Haha. Anyway I think I won't fix minor errors that the reader can infer until I've collected a bunch of them. =)

shredalert

15:46

@user21820 I think another solution would be to start up a blog on something like wordpress.

It would make for easier reference as well

after the presentation is done

user21820

@shredalert Definitely that's one way. I'll consider it. I've never used a blog before though.

shredalert

The problem with chat here is that everything is very condensed, and it's easy to lose stuff, even with the search facility provided. I know it loves to bug out every now and then

@user21820 wordpress is very easy to set up, and it's free.

you use latex on wordpress by typing $latex<space><input>$

and you can format it however you like because wordpress lets you write your posts with html

user21820

@shredalert I know; it's just that I've never used any social media websites. I prefer not having a 'public face' kind of thing.

shredalert

@user21820 you don't need to use any real names to make a wordpress account. You can remain anonymous.

Just letting you know, ofc, it's up to you whether you want to take up that option or not

user21820

@shredalert Of course, which is why I'll consider it for the above kind of purpose. It's just that last time I never had any reason for an anonymous blog. =)

shredalert

15:54

Btw, have you ever used Foundations of Mathematical Logic by Curry? @user21820

user21820

@shredalert I've not. Trying to find it online now.

shredalert

I was just wondering, because it looks like it has a lot of content not explicitly stated in many other textbooks devoted to mathematical logic. It's copiously referenced as well.

there are very clear sections on induction (and Curry talks about structural vs mathematical)

and a host of other things like lattices and combinators

user21820

I just had a glance at this review, and it seems that it would be very interesting for more in-depth study of logic, but may be too much for an introduction to logic.

Lol just after I said the above I reached the sentence in the review that says:

shredalert

Oh yes, I'm reading it more as an in-dept study

user21820

> Although the book was written to be a graduate level textbook, it
should be used with some caution, since it is difficult to read. This is
partly because Curry was not a good expository writer. (Curry knew
this about himself: he once criticized an early version of Seldin
(1975), which is an expository paper, for sounding too much like
him!)

shredalert

16:00

lol

I think Suppes, Lemmon, and Henle & co. take the top spots for introductions

just because they all use fitch-style natural deduction

I don't think a beginner will understand sequent calculus, and Hilbert style requires understanding the motivations to appreciate

user21820

@shredalert Yeap. Of course, Hilbert-style is extremely convenient for meta-theorems, so for a second-level logic course (Fitch-style ND should be for first-level) it's okay to introduce a Hilbert-style calculus (whose axioms would now be easy to explain in terms of the Fitch-style contexts) and then use it to prove meta-theorems.

shredalert

@user21820 That's exactly how I'm interpreting the Hilbert axioms.

user21820

The alternative is to vastly generalize (to all computable formal systems) so that one doesn't have to worry anymore about having many deductive rules, since the whole lot is simply one arbitrary proof verifier program.

shredalert

I've got time between my assignments now to get into a more mature exploration of logic. So I've been picking up some books to carry me there.

user21820

That's great to hear!

If you come across anything interesting, I'd be glad for you to share it! =)

shredalert

16:09

So far I've got Kleene's Introduction to Metamathematics. I'm thinking of picking up a physical copy of Curry's book (it's got an affordable dover edition).

@user21820 Will definitely share if I come across good finds.

I'm debating whether or not to at least skim through an electronic version of Church's Introduction to Mathematical Logic

user21820

@Raute: Hello and welcome! If you're interested in (mathematical) logic, feel free to ask/discuss related stuff here. Also, as pinned I'll be holding a discussion session on a generalized incompleteness theorem and a simple proof. You're welcome to attend if you can make it. =)

@shredalert If you find an online version, let me know where and I'll take a look too.

Sounds interesting, not least because of his currious word choice.

> For example, his use of the prefix "epi-" instead of "meta-" [for meta-theory] is a result of the fact that Kleene, in a review of one of his papers from the early 1940s, objected to his use of the prefix "meta".

shredalert

@user21820 e-version of which book?

user21820

Oh wait. I meant Curry's.

I think we mentioned before that Church's was available online right?

shredalert

Yes, we did.

Curry's can be found on libgen

It is written in a very messy way though, so having a physical copy would greatly improve readability

user21820

I see.

shredalert

16:15

The fact that it's a scan of the Dover edition makes matters worse, because they print everything in a very condensed fashion to save on space.

user21820

Lol!

shredalert

Yeah, it's why Kleene's Mathematical Logic (the book he wrote for undergraduates) is pretty much unreadable

His other more advanced book is a lot cleaner and better-written though.

I think he wrote the undergrad book just because his grad book didn't have any model theory in it. Although I think that's an advantage from a certain point of view.

user21820

Which one? I actually downloaded the "Introduction to Metamathematics" (scanned), but didn't really refer to it much.

shredalert

Mathematical Logic is the one for undergrads

Introduction to Metamathematics is for grad students

But he says in the preface to IMM that it can be read regardless of knowledge of any specific mathematical content.

user21820

Ah.

shredalert

16:20

and I'd say it's pretty true.

But Kleene's books are about meta-mathematics

Curry's is about the foundations of meta-mathematics

For example, in Kleene's IMM he doesn't really talk about structural induction at all, while Curry explicitly discusses it and how it fits into the whole "induction" idea.

In the following months I'll keep you updated, @user21820, as to how my reading of Kleene's and Curry's books are going.

user21820

@shredalert Hmm. I suppose Curry would say something about it being circular?

Anyway yup thanks in advance for telling me about how it goes! I'll be off soon. See you!

shredalert

see you later! @user21820

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