Logic

[ChrisK]

I've recently completed an introductory logic course. It only left me with a little taste and I want to learn more but don't have any more logic courses I can take till the fall.

My question is, does anyone know of any good books that I can learn logic from on my own? I bought Quine's Methods of Logic and was wondering if it is a good one to use.

[Rosa Lichtenstein]

Quine's book is excellent, but if you really want to get stuck in get hold of Metalogic by Geoffrey Hunter and then Intermediate Logic by David Bostock (but you might need to know some mathematics for these two).

You should also get to know some Natural Deduction (http://en.wikipedia.org/wiki/Natural_deduction), so you need to work through Beginning Logic by E J Lemmon.

This should be in learning or in Research.

[ChrisK]

Quine's book is excellent, but if you really want to get stuck in get hold of Metalogic by Geoffrey Hunter and then Intermediate Logic by David Bostock (but you might need to know some mathematics for these two).

You should also get to know some Natural Deduction (http://en.wikipedia.org/wiki/Natural_deduction), so you need to work through Beginning Logic by E J Lemmon.

This should be in learning or in Research.

Thank you for the help!

How advanced of mathematics would I need to know?

Can a mod move this to learning?

[Rosa Lichtenstein]

Well, much of the first chapter of Metalogic is based on post-Cantorian set theory, but he does a good job of explaining what you need to know.

Put it this way, I studied this book before I did my mathematics degree (my knowledge of mathematics at that point was pretty basic) and I followed most of it. In fact, the ease with which I followed Hunter's explanation helped convince me that I might be able to do a degree in the subject!

You can study Quine's book with very little knowledge of mathematics, but if you really want to get to grips with modern logic, you really do need to know set theory (and some number theory, at least).

[ChrisK]

Well, much of the first chapter of Metalogic is based on post-Cantorian set theory, but he does a good job of explaining what you need to know.

Put it this way, I studied this book before I did my mathematics degree (my knowledge of mathematics at that point was pretty basic) and I followed most of it. In fact, the ease with which I followed Hunter's explanation helped convince me that I might be able to do a degree in the subject!

You can study Quine's book with very little knowledge of mathematics, but if you really want to get to grips with modern logic, you really do need to know set theory (and some number theory, at least).

Alright, well I was planning on a math minor, so I guess these will go well together.

[Rosa Lichtenstein]

Sure will!!:)

You might even get some mathematical logic thrown on that course.

[Rosa Lichtenstein]

You'll also find useful summary of set theory (and the logic of relations) in Lemmon's book

[syndicat]

if you want to check out inductive logic, I'd recommend Kathleen Mooore's "Inductive Arguments."

[Dooga Aetrus Blackrazor]

I don't know if my textbooks are the best, but I'd be curious what text/content you studied. It would give me a better idea of what to recommend. My experience is mostly involving overview courses, but I have encountered both Quine and Lemmon.

I should point out that Quine has strong oppositions to Modal Logic, and I believe many "followers" of Quine and Wittgenstein share this sentiment. So if you want both sides of the coin with respect to Modal Logic, you'd have to read someone in addition to Quine. I'm not sure if Quine is right or not. My professor disagreed with him so I obviously have a biased view. That and modal logic has lots of fun symbols and shapes so I don't want to go back to classical logic.

Godel's work on soundness and completeness is interesting. Kripke is absolutely everywhere these days. Necessity of Identity is quite an interesting conclusion.

There is that principle I forget the name of. It claims you can derive anything from a contradiction. Epistemic logic has people that believe you can know something without knowing you know it simply by virtue of having the "theoretical means to arrive at the truth."

I am rambling as my information is all over the place due to just doing a Modal Logic final this morning. Logic is interesting, but I have a hard time with it sometimes because of the poor quality of the writing/examples. That's true of a lot of philosophy and academia though. If only people would learn to write and draw pictures for me, I'd be set.

[Rosa Lichtenstein]

Dooga:


There is that principle I forget the name of. It claims you can derive anything from a contradiction.

It's called ex falso quodlibet (from a falsehood anything follows), or the principle of explosion (http://en.wikipedia.org/wiki/Principle_of_explosion).

I agree with you about this, though:


the poor quality of the writing/examples. That's true of a lot of philosophy and academia though.

It's largely the same in mathematics, and I think this is because such books are written by those who find this stuff laughably easy, hence they can't exaplin it to anyone since they have no idea of the difficulties ordinary students face.

[Dean]

Moved to learning forum. - 04-23-10 Dean

[ChrisK]

if you want to check out inductive logic, I'd recommend Kathleen Mooore's "Inductive Arguments."

Thanks, I'll get that one as well!

[syndicat]

It's largely the same in mathematics, and I think this is because such books are written by those who find this stuff laughably easy, hence they can't exaplin it to anyone since they have no idea of the difficulties ordinary students face.

yep. when I started teaching logic to students at state colleges i had overwhelmingly working class students, and just couldn't use any of the usual logic texts. fortunately there is a natural deduction symbolic logic series in the USA that was written exactly for this purpose, by Howard Pospesel. Uses examples drawn from newspapers, comic strips, etc. Everything is completely simplified. Made a big difference.

[RebelDog]

If you cannot compare something with another thing how does one define that thing?

[Rosa Lichtenstein]

RebelDog:


If you cannot compare something with another thing how does one define that thing?

Who here has alleged this?


you cannot compare something with another thing

[RebelDog]

RebelDog:



Who here has alleged this?

Sorry. I looked up the guy Syndicat mentioned and this is a page I found:
http://ifenglishthenlogic.blogspot.com/2010/02/predicate-logic-howard-pospesel.html

I must have thought someone posted it in a momentary lapse of reason. My origianal post was my thought after reading it. I thought the guy was stating the bleeding obvious. I suppose that is why it is called 'logic'.

[Rosa Lichtenstein]

Well, you seem to be operating with an idiosycratic notion of modern logic. Logic in general is concerned with inference, and it often considers simple, seemingly 'obvious' inferences so that we might learn how to study more complex examples.

It's effectivenes can be seen from the additional fact that had logicians not started doing this in the mid-19th century, you would not now have a computer by means of which to raise this question -- from very simple inferences we can construct massively complex and (surely) non-'obvious' inferences, and thus equivalently complex software.

[RebelDog]

Well, you seem to be operating with an idiosycratic notion of modern logic. Logic in general is concerned with inference, and it often considers simple, seemingly 'obvious' inferences so that we might learn how to study more complex examples.

It's effectivenes can be seen from the additional fact that had logicians not started doing this in the mid-19th century, you would not now have a computer by means of which to raise this question -- from very simple inferences we can construct massively complex and (surely) non-'obvious' inferences, and thus equivalently complex software.

I see the logic in that. I read it out of context.

[syndicat]

yes, in logic we start with what is blindingly obvious. so obvious you might not have thought to state it. the method is, as Rosa says, to try to establish or justify complex chains of reasoning in a step ty step way where each step appeals to some blindingly obvious principle. that's the beauty of it.

[Rosa Lichtenstein]

We can also reason from falsehood to truth in logic, so we do not always begin with the obvious.

And we can reason hypothetically, where we are unsure of the truth of our premises, or we suspect one of them is false.

[syndicat]

yeah, i wasn't being clear. I meant that the principles of inference used to validate each step are blindingly obvious, not that the premises in an argument have to be. rosa is, i think, referring to the fact that in deductive logic there are three inferential strategies: direct proof, indirect proof, and hypothetical proof.

that said, logicians do challenge inference rules at times, and they will debate among themselves whether certain rules should be accepted.

[RebelDog]

Maybe off topic. Can truely random numbers exist, or randomness per-se?

[Rosa Lichtenstein]

They can be generated by random quantum effects. By any other method they are merely 'pseudo-random'.

http://en.wikipedia.org/wiki/Random_number_generation#.22True.22_random_numbers _vs._pseudorandom_numbers

[red cat]

Maybe off topic. Can truely random numbers exist, or randomness per-se?

We often believe that the state of the universe at any given time uniquely determines its subsequent stages, and this belief seems to hold true for most things in our daily lives. But this is really impossible to verify as we have to affect a system in order to obtain information about it.

Numbers based on certain aspects of microscopic and macroscopic physical phenomena can be called random. However, since such random number generators are very slow, we use pseudo-random generators which are as good as random ones for practical applications.

[ChrisK]

I don't know if my textbooks are the best, but I'd be curious what text/content you studied. It would give me a better idea of what to recommend. My experience is mostly involving overview courses, but I have encountered both Quine and Lemmon.

I should point out that Quine has strong oppositions to Modal Logic, and I believe many "followers" of Quine and Wittgenstein share this sentiment. So if you want both sides of the coin with respect to Modal Logic, you'd have to read someone in addition to Quine. I'm not sure if Quine is right or not. My professor disagreed with him so I obviously have a biased view. That and modal logic has lots of fun symbols and shapes so I don't want to go back to classical logic.

Godel's work on soundness and completeness is interesting. Kripke is absolutely everywhere these days. Necessity of Identity is quite an interesting conclusion.

There is that principle I forget the name of. It claims you can derive anything from a contradiction. Epistemic logic has people that believe you can know something without knowing you know it simply by virtue of having the "theoretical means to arrive at the truth."

I am rambling as my information is all over the place due to just doing a Modal Logic final this morning. Logic is interesting, but I have a hard time with it sometimes because of the poor quality of the writing/examples. That's true of a lot of philosophy and academia though. If only people would learn to write and draw pictures for me, I'd be set.

I've just seen this and I have a question. What exactly is Modal logic and why do wittgensteinians dislike it?

As for the textbooks I've used, I've only had one class in logic so besides Quine's book I have "A Concise Introduction to Logic" by Patrick Hurley

[syndicat]

Modal logic is the logic possibility, contingency and necessity. So for example some basic principles:

If necessarily P, then P. (what is necessary is actual)
If P, then possibly P. (what is actual is possible)

We often attribute modal properties to things. For example, susceptibilities, abilities, capacities, potentialities, tendencies. These all imply possibility.

One argument for modality is the inability of acconting for the ordinary conditional without it because the relationship between the "if" part of a conditional and the "then" part is not adequately thought of as a mere correlation without connection, but in the classic Frege/Russell propositional logic it is a mere correlation.

Hughes & Cresswell is a standard text in modal logic...which i used to use when i taught modal logic classes.

[Rosa Lichtenstein]

ChristopherKoch:


wittgensteinians dislike it?

I have yet to meet/read any who do.