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Foundations of Logic

sagardipak
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Posted 05/12/08 - 01:51 PM: Subject: Foundations of Logic	#1
Hi everybody! My name is Sagar and I'm new to this forum. I'm sort of new to philosophy... The only philosophy I've had started in my 10th grade (in Portugal) and it's going to end this year, the 11th. Anyway, I wanted to learn Mathematical Logic. I'm aware that there are many kinds of logic, but I wanted to learn a solid one... Does anyone know of any book that could teach this? Preferrably, with some history and discussion of logic to go... Thank you! Sorry if my english is not that correct...

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Posted 05/12/08 - 03:31 PM:	#2
sagardipak wrote: Hi everybody! My name is Sagar and I'm new to this forum. I'm sort of new to philosophy... The only philosophy I've had started in my 10th grade (in Portugal) and it's going to end this year, the 11th. Anyway, I wanted to learn Mathematical Logic. I'm aware that there are many kinds of logic, but I wanted to learn a solid one... Does anyone know of any book that could teach this? Preferrably, with some history and discussion of logic to go... Thank you! Sorry if my english is not that correct... To my knowledge, logicians have basically given up on tring to establish a form of universal or complete logic. Instead, they work on developing certain forms of logic which are context-dependent, working in certain areas. This is less grandiose, but it is more practical, because it can actually be used for things like computers and other machines which work in very narrow fields, not figuring out "the answer to everything." In my opinion, logic which is very useful for everyday discussion is studying the fallacies of formal and informal logic: http://en.wikipedia.org/wiki/List_of_fallacies These all tend to correspond to cognitive biases in Psychology: http://en.wikipedia.org/wiki/List_of_cognitive_biases I took an introductory course in logic in college and the text we used was Introduction to Logic by Irving Copi and Carl Cohen. It seems to be a pretty decent book.

Prime_Mover
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Posted 05/12/08 - 04:00 PM:	#3
For the most basic introduction to Western logic, pick up the most basic foundation: Aristotle's Organon. It is Aristotle's collection of works on logic, made up of the six treatises "De Interpretatione", "Categories", "Prior Analytics", "Topics", "Sophistical Refutations", and the "Posterior Analytics". If you have trouble with the book, supplement it with notes from SparkNotes and information from the Stanford Encyclopedia of Philosophy, found here: http://plato.stanford.edu/entries/aristotle-logic/ After you finish the basics of Aristotle, you can move on to the more specific areas of logic with content-specific books on such topics. (don't trust Wikipedia)
The Promethean Movement http://www.promethea.org

7
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Posted 05/12/08 - 07:15 PM:	#4
There's a list of books on math logic here: http://forums.philosophyforums.com/threads/recomm... It is hard for me to make a recommendation because I don't know what you're looking for. Do you want metatheory (completeness, compactness, lowenheim skolem, incompleteness, undecidability, etc.) or do you just want the very basics? Are you interested in higher order logics? Modal logic? Fuzzy logic? Some other non-classical logic? Do you want to learn tableau-style proof procedures (I find them extremely useful)? If you want to move into metalogic, you'll want some set theory. How much? BTW, if you want mathematical logic, I don't think reading Aristotle will meet your needs. You can jump into a book on contemporary mathematical logic, if you have a bit of mathematical experience. The Copi and Cohen is ok, but it's lightweight. You'll probably want something more in-depth and without the IMO useless material about syllogisms.

sagardipak
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Posted 05/13/08 - 05:57 AM:	#5
Thank you for all your answers. 7 wrote: There's a list of books on math logic here: http://forums.philosophyforums.com/threads/recomm... It is hard for me to make a recommendation because I don't know what you're looking for. Do you want metatheory (completeness, compactness, lowenheim skolem, incompleteness, undecidability, etc.) or do you just want the very basics? Are you interested in higher order logics? Modal logic? Fuzzy logic? Some other non-classical logic? Do you want to learn tableau-style proof procedures (I find them extremely useful)? If you want to move into metalogic, you'll want some set theory. How much? BTW, if you want mathematical logic, I don't think reading Aristotle will meet your needs. You can jump into a book on contemporary mathematical logic, if you have a bit of mathematical experience. The Copi and Cohen is ok, but it's lightweight. You'll probably want something more in-depth and without the IMO useless material about syllogisms. Yes, I'm looking for a more modern logic. I have some books about Set Theory (both naive and axiomatic), but that's not what I'm searching for. I want to learn the logic that maths use (the propositional, symbolic). And I'm also interested in Godel's completeness theorem and Hilbert's view on quantifiers, which I think it's different (something to do with epsilon calculus). But what I really want is something like the deduction of logic. Giving the axioms of logic and then deducing it. Edited by sagardipak on 05/13/08 - 06:10 AM

7
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Posted 05/14/08 - 01:38 PM:	#6
Any book on metalogic will have the completeness theorem. The presentation in Enderton's book is pretty good, as is the one in Christopher Leary's A Friendly Introduction to Mathematical Logic. The latter is somewhat easier to read, but the Enderton has greater detail. Either one or a bit of both is good for an introduction. The Enderton has things that aren't in the other book, but Leary has a better treatment of Godel's first incompleteness theorem. If you are interested in Godel's incompleteness theorems, Peter Smith has an excellent book called An Introduction to Godel's Theorems. Most books prove the Completeness Theorem using Henkin's proof. A notable exception is Smullyan's First Order Logic, which features tableau-style completeness proofs. Most books do not cover the epsilon calculus. Here are a few sources: http://plato.stanford.edu/entries/epsilon-calculus/ http://www.utm.edu/research/iep/e/ep-calc.htm There are references at the bottom of each page.

sagardipak
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Posted 05/20/08 - 01:52 PM:	#7
7 wrote: Any book on metalogic will have the completeness theorem. The presentation in Enderton's book is pretty good, as is the one in Christopher Leary's A Friendly Introduction to Mathematical Logic. The latter is somewhat easier to read, but the Enderton has greater detail. Either one or a bit of both is good for an introduction. The Enderton has things that aren't in the other book, but Leary has a better treatment of Godel's first incompleteness theorem. If you are interested in Godel's incompleteness theorems, Peter Smith has an excellent book called An Introduction to Godel's Theorems. Most books prove the Completeness Theorem using Henkin's proof. A notable exception is Smullyan's First Order Logic, which features tableau-style completeness proofs. Most books do not cover the epsilon calculus. Here are a few sources: http://plato.stanford.edu/entries/epsilon-calculus/ http://www.utm.edu/research/iep/e/ep-calc.htm There are references at the bottom of each page. Thank you very much! I'm going to look for these books, and hopefully learn something from them. Thanks again, Sagar Pratapsi

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