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2010-08-10
Graduate Logic Requirements
I am starting to apply to PhD programs, and I hope to specialize in philosophy of science (particularly information science). I have a strong interest in logic, and I know that I have to complete certain requirements for universities teaching in the analytic tradition. I did not have logic as an undergrad (I was on the religious studies side of the department). I have been diligently studying by myself, but I am trying to get an idea of what level of study I should be comfortable with. I am currently working through Symbolic Logic I, available from MIT though open courseware. I have also worked through a couple other symbolic logic texts (Logic for Dummies, and Introduction to Logic by PD Magnus). I have mostly been working with sentential and predicate logic, truth tables, and some proofs. Should I worry about set theory, incompleteness, or other logics (many-valued, fuzzy, modal, etc). I might be over worrying, but I want to be a strong student and be sure that I am prepared.

Thanks

Justin Charles Hite, BA, MLIS

2010-08-13
Graduate Logic Requirements
Reply to Justin Hite
(Note that I've moved this thread to a more appropriate forum.)
Judging from what I've seen at the two unis I've attended as a grad student in philosophy (ANU and UofT), you don't need more knowledge of logic to be accepted in a phd program in philosophy than in any other discipline. However, in some places they want you to have at least a good command of propositional and predicate logic by the time you get out, so they'll make you take an undergraduate course in logic if required (this was the case at UofT a few years ago). I don't think that training includes any set theory, alternate logics, etc -- it was the most basic course focused exclusively on logic (there were also softer courses like 'critical thinking' with a logic component, but these weren't enough to qualify for graduation). 

So, I wouldn't worry more about this for now. You've already learned what you really need to know for practical purposes, and doing more independent training isn't really going to help you for graduation purposes because they'll make you take a course anyway if you go to a place like UofT. That said, I would recommended reading the graduate prospectus of the programs you're thinking of applying to. 

Good luck!

2010-08-16
Graduate Logic Requirements
Reply to Justin Hite
One can loose much time and hair on bad logic manuals. A safe bet for first order logic is always Quine's Methods of logic (1950 - republished many times). Many valued logic reveals easy when explained by his inventor Jan Lukasiewicz for example in the short System of logic (1953 - see the book Selected Works). On the same topic and by the same author, the article Arithmetic and modal logic offers a memorable thought experiment and illustrates the relation between modal and many valued logics. Kenneth Konyndyk's Introductory modal logic (1986 - many republishings) is certainly the book you would take with you on a trip to another possible world as a means to keep your head on.

This set of references represents less than 500 pages to read with no boredom.

Now I gladly join you in this thread to request a likewise enlightening reference on the topic of higher order logic.

Best regards,

Emmanuel

2010-08-17
Graduate Logic Requirements
Reply to Emmanuel Rens
P.S. I don't mean that the books you mention are bad.

2010-08-17
Graduate Logic Requirements
Reply to Justin Hite
Thanks for the insight guys. I think that I am definitely over-worrying, but I feel like logic is the first thing I've ever been challenged by, and so that intrigues me. I have mostly been going with what was available for free online and cheap at my local Borders. My next book buying will have to be from Amazon. But I've already learned about the "hair loss effect", when trying to read Hegel's Logic (luckily, one of my old philosophy professors quick shoo-ed me away from this book.) I think the crux of my worry comes from a slight inferiority complex. I was looking at some of the current students at one of the universities I am thinking of applying to (Carnegie Mellon), and a majority of the students double majored in philosophy and mathematics, as opposed to me who studied religion and music theory. 
As for higher-order logic, I get the idea, I'm still working on the practice haha. Give me a little time, and I'll be asking for the best texts on lambda calculus, I promise. 

Justin

2010-08-17
Graduate Logic Requirements
Reply to Justin Hite
I'm happy if my list of best sellers can help you. None of them requires the slightest knowledge in mathematics: Quine hardly reaches number definition, Lukasiewicz only requires you to recognize when a number is greater than another, Konyndyk doesn't care about numbers. You might have to borrow Lukasiewicz's Selected works from a library.


All the best!

Emmanuel

P.S. By the way, you would do me a great favour if you could participate in my experiment on musical perception: people seem shy (or bored), a first tester could make the start. Cf. http://philpapers.org/post/4340 . Many thanks in advance!

2010-08-19
Graduate Logic Requirements
Reply to Emmanuel Rens
The experiment looks interesting. I'll give the paper a read. I composed my fair share of 12-tone music while in school, and I am interested in the foundations of aestetics. I'll get you my response/results ASAP.

Many thanks

Justin

2010-08-25
Graduate Logic Requirements
Reply to Justin Hite
Here in Spain ,Logics are taught at the first years , mostly the book of Suppes and XXth century Logics are reserved for those that specialize in Logics, at the Doctorate courses.

By the way, I hate XXth century Logics, I think that they are just an experiment without other meaning, too often XXth century Logics are "ilogical" in the sense that nobody can understand them
and are a forceful twist of Aristotelian Logics which must be learned as a creed as each Logician says that his  sillogism conclusions are as he says.

2011-02-02
Graduate Logic Requirements
I don't think that 'nobody can understand' XXth century Logics, in what basis do you make such a claim?

2011-05-14
Graduate Logic Requirements
I replied before but it was erased by an editor of this web.

I try again:XXth logics are experimental,not related with   the "natural" way of thinking of the  humans (which was stated by Aristotle in his Logics) and it is i-logical, in the sense  that XXth Logics rapes the natural way of thinking.

 XXth Logics is interesting only as an experiment  and nothing else.

And too often the  XXth Logicians use to demonstrate  their conclussions after a long chain of sillogisms just by saying "this is the way it is because I say it is " and that ś all.

 We must accept what the XXth logicians say, just because    they say that we must accept it, not by  demostration.

2012-07-23
Graduate Logic Requirements
Why do you think that logic ought to conform to the natural way of thinking? What reason is there for the human brain to have evolved in a perfectly logically-consistent way? 

Russell's Paradox shows that our natural intuition to categorize groups of things as merely extensions of predicates is illogical. This was the starting point for 20th Century logic. So in a way I agree with you--modern logic IS counter-intuitive. But we've also shown that our intuitions are not entirely logical, so who cares?

2013-07-05
Graduate Logic Requirements
Reply to Justin Hite
Justin,
There are many excellent textbooks on these topics (as old as Tarski, Intro to Logic and brand new).

Since you have a strong interest in Logic and want to specialize in the philosophy of information sciences, you really should develop a high level of competence in Philosophical Logic, Set Theory and some related mathematics.  For Logic, I suggest the following:  "Classical and Non-classical Logics" by Eric Schechter.  You would study the classical, many-valued, fuzzy, Zadeh, relevance (relevant), Abelian, Sugihara and other propositional logics from semantical (model theoretic) and syntactical (proofs) views of each topic.  You would not study modal or applied mathematical logics (groups, rings, advanced topological notions, etc.) or set theory (beyond what is necessary for this book) nor would you study quantification theory in any logic.  Three attractive attributes of this book are 1) explication of both semantics and syntactics of each type of logic and comparisons of the two methods, 2)  extensive use of diagrams to depict relationships among logics and of truth tables for each logic as well as for comparisons, and 3) the author takes great care to provide excellent exercises.  There is an errata page, too.  To study logic from a mathematical perspective or set theory in some depth, I recommend two books by Herbert Enderton, "A Mathematical Introduction to Logic," and "Elements of Set Theory."  Both cover the waterfront and are accessible for self study (my avenue, likewise for Schechter).

For a philosophical approach, (Quine, Fitch and Barwise&Etchemendy are very good, too), "Logic:  Techniques of Formal Reasoning," by Kalish, Montague and Mar is an excellent alternative.  They present logic as:  1) a tool for analyzing English arguments (heavy emphasis) as well as 2) a tool for analyzing formal languages.  They develop a detailed theory of translation from English to symbols and back for the propositional logic and for quantificational logic.  They develop the theory of identity (=), a theory of descriptions (a la Russell), theory of formal theories and their languages, and extend first-order logic to develop a theory of variable-binding operators.  This book goes from soup to nuts:  the very beginning to a very advanced discussion.  It is rigorous (no hand-waving); the authors develop a "natural deduction" vs. an "axiomatic" system.  The former has rules and definitions only; the latter has axioms, definitions and rules.  Personally, I like this book a great deal for the study of philosophical logic.

For modal logic and other non-classical logics, including quantification, I recommend Priest, "Non-classical Logics".  It's detailed and encyclopedic.  Compared to Schechter, it's more complete in that it develops quantification theory in modal, many-valued and intuitionistic logics.  But, I prefer Schechter's use of a dual approach (model theoretic and proof theoretic) to the same material.


2013-07-05
Graduate Logic Requirements
Reply to Justin Hite
Justin,
There are many excellent textbooks on these topics (as old as Tarski, Intro to Logic and brand new).

Since you have a strong interest in Logic and want to specialize in the philosophy of information sciences, you really should develop a high level of competence in Philosophical Logic, Set Theory and some related mathematics.  For Logic, I suggest the following:  "Classical and Non-classical Logics" by Eric Schechter.  You would study the classical, many-valued, fuzzy, Zadeh, relevance (relevant), Abelian, Sugihara and other propositional logics from semantical (model theoretic) and syntactical (proofs) views of each topic.  You would not study modal or applied mathematical logics (groups, rings, advanced topological notions, etc.) or set theory (beyond what is necessary for this book) nor would you study quantification theory in any logic.  Three attractive attributes of this book are 1) explication of both semantics and syntactics of each type of logic and comparisons of the two methods, 2)  extensive use of diagrams to depict relationships among logics and of truth tables for each logic as well as for comparisons, and 3) the author takes great care to provide excellent exercises.  There is an errata page, too.  To study logic from a mathematical perspective or set theory in some depth, I recommend two books by Herbert Enderton, "A Mathematical Introduction to Logic," and "Elements of Set Theory."  Both cover the waterfront and are accessible for self study (my avenue, likewise for Schechter).

For a philosophical approach, (Quine, Fitch and Barwise&Etchemendy are very good, too), "Logic:  Techniques of Formal Reasoning," by Kalish, Montague and Mar is an excellent alternative.  They present logic as:  1) a tool for analyzing English arguments (heavy emphasis) as well as 2) a tool for analyzing formal languages.  They develop a detailed theory of translation from English to symbols and back for the propositional logic and for quantificational logic.  They develop the theory of identity (=), a theory of descriptions (a la Russell), theory of formal theories and their languages, and extend first-order logic to develop a theory of variable-binding operators.  This book goes from soup to nuts:  the very beginning to a very advanced discussion.  It is rigorous (no hand-waving); the authors develop a "natural deduction" vs. an "axiomatic" system.  The former has rules and definitions only; the latter has axioms, definitions and rules.  Personally, I like this book a great deal for the study of philosophical logic.

For modal logic and other non-classical logics, including quantification, I recommend Priest, "Non-classical Logics".  It's detailed and encyclopedic.  Compared to Schechter, it's more complete in that it develops quantification theory in modal, many-valued and intuitionistic logics.  But, I prefer Schechter's use of a dual approach (model theoretic and proof theoretic) to the same material.