I'm currently studying mathematical logic and I'd like some recommendations on more classical logic and philosophy.
Mathematical logic is relatively new, and vastly different from its predecessors. In fact, modern logic has much more in common with math today than it does with philosophy.
Nevertheless I want to be able to understand my subject in a broader sense, so if any of you know of any books both on the history of logic and philosophy, as well as actual "textbooks" I guess you could call them, that would be appreciated.
An Introduction to Philosophical Logic: Anthony C. Grayling is decent.
Alexander Diaz
'The Development of Logic' by William Kneale (1962) 'From Frege to Godel: A Source Book in Mathematical Logic, 1879-1931' by Jean van Heijenoort
Jace Thompson
I've said this before and I'll say it again for those that have been seduced by ML: you'll never understand the deepest results of ML unless you're confident in your mathematical ability. This means having the knowledge of a 4-year maths education. Do you have it? If not, get it. If you do, then Schoenfield's book is the standard graduate textbook in ML.
>In fact, modern logic has much more in common with math today than it does with philosophy. It's not a fact, unless by "fact" you mean "something that I pulled out of my ass". When you state that something has something "much more in common" with something else you need to say just what it is that they have in common and provide the statistics that justify it. It is nonsense to talk about something being "much more" than something else without defining a method for establishing this. ML lies in the foundations of mathematics and it overlaps with mathematics just as it does with philosophy.
>vastly different from its predecessors Predecessors? *What* predecessors?
Connor Watson
psh, kid, i now the difference between a union and an intersection
Robert Peterson
>It's not a fact, unless by "fact" you mean "something that I pulled out of my ass" Figure of speech my man. I'm not going to lay out my definitions in everyday speech. No one does. Turn down your autism dial just a bit. I was saying that as a kind of introduction to the uninitiated. Perhaps philosophy students who had studied logic in an informal sense.
>Predecessors? *What* predecessors? Do you honestly not understand what I meant by this? I don't really feel like getting into an argument. You seem like a clever guy, try to use common sense when reading what others write. The rest of us is doing you that courtesy.
Kevin Myers
The most well-researched areas in logic nowadays belong inside Computer Science departments and Mathematics departments. In the U.S. students are expected to have a reading comprehension of first-order logic and modal logic, but not much more than that.
Well, the development of modern logic can be traced back to the end of the XIX century and the first half of the XX century.
Now, the first thing that I say is this: for the technical part of ML, use modern textbooks. A good starting place is reading Peter Smith's blog and his Learning Logic Guide (logicmatters.net). If you feel comfortable with mathematics, I would recommend that you use Elliot Mendelson's 'Introduction to Mathematical Logic', I think the last edition was released in 2015. If you are less mathematically-inclined, you could use Ian Chiswell and Wilfrid Hodges' 'Mathematical Logic'.
For starters, this material should keep you busy for at least a semester.
Now, on the history side, a very good starting point (although not a terribly serious one) is to get a hold of a graphic novel called 'Logicomix'. It will introduce you to some of the key figures of early mathematical logic, and it is a nice, light-hearted read. After reading that, you could learn more about the key figures in mathematical logic. I don't know of any comprehensive books about the history of the subject, but there are many well-researched biographies out there. If you don't want to commit yourself to the study of someone's whole biography, at least read about these people:
- Georg Cantor - David Hilbert - Gottlob Frege - Bertrand Russell - Alfred Whitehead - Kurt Gödel - Gherard Gentzen - Alfred Tarski
All of these people (with the exception of Tarski and Whitehead) have very well-written biographies. Since their lives are very much tangled, reading any such biography would give you insight into the birth of the discipline.
Please feel free to ask for more recommendations or additional information.
Nathan Baker
So you can't account for your words. Okay. At any rate, you know what to read, given that you satisfy the requisites. If not, you know what to do. And please, don't ever back-pedal like a juvenile teenager.
>The most well-researched areas in logic nowadays belong inside Computer Science departments and Mathematics departments. That's all nice and all princess, but please: no one here wants to hear your anecdotes. If you want to to make a case for compsci and maths here, provide some accompanying statistics. If you're ignorant of the contemporary landscape of Philosophy just say so. Comparing a thing whose value you don't know with an other thing whose value you do know is intellectually dishonest.
>is to get a hold of a graphic novel called 'Logicomix'. Jesus fucking Christ this board is hopeless.
>At any rate, you know what to read, given that you satisfy the requisites. No I don't know what to read. Maybe you have trouble understanding English, but I said I was studying mathematical logic, and wanted history of NON-mathematical logic. In what way is a 4+ year degree in mathematics necessary for that? Please enlighten me, great one. Never heard of history being that hard before.
Furthermore I don't think you had any issues understanding what I meant, I think you just get triggered whenever someone suggests modern logic is closer connected to mathematics than philosophy. It's well known logicians during the late 19th and early 20th century wanted to emulate the success of mathematics, and so tried to bring logic closer to it. Does this upset you in some way?
Also, take a look at John MacFarlanes dissertation "what does it mean to say that logic is formal?", okay?
Sebastian Wood
>any particular periods you are interested in? Well stuff like the Greeks is obviously interesting. Preferably something that compares it to more modern logic, since there are such large differences. Even a large volume on the general history of logic from the Greeks to modern day would also be great.
>Also, take a look at John MacFarlanes dissertation "what does it mean to say that logic is formal?", okay? Yes, I'm skimming through it now, it's rather long, so is there anything in it that's immediately important? What's the general gist of it?
Oliver Rodriguez
nerd
Alexander Jones
the development of logic by kneale and kneale is kind of a classic. macfarlane argues that the distinctive modern conception of logic as 'formal' (which has a few different meanings, he argues there are three of them as you can see), has its origins in kant's transcendental idealism, and divorced from that content it is no longer clear what it means to say that logic is distincively 'formal' (and in a certain sense this explains why people wh have accepted kant's understanding of formal (pure, general) logic but totally divorce it from the rest of Kant's philosophy have such a difficult time giving an account of what logic is about or concerned with)
some other classics: goldfarb's essay "logic in the twenties: the nature of the quantifier" is worth checking out. plus check out jonathan barnes truth. etc for ancient logic (plus james lennox, jonathan lear, terrence parsons for medieval)
i dunno if you are interested in early modern, or frege, or bolzano or whatever then let me know. history of logic is a fucking huge subject.
Elijah Watson
>studying some trendy philo bullshit instead of just studying mathematics
You're not going to make it.
Noah Ward
>OP: I'd like some recommendations on more classical logic >: wanted history of NON-mathematical logic Huh? What exactly did you mean by "classical logic" in your OP?
>Furthermore I don't think you had any issues understanding what I meant, I think you just get triggered whenever someone suggests modern logic is closer connected to mathematics than philosophy. To clarify, I don't have any problem with this as long as you give some evidence for your claims. You haven't given us any. If you don't have the evidence then you should have said something less strong and more modest: "ML overlaps with maths, philosophy, compsci, linguistics, ..." and not "ML overlaps with maths more than with philosophy": the former statement is common knowledge, but the latter is harder to establish.
> It's well known logicians during the late 19th and early 20th century wanted to emulate the success of mathematics "Emulate the success of mathematics"? Those are poor choice of words. They wanted to found classical mathematics on solid, safe, and rigorous foundations, just as Kronecker, Weierstrass, and Dedekind wanted and indeed provided the arithmetization of analysis. By and large, logicians scorn at mainstream mathematicians (e.g. some ML textbooks, written by logicians, make fun of many Analysis textbooks and how confused they are from the POV of ML), but that's a different can of worms.
>Go ahead It really irks me that you believe something like Wikipedia to be a good go-to source for the history of ML. Do you not know better sources? Linking me to would be a much better answer here; then again, I've already read both.
Brody Gonzalez
why are you being a prick instead of actually helping op? I've got my hands full grading papers etc but I took 2 mins to give him a list he/she seems genuinely interested and curious. why not just help them out?
Aaron Clark
Are you kidding me? How is >[Pursue] [...] ML unless you're confident in your mathematical ability. This means having the knowledge of a 4-year maths education. Do you have it? If not, get it. If you do, then Schoenfield's book is the standard graduate textbook in ML. that I provided in not helping OP?
This is silly advice. there is no reason not to to start studying logic and then learn the math you need to know if and when you need it, it certainly doesn't require 3-4 years of study before you begin logic. that's just ridiculous. for fuck sake schoenfields book isn't even that difficult, but if you have less of a math background check out boolos et al's computability and logic or enderton's mathematical introduction to logic and then move onto modal logic or modal theory or proof theory or whatever as need be, and pick up the math you need when and as you need it.
Aiden Miller
>But in our time, education is overwhelmed by mathematics and on more than one score. For, while a contemplative interest in the properties of shapes and numbers is almost completely extinct, an illiberal and utterly inhuman form of mathematics dominates the years of learning of our boys and girls, almost completely from the very first year of the primary school to the very last year of college. In place of arithmetic and geometry, whose relation to reality is definite and understandable, there is now an indefinite confusion of branches which go by the name of mathematics, the nature of whose objects nobody understands! Such topics as topology, non-Eudidean geometry, Boolean algebra, transfinite numbers, projective geometry; not to speak of other more recognizable subjects like algebra, trigonometry, integral calculus, vector analysis and the theory of equations. These new subjects are not only more confusing but much more difficult to acquire, and therefore much less likely to leave the mind at leisure for other liberal studies. But the predominance of mathematics today is not restricted to those courses which go by its name, because mathematics, in some form or other, in matter or in method, has crept into every other corner of the curriculum. According to the modern positivistic conception, mathematics and not wisdom is considered as the prototype of science. In subjects ranging from physics to education, covering every field of human learning, there is an evident tendency to assimilate all knowledge to mathematical knowledge and to resolve all realities into mathematical formulas. This trend reaches its apex in the development of symbolic logic, in which guise mathematics invades even the field of philosophy, to distort all the basic conceptions of the mind, and to deflect all the activities of thought from attaining their fulfillment in true wisdom which consists in knowledge about God, by keeping them whirling endlessly around the nihilistic circle of sheer mathematical emptiness.
Joshua Clark
stop spamming this shit
Jackson Jackson
this is fucking retarded
Blake Thompson
OP asked for classical logic / philosophy
Nathan Barnes
That paper looks really interesting, I'll definitely read through it.
I'm very much still a beginner when it comes to formal logic, but I often find that knowing the history and motivation behind ideas help me understand them. It's also interesting to me exactly how the current definition of formal when it comes to logic has come about (Which MacFarlane's paper seems to be a perfect fit to answer).
Since the history of logic is so immensely large, are there any general/overview books on it? Something that perhaps favors breadth of depth, so I can get a bird's eyes view over the history, and then dive in deeper where I want?
I'm also noting down all your recommendations as well, I'll make sure to check out all of them.
I'm not going to argue with you anymore. This discussion is off-topic to the thread.
Mason Gray
It really isn't silly advice. Mathematicians compared to non-mathematicians have plenty of time practising their proof skills before they get to ML. The more math you know the better prepared you'll be. Diving into ML as a non-mathematician is going to hurt. A lot. Schoenfield is pretty terse and more tough-going than Enderton and Mendelson. Boolos' book is ok for philosophers I guess.
Charles Sullivan
it's silly to tell someone to put off their studies for 4 years to practice proofs and learn fucking gallois theory or something.
better to start off with a more manageable text like boolos' or endertons, and then learn the math you need as you go along and move on to more complex stuff.
sure it will be hard, but better to jump in the deep end then wait for 4 years until you are ready. and there are plenty of books that help with proofs; daniel vellemans how to prove it: a structured approach is one nice example that isn't pitched at too high a level
truth etc, by barnes on ancient logic kneale and kneale's the development of logic two anthologies of primary sources: from frege to godel, and the lesser known from kant to hilbert
plus looking around in macfarlanes dissertation is great becaues it's good for further references, apart from being a great piece of work
outside of that there are just lots of papers and books etc. check out the stanford encyclopedia of course.
Ryder Peterson
also when you say you are a beginner in logic, how much of a beginner are you?
Juan Howard
I'll have a look at all of these.
In logic I'm pretty much only comfortable with first order logic, although I do have somewhat of a mathematical background (analysis, abstract algebra, etc.), so I also have experience in set theory. My original reason for going into logic in the first place is because I thought it'd be a fun supplement to my mathematical studies.
Bentley Bailey
he knows how to check soundness of arguments using truth-tables.
Jace Lee
>I'm pretty much only comfortable with first order logic Why is Henkin's proof for completeness of FOL preferred over Godel's?
Adrian Baker
i'd say that it's a lot more usefully to examine particular philosophical arguments rooted in formal logic than it is to read over histories or commentaries of logic as a discipline.
Check out Hofstader's Godel Escher Bach, Bertrand Russell's Principles of Mathematics, John Etchemendy's Concept of Logical Consequence, and Robert Nozick's Philosophical Explanations
Evan Martinez
>John Etchemendy's Concept of Logical Consequence
this is a classic OP. he fucking butchers bolzano and is wrong on a whole host of things, but it is a great book.
Logan Johnson
Holy shit, this philosophy kid has been awfully triggered and is in dire need of some proper spanking. Mathematical logic is mostly done - gasp! - in mathematics and Computer Science.
Gavin Fisher
>this philosophy kid No where did "this philosophy kid" identify as one.
>Mathematical logic is mostly done - gasp! - in mathematics and Computer Science. It seems that you're suffering from a similar disease as OP: Is there any particular reason why you're confusing blatant allegations with justified statements?
