Cool! I had to look that up. Thank you, @jeffsmith1798. I know Euclid has other proofs like that. Consider, in number theory, that there are infinitely many prime numbers.

Absolutely! I love this book. There's a lot of logic textbooks out there, even very traditional ones, but I know of none that approaches this level of, so to speak, "funness."

People have become hyper-specialists. That's partly why it is so easy for people to embrace a naïve scientism and reject ontology or general philosophy. Indeed, some scientists have gone so far as to claim "[traditional] philosophy is dead!" But the thing is, there is so much physics takes for granted when it comes to ontology and epistemology. While we can "bracket off" that grounding such that we don't need to think about it when studying something like F=ma, that grounding is STILL there.

Good comment, @codework-vb6er. Thank you! I was second guessing myself when I worked through that exercise and saw how the authors interpreted the proposition. You have a good grasp. You model and explain things well. At the same time, I perceive something like predicate logic or propositional logic as two different *models*. We need to interpret the proposition first as it stands and only secondarily consider how we should properly model it (if that makes sense). In other words, natural language and natural reasoning comes before, and takes priority over, the symbolic language. It is in this sense, for example, that I disagree with someone like Bertrand Russell. It also explains why I think traditional Scholastic logic is not out-of-date nor replaceable.

To your point "natural language and natural reasoning comes before, and takes priority over, the symbolic language." There exist arguments that reason or intuition (natural language and natural reasoning) knows is true, but that the formal reasoning and formal language, such as Propositional Logic, cannot prove true. That is, the equipment of Propositional Logic cannot move from true premises to a true conclusion for these particular forms of an argument. It does not mean the argument is invalid. Instead it means, Propositional Logic, as a formal system of reasoning, is not sufficient to show the argument is valid -- So we create a better mouse trap, Predicate Logic.

"A Beginner's Guide to Mathematical Logic" by Raymond M. Smullyan: amzn.to/4aw3mlG He's a legend!

There are several! Many I have not seen (or read). But for a contemporary approach, try "Introduction to Mathematical Logic" by Elliott Mendelson: amzn.to/4bR8Qs5

Yes, exactly! That's my new motto. :) Thank you!

Thank you, @SeatCushion!

Hello, @divinefavour1289. Oh, I think it DOES help. There are different areas of logic to explore. Some books are better in certain areas than others. And there are different, so to speak, branches of logic. A formal logic textbook is different than an informal logic textbook. Mathematical logic is different from traditional, verbal style logic. Etc. It’s not that much different than math books. Math is a huge topic! There are all sorts of different branches to explore. Different books specialize in different areas. They offer different, so to speak, perspectives. Etc.

@@AmateurLogician i see. that does make sense

@@divinefavour1289 not to mention, different authors have different perspectives on logic, similarly to every other discipline. People may define things differently, establish different systems, etc.

@@ninja_raven512 i see. that makes sense

First do a good single book on logic. Then you'll be able to judge and read other books

Hey, @SaintBusiness. I think most people find it a hard book to read! It's not impossible, mind you, but very hard. I've used it more as a reference. Other books helped fill in various pieces for me.

You could try this: kzbin.info/aero/PL6CXV84lIvr4NNOmvTGqwraSsWlzE_EsG Other books I recommend can be found here: amateurlogician.com/trivium-logic/ and here: amateurlogician.com/propositional-logic/ Good luck to you!

I'll second @AmateurLogician suggestion for "First Course in Mathematical Logic." Despite the intimidating title, it actually baby steps you through the material. It's also not very expensive to buy the book either. I also highly suggest you watch his video series on this book. He not only goes over some of the exercises, but also has helpful hints. For example, being an older book, Suppes and Hill sometimes uses terms or conventions that aren't used by modern books. @AmateurLogician videos point out when that occurs and elaborates on how the topic is presented in most modern texts.

Many Thanks Team 👍👍👍

Thank you, @chet3030!

Well, sometimes I think Peter Kreeft (and editor Trent Dougherty) go too far in their criticism of mathematical logic, but they are not far from the truth. Paradoxes of material implication are mentioned, for example. Still, one thing all logicians can agree on is this: mathematical-symbolic logic doesn't capture all forms of natural language argumentation out there. Mathematical logics are just models, so to speak. There are limits to what those models can do. Also, what takes priority: natural language and reasoning or symbolic language and reasoning? What should accommodate itself to what? Bertrand Russell would answer one way, someone like Peter Kreeft would answer another way.

@@AmateurLogician great points. If I may generalize, natural language is like classical mechanics: it works on the day to day level but doesn’t fare well at the sub atomic level.

You can study logic in a more-or-less linear progression, but I've always jumped about into different areas or branches. The Logicist Project, as you may know, ultimately failed with Godel's Incompleteness Theorem. The irony is that Russell's Paradox destroyed Frege's system, and Godel's Incompleteness Theorem destroyed Russell's and White's. You could take a more historical approach. But, first, read some "standard" college textbooks in metalogic and modal logic. Then read Frege's books, Russell's, Quine's, Kripke's, etc.

Yeah, I've heard people say that Epp's book is better. (Though I don't own a copy of it!)

Thank you! I'm glad the video is helpful. If you have questions, let me know.

Hi, @ignacioschulz8182. Logic is necessary, I think, but not sufficient in making good decisions. You need good premises to work with in order to logically derive what follows from them. So, more than pure logic is required! Decisions in life, for example, require thinking about what is morally right. What you and I both need is to ground ourselves in good philosophy. Logic alone will not tell you, e.g., "be charitable to others" or "murder is wrong." What I really think is required is getting in touch with basic philosophy. Aristotle was the first true logician. His most readable book (or lecture notes) is "The Nicomachean Ethics." Or start reading something opinionated like "Ten Philosophical Mistakes" by Mortimer J. Adler. He talks about how small errors in a worldview logically lead to big errors later. amateurlogician.com/philosophy/ In any case, logic can help us think better. In that sense, it can help us make decisions. We can hear the pros and cons of an argument that tells us to do one thing versus another. Or we can use logic to listen to the arguments of some person who is giving us advice on what "best to do." Maybe that argument is fallacious? Learning about the fallacies can help us with that. There's no one book, that I can think of, that will be right here. My advice is to read deeply in philosophy, formal logic, and informal logic. It's something I'm trying to do. There's always so much more to learn!

@@AmateurLogician thanks

Hi, it depends upon what you want to focus on. Logic is a richer, vaster subject that a lot seem to believe. For traditional logic, I have some book recommendations here: amateurlogician.com/trivium-logic/ For the mathematical logic, I have some book recommendations here: amateurlogician.com/propositional-logic/ All the books listed can be self-studied. Some are more advanced than others. Much of traditional logic can be studied, for free, with my tutorial in the first link. We can try to narrow things down with the books, though, if you can be more specific on your exact needs. Best of luck! And thanks for watching.

@@AmateurLogician So i am thinking of purchasing 'The Trivium by Sister Miriam and I have been not able to figure out on formal/symbolic logic, someone recommended me 'Essentials of Symbolic Logic by R.L. Simpson.' can you also recommend me other books since I am from India and the books you mentioned are somewhat rare here and expensive and I am coming to America for vacation next week so I will be able to purchase other books.

@@righteouszzy Sister Miriam Joseph's book is outstanding, though be aware it's an older book written in a somewhat dry style. You might want to supplement that with an additional book. Either "Socratic Logic" by Peter Kreeft or (an easier book) "Logic as a Liberal Art" by R. E. Houser. Note there’s also great books you can read freely online! For example, I've done videos on "Introduction to Logic" by Andrew H. Bachhuber: kzbin.info/www/bejne/qKWXqamefNtmgqs For mathematical logic, there’s my KZbin series on "First Course in Mathematical Logic" by Patrick Suppes and Shirley Hill: kzbin.info/aero/PL6CXV84lIvr4NNOmvTGqwraSsWlzE_EsG You can get the book and "follow along." A good follow-up to that book might be E. J. Lemmon's "Beginning Logic." It's more advanced. Enjoy your time in America! Where are you from, if I may ask? Where are you staying?

@@AmateurLogician i am from Gujarat, India and i will be staying in New York, can you recommend me a bookstore where i can purchase this books??

@@righteouszzy I’m not in the NY area, alas. For me personally, I usually buy my books online. For example, there is www.bookfinder.com/

:)

Some problems I make up on my own. This TYPE of problem, however, will be encountered in some discrete math textbooks. For example, see "Discrete Mathematics and Its Applications" by Kenneth Rosen.

@@AmateurLogician hi also just a random quick question is there a book you would recommend to pair with suppes and hills for predicate Logic because I remember in a video you mentioned it was a weak area of the book? And what would your recommend reading be for a beginner new to the study of Logic? My goal is that of the more mathematical side of Logic but I was curious would you recommend to start from the philosophical side and then move onto a book like suppes n hills for symbolic logic as I am new to this and have just started myself I would appreciate any advice and guidance you can give . Also I really enjoy your videos and it motivates me more and more to study Logic as I have been considering putting in proper time and effort into its study over the last few years and now I think I will go full steam ahead so thank you for motivating me I hope you keep up the good videos

@@leoduckworth8932 Logic is very diverse, more so than a lot of people realize. You can specialize in the mathematical logic without touching much or any of, e.g., informal logic or logic that’s more on the philosophical side. However, while you CAN do that, I think someone would be doing a disservice to themselves. I must admit: I'm biased toward traditional logic and informal logic. Mathematical logic alone is not sufficient. In any case, The Propositional Logic Tutorial has some recommendations: amateurlogician.com/propositional-logic/ Once you get through the Suppes and Hill text, "Beginning Logic" by E. J. Lemmon is a classic that's another step up in difficulty. For something at about the same level as Suppes and Hill, yet will definitely fill in the missing predicate logic pieces, you can try a standard textbook like "A Concise Introduction to Logic" by Patrick Hurley or Irving Copi's "Introduction to Logic." I hope this helps! And good luck to you!

Howdy, @alvaropalomino5525! Thanks for the question. Logic is a fantastic subject to study! Yet it depends upon what you want to focus in on. Traditional or verbal style logic is a different approach than modern symbolic logic. The stuff in this video, of course, is the latter and not the former. The video “Studying Logic with Used Books” gives starting recommendations for traditional logic. A lot of people like the Andrew H. Bachhuber book. Another book is "Socratic Logic" by Peter Kreeft. I also have a tutorial at my website: amateurlogician.com/trivium-logic/ There’s even more recommendations there. For a more modern approach that will get you into symbolic logic, "The Art of Reasoning" by David Kelley and Debby Hutchins is really good and very, very readable. See the video "Self-Teach Yourself College Logic with THIS book." Another good one, for example, is Patrick Hurley's "A Concise Introduction to Logic." Finally, for a symbolic approach, perhaps the easiest book out there is "First Course in Mathematical Logic" by Patrick Suppes and Shirley Hill. And you can "follow along" with me on this KZbin channel: kzbin.info/aero/PL6CXV84lIvr4NNOmvTGqwraSsWlzE_EsG This is a much more work in progress tutorial: amateurlogician.com/propositional-logic/ I’m more partial to traditional logic than mathematical logic. That's partly because it is more "grounded" in natural language reasoning. It ties both into "formal" logic and "informal" logic. It allows us to think more philosophically, and to do philosophical argumentation in a more direct way. Mathematical logic, of course, is great. It's something to learn "on top of" traditional logic, in my view. However, if one just wants to get into proof making in mathematics, then, of course, learning some mathematical logic is paramount. Traditional logic can then be totally skipped. But you’'e also skipping informal logic and thereby skipping cool things like informal fallacies, etc.

@@AmateurLogician Thank you so much for responding in such detail sir! You are a wonderful person!

@@alvaropalomino5525 You're welcome! Good luck to you in your studies. :)

No, because here I'm addressing traditional verbal style logic. It's another beast! Yet, even if you want to do mathematical logic, I would recommend at least learning SOME traditional logic too. It's a neglected subject for far too many, including math majors.

Thanks, @codework-vb6er! Time flies. Before we know it, we'll be done with the entire textbook. Predicate logic is, in my view, a weakness in this book. So, I really will be "filling in" important gaps.

That’s funny! Who is "Ben Shaprio but smart"? Me or Anthony Rizzi? (Or both!?) If me, I should use that quote and put it on my website AmateurLogician.com. ;)

Good comment. Yeah, I usually use the term "paradox" different than "contradiction." It's not a contradiction to claim "if p, then q" and "if p, then not q." However, it would be a contradiction to claim "if p, then q," "if p, then not q," and "p is the case."

Of course, the point being that the "strict logic" of the if-then construction is NOT equivalent to the ordinary English claim of if-then. Yet there's nothing wrong whatsoever with the latter usage in the right context. Formal logic and "natural" reasoning (and "natural" propositions) are not something that have a perfect one-to-one-correspondence. What takes priority is a matter that philosophers differ over. Logic took off from our "natural" reasoning in practice. Some of that is easy to capture in a formal structure, some of that is not easy to capture. I believe (pace Bertrand Russell) theory should be secondary to natural practices as a rule. How to think about conditionals is a complex subject, e.g., see "A Philosophical Guide to Conditionals" by Jonathan Bennett. This I discovered through philosopher David Papineau, who also has commented on the differences between the ordinary language version and the mathematical version of the if-then.

No. I don’t think directly. It’s a very interesting thought, though! Basically, without going too much on a tangent here, sometimes a certain metaphysics is being "read into" logic. Perhaps contemporary logic more easily accommodates a position that wants not to think about cause-and-effect relationships a la David Hume. See this blog article by Dr. Edward Feser: edwardfeser.blogspot.com/2021/07/the-metaphysical-presuppositions-of.html

You're welcome. I'm glad the video helped. And thank you for watching! :)

Good comment. I agree. However, there is a proof concerning (-1)(-1) in the book.

To error is human. You're right! Thank you. Sorry that I missed that.