The way you prove something in this system is you start with your premises and you end with your conclusion. Read. That’s pretty much definitional of this conception of formal logic. Category: Overview | Length: 816 pages | Published: 2002. It’s interesting. Here are the best books on formal logic in no particular order. This book sets logic more in the context of the humanities than mathematics. This collection of newly commissioned essays by international contributors offers a representative overview of the most important developments in contemporary philosophical logic. The first one is called Logic Primer. Philosophy of Logic Its scrupulous attention to detail and precision in exposition and explanation is matched by the greatest accuracy in all associated detail. These properties of logical truth, of validity, occur in every language that can be used to speak truths or falsehoods. When trying to prove that some conclusion follows from certain premises—if you accept these premises, then you must accept this conclusion—that’s equivalent (nice logician’s term there) to saying that if you accept these premises and deny this conclusion, you’re committed to a contradiction. One of the interesting things about teaching logic at a university is that no logic teacher at a university is happy with anyone else’s textbook. So if it’s true, it’s false. The Daily Idea aims to make learning about philosophy as easy as possible by bringing together the best philosophy resources from across the internet. He goes on to say, “[Wittgenstein] is concerned with the conditions for accurate Symbolism [Russell’s using ‘Symbolism’ here to mean symbolic representation of the world] i.e. Now, I’m quite lazy, and I didn’t. The accompanying technological resources offered through MindTap, a highly robust online platform, include self-grading interactive exercises, a new digital activity that allows you to apply the skills you learn to a real-world problem, and videos to reinforce what you learn in the book and hear in class. It’s not both and it’s not neither. It’s less about which statements are true than how to keep to the truth once you’ve got some. But how does it work and what are its limitations? Maybe the context given by Ray Monk’s biography would be useful, and also culturally explain why he wrote it in the style that he did, which is aphoristic. Follow The Daily Idea on Facebook and Twitter for updates. In natural languages we let meaning develop and emerge and then dictionaries try to capture some of that and we discover how rich and complex it is, and so on. So let’s take those bits of the language where we’re concerned with truth and falsity and the relationships between truths, and see if we can make those properties explicit. With the liar paradox, the problem is if it’s true it’s false and if it’s false it’s true, and that looks like an unacceptable conclusion, because we can’t allow that it’s both true and false. For me that’s the fascination of the book, but I should warn that there are very different interpretations of it around. You’re going to have to say, ‘Some statements can fail to be either true or false.’ Once you have done that, you will have to make other choices in your logic to keep it consistent. Read. In fact, I was given it by a maths teacher while I was at school, who thought I was getting bored in maths lessons. Then what formal logic does is allow us to say, ‘Here’s another tool. You might think that means it feels very natural when you use it. You don’t need to know formal logic to grasp this book. If you’re okay with basic algebra, it won’t be unfamiliar. It can also be immensely irritating for your partner. When will a formal language allow me to do something better or more easily than a natural language? Often when philosophers are asked this, they’ll either say it helps you reason better, or it helps you do science better, or something like that. And that’s it. If that’s not the case, it’s not false, so it must be true. “Effectively, formal logic is a very general form of algebra.”. And we can use them for some purposes. In that sense, yes, it’s still doing logic; it’s still going to be formal; it’s still going to have symbols; but it’s a much softer, gentler introduction, appealing to a different curiosity. Read We can say, ‘If John is taller than Peter, and Peter is taller than Fred, then John is taller than Fred.’ That’s an inference in natural language and when we start using formal logic we also want to use such inferences. Why do logicians want to study that? It’s important to note that there is no single best book on formal logic. Or it might be that the conclusion that we thought was unacceptable is something we just have to end up accepting and bite the bullet. The statement ‘either the moon orbits the earth, or the moon does not orbit the earth’ is true by virtue of logic alone. Of course, the law of contradiction only holds in some circumstances’? And personally I think you’re right, there are different logics. That can be very useful. So it looks like our statement has failed to say anything true or anything false. It’s called the liar paradox because of a variation in which the Cretan Epimenides says ‘All Cretans are liars.’ If what he says is true, then he’s a liar, and so what he says is false…. The question of, ‘Is this a correct or accurate translation/symbolization/formalization?’ isn’t important. All these technical tools are fascinating, and enjoyable to study for their own sake, but the driving question should be: what can I use this one for and what can I use that one for? Another (in)famous one is the paradox of the heap. They are more like computer programming languages, as you said earlier. Take the paradox of the heap. The best book for you will depend heavily on your preferred learning style and the amount of time/energy you’re willing to spend reading. From my point of view, it also forces a kind of precision on you as a thinker, because you can’t do it unless you’re extremely precise about what you mean by the terms that you’re using. But then we get 1.1.1, so this is going into an elucidation of 1.1, and so on. I’ve talked about validity and defined it as a logical property. So on this conception, what logicians do is create artificial languages with lots of explicit definitions and rules. I stuck to this book, though actually I changed it in lots of ways. Its simplest formulation is the statement, ‘This sentence is false.’ Now ask yourself, is that statement true or false? In contrast, Quine’s book is about when we construct a formal logic, when we create these formal languages, then we’re making philosophical decisions or choices about how we do it. It’s interesting you’re talking about truth, because that makes it sound a bit like epistemology—as in, how do we know that things are true? At one point in the history of astronomy, in order to explain some unusual features of the motions of Mercury, it was postulated that there was an unobserved planet which exerted a gravitational pull on Mercury. Throughout this discussion, it’s almost as if we’ve been talking about logics plural. We make all the meanings and the grammatical rules absolutely explicit. What is important is that we choose the correct linguistic tool for the job. Others might say it’s neither true nor false. 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