PHL2140 Introducing Logic
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Handbook entry- a brief description of the subject can be found in the handbook entry. The handbook also provides information about the unit leader, the semester and mode in which the unit is available, the contact hours and the assessment requirements.
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MUSO/Blackboard site - there is a MUSO/Blackboard site for this unit where assessment tasks, lecture notes and other unit resources will be posted. Once enrolled, students taking this unit are advised to check MUSO/Blackboard regularly.
What is formal logic?
Formal logic is all about the idea of consequences – what follows from what. Given some information, logic tells you what other information must also be true. Formal logic provides both a theory of what follows from what and a set of useful techniques and methods for working out whether something follows from a given body of information or not. That’s what you’ll be learning about in this course.
An example
As an example, see if you can work out the answer to the following little puzzle. I’ll supply you with some information. To solve the puzzle, you have to think about what would follow from that information. Imagine that you have before you a hand of four ordinary playing cards, face down. I’m not going to tell you what the cards are, but I will tell you that only one of the following two statements about them is true:
(1) There is a king or an ace (or both) in the hand.
(2) There is an ace and a queen in the hand.
Here is the puzzle: supposing that the information I’ve just given you is true, is it possible that there is an ace and a queen in the hand? (I’m not asking if there actually is an ace and a queen in the hand. I’m just asking if that possibility is consistent with the information I’ve given you). Think about it for a minute before reading on.
The intuitively correct answer is ‘yes, it is possible’. If that’s the answer you gave, you’re in good company – that’s the answer most people give (even very very smart people). But it’s not the right answer. In fact, the information provided implies that it is impossible for statement (2) to be true, given that only one of the two statements is true. By taking this course, you’ll discover why that is.
This puzzle provides a good example of the fact that our intuitive judgments are often quite misleading. Modern psychology and cognitive science are revealing that human beings are susceptible to certain logical illusions, in much the same way that we are all susceptible to certain visual illusions. Sometimes things seem like they ought to follow from given information even when they don’t, just as one line sometimes looks longer than another line even when it isn’t. By studying formal logic, you’ll become more resistant to these pervasive and potentially dangerous logical illusions.
What you’ll learn about in this course
Long ago, the philosopher Leibniz dreamed of an artificial language in which problems and questions could be clearly and unambiguously stated and then actually answered by carrying out something like a mathematical calculation. It won’t surprise you to learn that we are a long, long way from achieving Leibniz’s philosophical dream. Nonetheless, Leibniz’s idea led directly to the invention of modern systems of logic that come about as close to achieving that dream as it now seems possible to get. (What’s more, these ideas were highly influential in the development of the modern computer. Not a bad result for a bit of philosophy).
In this course, you’ll be learning how to use a simple and powerful logical system that allows you to (a) represent information concisely and unambiguously and then (b) apply a set of simple rules that will tell you whether or not something else follows logically from that information.
We will also occasionally be taking a critical look at some of the philosophical assumptions that are built into this system of rules. That will give you a glimpse of some philosophically exciting alternatives to standard (or ‘classical’) logic.
You can think of these rules as a bit like a kind of abstract machine or calculating device – a tool for working out the commitments of your current beliefs and convictions. You plug in the information and the machine does most of the work for you, spitting out the answer at the end. That’s a very useful tool to have in your intellectual tool box.
Why should I bother?
The study of logic can extend your reasoning skills, help you to think and write with greater rigour and clarity, and so help in the countless areas where these are important skills to have. In short, studying logic works like a session at the gym: the difference is that it exercises and strengthens your intellectual muscles.
And knowing a little bit of logic is essential if you want to study philosophy. Philosophy is about analysing, demolishing and constructing arguments. Logic helps you understand the structure of arguments. It helps you to identify flaws and missing premises in arguments. It helps you clarify what you think and how to argue for it. It helps clarify the relationships between different philosophical theories and suggests places where there may be room for a new kind of theory.
Logic is also more directly relevant to many important philosophical problems. For example, many philosophers think that the logical representation of what we say and think is the key to understanding our metaphysical and ontological commitments – the key that is, to understanding what there is in the universe. It’s not that logic can solve all philosophical problems, but it can certainly sharpen your understanding of many of them!