PHIL20020 Logic

Academic Year 2022/2023

Logic is the study of arguments and formal logic is the study of formal features of arguments. We will look at the formal elements that distinguish good arguments from bad arguments.

Consider the argument:
If statues are constituted of lumps of clay, then two objects can be in the same place at the same time.
Statues aren’t constituted by lumps of clay.
Therefore, two objects cannot be in the same place at the same time.

It’s a bad argument. Its reasoning is flawed. But what is going wrong in this argument? The argument has a bad form. Moreover, any argument of the same form is equally bad.

In this course, you will see why arguments such as the one above are formally flawed, and you will learn a language that will help you uncover the logical form of arguments.
You will first see how to translate ordinary English sentences into the language of propositional logic. With the help of truth tables, we will determine whether a complex argument is formally good or bad.
Once you have familiarized yourself with the language of propositional logic, we will extend the language by a few symbols and rules. This extended language is called the language of quantificational logic. We will translate ordinary English sentences into the language of quantificational logic. This way, it will be easier to spot formally flawed arguments.

Deductive arguments are very common in philosophy where a priori reasoning plays a significant role. As philosophers, we often want our conclusions to strictly follow from our premises. We don’t want our conclusions to be just very likely to be true - we want them to be necessarily true. But no conclusion can strictly follow from its premises unless the argument has a good form (or can be easily turned into an argument that has a good form). This is why the study of formal logic is strongly recommended to philosophy students.

Logical symbols are also frequently used in articles and books in analytic philosophy, especially in the theoretical subdisciplines, such as metaphysics, philosophy of language, philosophy of mind, or epistemology. You might read ~∃x (x=a) in an article on the ontology of numbers or the semantics of fictional names. This course will show you how to read and interpret such symbols.

This module is skills-focused. What that means is that learning mainly happens through practice.
Although formal logic is mathematical in its appearance, it is more like a very simple artificial language to learn, with a handful of symbols and even fewer syntactic rules. No special aptitude for math is necessary for this course. But as with any new language, a willingness to practise is essential to learn it.