1. The Nature of Argument
In this unit we' learn how to recognize arguments and distinguish them from other sets of sentences, and from assertions, especially conditional assertions.
- Defining argument
- The principle of charity
- Personality types
- Asking for explanations
- Background: declarative sentences
- Truth values and truth conditions
- Simple and complex sentences
- Arguments as sets of sentences
2. Analysing Arguments
In this unit we' look at how to analyse arguments and set them out 'logic-book style'. This makes it much easier to see the structure of the argument (which in turn makes it much easier to evaluate the argument).
- Ambiguity: what it is and why it is important
- Types of ambiguity
- The importance of clarity
- Identifying premises and conclusions
- Setting out arguments logic-book style
- Making terms consistent
- Eliminating irrelevancies
- Explicating suppressed premises
- Suppressed premises
3. Deduction and Induction
This is the unit in which we learn how to distinguish deductive arguments from inductive arguments. Deduction and induction are two quite different types of argument. All arguments fall into one category or the other. The two types of argument are evaluated quite differently.
- Two types of 'following from'
- Logical and empirical possibility: epistemology and metaphysics
- Deductive arguments are good or bad
- Inductive arguments are strong or weak
- Conclusivity, monotonicity and certainty
- A priori versus a posteriori
- Induction and necessity of empirical experience and observation
- Distinguishing deductive arguments from inductive arguments
4. Induction, Popper and the Paradoxes of Confirmation
In this unit we will be stepping back from critical reasoning to consider the philosophy of critical reasoning. In particular we will be considering the nature of induction and some problems endemic to inductive reasoning.
- David Hume and the first problem of induction
- The principle of the uniformity of nature
- Justifying the PUN
- The rationality of induction
- Karl Popper and the rejection of induction
- A model of the scientific method
- Is induction less valuable than deduction?
- Concluding comments and questions
- First assignment
5. Types Of Induction
Having got to grips with the problems endemic to inductive reasoning we shall now consider the different types of inductive reasoning, and look at how to evaluate them.
- Inductive generalisations
- Evaluating inductive generalisations
- Causal generalisations
- Evaluating causal generalisations
- Abductive arguments
- Evaluating abductive arguments
- Analogies and evaluating analogies
- Arguments from authority and evaluating arguments from authority
6. Deduction, Validity And Truth
In this unit we will consider how to evaluate deductive arguments. We will start by reflecting on the notions of validity, entailment and truth. Then we wi'll look at the process by which all deductive arguments are evaluated.
- Validity, truth and soundness
- Validity and knowledge
- The paradoxes of entailment
- Evaluating deductive arguments
- Testing for consistency
- Testing for consistency with Venn diagrams
- Testing for consistency with semi-formalisation
- (In)consistency and (in)validity
7. The Rudiments, Purpose and Limits of Formalisation
In this unit and the next we shall be looking at the rudiments of formalisation. Why do logicians use symbols? How do they help? In unit seven we shall ourselves learn how to formalise simple arguments.
- The purpose of propositional logic
- The limits of propositional logic
- Constructing interpretations
- Sentence functors and truth functors
- Truth functor symbols
- Problems with ‘not’ and ‘~’
- Problems with ‘and’ and ‘&’
- Problems with ‘or’ and ‘∨’
- Problems with ‘If/then’ and ‘→’
- Problems with ‘iff’ and ‘↔’
- Expressing English sentences in truth functor symbols
8. The Rules of Propositional Logic
Having learned in the last unit how to formalize simple arguments we shall now learn how to apply a set of mechanical rules by which to test these formalized arguments.
- Testing semantic sequents
- Testing syntactic sequents
- Concluding comments and questions
- Second assignment
The last two units have been tough. This unit will be a bit of relaxation. In this unit we wi'll learn about fallacies. These are bad arguments that look like, and can easily be mistaken for, good arguments. You' will do some research of your own into particular types of fallacy.
- Formal fallacies
- Informal fallacies
- Reflections on the course so far
10. Analysing Complex Arguments
In this, our final unit, you wi'll be set the task of analyzing a complex argument. Half of you will analyse a complex inductive argument, the other half a complex deductive argument.
- Activity one: Analysing and evaluating arguments
- Activity two: Checking the work of other students
- Activity three: Self-assessment
- Activity four: The Glossary
- Activity five: Summing up your thoughts
- What next?
We strongly recommend that you try to find a little time each week to engage in the online conversations (at times that are convenient to you) as the forums are an integral, and very rewarding, part of the course and the online learning experience.