Logic and critical thinking

 

 

Course Description

This course is split into two components. The first aims to introduce students to practices of argumentation, critical analysis, and evaluation. Such skills in critical thinking are integral to the discipline of philosophy. They are also tremendously useful in other academic domains, in the workplace, and in everyday life. The course aims to help students to understand and develop the skills required for critical thinking, and to encourage them to explore the ways in which these skills can further the pursuit of both their academic and nonacademic projects. Topics covered may include: inductive and deductive reasoning, common fallacies, the use of rhetoric. The second component of this course introduces students to elementary propositional logic.

Learning Outcomes

On satisfying the requirements of this course students will have the knowledge and skills to:

  1. Critically analyse beliefs, including their own beliefs, to identify underlying assumptions and unforeseen consequences.
  2. Analyse others’ arguments – especially the arguments of philosophers – presented in both written and oral forms, and identify where they have committed informal fallacies and where their arguments are vulnerable to particular critical strategies identified in the course, such as counterexamples or questioning the use of a definite description.
  3. Analyse others’ arguments and identify where they have successfully used the strategies and techniques from the course.
  4. Formulate arguments that appropriately incorporate techniques from the course.
  5. Communicate these arguments clearly in both written and oral form, drawing where relevant on strategies for clear written and oral communication from the course.
  6.  Use elementary formal logic to represent arguments and determine whether they are deductively valid or invalid
  7. Reflect on their own set of strategies for philosophical analysis and argument, and identify the improvement and growth that has taken place during the course.
  • Course Schedule

 

  Lectures Tutorials Assessment
Week 1 a. Why Critical Thinking? no tutorial
b. Arguments, premises, conclusions.
Week 2 a. Inductive and deductive reasoning Critically examining beliefs (also possible to discuss ‘what is an argument?’ and habits of good communication.)
b. Positive Strategies/Argument Mapping 1
Week 3 a. Argument Mapping 2 Argument mapping 1 *short belief exercise due
b. Argument Mapping 3
Week 4 a. Fallacies of Relevance 1 Argument mapping 2 *argument mapping quiz in lecture
b. Argument mapping quiz + Fallacies of Relevance 2
Week 5 a. Fallacies of Presumption Fallacies of Relevance
b. Fallacies of Vagueness, Ambiguity and Probabilistic fallacies
Week 6 a. Positive Strategies Fallacies of Vagueness, Presumption, Ambiguity, Probabilistic fallacies
b. Rhetoric, Persuasion, Emotion
Week 7 a. Overview of elementary logic Positive Strategies, Rhetoric, Emotion, Persuasion *critical analysis of an argument due
b. Connectives & truth-tables
Week 8 a. Conditional The second part of the course will involve working through chapters of Brian Garrett’s textbook on elementary logic. In tutorials we will work through logic exercises and discuss proof strategies. *short written argument due
b. Conjunction
Week 9 a.
b. Conditional proof
Week 10 a. *exam in lecture
b. First exam – 55 minutes
Week 11 a. Negation
b. Disjunction
Week 12 a. Derived rules
b. Truth-trees
Week 13 a. Review and reflections *exam in lecture
b. Second exam – 55 minutes

 

 

 2. Proposed Assessment Items

  • 1. Tutorial attendance and participation (whole course) – 10%
  • 2. Short belief exercise (500 words) – 10%
  • 3. In-lecture quiz – 10%
  • 4. Short argument (500 words) – 10%
  • 5. Argument analysis (750 words) – 20%
  • 6. Exam 1 (for Part 2: intro logic) – 20%
  • 7. Exam 2 (for Part 2: intro logic) – 20%

 

Assessment Item Details

Assessment Item 1: Tutorial attendance and participation

Weighting: 10%

Learning Outcomes: 1, 2, 3, 4, 5b, 6

During tutorials you will work through practice exercises, discuss ideas from the course with your peers, and have the opportunity to ask your tutor questions about the material covered in lectures and readings.  You will find that attending tutorials is a great way to improve your assessment outcomes, because it gives you a chance to practice the sorts of activities you need to do for the assessment, and to receive feedback on your efforts.  There will also be opportunities to discuss the assigned readings, and to share your own observations and discoveries with other students. To receive any of the possible marks, students must attend a minimum of 10 tutorials (out of 12). Half of the marks for each tutorial will be granted on the basis of the quality of students’ participation. Quality will judged both on the merit of the student’s contributions to the tutorial, and on the student’s willingness to listen to and consider the ideas of others, and to apply the principle of charity to other students’ arguments. The other half will be granted to students who complete tutorial tasks prior to the tutorial. These tasks will be initialed by your tutor at the beginning of the tutorial, and then returned to you.

Critical Thinking (first half of course):

 

Assessment item 2: “I believe….” Task

Weighting: 10%

Word Count: 500 words

Learning Outcomes: 1, 5, 7

For this task you choose one of the belief statements listed below and identify (1) underlying assumptions and (2) unforeseen consequences of holding that belief. Note that for this exercise you are not to provide an argument for or against the belief, but simply to analyze what holding this belief involves or commits you to. The idea is to choose a statement that you do in fact believe. You may contact me (kelvin.mcqueen@anu.edu.au) for approval of an alternative statement if you do not feel you can do the activity with one of the options below. We will have a go at a version of this activity in tutorials the week before it is due.

  1. That Australia should have a carbon tax.
  2. That Australia should not have a carbon tax.
  3. That there is a God.
  4. That there is not a God.
  5. That abortion is permissible.
  6. That abortion is impermissible.
  7. That all moral judgments are subjective, i.e. there are no moral absolutes.
  8. That at least some moral judgments are objective, i.e. there are some moral absolutes.

Assessment Item 3: Argument mapping quiz

Weighting: 10%

Duration: 30 minutes

Learning Outcomes: 1, 2, 5

This assessment item will be composed of multiple-choice, mapping and short answer questions aimed at helping students to clarify arguments by identifying conclusions, premises, objections, and suppressed premises and objections.

 

 

Assessment Item 4: Critical analysis task

Weighting: 20%

Word Count: 750

Learning Outcomes: 1, 2, 3, 5, 7

You will need to find a nontechnical newspaper or magazine editorial (or section of an editorial – no more than 250 words) to analyse. Include this editorial or excerpt at the beginning of your essay, using the remaining word count to respond to it. You should identify the premises and conclusion of the argument, identifying suppressed premises (if any). You should then identify and name any fallacies that you can find in the argument, with brief explanations for each one that you identify. You will also be expected to identify any of the positive strategies discussed in the course that you can find in it, with brief explanations for each. Finally, you should indicate whether or not the argument is sound in your opinion, or, if it is not possible to decide (for example because you cannot judge the truth of a key premise) you should indicate what further information would be required for you to decide.

Assessment Item 5: Short argument

Weighting: 10%

Word Count: 500

Learning Outcomes: 1, 4, 5, 7

For this assignment, you will take the belief claim that you analysed in the first assignment and write an argument against it. So, if you analysed the statement “That there is a God” in the first assignment, you will be arguing in this assignment that there is not a God. One reason for this is to help you occupy other points of view than your own. Completing the earlier assignment should have helped you discover ways in which the claim is vulnerable (for example because one of its underlying assumptions is, or because it has hard-to-swallow consequences).

 

Elementary Logic (second half of course)

 

Assessment Item 6:  Exam 1

Weighting: 20%

Duration: 55 minutes

Learning Outcome: 6

Assessment Item 7:  Exam 2

Weighting: 20%

Duration: 55 minutes

Learning Outcome: 6

  • Prescribed readings

Readings and resources for the first part of the course (on critical thinking) will be posted to the Wattle site. The readings for the first part of the course are optional, but will often be quite helpful. The second part of the course (on elementary logic) will involve working through chapters from Brian Garrett’s textbook Elementary Logic. You must read these chapters; they are not optional. Further information about the textbook will be provided later in the semester.

 

Week 1 optional reading:

Nussbaum, Martha.  “Socratic Pedagogy: The Importance of Argument” in Not for Profit: Why Democracy Needs the Humanities, Princeton University Press, 2010, pp. 47-77.

 

Tutorial 1 (Week 2): Critically Examining Beliefs

Task: Choose one of the following positions and identify the assumptions and consequences of holding it: “Australia should seek to limit its immigrant population” or “Australia should not seek to limit its immigrant population”.

Optional Readings:

Hughs, Lavery and Doran.  “Deductive Reasoning” in Critical Thinking: An Introduction to the Basic Skills, 6th edition, Broadview Press, 2010, pp. 185-202.

Hughs, Lavery and Doran.  “Inductive Reasoning” in Critical Thinking: An Introduction to the Basic Skills, 6th edition, Broadview Press, 2010, pp. 203-223.

Tutorial 2 (Week 3): Argument Mapping 1

Task: A brief passage will be posted online. Map this argument.

Optional Readings: Hughs, Lavery and Doran.  “Strategies for Assessing Arguments” in Critical Thinking: An Introduction to the Basic Skills, 6th edition, Broadview Press, 2010, pp. 113-119.

Tutorial 3 (Week 4): Argument Mapping 2

Task: A brief passage will be posted online. Map this argument.

Optional Readings: None.

Tutorial 4 (Week 5): Fallacies of Relevance

Task: Bring to the tute an example of one of the discussed Fallacies of Relevance in the popular media (newspaper, magazine, blog, etc). Come prepared to discuss your example.

Optional Readings:

Copi, Irving M.  Extracts from chapter 3, “Informal Fallacies”, in Introduction to Logic 10th Edition, Macmillan, 1998.

Tutorial 5 (Week 6): Fallacies of Ambiguity, Vagueness, Presumption, and Probabilistic Fallacies

Task: Bring to the tute an example of one of the fallacies discussed in the previous week’s lectures. The example should be from the popular media (newspaper, magazine, blog, etc). Come prepared to discuss your example.

Optional Readings:

Copi, Irving M.  Extracts from chapter 3, “Informal Fallacies”, in Introduction to Logic 10th Edition, Macmillan, 1998, pp. 110-117.

Tutorial 6 (Week 7): Emotion, Rhetoric, the Place of Critical Thinking

Task: When our emotions and our critical reflection come into conflict, should we ever act on our emotion? If yes, give an example and defend with reasons. If no, say why not. Come to the tute prepared to discuss your answers. (No more than one paragraph, please!)

Optional Readings:

Small, D., Loewenstein, G., and Slovic, P. (2007) “Sympathy and Callousness: The impact of deliberative thought on donations to identifiable and statistical victims” Organizational Behavior and Human Decision Processes 102, p. 143-153.

Martha Nussbaum (2001) Upheavals of Thought: The Intelligence of Emotions, Cambridge: Cambridge University Press, Chapter 1.

 

Tutorials 7 – 12 (Week 8 – 13): Elementary Logic

The second half of PHIL1005 involves working through chapters of Brian Garrett’s textbook Elementary Logic. You must read them; they are not optional.

Below you will find information about the prescribed weekly readings and tutorial tasks, as well as the slides for the lectures. You should do the readings before each lecture. In addition to the tutorial tasks, you should try to complete all of the exercises at the end of every chapter. If you want to do well in formal logic, then you must practise doing it.

Week 7 – Elementary Logic

Lecture 1: Overview

Read chapter 1 of Garrett’s Elementary Logic.

Lecture 2: Logical connectives and truth-tables

Read chapter 2 of Garrett’s Elementary Logic.

Additional resources

The Critical Thinking Web (CTW) website has some useful tutorials with exercises.

(Note: CTW uses brackets in a slightly different way than we do. For example, we would write the conjunction A&B without brackets. But CTW would write it with brackets, like this: (A&B). As long as you keep this slight difference of notation in mind, the CTW website is very useful.)

– Symbolic representation: http://philosophy.hku.hk/think/sl/formal1.php

– Connectives: http://philosophy.hku.hk/think/sl/connectives.php

– Truth-tables: http://philosophy.hku.hk/think/sl/complex.php

There is an excellent online generator of random truth-table problems on the California State University website. You can do the exercises online and the program tells you whether your answers are right or wrong. (Note: the program uses slightly different symbolism to ours. You will often encounter different symbolism when looking through different textbooks and websites. You can find a list of the most common symbols in the pdf document below called “Other common symbols“.)

– Random truth-table problem generator: http://www.math.csusb.edu/notes/quizzes/tablequiz/tablepractice.html

 

Tutorial 6:

This tutorial is not about formal logic; see above for information about your tutorial task

 

Week 8 – Elementary Logic

Lecture 3: Conditional

Read chapter 3 of Garrett’s Elementary Logic.

Additional resources

It is perfectly natural to feel puzzled by the material conditional interpretation of the English indicative conditional. The material conditional is discussed on Critical Thinking Web.

– CTW on the material conditional: http://philosophy.hku.hk/think/sl/ifthen.php

Another useful and gentle discussion of the material conditional may be found on Peter Suber’s website.

– Suber on the material conditional: http://www.earlham.edu/~peters/courses/log/mat-imp.htm

A more sophisticated discussion, with lots of references for further reading, may be found in the Stanford Encyclopedia of Philosophy entry “Conditionals”. Section 2 contains the most relevant discussion.

– SEP entry: http://plato.stanford.edu/entries/conditionals/

Lecture 4: Conjunction

Read chapter 4 of Garrett’s Elementary Logic.

Tutorial 7: Key concepts, logical connectives, symbolic representation, and truth-tables.

Look at the English sentence that has been posted online. Translate the sentence into a formula of our logical language. Determine which connective is the main connective of the formula. Write out the truth-table for the formula. Determine whether the formula is contingent, a tautology, or a contradiction. Reality corresponds to one of the rows on the formula’ truth-table. Find the row and determine whether or not the formula is actually true.

 

Week 9 – Elementary Logic

Lecture 5: Conditional proof

Read chapter 5 of Garrett’s Elementary Logic.

Tutorial 8: Conditional and conjunction

Look at the deductively valid English argument that has been posted online. Translate the English argument into a sequent. Using the rules àO, &O, and &I, construct a natural deduction proof which shows that the argument is valid. Do you think the argument is sound? Briefly explain your answer.

Week 10 – Elementary Logic

Lecture 6: Examination 1

This examination will cover material from Chapters 1 – 5

Tutorial 9: Conditional proof

Look at the deductively valid English argument that has been posted online. Translate the English argument into a sequent. Construct a natural deduction proof which shows that the argument is valid. You should use the rule àI in your proof.

Week 11 – Elementary Logic

Lecture 7: Negation

Read chapter 7 of Garrett’s Elementary Logic.

Lecture 8: Disjunction and biconditional

Read chapters 8 and 9 of Garrett’s Elementary Logic.

Tutorial 10: Negation

Look at the deductively valid English argument that has been posted online. Translate the English argument into a sequent. Construct a natural deduction proof which shows that the argument is valid.

Week 12 – Elementary Logic

Lecture 9: Logical truths and derived rules

Read chapter 11 of Garrett’s Elementary Logic.

Lecture 10: Testing for validity and invalidity with truth-tables and truth-trees

Read chapter 12 of Garrett’s Elementary Logic.

Tutorial 11: Disjunction, biconditional, and derived rules

Look at the deductively valid English argument that has been posted online. Translate the English argument into a sequent. Using only primitive inference rules (i.e. without using any derived rules) construct a natural deduction proof which shows that the argument is valid.

 

 Week 13 – Elementary Logic

Lecture 11: Review and reflections

Read chapter 13 of Garrett’s Elementary Logic

Lecture 12: Examination 2

This examination will cover material from the whole second half of the course

Tutorial 11: Testing for validity and invalidity with truth-tables and truth-trees

Look at the deductively valid English argument that has been posted online. Translate the English argument into a sequent. Using derived rules where possible, construct a natural deduction proof which shows that the argument is valid. Construct a truth-tree which also shows that the argument is valid.

 

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