[PEC] Critical Thinking

Need for Critical Thinking

To motivate critical thinking and identify risks of ‘non critical thinking’

Developing Critical Thinking

What is critical thinking?

• Abilities to think clearly and rationally about what to do or what to believe
• Abilities to engage in reflective and independent thinking
  • Understand the logical connections between ideas
  • Identify, construct and evaluate arguments
  • Detect inconsistencies and common mistakes in reasoning
  • Solve problems systematically
  • Identify the relevance and importance of ideas
  • Reflect on the justification of one’s own beliefs and values
    Critical thinking is the foundation of Science and Democracy

Process

Analyze-> Evaluate-> Conclude

Rationality

• Rationality is the quality or state of being reasonable, based on facts or reason
• Rationality implies that one’s beliefs are aligned with one’s reasons to believe or one’s actions are congruent with one’s reasons for action

Logic and reasoning

• Logic is concerned with the principle of correct reasoning
  • How do we make conclusions? How do we justify decisions?
• We focus on principles that govern validity of arguments: whether certain conclusions follow from some given assumptions.

Assertions, arguments, premises

Assertions and Arguments

• Assertion is a statement: “Shakespeare wrote the play Hamlet”.
• A proposition is informational content of any statement or assertion, i.e. a statement that can be judged true or false.
• Argument offers a series of related statements to support an assertion - to give others good reasons to believe that the assertion is true rather than false. e.g.
  • Doctors help people
  • I want to help people
  • I should become a doctor

A strong proposition has five characteristics

It is NOT matters of verifiable fact or matters of taste

for example, Peter: “We have to get a train to Paris. It is the fastest way to get there.”
Tom: “No, it is fastest to fly from Birmingham.”

It makes an assertion or urges a course of action in a declarative sentence.

• “Should hotels allow dogs in the rooms?” NOT STRONG PROPOSITION
• “Hotels should allow dogs in the rooms.” STRONG PROPOSITION
• “Hotels should not allow dogs in the rooms.” STRONG PROPOSITION

It should not include words that reflect a position on the proposition, i.e. introduce bias.

• e.g. “The inadequate care of parks in the city must be improved”
• It is necessary to verify that “inadequate” care exists in order to have a proper debate. If the care is inadequate then there is no debate.
• The debate is about whether they are inadequate and, thus, further action is required, e.g. improved based on community funds.

It is un-ambiguous, i.e. clear about the idea it states. It should not allow for multiple interpretations.

• e.g. High-school students are given scholarship to study ‘data science’. All
  students with B average would qualify. That is put forward for discussion.
• The staff is asking what ‘B average’ means. B average in all subjects or only relevant
  subjects? For example, if a student may have A in French and C in mathematics.
  Would the student be eligible for a technical scholarship?

It must be singular. One cannot reasonably argue two ideas at once.

• e.g. The school should cover costs of internet access for students living off
  campus and allow online gaming on school computers.
• These two requests are independent and it should be separated.

Turning propositions into arguments

• Once an arguable proposition is created, we need to identify the minor propositions to support the argument
• A minor premise shows the sense of the major proposition - a reason to support the major proposition
• The minor premise itself maybe debatable, in which case one has to argue it individually
• In the context of debating, each minor premise is called an issue

Informal logic, valid and sound arguments

Deductive and Inductive Reasoning

• Deduction and induction used to be differentiated in terms of argument flow, from general to specific and vice-versa
• Deduction was seen as flowing from a general towards specific statements.

Deduction

• In a deductive argument, it is impossible for the premise to be true and the conclusion to be false.
• The conclusion follows necessarily from the premises and inferences.
  • for example All men are mortal
  • Socrates is a man
  • Therefore, Socrates is mortal

Induction

• Induction was seen as flow from particular facts to general statements
  • Socrates was Greek
  • Most Greeks eat fish
  • Socrates ate fish
• In an inductive argument the premises are supposed to support the conclusion so that if the premise are true, it is improbable that the conclusion would be false.
• Like the above example, Socrates ate fish is probably true.

Informal and formal logic

• Informal logic is often used to mean critical thinking
• Formal logic involves systems that are constructed to carry out proofs, where the languages and rules of reasoning are precisely and carefully defined.
• Studying basic formal logic can help improve critical thinking

Valid and invalid argument

• The argument is valid if the premises entail their conclusion, i.e. it is logically impossible for its premises to be true and the conclusion to be false.
  • Paul and John are skeptics
  • Paul and John are writers
  • So, some skeptics are writers
• Relationship between the premises and conclusion is implication or inference
• A valid argument may have false premises. In that case, the implication is valid but the argument is not sound.
  • All Protestants are dogmatists
  • All dogmatists are Italian
  • So, all Protestants are Italian
• Note, the premises are false. The structure of the argument is valid. The show argument is not sound.

Fallacies

Detail please have a look at slides.

Negation and Inference

“If A then B” is equivalent to “If NOT B then NOT A”
“If A then B” is not equivalent to “If NOT A then NOT B”