PHIL102: Introduction to Critical Thinking and Logic

7a. Illustrate several types of problems and explain how to understand and problem-solve for each

• What are several types of problems and how do we begin to solve them?
• What are some problem solving strategies?

When we have a real problem to solve – there is evidence of a problem, as opposed to mere speculation – organizing our thinking about it is the first step toward solving it. First, let's consider the difference between a proposed problem versus a real problem. The 2020 U.S. Presidential Election proceeded according to the practices of previous elections. There were no significant abnormalities that would suggest problems such as election fraud. Officials from both parties oversaw the process and conducted the usual quality control checks. Nevertheless, then-president Donald J. Trump claimed there were numerous problems. Even after he was presented with myriad evidence to the contrary, Trump and his supporters insisted that the U.S. election system is rife with corruption and other problems. The question before citizens is one of evidence. If we say we have a problem, we need evidence of such.

One of the first steps toward problem solving is to ascertain the type of problem we face. To do so, we ask empirical questions, conceptual questions, and evaluative questions:

• Empirical questions are questions about the facts; typically, these questions are answered by observation or experiment (Are COVID-vaccinated individuals more or less likely than non-vaccinated individuals to contract the Delta variant?)
• Conceptual questions are questions about the meanings of words and the reasoning involved in arriving at an answer without observation and experimentation (What is justice?)
• Evaluative questions are questions about moral norms and judgments (Is this political system just?)

Sometimes, combinations of these question types are enlisted in clarifying the problem (Are poor people more likely to contract COVID than non-poor people?).

Mathematician George Pólya's 1971 book, How to Solve It, lays out a four-step process for problem solving:

1. Understand the nature of the problem (look at the classifying questions above).
2. Draw up a plan: The systematic approach to solving a problem includes a plan for action involving time, resources, and preparation.
3. Try out the plan: Monitoring the progress of the plan and recording errors and special considerations will help you understand the outcome.
4. Monitor the outcome: Results will inform next steps.
   

To review, see Classifying Problems and Solving Problems. 

 

7b. Use visualization tools to analyze problems

• What are some visualization tools used to analyze problems?

There are several visualization tools used to analyze problems.

• Flowcharts use shapes to a process or plan:

The meanings of some of the more common shapes are as follows:

The terminator symbol represents the starting or ending point of the system.

A box indicates some particular operation

This represents a printout, such as a document or report.

A diamond represents a decision or branching point. Lines coming out from the diamond indicates different possible situations, leading to different sub-processes.

It represents material or information entering or leaving the system. An input might be an order from a customer. An output can be a product to be delivered.

This symbol would contain a letter inside. It indicates that the flow continues on a matching symbol containing the same letter somewhere else on the page.

As above, except that the flow continues at the matching symbol on a different page.

Identifies a delay or bottleneck.

Lines represent the sequence and direction of a process.

For further information, please refer to:

• International Organization for Standardization (ISO), ISO 5807, Information processing – Documentation symbols and conventions; program and system flowcharts.
• American National Standard, ANSI X3.6-1970, Flowchart Symbols and their Usage in Information Processing.

• Decision trees represent possible consequences of a decision:
  

  
  

  
  

• Causal diagrams (see 6f)

To review, see Charts and Diagrams.

 

7c. Explain the principles of creative thinking and their implications

• What are some principles of creative thinking?
• What are some implications of creative thinking?

Creative thinking can be methodical, rather than haphazard (or inspirational). Developing creative skills generally follows these principles:

• Build new ideas from old elements: Ideas don't occur in a vacuum. They're typically innovations on and novel creations from existing ideas.
• Critically evaluate new ideas: Don't believe every idea is as good as every other.
• Seek connections between ideas: What may seem like disconnected ideas can actually work together to generate something novel or innovative.

Creative thinking is not simply for artistic endeavors. It works across subjects and problems. Many scientists, for example, actively engage these principles as part of their larger research projects.

To review, see Three Basic Principles of Creative Thinking. 

 

7d. Compare the methods for approaching problems creatively as a means to think creatively about real-world problems

• What are some methods for approaching problems creatively?

The principles outlined in the previous section can be followed in a stepwise fashion:

1. Conduct research, so you know what others are thinking and have done to solve the problem.
2. Explore connections between ideas, which likely involves studying otherwise disparate fields.
3. Give yourself time to "digest" what you've researched and studied, since intellectual development takes time, similarly to digesting food.
4. Apply the idea to a relevant problem, review the results, and follow-up, so you have some practical and actionable outcomes.

Some other methods offer additional specifics for problem solving:

• Create a feature list, which is a list of an object or process' features. Once generated, you can think of the features in isolation and in connection with the other features.
• Construct an analogy, which compares two objects or events, with the aim of drawing a conclusion about one on the basis of that comparison.
• Create a systematic search method of other possible solutions, which can help you narrow or broaden your thinking.
• Try a shift in perspective, which can help you see the problem and potential solution(s) in new ways.
• Take advantage of the numbers using group creativity, whose brainstorming, for example, can produce new ideas.

To review, see The Creativity Cycle and Creative Heuristics and Group Creativity.

 

Unit 7 Vocabulary

This vocabulary list includes the terms listed above that you will need to know to successfully complete the final exam.

• causal diagrams
  
• conceptual questions
• creative thinking principles
• decision trees
• empirical questions
• evaluative questions
• flowcharts
• problem-solving
• proposed problem
• real problem