|•||Using quantifiers in reasoning.|
|•||Solving categorical syllogisms with circle diagrams.|
|•||Solving categorical syllogisms with verbal rules.|
|•||Understanding the difference between truth and validity.|
|•||Recognizing when syllogisms are being used to change attitudes.|
|•||Using linear diagrams to solve linear syllogisms.|
|•||Watching for marked adjectives.|
|•||Using the principles of linear orderings as an aid to clear communication.|
|•||Reasoning with "if, then" statements.|
|•||Using tree diagrams with "if, then" statements.|
|•||Avoiding the fallacies of confirming the consequent and denying the antecedent.|
|•||Using circles with either/or statements.|
|•||Examining reasoning in everyday contexts for missing quantifiers.|
4. Have you reached your goal? This is an accuracy check on your work. When determining valid conclusions from categorical syllogisms, did you get the same answer with both the rules for syllogisms and the circle diagrams? Did you consider all combinations of representations when drawing your diagrams? Does your answer make sense?
1. Deductive reasoning (the type of reasoning considered in this chapter) is the use of premises or statements that we accept as true to derive valid conclusions.
2. People don't approach reasoning problems according to the laws of formal logic. Instead of determining whether a conclusion logically follows from the premises as they are stated, there is a tendency to alter the premises according to one's own beliefs and then decide whether a conclusion follows from the altered statements.
3. Human reasoning is often biased by beliefs about emotional issues.
4. People often confuse truth with validity. Validity refers to the form of an argument and is unrelated to content. If a conclusion necessarily follows from the premises, then it is valid. The topic of truth and believability of premises is addressed in the next chapter.
5. In linear orderings, we use premises to establish conclusions about ordered relationships. A good strategy for solving linear orderings is to utilize a spatial representation with the items arranged in an ordered manner.
6. In "if, then" statements a conditional relationship is established. As in syllogisms and linear orderings, the premises that are given are used to determine valid conclusions.
7. "If" is frequently interpreted as "if and only if" in "if, then" statements. Although this conversion is an error according to the rules of formal logic, sometimes it is justified by the context in which it is embedded.
8. Confirmation bias is the predilection or tendency to seek and utilize information that supports or confirms the hypothesis or premise that is being considered. The four-card selection task is a demonstration of this robust bias.
9. Quantitative syllogisms indicate which terms belong in the categories that are specified. Statements in syllogisms can take one of four different moods: universal affirmative, particular affirmative, universal negative, and particular negative.