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Questions and Answers
What does a Venn diagram of a syllogism need to demonstrate for the syllogism to be valid?
What does a Venn diagram of a syllogism need to demonstrate for the syllogism to be valid?
- It must include all terms in the premises.
- It must exclude the possibility of the conclusion being false. (correct)
- It must include a representation of the subject term.
- It must demonstrate at least one true premise.
In the claim 'The only people admitted are people over twenty-one', which term is introduced by the phrase 'the only'?
In the claim 'The only people admitted are people over twenty-one', which term is introduced by the phrase 'the only'?
- The subject term. (correct)
- The middle term.
- The predicate term.
- The minor term.
What type of syllogism involves reasoning from a general premise to a specific conclusion?
What type of syllogism involves reasoning from a general premise to a specific conclusion?
- Argument by elimination
- Hypothetical syllogism
- Categorical syllogism (correct)
- Argument from definition
When diagramming the argument 'All fish are swimmers. All bass are fish. All bass are swimmers', what area in the Venn diagram represents the conclusion 'All bass are swimmers'?
When diagramming the argument 'All fish are swimmers. All bass are fish. All bass are swimmers', what area in the Venn diagram represents the conclusion 'All bass are swimmers'?
How should claims about single individuals be treated in categorical logic?
How should claims about single individuals be treated in categorical logic?
In a group exercise focused on propositional logic, what is the primary task of each individual member?
In a group exercise focused on propositional logic, what is the primary task of each individual member?
Which argument type specifically utilizes mathematical reasoning?
Which argument type specifically utilizes mathematical reasoning?
What is the significance of translating claims into standard form in categorical logic?
What is the significance of translating claims into standard form in categorical logic?
What is the central focus of the group discussion exercise detailed in the content?
What is the central focus of the group discussion exercise detailed in the content?
What must be present in the Venn diagram to affirm that 'Some dogs are not brown' as a true statement?
What must be present in the Venn diagram to affirm that 'Some dogs are not brown' as a true statement?
What is required for two claims to be considered equivalent?
What is required for two claims to be considered equivalent?
How is each properly categorized argument evaluated in the group activity?
How is each properly categorized argument evaluated in the group activity?
Which term is represented in the left circle of a standard Venn diagram for syllogisms?
Which term is represented in the left circle of a standard Venn diagram for syllogisms?
What is an example of an argument based on mathematics?
What is an example of an argument based on mathematics?
Identify the structure of a standard-form categorical claim.
Identify the structure of a standard-form categorical claim.
Which of the following statements is a categorical claim?
Which of the following statements is a categorical claim?
What type of argument is presented when a conclusion is derived from definitions?
What type of argument is presented when a conclusion is derived from definitions?
In categorical logic, what is the term used for the claim structure that states 'No A are B'?
In categorical logic, what is the term used for the claim structure that states 'No A are B'?
Which of the following is NOT a valid term to use in a standard-form categorical claim?
Which of the following is NOT a valid term to use in a standard-form categorical claim?
What kind of reasoning does an argument based on statistics employ?
What kind of reasoning does an argument based on statistics employ?
Which option accurately describes the nature of categorical claims?
Which option accurately describes the nature of categorical claims?
What is a hypothetical syllogism primarily characterized by?
What is a hypothetical syllogism primarily characterized by?
Which pattern of deductive reasoning comprises a two-premise argument?
Which pattern of deductive reasoning comprises a two-premise argument?
In a hypothetical syllogism, which of the following best describes modus ponens?
In a hypothetical syllogism, which of the following best describes modus ponens?
Which argument relies on mathematical reasoning to draw conclusions?
Which argument relies on mathematical reasoning to draw conclusions?
What pattern of deductive reasoning is used when concluding an outcome from multiple conditional premises?
What pattern of deductive reasoning is used when concluding an outcome from multiple conditional premises?
Which common variety of hypothetical syllogisms asserts the consequent to reach a conclusion?
Which common variety of hypothetical syllogisms asserts the consequent to reach a conclusion?
What does a categorical syllogism primarily involve?
What does a categorical syllogism primarily involve?
Which argument is likely to be classified under the category of arguments from elimination?
Which argument is likely to be classified under the category of arguments from elimination?
What should be done to handle ambiguity when placing 'x' in a segmented area?
What should be done to handle ambiguity when placing 'x' in a segmented area?
Which of the following statements is true regarding syllogisms?
Which of the following statements is true regarding syllogisms?
In a syllogism, which premise should be diagrammed first when one is universal and the other is particular?
In a syllogism, which premise should be diagrammed first when one is universal and the other is particular?
What is a requirement for a term that is distributed in the conclusion of a syllogism?
What is a requirement for a term that is distributed in the conclusion of a syllogism?
Which claim distributes its subject term?
Which claim distributes its subject term?
How many negative claims must be present in the conclusion of a valid syllogism?
How many negative claims must be present in the conclusion of a valid syllogism?
Which claim does not distribute any terms?
Which claim does not distribute any terms?
What is necessary for at least one premise in a valid syllogism?
What is necessary for at least one premise in a valid syllogism?
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Study Notes
Module 3 Pt. 1: Common Patterns of Deductive Reasoning
- This module identifies common patterns in deductive and inductive reasoning
- By understanding these patterns, you build familiarity with necessary inferential relations (deductive) and probabilistic inferential relations (inductive)
Common Patterns of Deductive Reasoning
- This section explores 5 common patterns of deductive reasoning:
- Hypothetical Syllogism
- Categorical Syllogism
- Argument by Elimination
- Argument Based on Mathematics
- Argument from Definition
Hypothetical Syllogism
- A syllogism is a two-premise deductive argument
- In hypothetical syllogisms, one premise is a conditional statement (If A, then B)
- Example: "If it rains, the streets get wet. It rained."
- This leads to the conclusion: "So, the streets are wet."
- This pattern is known as Modus Ponens and it follows this structure:
- A conditional premise (If A, then B)
- A second premise asserting the antecedent (A) is true
- A conclusion asserting the consequent (B) is true
Other Common Hypothetical Syllogism Varieties
- Chain Argument: Three conditional statements linked together
- Modus Tollens (Denying the Consequent): If A, then B. Not B. Therefore, not A.
- Denying the Antecedent: If A, then B. Not A. Therefore, not necessarily B.
- Affirming the Consequent: If A, then B. B. Therefore, not necessarily A.
Argument Based on Mathematics
- Conclusions rely heavily on mathematical calculations or measurements (often combined with non-mathematical premises)
- Example: "Light travels at 186,000 miles per second. The sun is more than 93 million miles away from the Earth."
- This leads to the conclusion: "Therefore, it takes more than eight minutes for the sun’s light to reach the earth."
- Arguments based on mathematics can also be inductive, utilizing statistics or generalizations from samples
Argument from Definition
- The conclusion is presented as being "true by definition"
- It follows directly from the meaning of a keyword or phrase used in the argument
- Example: "Bachelors are unmarried men. Jose is an unmarried man. So, Jose is a bachelor."
Categorical Logic
- Logic based on relations of inclusion and exclusion among classes (or "categories") stated in categorical claims
- Categorical claims make statements about classes of things
- Standard-Form Categorical Claims:
- A (All): "All _________ are _________. (All Lasallians are Career-oriented persons.)"
- E (No): "No _________ are _________. (No Muslims are Christians.)"
- I (Some): "Some _______ are _________. (Some Christians are Filipinos.)"
- O (Some are not): "Some ______ are not _____. (Some critical thinkers are not philosophers.)"
Important Notes about Categorical Claims
- Terms: The words or phrases in the blanks are called "terms," with the first being the subject term and the second being the predicate term.
- Standard Form: Translation is crucial to apply the mechanism of Categorical Logic
Testing Syllogisms for Validity Using Venn Diagrams
- To test if a syllogism is valid, Venn Diagrams represent the premises and analyze the result.
- If the premises eliminate the possibility of the conclusion being false, the syllogism is valid.
- If the Venn Diagram represents the conclusion, the syllogism is valid.
- Each syllogism uses three terms, so a Venn diagram needs three circles (minor, major, and middle terms).
Rules Method for Testing Validity
- Based on two ideas:
- Affirmative and Negative Categorical Claims (A and I are affirmative, E and O are negative)
- Distribution: A term is distributed if the claim applies to EVERY member of that class, if not, it's undistributed
- A-claims distribute the subject term
- O-claims distribute the predicate term
- E-claims distribute both terms
- I-claims distribute neither term
Three Rules of the Syllogism
- For a syllogism to be valid, ALL of these conditions must be met:
- The number of negative claims in the premises must match the number of negative claims in the conclusion (no valid syllogism has two negative premises).
- At least one premise must distribute the middle term.
- Any term distributed in the conclusion must also be distributed in its premises.
Propositional Logic
- This topic will be explored in more detail in future discussions.
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