Syllogisms Flashcards
Syllogisms
- Syllogisms have been used since Aristotle to establish truths or validate points in an orderly and reasoned matter.
- Formal argument that contains two premises and a conclusion that logically follows those premises.
4 Main types of syllogisms
- conditional
- categorical
- disjunctive
- conjunctive
Conditional Syllogisms
- If P then Q. (major premise)
– P. (minor premise)
– Therefore, Q. (conclusion)
- Also called an “if-then” argument
- Other types of conditional syllogisms are:
— “only-if” (P only if Q) It only rains if it is cloudy, it is raining, therefore it is cloudy
— Biconditional (P if and only if Q) arguments
—— It only rains if its cloudy and only if I don’t have an umbrella, it is raining, therefore it is cloudy and I don’t have an umbrella
Categorical Syllogism
- With a valid syllogism, the major premise makes a general statement, beginning with an inclusive term such as “all, every or any.”
- The minor premise makes a statement about a specific instance of P, and the conclusion follows logically from the two premises.
- Each term (P,Q,R) can occur only once in any premise, and each term must be used twice throughout the argument.
- All Ps are Qs. (major premise)
- R is a P. ( minor premise)
- Therefore, R is a Q (conclusion)
- All classes are hard. Anatomy is a class.
- Therefore, Anatomy is hard.
Disjunctive Syllogism
- Presents two alternatives in the major premise, separated by the word “or.”
- The minor premise makes a statement about one of the alternatives and the conclusion follows logically.
- We will go on a run or go to yoga class.
We went to yoga class.
Therefore, we did not go on a run. - Can either be exclusive or inclusive:
- Exclusive argument = “P or Q but not both” I’ll take cake or pie but not both
- Inclusive argument= allows both alternatives “P or Q or Both” I’ll take cake or pie or both.
Conjunctive Syllogisms
- States that two conclusions can co-occur
- P and Q (major premise)
- P. (minor premise)
- Therefore, Q. (conclusion)
- Can be used to explain the rules to a game:
- White beads move diagonally, and red beads move horizontally. The white bead moves diagonally. The red bead moves horizontally.
Real world applications
- Syllogistic reasoning is used in many academic, vocational and personal endeavors in any given person’s life.
- Individuals must be able to produce valid arguments and detect invalid ones.
Development of Syllogistic Reasoning
- Attention has been focused on the manner in which children and adolescents learn to understand valid and invalid forms of syllogisms.
- Studies have shown that syllogistic reasoning begins in early childhood and improves throughout the school-age and adolescent years and into adulthood.
- Despite the improvement with age, even adults sometimes make errors, drawing invalid conclusions with respect to modus pollens (affirming the consequent) and modus tollens (denying the antecedent)
Syllogistic Reasoning
- Syllogistic reasoning is related to:
– Internal factors
—— Cognitive and linguistic development
– External
—— Type of argument (ex. Categorical vs. conditional syllogism)
- Content dimensions
– Ex. Common objects vs. abstract symbols, object present vs. object absent)
- Presentation mode (ex. Written vs. conversational tasks)
Internal Factors
- Keating and Caramazza (1975) developed a study that examined factors of age, intelligence, and language ability.
— They aimed to measure understanding of conditional syllogisms in 4 subgroups (11 y/o boys with low intelligence, 11 y/o boys with high intelligence, 13 y/o boys with low intelligence, 13 y/o boys with high intelligence)
— Results showed that the 13 y/0 group performed higher than 11 y/0 group, as well as the 2 groups with high intelligence performed better than the 2 groups with low intelligence.
Research
- Sternberg (1980) examined changes in speed and accuracy in syllogistic reasoning during the school-age and adolescent years.
— The study tested students of ages 8 to 16 years.
— Results revealed that accuracy improved as age increased. Response latency was also found to steadily decline with each successive age group.
- Roberge and Flexer developed a study to determine if syllogistic reasoning was related to vocab level.
— Results concluded that the correlation was not significant, however other studies support this association. It’s noted that the possibility of the words contained in the syllogisms were too simple to reveal individual differences in vocabulary knowledge.
External Factors
- Researchers have compared the difficulty of valid and invalid syllogistic arguments. These studies have indicated that children, adolescents, and adults have greater difficulty understanding invalid arguments.
- Taplin et al. (1974) showed that even by late adolescence, valid and invalid syllogisms can be difficult to understand.
Additional Study Results
- Children demonstrate greater accuracy on problems for which they are able to generate more alternative conditions.
- Performance on all type of syllogisms improved in relation to age
- Modus ponens and Modus tollens problems were easier than AC (affirming consequence) and DA (denying antecedent) problems.
- Even young adults can be challenged by AC and DA arguments.
Tasks with concrete objects
Syllogisms are easier to solve when accompanied by concrete objects
Content Dimensions
- Concrete-familiar
— Common objects used in the problems in unimaginative ways
- Suggestive
— Common objects used in imaginative ways
- Abstract
— Letters, symbols, or nonsense words were used
Additional evidence
- Additional evidence of greater difficulty of conditional syllogisms compared to other types
- As a whole:
— Conjunctive syllogisms where easiest, followed by exclusive disjunctive
— Only-if conditional and biconditional were intermediate in difficulty
— Inclusive disjunctive and if-then conditional were most difficult
- Results also indicated that performance steadily improved with age, however even the oldest students did not approach mastery
- No developmental differences as a function of increasing age
Conclusions
- Syllogistic reasoning is present in early childhood and gradually improves during school-age and adolescent years.
- Performance improves into adulthood, but certain types of syllogisms may even challenge college students.
- Individuals of all ages are better able to detect/explain valid arguments than invalid ones that are marked by insufficient information or illogical connections between premises.
- Developmental gains in solving invalid syllogisms may result from age-related improvements in the efficiency with which alternative conditions can be retrieved from semantic memory and expanding knowledge
base - Syllogisms that express conjunctive, exclusive disjunctive, and categorical relationships are generally easier than those that express inclusive disjunctive and if-then conditional arguments.
- Mode of presentation has also been found to affect performance
—- Formal, written syllogisms are more difficult than those that occur in conversational contexts.
Assessments
- Several standardized tests assess verbal reasoning:
— Cornell Reasoning Tests
— Matrix Analogies Test
- Subtests of comprehensive assessments with verbal reasoning sections:
— The Woodcock Language Proficiency Battery-Revised
— The Illinois Test of Psycholinguistic Abilities- 3rd Edition
— Wechsler Intelligence Scale for Children- 4th Edition
— Differential Aptitude Test- 5th Edition
— Test of Problem Solving-2
Intervention
- Focus intervention on targeting verbal reasoning with analogies, syllogisms, and using language to work through logical problems.
- Persuasive writing contexts can be used to scaffold students’ verbal reasoning abilities.
Teaching Syllogisms
- Begin by explaining what a syllogism is.
- Explain that syllogisms have 3 parts:
— Major premise (generally, a universally accepted fact.)
— Minor premise (a more specific, related fact.)
— Conclusion (Necessary truth drawn about the minor premise in consideration of the major premise)
- Provide examples
— Major premise: All mammals are warm-blooded.
— Minor premise: A whale is a mammal.
— Conclusion: Whales are warm-blooded.
- Provide problems for the students to do.
