Lecture 9

Question 1

deductive reasoning and categorical logic

Answer 1

• a branch of logic focusing on the inclusion and exclusion of classes as expressd in categorical claims
• track back to aristotle
• understanding everyday language and analyzing logical structure
• deductive arguments depend on word meanings for validity
• words like “all” “and” “or” “if then” cary the burden of validity
  - to narrow down to specific conclusions
• valid deductive arguments prve their conclusions beyond possible doubt
• categorical logic focuses on relations of inclusion and exclusion among classes
• studying categorical and truth-functional logical helps improve thinking precision

use categorical (deductive) logic to fil in venn diagram

general —> specific

Question 2

categorical claims

Answer 2

A-claims: all S are P (universal affirmative)

E-claims: no S and P (universal ngative)

I-claims: some S and P (particular affirmative)

O-claims: some S are not P (particular negative)

Question 3

tranlating claims into standard form

Answer 3

• process of turning ordinary language into categoical claims
• importance of precision in terms: using noun phrases for clarity
• addressing “only”: how to correctly translate claims involving this term
• examples: precise language

Question 4

the square of opposition

Answer 4

make an argument with opposition

• contraries:
  - can’t both be true at the same time
  - can both be false
  - example: “all dogs are pets” adn “no dogs are pets” —> 1 true, 1 false
• subcontraries:
  - can’t both be false at the same time
  - can both be true
  - example: “some dogs are pets” and “some dogs are not pets”
• contradictories:
  - always have opposie truth values
  - if one is true, the other must be false, and vice versa
  - examples: “all dogs are pets” and “some dogs are not pets”; “no dogs are pets” and “some dogs are pets”

Question 5

categorical syllogisms

Answer 5

definition: a deductive argument consisting of two premises and a conclusion, each in standard form

components: major term, minor term, middle term

1. major term: (general)
   - appears in the predicate of the conclusion
   - represents the larger category or group being discussed
   - deductive
2. minor term: (specific)
   - appears in the subject of the conclusion
   - represents a specific instance or subset of the major term
3. midle term: (repeats —> links both premises together)
   - appears in both premises but not in the conclusion
   - serves as a link connecting the major and minor terms

example:
premise 1: all dogs are animals
premise 2: some pets are dogs
conclusion: some pets are animals

• major term (animals):
  - appears in the predicate of the conclusion “ some pets are animals”
  - represents the larger category being discussed, which is “animals”
• minor terms (pets):
  - appears in the subject of the conclusion “some pets are animals”
  - represents a specific instance or subset of the major term “animals” indicating a more specific group within the larger category
• middle term (dogs):
  - appears in both premises but not in the conclusion: “all dogs are animals” and “some pets are dogs”
  - serves as the link between “pets” (minor term) and “animals” (major term), showing the relationship that some mebers of the minor category “pets” fall under the major category “animals” through their identification as “dogs”

Question 6

rules method for testing validity

Answer 6

rule 1:
- negative premises vs. conclusion:
- an argument must have the same number of negative claims in its premises as in its conclusion for validity. specifically, no valid syllogism has two negative premises

invalid example:
- premise 1: no cats are dogs
- premise 2: some pets are not dogs
- conclusion: some pets are cats

exaplanation: this example violates Rule 1 because both premises are negative, but the conclusion is affirmative. the mismatch is negativity makes the syllogism invalid

Rule 2:
- distribution of the middle term: at least one premise must distribute the middle term to ensure a valid connection between the major and minor terms. if the middle term is not distributed in at least one premise, the argument cannot validly connect the major and minor terms

invalid example:
- premise 1: all dgs are mammals (dogs = middle term, mammals = major term)
- premise 2: some pets are mammals (pets = minor term, mammals = major term)
- conclusion: some pets are dogs

explanation: this example violates Rule 1 becausethe middle term “mammals” is not distributed in the second premise. without the middle term being distributed in at least one premise, there’s no valid connection between “pets” and “dogs”, rendering the argument invalid

Rule 3:
- distribution in conclusion:
- any term distributed in the conclusion must also be distributed in its respective premise. this ensures that the conclusion does not make broader claims than supported by the premises

invalid example:
- premise 1: all flowers are plants (flowers = minor term, plants = major term)
- premise 2: some roses are flowers (roses = undistributed minor term, flowers = middle term)
- conclusion: all roses are plants

explanation:
- this example violates Rule 3 because the minor term “rses” is not distributed in the premises but is distributed in the conclusion. the premise “some roses are flowers” des not distribute “rose” yet the conclusion makes a universal claim about all “roses” being “plants”. this overextension in the conclusion without support from the premises reslts in an invalid argument

Question 7

categorize the relationship between ‘sportsmanship/sportspersonship’ and ‘fair play’ defend your statement

Answer 7

fair play is just one part of sportsmanship, however all sportsmanship persons use fair play

categorical logic with venn diagram
- define terms
- example
- make argument