Categoral statements make statements about categories
“All cows are herbivores
“Some business people are cheaters”
There are four standard forms of categorical statements:
All S and P (All cats are carnivores)
No S are P. (No cats are carnivores)
Some S are P (Some cats are carnivores)
Some S are not P (Some cats are not carnivores)
Two types: Universal and Particular
Universal Examples: 1. All students are trouble markers. 2. No A-students are slackers.
1. Venn Diagram of 2 circles. Shade out the “All Students” without touching the overlap
2. Venn Diagram of 2 circles. Shade out the overlapping part
Particular Examples: 1. Some people are liars. 2. Some professors are not mean. (Negation)
1. Venn Diagram of 2 circles with an asterisk (*) in the overlap area
2. Venn Diagram of 2 circles with the asterisk is in the professor circle. Not in the mean circle.
A valid categorical syllogism is such that if its premises are true, then its conclusion must be true. We
can check the validity by using a venn diagram.
If, after representing the premises, the conclusion is already represented on the diagram, then the
argument is deductively valid.
NOTE: You only ever diagram the premises, you never ever diagram the conclusion
Example: All egomaniacs are warmongers. All dictators are egomaniacs. Therefore, all dictators are
Draw three circles that overlap (for dictators, warmongers, and egomaniacs)
Premise 1: Shade in the egomaniacs circle. Premise 2: shade in the dictator circle. The conclusion has
been represented and present from the two premises. It is a valid argument. Example: All NBA players are fine athletes
No professor is an NBA player
No professor is a fine athlete.
Premise 1: fill in the circle that is for professional basketball players.
Premise 2: fill in the space in the middle that combines basketball players and professors
It is not fully filled in so the argument is invalid. (There is a space in between professors and athletes)
Universal receives priority over particular when both forms are present Example:
Example: Some snakes are poisonous
Anything that is poisonous should be destroyed
Some snakes should be destroyed
Premise 2: fill in the circle of poisonous. Premise 1: asterisk in the area between snakes and poisonous
Conclusion: Since there is an asterisk in the period between snakes and destroyed (resulting from the
premise one) then it is a valid argument.
Example: All learners require extra attention
Some who require extra attention in school need to be in specialized classrooms
Some slow learners need to be in specialized classrooms
Premise 1: shade in the area for slow learners. Premise 2: Asterisk between extra attention in school and
specialized classrooms on the very line in the middle because we’re saying that some that need extra
attention are slow learners and may need specialized classrooms.
Conclusion: Indeterminate / Invalid Argument because the asterisk is on the line.
Example: All tortoises are terrestrial. Some turtles are not terrestrial. Some turtles are not tortoises.
Premise 1: shade in the circle that applies to tortoises. Put an asterisk in the turtles circle.
Conclusion: It is valid because there is an asterisk in the turtle section
Example: All tortoises are terrestrial. Some turtles are not tortoises. Some turtles are not terrestrial.
Premise 1: Shade in the circle that is tortoises. Put an asterisk in the turtle section on the line that
overlaps towards the overlapping section between turtles and terrestrial.
Conclusion: It is invalid because there is an asterisk on the line so it is invalid. Example: No spiders are insects. No insects are lizards. No spiders are lizards.
Shade in the cross section between spiders and insects on the venn diagr