CT7 Classical Logic: Categorical Propositions
Lecture Slide
Introduction to Logic
principle of non-contradiction
a syllogism is a formalized appeal to the principle of non-contradiction
categorical
propositions
quality
affirmative proposition
negative proposition
quantity
universal propositions
particular propositions
distribution
a term is said to be distributed if the propositions makes an assertion about every member of the class denoted by the term
subject term
predicate term
modern square of opposition
immediate inferences
operations
conversion
switching subject and predicate term
E&I: same
A&O: undetermined
Two statements are said to be logically
equivalent statements when they necessarily have the same truth value.
(illicit conversion)
obversion
(1) changing the
quality (without changing the quantity), and
(2) replacing the predicate with its term
complement.
A&I&E&O: same
contraposition
two steps: (1) switching the subject and
predicate terms and (2) replacing the subject and predicate terms with their term
complements.
A&O: Same
E&I: undetermined
Two statements are said to be logically
equivalent statements when they necessarily have the same truth value (as we will see
???
same results as the modern square. Accordingly, the existential fallacy is committed from the Aristotelian standpoint when and only when contrary, subcontrary, and subalternation are used (in an oth- erwise correct way) to draw a conclusion from a premise about things that do not exist. All such inferences begin with a universal proposition, which has no existential import, and they conclude with a particular proposition, which has existential import.
Exercises
Exercise 1
For each of the following propositions, identify the letter it can be abbreviated with, the quantity and the quality; then indicate whether the predicate is particular (undistributed) or universal (distributed).
Some symphony orchestras are on the brink of bankruptcy.
All drunk drivers are a menace to their fellow road users.
Exercise 2
Draw Venn diagrams of the following propositions on the board:
Every human being is mortal.
Some people are annoying.
No student is well-rested.
Some test questions are not hard.
Use a Venn diagram to see whether these inferences are valid:
Some country doctors are altruistic healers.
Therefore, some country doctors are not altruistic healers.
No radio talk shows are reliable sources of information.
Therefore, some radio talk shows are unreliable sources of information.
All cocktails are dangerous mixtures.
Therefore, it is not the case that some cocktails are not dangerous mixtures.
Exercise 3,4,5
check logical equivalence for A,I,E&O propositions after they have been converted/obverted/contrapositioned
Exercise 6
Use the classical logical square to test whether the following inferences are valid:
A
All Swiss watches are true works of art. It is therefore not the case that no Swiss watches are true works of art.
B
Some viruses are structures that attack T cells. Therefore, some viruses are not structures that attack T cells.
C
It is not the case that all dogs bark.
Therefore, there are no dogs that bark.
H
If it is not the case that some cats are stupid
Then it is not the case that all cats are stupid.
G
All carps like bread.
Therefore, some carps like bread.
F
Some birds do not have wings.
Therefore, no birds have wings.
E
Some dinosaurs can fly.
Therefore, it is not the case that some dinosaurs cannot fly.
D
It is not the case that no student is stupid.
Therefore, all students are stupid.