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.