2.1.3 The A E I O Statements
Given two sets, it is possible that every member of the first set is also a member of the second
set. It is also possible that none of the member of the first set is a member of the second set.
The third possibility is that th
The Venn Diagram for the E Statement
In the Venn Diagram for the E statement No bats are birds, the area is shaded. This means
that the area is empty. Therefore, all members of the set B (the set of bats) must be in the area
. But if they are in the area
In order to make obvious the similarities of structure shared by different syllogisms, we will
always present each of them in the same fashion. A categorical syllogism in standard form
always begins with the premises, major first and then mi
Form and Validity
This method of differentiating syllogisms is significant because the validity of a categorical
syllogism depends solely upon its logical form. Remember our earlier definition: an argument
is valid when, if its premises were true, then it
The modern interpretation offers a more efficient method of evaluating the validity of
categorical syllogisms. By combining the drawings of individual propositions, we can use
Venn diagrams to assess the validity of categorical syll
Now, on to the next level, at which we combine more than one categorical proposition to
fashion logical arguments. A categorical syllogism is an argument consisting of exactly three
categorical propositions (two premises and a conclusion) in which there a
Exercise 1.1 (Questions 1, 8, 11, & 14)
1.) What is critical thinking? The systematic evaluation or formulation of beliefs or
statements, by rational standards.
8.) What is a statement? An assertion that something is or is not the case.
11.) What is an ar
Exercise 2.1 (Questions 2, 8, & 10)
2.) Hindrances that arise because of how we think (psychological obstacles) and
those that occur because of what we think (philosophical obstacles).
8.) If you sense a rush of emotions when you deal with a particular is
Exercise 3.1 (Questions 1, 2, & 10)
1.) A deductive argument is intended to provide logically conclusive support for its
2.) An inductive argument is intended to provide probablenot conclusive
support for its conclusion.
10.). Deductively vali
Exercise 4.1 (Questions 1, 5, & 14)
1.) Background information is that huge collection of very well supported beliefs
that we all rely on to inform our actions and choices.
5.) An expert is someone who is more knowledgeable in a particular subject area
A set is a group or class of things that share certain properties in common. For example, the
set of ravens is a group of large birds that have black feathers and a croaking cry. Each of
such a bird is said to be a member of the set.