Deductive logic related to the consistency of statements and beliefs and the validity of arguments.


I. Definition

The term "logic" is often used in many different ways.  It is sometimes understood broadly as the systematic study of the principles of good reasoning.  But sometimes "logic" is understood more narrowly as what we might call "deductive logic".  Roughly speaking, deductive logic is mainly about the consistency of statements and beliefs as well as the validity of arguments.

Deductive arguments are attempts to show that a conclusion necessarily follows from a set of premises.  A deductive argument is valid if the conclusion follows necessarily from the premises, i.e., if the conclusion must be true provided that the premises are true.  A deductive argument is sound if it is valid and its premises are true.  Deductive arguments are valid or invalid, sound or unsound, but are never considered true or false.  

Deductive reasoning is a method of gaining knowledge.  The following is an example of a deductive argument:

All people are mortal.
Socrates is a person.
Therefore, Socrates is mortal.

The first premise states that all objects classified as 'people' have the attribute 'mortal'.  The second premise states that 'Socrates' is classified as a man—a member of the set 'people'.  The conclusion states that 'Socrates' must be mortal because he inherits this attribute from his classification as a person.

 

II. Simplified example of basic logic

Question ID: 20700121100

You and your friends play a new card game.  One side of each card shows an integer number while the other side is either white or gray.  After playing for a while, one of your friends discovers that if a card shows an even number on one side, it will always be gray on the other side.  Your friend lays out four cards in front of you as shown. If you want to test whether the rule your friend discovered is true or not, which cards should you turn over (choose as few cards as possible)?

 

 

 

 

  1. 3 only
  2. 8 only
  3. 3 and white
  4. 3 and gray
  5. 8 and white
  6. 8 and gray
  7. all four cards

Answer: E

 

III. Importance of basic logic

1. The importance of basic logic in learning

Hempel (1965) proposed the deductive model of explanation.  He stated that the occurrence of any event E can be explained deductively from general laws and initial conditions (see Figure 1).

Given general causal laws and statements describing initial conditions as two premises of deduction, a statement describing the event to be explained (not the event itself) follows as a logical conclusion drawn from the given premises.

Park & Han (2002) claim that deductive reasoning can be a factor which can help students recognize cognitive conflict and resolve it.  They use deductive reasoning to help students to learn the direction of force acting on a moving object.  For example, they show these two premises to students:

Premise 1:  If an object is moving more and more slowly, then the net force acts on that object in the opposite direction to that of its motion.
Premise 2:  A ball which is thrown vertically upward is moving upward more and more slowly.

They then ask what conclusion can be drawn from these premises.  Their research shows that using deductive reasoning can help students change their preconceptions.

2. The importance of basic logic in everyday life

Deductive reasoning is a basic logic skill and is very useful in our daily life. We make many deductions from what we already know.  For example, say you receive a flower as Christmas gift.  You need to put it somewhere.  You know all plants need sunshine.  Your flower is plant.  The flower needs sunshine, so you put it beside the window.

 

IV. Research on basic logic

JJ Roberge. A study of children's abilities to reason with basic principles of deductive reasoning. American Educational Research Journal, 1970

TC O'Brien. Logical thinking in college students. Educational Studies in Mathematics, 1973

TC O'Brien. Logical thinking in adolescents. Educational Studies in Mathematics, 1972

Park, J. and Han, S. Using deductive reasoning to promote the change of students'conceptions about force and motion. International Journal of Science Education.2002

Dimitris K. Psillos; Odisseas Valassiadis; Peter F. W. Preece; Donald A. Bligh. Deductive and inductive modes of preservice physics teacher education.International Journal of Science Education, 1464-5289, Volume 6, Issue 2, 1984, Pages 179 – 183