(4) Deduction versus Induction

Deduction and induction are the two broad methods of reason in logic.  Deductive reasoning takes a “top-down” approach whereas inductive reasoning take a “bottom-up” approach.  Simply put, deduction is focused with confirming a theory whereas induction is focused with how a theory is developed.

Deductive reasoning starts with accepted theory (general explanation) and narrows down to specific observations of truth.  This method of reasoning is often used to confirm or contradict the underlying theory.  Deductive reasoning follows accepted truths (premises) and infers from those a necessary conclusion.  If the premises are true and rules of logic are followed, the conclusion holds true.  If the conclusion turns out to be false, one or more of the premises must be false.

Inductive reasoning starts with observing specific patterns and then developing a theory (general explanation) to explain the observations.  Because there are no accepted truths to build upon with inductive reasoning, arguments are considered strong or weak as opposed to valid or invalid and conclusions are not stated as necessary and certain but rather as probable.   The strength of the inductive argument centers around the value of provided evidence.

When seeking out what is true, it is best to employ both methods of reasoning.  This has been demonstrated over time with the advancement of scientific understanding.  An individual employs inductive reasoning to create a theory to explain observations or patterns.  Other individuals then work to disprove parts of the theory or its entirety using deductive reasoning.  Theories become accepted as truth if they are strong enough to withstand years of attempts at disproving its tenets.  It is noteworthy to recognize that accepting that a theory as true does not necessarily imply that the theory is true but rather that it is highly probable that the theory is true.

The following shows an example that demonstrates inductive reasoning versus deductive reasoning.

  1. Inductive Process
    1. An observation is made that all crows seem to be black.
    2. An attempt to is made to determine a pattern by observing the color of crows at multiple locations in the world.
    3. A generalization is made that ALL crows are black.  The argument can only strongly infer that all crows are black.  It does not and cannot prove this with certainty because all crows were not observed to confirm the black color.
  2. Deductive Process
    1. To disprove the generalization that ALL crows are black one only need find a single non-black crow.
    2. The theory (generalization) that ALL crows are black will continue to gain acceptance as long as continued searches fail to discover a single non-black crow.

(3) The Structure of a Logical Argument

A logical argument is much different than a situational argument such as when a parent confronts a child about not cleaning up his or her room.  There is no emotional language in a logical argument but rather it demonstrates a proof by using clear and concise language that follows a series of agreed upon statements of supporting truths.

The central parts of the logical argument are comprised of one or more premises and a conclusion.  Premises are series of statements which can be somewhat easily agreed upon.  These are brought together to give support for an ultimate proposition which is the conclusion of the argument.

In order to make one’s viewpoint pursuasive, it is often necessary to construct multiple supporting arguments.  As a demonstration of this, consider the following example in the form of a syllogism.

  • Premise: There is a volcano nearby that is getting ready to erupt
  • Premise: Erupting volcanoes kill everything close by
  • Conclusion: If we don’t evacuate the area soon we will die when the volcano erupts

In the previous example, the conclusion would hold true if the supporting premises are accepted as true.  However, it is likely that to gain acceptance of the first premise, it will be necessary to construct an additional supporting argment that proves that indeed a volcano is nearby and that it is likely to erupt.                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       .

(2) Dialectic Reasoning

Dialectic is an oscillation between opposing ideas within a dialogue.  It is a line of thinking that takes the form of argument and rebuttal to reach a better understanding of what is true.  The word and concept originates from the ancient Greek thinkers and is the basis for today’s use of logic when seeking out what is true.

The strength of the dialectic method of reasoning is built from a rational discussion that includes multiple opposing points of view.  Offering multiple propositions and counter propositions and then having them skillfully negated or confirmed, brings about resolutions of disagreements that lead reasonable participants closer to the truth.

Discussions involving singular points of view that have not been skillfully and rationally challenged often have fatal flaws which can lead to accepting false assertions.  Even a well constructed point of view, supporting a true assertion, benefits from the rigors of being challenged in that it contributes toward strengthening support for the assertions being made.

In the court of law where two skillful lawyers argue a case before a jury, it is not uncommon to be pursuaded of the guilt beyond reasonable doubt of an alleged defendant during the presentation of the prosecutor only later to be pursuaded by the defense that there is enough reasonable doubt to acquit the accused.  This exemplifies both the necessity of examining multiple points of view to develop a better understanding that more closely aligns with what is true as well as how much dialectic reasoning has shaped important processes that affect our lives even today.

(1) True or False vs. Valid or Invalid

True/False

It is common understanding that for an individual to believe or feel that something is true does not in itself imply that the something is indeed true.  Truth is something to be understood outside of our own experience.  It is true whether we believe it or not.

For example, it is true that objects in the dark are still there even if we cannot hear or see them.  A statement that that implies that when in the absence of light an object no longer exists is false and can be proven so by someone reaching out into the dark to touch that object.

Valid/Invalid

Validity focuses not upon whether the conclusion is true or false but rather on whether the process (argument) leading up to and supporting the conclusion is free from mistakes.

The following for example, shows how an argument can have a true conclusion but yet still be invalid.

Premise: The Sun is yellow
Premise: Fire is yellow
Premise: Fire is hot
Conclusion: Therefore the sun is hot

In this example, the conclusion is true yet the process is invalid as it proposes that a reason for the sun being hot is that it is yellow.

In the search for truth it is most important that both the conclusion is true and the supporting argument is valid.  A valid argument is helpful for ensuring that ones own understanding of the truth is supported by reason as well as for pursuading others to accept and agree with your conclusions of what is true.