Logical consistency

Extract from “Practical Thinking skills” (A.Adedapo) 

Chapter 9: Thinking logically; 9.1 Logical consistency.

Andrew: Computer, give us a summary of human logic.

Computer: Yes….

Ava: Start with what humans call logical consistency:

Computer: This is when a set of statements can all be logically true at the same time.Otherwise the group “(or set) is inconsistent

For example, the statements in (A) and (B):

1. Inconsistent statement: Tom is seven-years-old. Helen is holding an apple. Tom is not seven-years-old,

2. Consistent: Peter is a chair; Peter is 10-years-old.
3. Inconsistent: Peter is a chair; Peter is a 10-year-old boy

The reason why the statements A and C are inconsistent is due to logical inconsistencies.

Example 1: Let us apply this to the following statements:

A= All World-views lead to God; B= No world-view leads to God;

C= World-view X says there is only one god; D= World-view D says there are many gods,

E= World-view E is the only way to God; F= World-view F says F is the only way to God;

G = World-view G says whatever  World-view you believe in leads to God;

H = World-view H says that there is no such thing as God;

I = “I am the first and the last; apart from; me there is no God” [Chan^1,2]

Conclusion: All these statements are logically inconsistent.

For example, if statement A is true, then statement B cannot be true. According to Liu and Chan: “Every statement is inconsistent with its negation”.

Please note also that if statements F or G are true, statements A and B cannot be true. So there are statements, that are inconsistent with each other.

Ava: But, is it true that they cannot all be false?

Computer: To answer this I will give a second example:

Example 2: Let us apply this to the following statements:

{A = I only point to the way, I am not the way; B = There are no ways to heaven;

C = I am the Way, the Truth, and the Life;  D = Heaven does not exist;

E = Heaven does exist;  F = There is such a thing as truth;

G = There is no such thing as truth}

These statements are logically inconsistent e.g. D and E cannot both be true at the same time. Either heaven exists or heaven does not exist. Also, G contradicts itself because it asks us to accept the statement “There is no such thing as truth” to be true!

Andrew: Computer, what else is an example of logical inconsistency?

Computer: To answer this I will give a third example:

Example 3: Let us apply this to the following statements:

{A = People are destined to die once, and after that face judgment,

B = People are destined to be re-incarnated;

C = There is no life after death. D = There is life after death

E = There is a resurrection of all those who have ever lived.

F = There is no resurrection of all those who have ever lived}

Computer: These statements are logically inconsistent e.g. C and D cannot both be true at the same time. Either there is or there is no life after death.

Ava: Dear Reader, what do you think?

Sources:

[1]Isaiah 44 verse 6b “New International Version from “BibleGateway.” Isaiah 44:6 NIV – – Bible Gateway, www.Biblegateway.com/passage/? search=Isaiah44 verse 6bNIV. Accessed 10 October 2020

[2]  L04] Lau, Joe, and Jonathan Chan. “Critical Thinking Web.” Logical Relations.” [C01] What Is Critical Thinking?, Phileo ophy.hku.hk/think/logic/ relations.php. Accessed 6th August 2018 at 18:22

Share this post: on Twitter on Facebook