Logical Confusion: A is True or False?

  • Context: Graduate 
  • Thread starter Thread starter varadgautam
  • Start date Start date
  • Tags Tags
    Confusion
Click For Summary
SUMMARY

The discussion centers on the logical paradox involving the statement A: "Negation of A (~A) is true." It establishes that if A is true, then ~A must also be true, leading to a contradiction. Conversely, if A is false, then A must be true due to double negation, creating a logical inconsistency. The core conclusion is that the statement "the negation of this statement is false" does not qualify as a proposition, similar to the classic example "this statement is false," which also fails to meet the criteria for a valid proposition.

PREREQUISITES
  • Understanding of propositional logic
  • Familiarity with logical negation
  • Knowledge of paradoxes in logic
  • Basic concepts of truth values
NEXT STEPS
  • Research the principles of propositional logic
  • Study the concept of logical paradoxes, including the Liar Paradox
  • Explore the implications of double negation in logic
  • Learn about the distinction between propositions and non-propositions
USEFUL FOR

Students of philosophy, mathematicians, and anyone interested in the foundations of logic and reasoning.

varadgautam
Messages
10
Reaction score
0
Consider a statement
A: Negation of A (~A) is true

Then,
~A: Negation of A is false


If A is true, that means that ~A is true too, but these can't be simultaneously true.
If A is false, ~~A is true, i.e. A is true. What is the problem?
 
Physics news on Phys.org
The problem is that logic only applies to "propositions" which are defined as statements that are either true of false. What you have done is show that "the negation of this statement is false" is not a proposition.

It is, in fact, exactly the same as the common example of a statement that is not a proposition: "this statement is false".
 

Similar threads

High School Vacuously true statements and why false implies truth
  • · Replies 10 ·
Replies
10
Views
7K
MHB Is Theorem 5.2 in SET THEORY AND LOGIC True or False?
  • · Replies 2 ·
Replies
2
Views
1K
High School Why "the conditional in which the antecedent is false" is always true?
  • · Replies 14 ·
Replies
14
Views
3K
MHB Can Predicate Properties Be Neither True nor False?
  • · Replies 1 ·
Replies
1
Views
1K
Undergrad [(Linear) Temporal Logic] Are the given sentences consistent or not?
  • · Replies 8 ·
Replies
8
Views
2K
Undergrad Question about about halting problem and this particular function
  • · Replies 54 ·
2
Replies
54
Views
7K
Undergrad Why are the inverse and converse of an implication not equivalent?
  • · Replies 39 ·
2
Replies
39
Views
5K
Undergrad Syntactic vs semantic logical consequence (entailment)
  • · Replies 5 ·
Replies
5
Views
3K
Undergrad On the meaning of logical implication within specific context/models
  • · Replies 22 ·
Replies
22
Views
4K
Graduate What are your insights on The Hardest Logic Puzzle Ever?
  • · Replies 2 ·
Replies
2
Views
3K