• Source: Negation introduction

Negation introduction is a rule of inference, or transformation rule, in the field of propositional calculus.
Negation introduction states that if a given antecedent implies both the consequent and its complement, then the antecedent is a contradiction.




Formal notation


This can be written as:



(
P
→
Q
)
∧
(
P
→
¬
Q
)
→
¬
P


{\displaystyle (P\rightarrow Q)\land (P\rightarrow \neg Q)\rightarrow \neg P}


An example of its use would be an attempt to prove two contradictory statements from a single fact. For example, if a person were to state "Whenever I hear the phone ringing I am happy" and then state "Whenever I hear the phone ringing I am not happy", one can infer that the person never hears the phone ringing.
Many proofs by contradiction use negation introduction as reasoning scheme: to prove ¬P, assume for contradiction P, then derive from it two contradictory inferences Q and ¬Q. Since the latter contradiction renders P impossible, ¬P must hold.




Proof






See also


Reductio ad absurdum




References

Kata Kunci Pencarian:

• Nihilisme
• Absolut (filsafat)
• Yoshishige Yoshida
• Bahasa Saisiyat
• Daftar teori konspirasi
• The Memoirs of Naim Bey
• Belgia pada Perang Dunia II
• Aljabar Boolean (struktur)
• Negation introduction
• Double negation
• Negation
• De Morgan's laws
• List of rules of inference
• Existential quantification
• Minimal logic
• Reductio ad absurdum
• Disjunction introduction
• Rule of inference