Pigs would fly: Difference between revisions

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The phrase '''Pigs would fly''' is used as a conclusion to show that the corresponding assumption is impossible.  
'''"Pigs would fly."''' is a phrase used as a conclusion to show that the corresponding assumption is impossible.  


==Mainly about==
==Mainly about==
In conditional sentences<ref>In this context, a statement with an assumption and a conclusion. </ref>, it is a kind of wordplay or rhetoric used in the concluding part to show that an assumption is improbable.
In conditional sentences<ref>In this context, it is a statement with an assumption and a conclusion. </ref>, it is a kind of wordplay or rhetoric used in the concluding part to show that an assumption is improbable.


For example, considering the case that there is a given assumption "[[User:Notorious]] is a genius" and a person says "If [[User:Notorious]] were a genius, pigs would fly", we can see that the person thinks that "[[User:Notorious]] can't be a genius.<ref>But why? He is a genius.</ref>
For example, considering the case that there is a given assumption "[[User:Notorious|Notorious]] is a genius" and a person says "If [[User:Notorious|Notorious]] were a genius, pigs would fly", we can see that the person thinks that "[[User:Notorious|Notorious]] can't be a genius.<ref>But why? He is a genius.</ref>


==The logical consistency of saying it==
==The logical consistency of saying it==
Is there any consistency in concluding that "pigs fly" when the assumption is impossible? This question has only recently begun to be pointed out, and since ancient times it has continued to trouble the minds of logicians, philosophers, physicists, mathematicians, or cultists <del>who like to fantasize about things that are useless in reality</del>. However, it is now known that it can be proven by the [[Contrapositive]] argument.
The problem if there is any consistency in concluding that "pigs fly" when the assumption is impossible (called "''Pigs! Would! Fly!''" Problem) has only recently begun to be pointed out, and since ancient times it has continued to trouble the minds of logicians, philosophers, physicists, mathematicians, or cultists <del>who like to fantasize about things that are totally useless in reality</del>. However, it is now known that this "Pigs! Would! Fly!" Problem can be proven by the contrapositive argument.


Let an improbable assumption be symbolically "Mn". Now, we are supposed to determine whether the proposition "If Mn, then pigs will fly." is true or not.


仮定が有り得ないときに「豚が飛ぶ」と結論づけることに、整合性はあるのだろうか(=「豚!が!飛!ぶ!」問題)。「豚!が!飛!ぶ!」問題は近年になって指摘され始め、古来より{{矛盾}}論理学者や哲学者、物理学者、数学者、あるいはカルト信者など、<del>現実には役に立たないことを妄想したがる、厄介な</del>人々の頭を悩ませ続けてきた。しかし現在では、それが[[対偶]]論法によって証明されることが知られている。
We can prove that the proposition "If Mn, then pigs fly." by proving that its contrapositive "If pigs do not fly, then not-Mn," because the truth values of a proposition P and its contraposition Q are equal.


Let an improbable assumption be symbolically "Mn". Now, all we are supposed to is verify whether the proposition "If Mn, then pigs will fly" is true or not.
For the assumption "Pigs do not fly." of the proposition "If pigs do not fly, then not-Mn," it always stands; in this world, a pig would never fly. For the conclusion "Not-Mn," it is always true because Mn is known to be always false. Thus, it is true that, in this contrapostion, the conclusion is true when the assumption is true. Now we have proved this contraposition. Therefore, the proposition "If Mn, pigs would fly." is also true.


ある有り得ない仮定{{矛盾}}を記号的に Mn とする。すなわち、命題「Mnならば豚が飛ぶ。」が[[利用者:芯|真]]であるかどうかを検証すればよい。
Now we have a consistency upon saying "Pigs would fly." as a conclusion of an improbable assumption, and upon expressing the improbabity itself by saying so.
 
命題「Mnならば豚が飛ぶ。」が真であることを証明するために、その[[対偶]]「豚が飛ばないならばMnでない。」が真であることを証明する。<ref>ことに、命題Pとその[[対偶]]の命題Qとの真理値は等しい。</ref>
 
命題「豚が飛ばないならばMnでない。」について、仮定「豚が飛ばない」は'''常に'''真である(通常、豚が飛ぶことは無い)。また、結論「Mnでない」も'''常に'''真である(Mn は有り得ない)。このことから、「豚が飛ばない」が成り立つとき、「Mnでない」もまた成り立っている、ということがいえる。従って、命題「豚が飛ばないならばMnでない。」は真となる。
 
よって、真である命題の対偶もまた真であるから、命題「Mnならば豚が飛ぶ。」は真である。
 
 
「豚!が!飛!ぶ!」問題の論理的整合性は、かくの如く証明されるのである。
 
==使用例==
{{大喜利|場所=この節}}
この節では、「豚が飛ぶ」の具体的な使用例を掲げる。
 
#「[[WikiWiki]]が素晴らしいサイトでなかったならば、豚が飛ぶ。」
#「[[Wikipedia]]が素晴らしいサイトであったならば、豚が飛ぶ。」
#「豚が飛ぶならば、豚が飛ぶ。」
#「[[ジョン]]が数学のテストで満点を取るならば、豚が飛ぶ。」
==派生形==
{{大喜利|場所=この節}}
この節では「豚が飛ぶ」という言葉から派生した言葉を掲げる。
#[[WikiWiki]]が廃れる
#[[Wikipedia]]が栄える


==Footnote==
==Footnote==
<references />
<references />
[[ja:豚が飛ぶ]]
[[nm:P2s w3d f1y]]

Latest revision as of 15:35, 17 February 2023

"Pigs would fly." is a phrase used as a conclusion to show that the corresponding assumption is impossible.

Mainly about[edit | edit source]

In conditional sentences[1], it is a kind of wordplay or rhetoric used in the concluding part to show that an assumption is improbable.

For example, considering the case that there is a given assumption "Notorious is a genius" and a person says "If Notorious were a genius, pigs would fly", we can see that the person thinks that "Notorious can't be a genius.[2]

The logical consistency of saying it[edit | edit source]

The problem if there is any consistency in concluding that "pigs fly" when the assumption is impossible (called "Pigs! Would! Fly!" Problem) has only recently begun to be pointed out, and since ancient times it has continued to trouble the minds of logicians, philosophers, physicists, mathematicians, or cultists who like to fantasize about things that are totally useless in reality. However, it is now known that this "Pigs! Would! Fly!" Problem can be proven by the contrapositive argument.

Let an improbable assumption be symbolically "Mn". Now, we are supposed to determine whether the proposition "If Mn, then pigs will fly." is true or not.

We can prove that the proposition "If Mn, then pigs fly." by proving that its contrapositive "If pigs do not fly, then not-Mn," because the truth values of a proposition P and its contraposition Q are equal.

For the assumption "Pigs do not fly." of the proposition "If pigs do not fly, then not-Mn," it always stands; in this world, a pig would never fly. For the conclusion "Not-Mn," it is always true because Mn is known to be always false. Thus, it is true that, in this contrapostion, the conclusion is true when the assumption is true. Now we have proved this contraposition. Therefore, the proposition "If Mn, pigs would fly." is also true.

Now we have a consistency upon saying "Pigs would fly." as a conclusion of an improbable assumption, and upon expressing the improbabity itself by saying so.

Footnote[edit | edit source]

  1. In this context, it is a statement with an assumption and a conclusion.
  2. But why? He is a genius.