only to unintentionally make a mistake,  so the meal didn't turn out right?

卻無意中犯了錯誤，導致成品不盡人意？

That's a bit like what happens with Propositional  Fallacies in thinking and reasoning.

這有點像是思考和推理中命題邏輯謬誤所發生的情況。

Even if you start with the right  facts (aka good ingredients),  

即使你從正確的事實（好的原料）開始，

if your way of thinking (aka  the recipe method) isn't right,  

如果你的思維方式（食譜方法）不正確，

you might end up with the wrong conclusion  (aka a meal that's not what you expected).

你最終可能會得到錯誤的結論（不是你所期望的飯菜）。

Let's dive into these fallacies  and see how they can trick us,  

讓我們深入研究這些謬論，看看它們如何欺騙我們，

just like a recipe that doesn't work out.

就像一個執行錯誤食譜一樣。

Hi, I am Shao Chieh Lo, welcome to What  People Also ask where I compiled some fun  

你好，我是Shao Chieh Lo，歡迎來到《What People Also Ask》，我整理了一些有趣的

facts to share with you, usually  by conducting a lot of Googling.

事實與你分享，通常是透過進行大量的谷歌搜尋。

Today I want to talk about 3 propositional  

今天我想談談 3 個命題謬誤

fallacies where the logical structure of  an argument leads to false conclusions,  

即使論證的內容可能部分正確

even when the content of the  argument might be partially correct.

，論證的邏輯結構也會導致錯誤的結論 。

For each fallacy, I will give one  everyday example, one historical example,  

對於每一個謬論，我都會舉一個日常例子、一個歷史例子以及

and one example of Coke vs Pepsi just  for fun and to demonstrate the concept.

一個可口可樂與百事可樂的例子，只是為了好玩並示範這個概念。

So let's start by defining

那麼讓我們先定義

What are Propositional fallacies?

什麼是命題謬誤？

Propositional fallacies are a type of logical  fallacy occurring in deductive reasoning,  

命題謬誤是演繹推理中發生的一種邏輯謬誤，

where errors in the logical structure of  an argument lead to false conclusions,  

其中論證的邏輯結構錯誤導致錯誤的結論，

despite having true premises.

儘管有正確的前提。

These fallacies are distinct because  they stem from errors in how propositions  

這些謬誤是截然不同的，因為它們源自於命題

(aka statements that can be true or  false) are combined or manipulated,  

（也稱為可以是真或假的陳述）如何組合或操縱的錯誤，

not from the content of the premises themselves.

而不是源自於前提本身的內容。

They are considered formal fallacies, which means  

它們被認為是形式謬誤，這意味著

it's identifiable by examining the argument's  form or structure, rather than its content.

可以透過檢查論證的形式或結構而不是其內容來識別它。

Examples include Affirming a Disjunct, Affirming  the Consequent, and Denying the Antecedent.

例子包括肯定選言、肯定後件和否定前件。

Unlike other fallacies that might involve  incorrect facts or irrelevant information,  

與其他可能涉及不正確事實或不相關資訊的謬誤不同，

propositional fallacies highlight  the critical importance of correct  

命題謬誤強調了演繹 推理中

logical formulation in deductive reasoning,  

正確邏輯表述的至關重要性 ，

demonstrating how true premises can still lead  to false conclusions if structured improperly.

表明如果結構不當，正確的前提仍然可能導致錯誤的結論。

So let's talk about our  first propositional fallacy: 

那麼讓我們來談談我們的第一個命題謬誤：

What is Affirming a Disjunct? Affirming a Disjunct is a logical  

什麼是肯定選言？肯定選言是一種邏輯謬誤

fallacy that occurs in a situation where  there are two possibilities (aka disjuncts),  

，發生在存在兩種可能性（又稱選言）的情況下，

and the confirmation of one is  incorrectly taken to deny the other.

並且錯誤地確認其中一種可能性來否定另一種可能性。

This fallacy follows the format: "A  or B is true; A is true; therefore,  

這種謬誤遵循以下格式：“A 或 B 為真；A 為真；因此，B 不為真。”

B is not true." It's a fallacy because  both A and B could be true simultaneously.

這是一個謬誤，因為 A 和 B 可能同時為真。

Everyday example:

日常例子：

A person said, "It's raining outside, so either  I take an umbrella or I will definitely get wet;  

有人說：“外面下雨了，要么我帶傘，要么我一定會被淋濕；

since I'm taking an umbrella, it's  impossible for me to get wet."

既然我帶傘，我就不可能被淋濕。”

This statement implies a false dichotomy:  either taking an umbrella or getting wet,  

這種說法暗示了一種錯誤的二分法：要麼帶雨傘，要麼被淋濕，這

suggesting these outcomes are mutually exclusive.

表明這些結果是相互排斥的。

However, this is an oversimplification.  In reality, taking an umbrella doesn't  

然而，這過於簡單化了。事實上，帶傘並不能

inherently prevent the possibility of  getting wet, as other factors like wind  

本質上防止被淋濕的可能性，因為風等其他因素

could still lead to one getting wet. The  fallacy lies in the assumption that by  

仍然可能導致被淋濕。此謬誤在於這樣的假設：

affirming one outcome (aka using an umbrella),  the other (aka getting wet) becomes impossible.

透過肯定一個結果（使用雨傘），另一個結果（被淋濕）就變得不可能。

This example showcases a common logical  error, where binary thinking obscures the  

這個例子展示了一個常見的邏輯錯誤，即二元思維掩蓋了

possibility of overlapping or multiple outcomes.

重疊或多個結果的可能性。

It highlights the need to recognize that  actions and consequences are often not  

它強調需要認識到行動和後果往往不是

strictly linear or exclusive, reminding us of the  complexities and nuances in everyday scenarios.

嚴格線性或排他性的，提醒我們日常場景中的複雜性和細微差別。

This fallacy demonstrates  how easy it is to overlook  

這個謬誤表明，我們在推理過程中很容易忽略

these subtleties in our reasoning processes.

這些微妙之處。

Historical example:

歷史例子：

The debate between determinism and free will is  a longstanding and central theme in philosophy,  

決定論和自由意誌之間的爭論是哲學中一個長期存在的中心主題，

engaging numerous thinkers over the centuries.

幾個世紀以來吸引了無數思想家。 決定論和自由意誌

The longstanding philosophical debate between  

之間長期存在的哲學爭論

determinism and free will exemplifies  the fallacy of affirming the disjunct.

例證了肯定選言的謬誤。

This discourse questions whether human actions are  

這個論述質疑人類的行為是否是

predetermined or if individuals have  the freedom to choose independently.

預先決定的，或是個人是否有獨立選擇的自由。

A common misinterpretation is the oversimplified  argument: "Either actions are determined,  

一個常見的誤解是過於簡單化的論點：“要么行動是被（因果關係）決定的，

or they result from free will. Since  causality exists, free will does not."

要么是自由意志的結果。既然因果關係存在，自由意志就不存在。”

This binary perspective fails to  consider the potential coexistence  

這種二元觀點未能考慮這些概念的

or complex interaction of these concepts. Enlightenment thinkers like David Hume and  

潛在共存或複雜的相互作用。大衛·休謨和伊曼紐爾·康德等啟蒙思想家

Immanuel Kant played pivotal roles in this  debate. Hume's compatibilism suggested that  

在這個主題的辯論中發揮了關鍵作用。休謨的相容論顯示

causality's existence doesn't negate free  will, while Kant's "Critique of Pure Reason"  

因果關係的存在並不否定自由意志，而康德的《純粹理性批判》則

proposed that free will could exist within moral  actions, even in a deterministic physical world. 

提出自由意志可以存在於道德行為中，甚至存在於決定論的物理世界中。

The 20th-century resurgence of this debate,  influenced by advancements in quantum mechanics  

受量子力學和神經科學進步的影響

and neuroscience, further questioned the strict  dichotomy between determinism and free will. 

，這場爭論在 20 世紀重新興起，進一步質疑了決定論和自由意誌之間的嚴格二分法。

Philosophers like A.J. Ayer and Daniel Dennett  explored the compatibility of these concepts,  

AJ Ayer 和 Daniel Dennett 等哲學家探索了這些概念的兼容性，

suggesting a framework where deterministic  and free-will principles coexist. 

提出了一個決定論和自由意志原則共存的框架。

This debate's history highlights  the error of affirming a disjunct,  

這場辯論的歷史凸顯了肯定選言的謬誤，

simplifying a nuanced issue into a binary  choice, and overlooking the complexities  

將微妙的問題簡化為二元選擇，並忽略了

and interplay between determinism and  free will in human agency and cognition. 

人類能動性和認知中的決定論與自由意誌之間的複雜性和相互作用。

Coke vs Pepsi example A Coke enthusiast might declare,  

可口可樂與百事可樂的例子 可口可樂愛好者可能會宣稱：

"I love Coke, so it's impossible for me to  enjoy Pepsi." This statement is an example  

“我喜歡可口可樂，所以我不可能喜歡百事可樂。”這個陳述是

of the logical fallacy known as affirming a  disjunct. The error lies in the assumption  

被稱為肯定選言的邏輯謬誤的一個例子。錯誤在於這樣的假設：

that a preference for Coke inherently  excludes the possibility of liking Pepsi. 

對可口可樂的偏好本質上排除了喜歡百事可樂的可能性。

However, personal tastes are not mutually  exclusive, and one can appreciate  

然而，個人品味並不互相排斥，人們可以欣賞

different brands for different qualities. On the other hand, a Pepsi supporter might  

不同品牌的不同品質。另一方面，百事可樂的支持者可能會

argue, "Pepsi is my absolute favorite,  which means Coke must taste awful." 

爭辯說：“百事可樂絕對是我的最愛，這意味著可口可樂的味道一定很糟糕。”

This is another instance of affirming a  disjunct. The belief that a fondness for  

這是肯定選言的另一個例子。相信對

Pepsi automatically translates to a disdain for  Coke is a flawed conclusion. Preferences are  

百事可樂的喜愛會自動轉化為對可口可樂的蔑視，這是一個有缺陷的結論。

subjective, and liking one product does not  necessarily mean disliking its competitors. 

偏好是主觀的，喜歡一種產品不一定代表不喜歡其競爭對手。

Both these instances show a common cognitive  error where individuals mistakenly assume  

這兩個例子都顯示了一種常見的認知錯誤，即人們錯誤地認為

that their preference for one option means an  automatic rejection of the alternative. This  

他們對一種選擇的偏好意味著自動拒絕另一種選擇。

fallacy overlooks the nuanced nature  of personal tastes and preferences.

這種謬論忽略了個人品味和偏好的微妙本質。

What is Affirming the consequent?

什麼是肯定後件？

Affirming the consequent is a logical  fallacy involving an incorrect inference  

肯定後件是一種邏輯謬誤，涉及

from a conditional statement. It occurs when one  reason that because the consequent (aka the "then"  

從條件陳述中得出錯誤的推論。當一個原因是由於結果

part of a conditional statement) is true, the  antecedent (aka the "if" part) must also be true. 

（條件語句的“所以”部分）為真，因此前件（又稱“如果”部分）也必須為真時，就會發生這種情況。

This reasoning is flawed because it ignores other  possible reasons for the consequent being true. 

這種推理是有缺陷的，因為它忽略了結果成立的其他可能原因。

Everyday example: Consider the statement:  

日常例子：考慮一下這句話：

"If it is raining, the ground will be wet." An  instance of affirming the consequent would be:  

“如果下雨，地面就會濕。”肯定後件的一個例子是：

"The ground is wet, therefore it must be raining."  

“地面是濕的，因此一定在下雨。”

This conclusion is fallacious because there  are other reasons the ground could be wet,  

這個結論是錯誤的，因為地面可能潮濕還有其他原因，

such as a sprinkler system or a spilled bucket  of water. The wet ground doesn't necessarily  

例如灑水系統或溢出的水桶。地面濕並不一定

mean it's raining; it's just consistent with  what would be the case if it were raining.

意味著正在下雨；而只是意味著如果下雨了，地面可能會是濕的。

Historical example:

歷史例子：

The Geocentric Theory rooted in ancient  Greek philosophy, notably Aristotle's ideas,  

地心說植根於古希臘哲學，特別是亞里斯多德的思想，

posited Earth at the universe's  center and was further developed  

將地球置於宇宙的中心，並由

by Ptolemy in his 2nd-century work "Almagest." Ptolemy's model, integrating complex concepts like  

托勒密在他的2世紀著作《天文學大成》中進一步發展。托勒密的模型整合了

epicycles, became the prevailing astronomical view  for over a millennium, intertwined with Christian  

本輪等複雜概念，成為千年以來流行的天文學觀點，與

theology in the Middle Ages and widely accepted  in Islamic and Christian scholarly circles. 

中世紀的基督教神學交織在一起，並被伊斯蘭和基督教學術界廣泛接受。

This theory's endurance exemplifies the fallacy  of affirming the consequent. Observations that  

這理論的持久性反映了肯定後見的謬誤。 天體似乎圍繞著地球旋轉的

celestial bodies appeared to revolve around  Earth led to the erroneous conclusion that  

觀察 導致了 地球必定是宇宙中心的 錯誤結論

Earth must be the universe's center. This reasoning assumes a direct  

。這種推理假設 從結果到原因之間 存在直接

causality from consequence to cause without  considering other possible explanations. 

因果關係，而不考慮其他可能的解釋。由哥白尼在 16

The shift to the heliocentric model,  initiated by Copernicus in the 16th  

世紀發起並由開普勒和伽利略在 17 世紀的發現所鞏固的向日

century and solidified by Kepler and Galileo's  17th-century findings, challenged this fallacy. 

心說模型的轉變 對這一謬論提出了挑戰。

Their work provided evidence that directly  contradicted the geocentric view, demonstrating  

他們的研究提供了直接與地心論觀點相矛盾的證據，展示了

the perils of affirming the consequent in  scientific inquiry and highlighting how entrenched  

在科學探究中肯定後件的危險，並強調根深蒂固的

beliefs, both religious and philosophical,  can hinder the acceptance of new paradigms.

宗教和哲學信仰如何阻礙對新範式的接受。

Coke vs Pepsi example

可口可樂與百事可樂的例子

A Coke enthusiast might say, "If a soda refreshes  you, it must be Coke. You feel refreshed,  

可口可樂愛好者可能會說，“如果蘇打水能讓你精神煥發，那一定是可口可樂。你感覺精神煥發，

so you must have had Coke." This argument is  flawed because feeling refreshed can result  

所以你一定喝過可口可樂。”這個論點是有缺陷的，因為各種蘇打水都可以帶來清爽感

from various sodas, not exclusively Coke. The  supporter is erroneously asserting that the effect  

，而不僅僅是可樂。支持者錯誤地斷言效果

(feeling refreshed) confirms the cause (drinking  Coke), disregarding other potential explanations. 

（感覺神清氣爽）證實了原因（喝可樂），而忽略了其他可能的解釋。

Similarly, a Pepsi advocate might argue, "A  bold tasting soda is definitely Pepsi. This  

同樣，百事可樂的擁護者可能會說：“味道大膽的蘇打水肯定是百事可樂。這種蘇打

soda has a bold taste, so it must be Pepsi."  This is a fallacious reasoning because boldness  

水的味道大膽，所以它一定是百事可樂。”這是一個錯誤的推理，因為大膽的

in taste can be attributed to many sodas, not  just Pepsi. The Pepsi supporter is mistakenly  

口味可以歸因於許多蘇打水，而不僅僅是百事可樂。百事可樂的支持者錯誤地

affirming that the effect (bold taste) is a  definitive indicator of the cause (being Pepsi),  

認為，結果（大膽的口味）是原因（百事可樂）的明確指標，

which is an oversimplification of the  possible causes for a bold taste in sodas.

這過於簡單化了蘇打水大膽口味的可能原因。

What is Denying the antecedent?

什麼是否定前件？

Denying the antecedent is a logical fallacy  that occurs when, from a conditional statement,  

否定前件是一種邏輯謬誤，當人們從條件語句中

one incorrectly infers that if the antecedent  (the "if" part) is false, then the consequent  

錯誤地推斷出如果先行詞（“如果”部分）為假，則結果

(the "then" part) must also be false. This form  of reasoning is flawed because the consequent can  

（“所以”部分）也必定為假時，就會發生這種邏輯謬誤。這種形式的推理是有缺陷的，因為

still be true even if the antecedent is false. Everyday example:

即使前件是假的，結果仍然可能是真的。日常例子：

Someone said "If I study hard, I will  pass the exam. I didn't study hard,  

有人說“如果我努力學習，我就會通過考試。我不努力學習，

so I will not pass the exam." This reasoning is fallacious  

所以我不會通過考試。”這種推理是錯誤的

because there are other ways to pass the exam  besides studying hard, such as already knowing  

，因為除了努力學習之外，還有其他方法可以通過考試，例如已經了解

the material or making educated guesses. The absence of studying doesn't necessarily  

素材或做出有根據的猜測。不學習不一定

guarantee a failure; it just negates  one specific path to success. 

意味著失敗；它只是否定了一條特定的成功之路。

This example demonstrates the error  in concluding that the failure of the  

這個例子說明了錯誤的結論，即條件（努力學習）的失敗會

condition (studying hard) automatically leads to  the failure of the outcome (passing the exam).

自動導致結果（通過考試）的失敗。

Historical example:

歷史例子：

Euclidean geometry, dating back to around  300 BC with the Greek mathematician Euclid,  

歐幾裡得幾何可以追溯到公元前 300 年左右，希臘數學家歐幾里德

forms the foundation of geometric understanding  through his work "Elements." A central aspect of  

透過他的著作《幾何原本》奠定了幾何理解的基礎。 歐幾里德幾何 的一個核心面向

Euclidean geometry is the parallel postulate,  stating that parallel lines never intersect.  

是平行公設，即平行線永遠不會相交。

However, a historical misinterpretation,  particularly in the early study of geometry,  

然而，歷史的誤解，特別是在幾何學的早期研究中，

involved the logical fallacy of denying  the antecedent. This fallacy manifested  

涉及否定前件的邏輯謬誤。這種謬誤表現

in the incorrect belief that if two lines are  not parallel, they must intersect, neglecting  

為錯誤地認為兩條線不平行，則必定相交，而忽略了

the possibility of skew lines in three-dimensional  space, which are non-parallel yet do not intersect  

三維空間中斜線的可能性，斜線雖然不平行但不相交，

as they lie in different planes. This early misconception underscores  

因為它們位於不同的平面。這種早期的誤解強調了

a limited understanding of geometry,  primarily confined to two dimensions.

對幾何學的有限理解，主要局限於二維。

The later development and formalization  of three-dimensional geometry clarified  

後來三維幾何的發展和形式化澄清了

this misunderstanding. Further advancements in  the 18th and 19th centuries by mathematicians  

這個誤解。 18 世紀和 19 世紀，

like Gauss, Riemann, and Lobachevsky,  who explored non-Euclidean geometries,  

高斯、黎曼和羅巴切夫斯基等數學家探索非歐幾里德幾何，取得了

significantly broadened the scope of geometric  principles beyond Euclid's original framework.

進一步的進展 ，顯著拓寬了幾何原理的範圍，超出了歐幾里德的原始框架。

This evolution of mathematical thought  highlights the dynamic nature of the field  

數學思想的演變凸顯了該領域的動態本質

and the rectification of misconceptions through  deeper investigation and expanded perspectives. 

，並透過更深入的研究和擴展的視角糾正了錯誤觀念。

Coke vs Pepsi example The Coke enthusiast, named Clara,  

可口可樂與百事可樂的例子 這位名叫克拉拉的可口可樂愛好者

was known for her unwavering belief in the  superiority of Coca-Cola. One sunny afternoon,  

以其對可口可樂優越性的堅定信念而聞名。一個陽光明媚的下午，

while sitting at a local café, she declared,  "If a drink is Coke, then it is undoubtedly  

她坐在當地一家咖啡館裡宣稱：“如果飲料是可樂，那麼它無疑是

delicious." However, when the waiter brought  a tray of Sprite for the table next to them,  

美味的。”然而，當服務生端上一盤雪碧給鄰桌時，

Clara scoffed, "Since Sprite is not  Coke, it cannot possibly be delicious." 

克拉拉嗤之以鼻：“雪碧不是可樂，不可能好喝。”

Across town, Peter, a die-hard Pepsi fan, was  equally staunch in his opinions. "If a drink is  

在城市的另一邊，百事可樂的鐵粉彼得也同樣堅定自己的觀點。 「如果飲料是

Pepsi, it's the epitome of refreshment," he  proclaimed at a neighborhood barbecue. When  

百事可樂，那麼它就是提神的縮影，」他在附近的燒烤會上宣稱。當

his friend offered him a chilled glass of  Fanta, Peter said, "Since that's not Pepsi,  

他的朋友遞給他一杯冰鎮芬達時，彼得說：“因為那不是百事可樂，所以

it can't be refreshing." In both scenarios,  

它不可能令人耳目一新。”在這兩種情況下，

Clara and Peter were victims of the logical  fallacy known as denying the antecedent. 

克拉拉和彼得都是被稱為否定前件的邏輯謬誤的受害者。

They each believed that if a drink  wasn't their preferred brand,  

他們每個人都相信，如果一種飲料不是他們喜歡的品牌，

it couldn't possess qualities like deliciousness  or refreshment. This belief created a rift  

那麼它就不可能具有美味或提神等品質。

in their understanding of the vast world of  flavors beyond the realms of Coke and Pepsi.

這種信念使 他們對可口可樂和百事可樂以外的廣闊口味世界的理解 產生了裂痕 。