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  • Have you ever gathered the correct ingredients  and tried to cook, following the recipe,  

    您是否曾經收集了所有正確的食材並嘗試按照食譜烹飪,

  • only to unintentionally make a mistakeso 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 dichotomyeither 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 oversimplificationIn 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 debateinfluenced 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 affirmingdisjunct. 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 favoritewhich 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 affirmingdisjunct. 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 modelinitiated 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 philosophicalcan 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) isdefinitive 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 postulatestating that parallel lines never intersect.  

    是平行公設,即平行線永遠不會相交。

  • However, a historical misinterpretationparticularly 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 geometryprimarily 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 Lobachevskywho 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. "