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

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

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

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

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

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

just like a recipe that doesn't work out.

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

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

Today I want to talk about 3 propositional  

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

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

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

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

So let's start by defining

What are Propositional fallacies?

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

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

despite having true premises.

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

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

not from the content of the premises themselves.

They are considered formal fallacies, which means  

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

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

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

propositional fallacies highlight  the critical importance of correct  

logical formulation in deductive reasoning,  

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

So let's talk about our  first propositional fallacy: 

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

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

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

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

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

Everyday example:

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

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

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

suggesting these outcomes are mutually exclusive.

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

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

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

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

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

possibility of overlapping or multiple outcomes.

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

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

This fallacy demonstrates  how easy it is to overlook  

these subtleties in our reasoning processes.

Historical example:

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

engaging numerous thinkers over the centuries.

The longstanding philosophical debate between  

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

This discourse questions whether human actions are  

predetermined or if individuals have  the freedom to choose independently.

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

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

This binary perspective fails to  consider the potential coexistence  

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

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

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

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

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

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

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

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

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

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

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

Coke vs Pepsi example A Coke enthusiast might declare,  

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

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

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

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

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

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

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

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

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

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

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

fallacy overlooks the nuanced nature  of personal tastes and preferences.

What is Affirming the consequent?

Affirming the consequent is a logical  fallacy involving an incorrect inference  

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

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

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

Everyday example: Consider the statement:  

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

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

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

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

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

Historical example:

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

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

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

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

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

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

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

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

causality from consequence to cause without  considering other possible explanations. 

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

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

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

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

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

Coke vs Pepsi example

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

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

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

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

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

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

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

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

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

What is Denying the antecedent?

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

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

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

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

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

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

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

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

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

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

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

Historical example:

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

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

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

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

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

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

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

as they lie in different planes. This early misconception underscores  

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

The later development and formalization  of three-dimensional geometry clarified  

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

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

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

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

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

Coke vs Pepsi example The Coke enthusiast, named Clara,  

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

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

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

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

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

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

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

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

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

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

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

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