Aristotelian Logic & Fashioning an Argument A Study of Deductive Reasoning

Why learn this stuff? Logic = Reasoning Logic = Reasoning Basis of academic thought Basis of academic thought Creation of argument Creation of argument

How do I demonstrate logic? Make obvious, explicit connections between your major thoughts and ideas Make obvious, explicit connections between your major thoughts and ideas You want someone to FOLLOW your train of thought. You want someone to FOLLOW your train of thought.

Aristotle Worked with syllogisms Worked with syllogisms Formal system of thought Formal system of thought Provides a method for connecting ideas together Provides a method for connecting ideas together

Syllogism Ex: Ex: 1) Wood floats in water. 2) Ships are made of wood 3) Therefore ships float in water.

Syllogisms #1 and #2 are both a premise. #1 and #2 are both a premise. #3 is a conclusion #3 is a conclusion

Syllogism Example Reiterated Premise #1: Wood floats in water. Premise #1: Wood floats in water. Premise #2: Ships are made of wood. Premise #2: Ships are made of wood. Conclusion: Therefore, ships float in water. Conclusion: Therefore, ships float in water.

Syllogism Practice If all humans are mortal, If all humans are mortal, and all Greeks are humans, and all Greeks are humans, then all Greeks are mortal. then all Greeks are mortal.

This type of logic isn’t perfect! All chickens have two legs. All chickens have two legs. Aristotle has two legs. Aristotle has two legs. Therefore, Aristotle is a chicken. Therefore, Aristotle is a chicken. =flawed However, this isn’t the point!

So? When you write an essay, watch your premises. They should lead to a valid conclusion. When you write an essay, watch your premises. They should lead to a valid conclusion.

Examples – Fill in the missing component All trees have root systems. All trees have root systems. Therefore, All trees need nitrogen. Therefore, All trees need nitrogen. All root systems need nitrogen. All root systems need nitrogen.

Examples – Fill in the missing component All fruits grow on trees All fruits grow on trees Therefore, all oranges grow on trees Therefore, all oranges grow on trees All oranges are fruits All oranges are fruits

Examples – Fill in the missing component All bachelor's are single All bachelor's are single Johnny is single, Johnny is single, Hence, Johnny is a bachelor Hence, Johnny is a bachelor

Ex: Logic w/o syllogism format Everyday I go to work. This journey from my home to my office takes one hour. My office starts at eight o' clock in the morning. So, if I leave my home at seven o' clock in the morning, I will reach the office in time. Everyday I go to work. This journey from my home to my office takes one hour. My office starts at eight o' clock in the morning. So, if I leave my home at seven o' clock in the morning, I will reach the office in time.

Argument Validity and Soundness

Argument: Validity A deductive argument is said to be valid if and only if it takes a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false. Otherwise, a deductive argument is said to be invalid. A deductive argument is said to be valid if and only if it takes a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false. Otherwise, a deductive argument is said to be invalid.

Argument: Validity Valid arguments do not require true premises. Valid arguments do not require true premises.

Ex: Valid Argument – True premises Either Elizabeth owns a Honda or she owns a Saturn. Either Elizabeth owns a Honda or she owns a Saturn. Elizabeth does not own a Honda. Elizabeth does not own a Honda. Therefore, Elizabeth owns a Saturn. Therefore, Elizabeth owns a Saturn.

Ex: Valid Argument – False premises All toasters are items made of gold. All toasters are items made of gold. All items made of gold are time- travel devices. All items made of gold are time- travel devices. Therefore, all toasters are time- travel devices. Therefore, all toasters are time- travel devices.

Argument - Soundness A sound argument is one that is not only valid, but begins with premises that are actually true A sound argument is one that is not only valid, but begins with premises that are actually true

Soundness A deductive argument is sound if and only if A deductive argument is sound if and only if 1) it is both valid, and 1) it is both valid, and 2) all of its premises are actually true. 2) all of its premises are actually true. Otherwise, a deductive argument is unsound. Otherwise, a deductive argument is unsound.

Ex: Sound argument No felons are eligible voters. No felons are eligible voters. Some professional athletes are felons. Some professional athletes are felons. Therefore, some professional athletes are not eligible voters. Therefore, some professional athletes are not eligible voters. QUANTIFIERS

Practice…