A Very Basic Introduction to Logic and Syllogistic Logic

Summary

This video script offers an elementary introduction to logic, emphasizing its importance in making informed decisions. It defines logic as the analysis and appraisal of arguments, distinguishing between 'valid' and 'sound' arguments. The script introduces syllogistic logic, explaining well-formed formulas and the star test for argument validity. The goal is to equip viewers with basic logical tools to critically assess information and form reasoned conclusions.

Takeaways

• 😀 The script emphasizes the importance of logic in winning arguments and making important life decisions.
• 📚 It introduces Harry J. Gensler's 'Introduction to Logic' as a foundational text for learning about logic.
• 🧐 Logic is defined as the analysis and appraisal of arguments, a tool rather than a fixed set of rules.
• 🔍 The script differentiates between an argument's validity and soundness, explaining that validity is about the logical structure, while soundness requires true premises.
• 📈 The concept of syllogistic logic is introduced, highlighting its structure with major and minor premises leading to a conclusion.
• 🔑 The script explains 'well-formed formulas' or 'woofs' as a method to represent arguments in syllogistic logic using letters and specific words.
• 📝 The importance of capitalization in 'woofs' is discussed, with rules for when to capitalize letters representing general terms versus specific entities.
• 🌟 The 'star test' is presented as a method to determine the validity of a syllogism by ensuring proper distribution and exclusivity of starred letters.
• 📉 The script acknowledges the complexity of the star test and suggests that practice and further reading are necessary to fully understand its application.
• 📑 The video encourages note-taking and revisiting sections for better comprehension of the information presented on logic.
• 🎓 The speaker shares personal insights on how learning basic logic has positively impacted their life, suggesting its practical value.

Q & A

What is the main purpose of the video script?

The main purpose of the video script is to provide a basic introduction to logic, explaining what logic is, the difference between a valid and sound argument, the basics of syllogisms, and how to test for the validity of a syllogism using the star test.

Why might someone want to learn logic?

Learning logic can help individuals analyze different arguments through logic, make important decisions in life, and come to their own conclusions by looking at various life philosophies and self-help advice more logically.

What does the author suggest as a resource for further reading on logic?

The author suggests 'Harry J Gensler's Introduction to Logic' as a resource for further reading on the subject.

What is the definition of logic according to Gensler?

According to Gensler, logic is defined as the analysis and appraisal of arguments.

What are the two components of an argument in the context of logic?

The two components of an argument are a set of premises, which can be seen as supporting evidence, and a conclusion, which is based on that evidence.

What is the difference between a valid argument and a sound argument?

A valid argument is one where it would be contradictory to have all the premises true and the conclusion false. A sound argument, on the other hand, is not only valid but also has true premises.

What is a syllogism and what are its parts?

A syllogism is a type of logical argument that applies deductive reasoning to arrive at a conclusion based on two or more propositions that are asserted or assumed to be true. It consists of a major premise, a minor premise, and a conclusion.

What are 'well-formed formulas' or 'woofs' in the context of syllogistic logic?

In syllogistic logic, 'well-formed formulas' or 'woofs' are formulas that follow a specific structure using the words 'all', 'no', 'some', 'is', and 'not', along with letters representing the terms in the argument.

What does the star test involve when determining the validity of a syllogism?

The star test involves underlining distributed letters in the premises and conclusion, starring distributed premise letters and non-distributed conclusion letters, and then checking if every capital letter is starred exactly once and if there is exactly one star on the right-hand side.

Why is it important to test the validity of an argument?

Testing the validity of an argument is important because it helps determine whether the conclusion necessarily follows from the premises, which is crucial for logical reasoning and making sound decisions.

How does the script suggest one can enhance their understanding of logic?

The script suggests that one can enhance their understanding of logic by learning the basics, such as the difference between valid and sound arguments, the structure of syllogisms, and practicing the star test for validity, as well as seeking further reading in books like Gensler's 'Introduction to Logic'.

Outlines

00:00

😀 Introduction to Logic and Argument Analysis

This paragraph introduces the concept of logic as a tool for analyzing and appraising arguments, contrasting it with the common misuse of the term in everyday language. The speaker emphasizes the importance of logic in making informed decisions and understanding conflicting life philosophies. The script is based on Harry J. Gensler's 'Introduction to Logic,' and the video aims to provide a basic introduction to logic for beginners. It also encourages viewers to take notes and revisit sections for better understanding.

05:00

🧐 Understanding Validity and Soundness in Arguments

The second paragraph delves into the distinction between a valid and a sound argument. A valid argument is one where it's impossible for the premises to be true and the conclusion false, focusing on the logical structure rather than the truth of the premises. Soundness, on the other hand, requires both validity and the truth of the premises. The paragraph uses examples to illustrate these concepts and highlights the importance of testing arguments for validity, with a promise to introduce a method for such testing later in the video.

10:01

📚 Exploring Syllogistic Logic and the Star Test

This paragraph introduces syllogistic logic, a type of deductive reasoning invented by Aristotle. It explains the structure of syllogisms, which consist of a major premise, a minor premise, and a conclusion. The speaker discusses the use of well-formed formulas, or 'woofs,' and the specific language used in syllogisms. The paragraph also outlines the star test method for determining the validity of a syllogism, which involves underlining distributed letters and starring certain letters to check if the argument meets specific criteria for validity.

Keywords

💡Argument

In the context of the video, an 'argument' is a set of statements, consisting of premises and a conclusion, used to persuade or logically deduce a point. The script uses the example 'All fish are animals, a salmon is a fish, therefore a salmon is an animal' to illustrate a valid argument structure. The concept is central to the video's theme of logical reasoning and analysis.

💡Logic

Defined by Harry J. Gensler in the video as 'the analysis and appraisal of arguments,' logic is presented as a method or tool for evaluating the strength of arguments. It's integral to the video's educational purpose, which is to introduce viewers to the basics of logical thinking and argument evaluation.

💡Premise

A 'premise' in the script refers to a statement or proposition that supports the conclusion in an argument. It is part of the argument's structure, serving as evidence that lends credibility to the conclusion. For example, 'All fish are animals' is a premise in the argument provided in the script.

💡Conclusion

The 'conclusion' is the final statement in an argument that follows from the premises. It is what the argument aims to establish as true based on the supporting evidence provided by the premises. In the script, 'a salmon is an animal' is the conclusion derived from the premises provided.

💡Validity

The script explains 'validity' as a property of an argument where it would be contradictory to have all the premises true and the conclusion false. Validity does not concern the truth of the premises but the logical relationship between them and the conclusion, as illustrated by the modified Socrates example.

💡Soundness

'Soundness' in the video is described as a higher standard for an argument, where not only is the argument valid, but all its premises are also true. The script uses the classic 'All men are mortal, Socrates is a man, therefore Socrates is mortal' as an example of a sound argument.

💡Syllogism

A 'syllogism' is a kind of logical argument that applies deductive reasoning to arrive at a conclusion based on two propositions that are asserted or assumed to be true. The script introduces syllogistic logic as a method invented by Aristotle, with a structure including a major premise, a minor premise, and a conclusion.

💡Well-formed Formula

In the context of syllogistic logic, a 'well-formed formula' or 'woof' as colloquially referred to in the script, is a formula that adheres to the specific language rules of syllogisms, using only certain words and following capitalization rules. The script provides examples and explanations of how to convert sentences into well-formed formulas.

💡Distribution

The term 'distribution' in the script refers to a property of a term within a well-formed formula that appears after 'all', 'no', 'not', or 'any'. The script explains that understanding distribution is important for applying the star test to determine the validity of a syllogism.

💡Star Test

The 'star test' is a method introduced in the script for testing the validity of a syllogism. It involves underlining distributed letters and starring certain letters to check if the syllogism follows the rules of validity, such as every capital letter being starred exactly once and having only one star on the right-hand side.

Highlights

The importance of logic in making important life decisions and analyzing conflicting self-help advice.

Introduction to logic as a fundamental tool for argument analysis and appraisal.

Defining an argument with its two components: premises and conclusion.

The distinction between a valid and sound argument in logical analysis.

The concept of syllogistic logic, introduced by Aristotle, and its structure.

Understanding 'well-formed formulas' or 'woofs' in syllogistic logic.

The use of specific language and capitalization rules in constructing syllogisms.

The process of converting sentences into well-formed formulas for logical analysis.

The method for testing the validity of a syllogism using the 'star test'.

The significance of distributed letters in well-formed formulas and their role in the star test.

How to properly star premise letters and conclusion letters for the star test.

The criteria for a valid syllogism according to the star test method.

The practical application of logic in everyday life beyond academic settings.

The recommendation of Harry J. Gensler's book for further reading on logic.

The emphasis on the importance of understanding the relationship between premises and conclusions in arguments.

The illustration of how to determine if an argument's conclusion necessarily follows from its premises.

The clarification on the difference between having a true premise and a conclusion that follows from the premises.

The encouragement for viewers to take notes and revisit sections for better understanding of logic concepts.

Transcripts

we all want to win arguments i mean sure

there are probably those people out

there that like losing arguments because

that means that they've learned

something

but usually we want to look cool and

smart in front of people that don't

really care

i mean come on i'd miss my own wedding

if it meant winning an internet argument

with some random guy in nebraska

but in all seriousness being able to

analyze different arguments through

logic will help us make important

decisions in life

there's different life philosophies and

self-help advice out there

some conflicting with others and perhaps

by looking at all this advice more

logically we could come to our own

conclusions

so this video is designed to provide a

very basic

elementary introduction to logic for

someone who knows literally nothing

about it

the text i'll be using which i was

taught in my logic class

is harry j gensler's introduction to

logic hopefully

if this video does its job and gets you

more interested in logic

you get the book yourself for further

reading also this video contains a lot

of information so feel free to pause it

take notes go back to earlier sections

or whatever else you gotta do

now without further ado let's actually

start talking about logic

so first off we should probably define

logic in contemporary culture we kind of

just use the word logic interchangeably

with reason

if anything the word is used as a

political tool you know people will talk

about how logical they are

and their side is while the other side

is illogical

they'll say their position is logical

without even talking about its validity

or anything

but what really is logic gensler defines

logic as

the analysis and appraisal of arguments

i think about logic less is a thing

but as a method a tool that you could

use to look at arguments and determine

certain things about that argument

we'll talk about those things later but

we might as well also understand what an

argument is since that's what we're

going to be dealing with when we do

logic

an argument has two components first it

has a set of premises which can be seen

as supporting evidence

and then a conclusion which is based on

that evidence now you could have a lot

of premises i've seen them go up to more

than a dozen personally

but for this video and for syllogistic

logic we're going to be dealing with two

premises and one conclusion

here's a more concrete example of an

argument all fish are animals

a salmon is a fish therefore a salmon is

an animal

also those three dots that form a

triangle that's just another way to say

therefore

i just use it instead of writing out

therefore because i'm lazy

so now we know what an argument is and

it might be helpful to think of some

argument examples of your own but we've

only just begun

we've actually got to test these things

i mean consider this example of an

argument

mcdonald's is healthy all frogs creep me

out

therefore biking should be illegal i

mean it's technically in the form of an

argument but something seems seriously

wrong here and i'm not talking about the

fact that i actually like frogs

so when we get an argument like this or

any other we have to put it through two

different tests

we have to test whether an argument is

valid and if an argument is sound

[Music]

so let's start with understanding what a

valid argument is

the book states an argument is valid if

it would be contradictory

impossible to have the premises all true

and the conclusion

false valid doesn't say that the

premises are true

but only that the conclusion follows

from them if the premises were all true

then the conclusion would have to be

true so to test for validity

we first don't concern ourselves about

whether the premises are true

we kind of just assume them to be true

for now so even if we get ridiculous

sounding premises like

all giraffes live on mars we don't worry

about whether it's true

what we do worry about is the

relationship to these assumed true

premises and the assumed true conclusion

to see if the conclusion necessarily

follows from the premises

this might sound weird so let's get an

example going all cats are evil

garfield is a cat therefore garfield is

evil

so again it may or may not be true that

all cats are evil or if garfield is a

cat

but that's all irrelevant we're only

concerned here with whether the

conclusion necessarily follows from

the premises now i'll explain an actual

test to test for validity later in this

video

but here's just an illustration i made

to show how this argument is valid

all cats are evil so the entire category

of cats

fits into the larger category of evil

garfield is a cat so he fits into the

cat category

and since the cat category is in the

evil category

it necessarily follows that garfield is

evil

therefore this is a valid argument but

what about an invalid argument what

might that look like

let's take a classic argument example

and modify it a bit to make it invalid

all men are mortal socrates is immortal

therefore

socrates is a man now this might sound

valid on its surface but it's really not

here's an illustration to show why so

all men are mortal

so the men category fits into the larger

mortal category

now socrates is immortal and while that

may mean socrates can fit into the man

category

he could also be somewhere else like in

this fish category because fish are also

mortal

so you see that even if it's possible

for the conclusion to follow from the

premises it isn't necessary or forced

the conclusion must follow necessarily

from the premises for an argument to be

valid

so that's what a valid argument is again

i'm actually going to give you a way to

test for validity later on in this video

but first i want to distinguish a valid

argument from a sound argument

now a sound argument doesn't need much

explanation basically a sound argument

is a valid argument but the premises are

also true

remember how we don't really care if the

premises are true when we test for

validity

well here we actually do care an

argument could be unsound in either two

ways

one it might have a false premise or two

its conclusion might not follow from the

premises

here's the classic example of a sound

argument all men are mortal

socrates is a man therefore socrates is

mortal

as you could see it is both valid as an

argument and the premises are true

don't worry yourself too much though

about sound arguments or determining

whether the premises are true

because in my experience the majority of

logic focuses around testing for valid

arguments

a critical reasoning class might be

better suited for judging if a premise

is false or not

anyway now that we have distinguished

between a valid and sound argument

let's now introduce a certain type of

logic which is arguably the most famous

and accessible

[Music]

shout out to aristotle it's surprising

that we haven't talked about him yet on

this channel

but he is the inventor of syllogistic

logic now there are three parts to an

argument in syllogistic logic or

syllogisms for short

there's the major premise such as all

men are mortal there's the minor premise

such as socrates as a man

then there's the conclusion such as

socrates mortal pretty straightforward

the thing is though when working with

logic you're probably not going to be

dealing with full

words but rather letters that represent

a word usually you just substitute the

word for the first letter

so instead of all men are mortal you'd

put all m

is o with o representing mortal because

we already have an

m but wait why are we saying all m is o

instead of all m r o well that's because

there's specific language used for

syllogisms

specifically there are five words used

in these sentences

those words are all no sum

is and not and when you combine the

letters that represent a thing

with these words you get stuff like all

f is

h or no g is d these are called

well-formed formulas but in class we

just called them woofs for short

here are some examples of wolves used in

syllogisms and underneath them are some

non-wolfs notice how the non-woofs

underneath use

language that isn't limited to our five

words now there's also the issue of

capitalization

because as you've probably noticed some

letters are capitalized and others

aren't

so in each wolf there are two letters

now for the first letter

if the wolf begins with a word such as

some all or no

then both letters get capitalized

however if the wolf begins with a letter

and not a word

then the first letter is lowercase but

in this second case where the first

letter is lowercase

what do we do about the second letter

well if the term you're representing is

a general term

then you use a capital letter so for

example eats ice cream

would be a capital e and soccer players

would be a capital s

now if the term you're representing is

singular and points to a specific person

or thing

then you should use a lowercase letter

for example amygdalavids would be a

lowercase a

and nietzsche would be a lowercase n now

with all this in mind

see if you could convert this sentence

here into a woof pause the video if you

need to

okay assuming you pause the video and

you have an answer here is the correct

answer

as you can see we only use those five

words that are available to us and our

letter capitalization meets the rules we

previously established

finally now that we understand wolf's

and syllogistic logic

we can now go over a method for testing

the validity of a syllogism

[Music]

so let's start by converting this

argument on the left into a syllogism

using wolves no rabbits eat meat bugs

bunny is a rabbit

therefore bugs bunny doesn't eat meat

for the first part

we could translate this into no r is e

with r representing rabbits and e

representing eat

meat remember we capitalize both because

this woof starts with a word

next we can translate the second part

into b is r

with b for bugs bunny being lower case

because this wolf begins with a letter

and r for rabbit being uppercase because

it is a general term

finally we could translate this

conclusion into b is not e

alright nice job guys we have our

syllogism next we want to underline

any letter that is distributed but what

does it mean for a letter to be

distributed

an instance of a letter is distributed

in a woof

if it occurs just after all or anywhere

after no

or not so here are some examples of

distributed letters and wolves that are

underlined

again pause the video if need be but

let's now look at our example

since our first wolf starts with no any

letter after that is distributed

so we underline both the r and the e our

next line has no distributed letters

according to our rules

so nothing gets underlined finally for

our conclusion

b is not underlined but e is because it

comes after the word

not so our syllogism with underlined

distributed letters should look like

this

next we need to star certain letters

star premise letters that are

distributed and conclusion letters that

aren't distributed

so for our example here our first

premise has both letters distributed

so we star both of them none of the

letters in our second premise is

distributed so nothing gets starred

finally in our conclusion we only star b

because it is not distributed

this is now what our syllogism looks

like both distributed and starred

last step here we check if every capital

letter is starred

exactly once and then we check if there

is exactly only one star on the right

hand side

so checking over our example we see that

r and e

our only capital letters are starred

exactly once

so it passes that test next we check if

there is exactly one star on the right

hand side

and there is on the e in our first

premise and since it passes those two

tests

the argument is valid the syllogism is

valid if and only if

every capital letter is starred exactly

once and there is exactly one star on

the right hand side

now i don't expect you all to get this

immediately which is why i highly

recommend the book of this stuff

interests you because there are also

practice problems to help you fully

grasp all this

as to why the star method works i really

don't know

and i would expect it to be extremely

tedious to try and learn how it just

does in the end

but just to recap hopefully you've

learned what logic is

the difference between a valid and sound

argument the basics of syllogisms and

well-formed formulas or wolves as we've

called them

and the star test to test for validity

don't ask me to go further with logic

because it's really not where i focus

much in my education

however just learning some basics has

really helped me greatly in life

if you got any value out of this video

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hit the like button if you've learned

anything and i wish you all a beautiful

rest of your day

you