A Very Basic Introduction to Logic and Syllogistic Logic
Summary
TLDRThis 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
😀 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.
🧐 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.
📚 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.
Mindmap
Keywords
💡Argument
💡Logic
💡Premise
💡Conclusion
💡Validity
💡Soundness
💡Syllogism
💡Well-formed Formula
💡Distribution
💡Star Test
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
then feel free to subscribe and hit the
bell to be the first ones notified when
i drop another video
hit the like button if you've learned
anything and i wish you all a beautiful
rest of your day
you
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