Video summary
Welcome to Introduction to Formal Logic, a course designed not only for philosophy and mathematics majors but also for anyone interested in systematic critical thinking across various fields like law, computer science, and everyday life. The primary focus of this class is deductive logic, which investigates the structure of arguments where the truth of the premises guarantees the truth of the conclusion. Unlike casual uses of "logic" that refer to common sense or the internal rules of a system, formal logic specifically evaluates whether an inference is valid based on its form rather than the content of its claims. The professor illustrates this by presenting examples such as conditional statements about God and life's meaning, syllogisms regarding whales and mammals, and arguments involving students carrying backpacks to demonstrate how logical validity depends entirely on the arrangement of terms.
To clarify these structures, the course introduces a formal language that translates ordinary English sentences into schematic symbols, making it easier to see whether an argument is logically sound or flawed. For instance, while one might intuitively reject a conclusion because they believe whales are not hairy, logic dictates that if we accept specific premises about mammals and hair, the conclusion must follow regardless of real-world facts until proven otherwise. Conversely, arguments like "All students carry backpacks; therefore, anyone carrying a backpack is a student" fail logically because the order of terms matters in universal statements. By converting natural language into formal notation using symbols for variables, quantifiers, and conditionals, students can objectively assess whether an argument's conclusion necessarily follows from its premises without being misled by emotional reactions or factual disagreements about the subject matter.
The course operates as a self-paced online module divided into units, each focusing on specific learning outcomes that must be mastered to progress. Students are expected to complete readings, watch video lectures, and solve practice problems before taking an exam; passing with a satisfactory score typically unlocks the next unit in this sequential process. Grading is based entirely on mastery levels rather than traditional letter grades for every assignment, where achieving an A requires satisfying scores on all seven exams corresponding to each of the course's units. If a student does not pass an initial attempt, they are allowed multiple retakes after waiting forty-eight hours and completing additional practice sets, ensuring that their final grade reflects genuine understanding rather than random chance or minimal effort.
Practical preparation for the class involves familiarizing oneself with the D2L learning platform, downloading the free open educational resource textbook (though a nominal fee may apply if one chooses not to opt out), and setting up an account on Carnap for homework assignments and exams. The professor strongly advises using a laptop or desktop computer rather than a mobile phone due to formatting issues that make reading difficult on smaller screens. Students are encouraged to carefully review the syllabus, explore available resources like print-on-demand options if desired, and utilize various communication channels such as email, Teams, and office hours for support. Additionally, references to an older course number or title in some materials should not cause confusion, as this is simply a legacy designation for the same current content intended for 205-level students rather than advanced graduate work.
Read the full video transcript
Hello. Welcome to Introduction to Formal
Logic, Phil 205, and Math 205. I'm Matt
Brown. I'll be your professor for this
course. What we're going to do today is
two things in this introductory lecture.
We're going to first talk about the
topic of the course. What is logic? And
specifically, what is formal logic? And
what is the types of formal logics that
we're going to mostly focus on in the
course, deductive logic? And know right
off the bat I want to say logic is not
only uh a sort of technical uh field of
interest to philosophy majors and
mathematics majors but also relevant
across a wide variety of areas. Logic
questions appear on law school entrance
exams. There's a lot of use of logic in
computer science and engineering.
um and I think a lot of relevance to
your everyday life. So um in terms of
analyzing ideas and engaging in
systematic and critical thinking. So I
look forward to sharing this with you.
Let's get into it. I want to start by
talking about what logic is. Now in
everyday language we use the term logic
in a few different ways. We you we we
say something is logical to mean that
it's like reasonable or common sensical.
Maybe we might also talk about logic in
the sense of the logic of some system or
activity, the the logic of the the this
business or the logic of capitalism, the
logic of war. Those aren't quite the
senses of logic we mean. Logic in our
sense means the investigation and
evaluation of arguments and inferences.
If we make an argument or we we make an
inference, what makes that a good or bad
one? By argument, by the way, I don't
mean a fight, yelling and hair pulling
and stuff. I mean presenting reasons or
ideas to try to convince someone of
something. Now, deductive logic, which
is our main focus in this class,
concerns those particularly strong kinds
of arguments or inferences where the
truth of the premises that you start
with guarantees the truth of your
conclusion, right? We'll talk more about
that in a minute. Let's look at some
examples of arguments. Here's one. So,
premise one, if God does not exist, then
life is meaningless. Premise two, if
chocolate exists, then life is not
meaningless. Premise three, chocolate
exists. Conclusion four, therefore, God
exists. Now, we can ask, is this a good
argument? And we can evaluate that in
different ways. The logical way of
evaluating it tells us that yes, it is a
good argument. If premises one through
through three were true, then conclusion
four would also have to be true. Maybe
you disagree with one of the premises,
right? Maybe you think premise one or
premise 2 is false. Maybe you think
premises like one and two cannot be true
or false because they deal with with
concepts that don't have that don't have
that kind of meaning. But those are not
logical issues. Those are issues of of
content. If you think on the other hand
that the premises are true, then you're
obligated to believe the conclusion.
That's what that's what formal logic
tell that's what logical reasoning
general deductive logical reasoning in
general tells us. Here's another
example. All whales are mammals. All
mammals are hairy. So all whales are
hairy. Again, this argument is a good
one logically [clears throat] speaking.
Now you might object. Whales, dolphins
aren't hairy, but they're mammals. So,
the argument must be bad. Well, in what
sense might you say it's bad? You could
deny
uh premise one, say that whales are
fish. Herman Melville seems to believe
that. Uh or you could deny premise two,
say some mammals are hairy, right? But
you but if you accept premise one and
two, you it seems like premise three
must or conclusion number three must be
right must be true. Actually, I think
the argument is right. Even whales and
dolphins have hair. Although sometimes
just in uterero before they're born and
[clears throat] and they lose it.
Depends, I guess, on what you mean by
hairy. Here's a third argument. [sighs]
All students carry a backpack. The
professor carries a backpack. Therefore,
the professor is a student. Now, this is
a bad argument. Not because the premises
are false. Suppose the premises are
true. Suppose it's true that all
students and the professor carry a
backpack. Can you see why? Even if all
students carry a backpack, that isn't
the same as saying that all backpack
carriers are students. The order matters
in this kind of statement. And the order
of the the order in these cases makes it
such that the conclusion doesn't follow
from the premises. And one of the tools
of formal logic is representing or
translating claims in ordinary language
into what we call a formal language that
makes more clear the form or structure
of the claim. We'll learn what the
symbols I'm about to show you uh mean in
future units. But we can we can
translate claims like if God does not
exist then life is meaningless into a
kind of schematic form. Right here I'm
using G to represent God and God exists
and M to represent life is meaningless.
And then the arrow indicates the if then
structure of the statement. All students
carry a backpack. We might represent
with a slightly more complicated set of
formal tools like this. For all X, if X
is a student, then X carries a backpack
would be how we would read that formal
statement. Consider another statement
like this. The person who knows the
combination to the safe is not a spy.
We'll learn much later in the class that
the probably best way to represent this
formally uh is a is a formula like this.
Now that's complicated and maybe a
little intimidating.
But by the time we get to it, it will be
clear to you what it means and and fair
and you'll learn to do this translation
work pretty easily. So, that's just a
very quick sort of introduction into the
basic ideas that we're going to be
working with in this class. Now, I want
to get into some of the mechanics of it,
how how you're going to work your way
through this class. It's an online
class. We're not going to have meetings
face to face. And so, it it's actually
going to work a little bit more in a
self-paced
way, independent way as follows. So the
class is divided into several units,
right? Based on the kind of core
learning outcomes that we're going to
focus on. To get more information about
the learning outcomes, you should
consult the syllabus. And you'll see
both the learning outcomes that you'll
achieve if you make the way through the
course and how they are tied to each of
the units. So for each unit you need to
do the readings, watch the video lecture
like this one and complete at least one
practice problem set with the exception
of this unit zero has no practice
problems. It's just the introduction. Um
so for the for this uh unit just read
the syllabus, watch this lecture and
that's what you do and this will unlock
the exam for that unit. In unit one,
there'll be reading from the textbook.
There'll be another video lecture.
There'll be a set of practice problems.
Um, I think we've got four practice
problem sets for the first unit. Um, and
then once you do that, you'll be able to
take the exam. If you get a satisfactory
score on the exam, and it's differs per
exam, but most of them it's an 80% or
better score, that will unlock the next
unit, and then you can start on the next
unit. If you don't get that score, it
doesn't mean you're done, right? You can
retake the exam many times if you need
to, although you do need to wait 48
hours and complete additional problem
sets in order to unlock the next re a
retake of the exam. So, you can take all
of the time you need to master each of
the units, which corresponds to
different learning outcomes for the
course. And however however far you make
it indicates your level of mastery in
the class. Your grade in the class is a
function of how many units and so how
many learning outcomes you gain mastery
over. For example, an A in the course
means that you get a satisfactory grade
on all seven exams. You've made it
through all seven units and a
satisfactory level. That's a level of
mastery. An A minus is exams 1 through
six.
A B+ is exams 1 through five plus giving
a good try on exam number six. You you
tried you tried once. It was more than
just a you know click on it and open it
and submit whatever. It's a a genuine
attempt, [clears throat]
right? The syllabus will give the full
breakdown of grades and and what you
have to do to achieve that grade.
Satisfactory as I said depends on the
assignment but is typically about 80%
correctness. That might seem low, but
the exams are not easy. And to get to
that level, it really shows that you
have basically mastered that that set of
concepts, right? Completion of an
assignment, and this is most relevant
for exams, but also for the practice
exercises, means making a reasonable
effort to complete it, which could
consider the number of questions
answered, the amount of time taken, um,
and the final score that you get. even
though it's not satisfactory, it's it's
not just uh it's better than random
chance, let's say. So, I'll look at your
attempts closely to determine whether
they meet this criterion whenever it's
potentially an issue. Now, I want to
talk about what comes next. What should
you be doing as part of this
introductory unit for the course? First,
you should spend some time poking around
D2L, making sure you understand how D2L
in general works if you're new to it and
how the course in particular is set up.
I'll go through in a minute some of the
features of that. You need to download
and print or buy a copy of the textbook.
The textbook is provided for free. Um,
it's an open educational resource. Uh,
so you don't have to buy the textbook
for this class, although you can buy a
print ondemand version and that that
link is in the syllabus and in D2L or
you can download it and print it. You
can also view it on your computer. By
the way, just because the textbook for
this course is an open educational
resource does not mean that you will not
pay the textbook fee for this class. you
have to intentionally opt out of that
fee for your classes. So, I would look
at this class and your other classes and
determine whether it makes sense for
you, whether it's worth it to pay the
textbook fee so you can opt out if you
need to. But just because there is no
textbook to buy for this class other
than maybe a moderate or nominal fee to
to print the book, uh doesn't mean you
won't pay that fee. So, so keep an eye
on that. I strongly recommend that you
do not look at the book on your on your
phone, on your cell phone. Um, it the
formatting is not really amanable to
that. It's going to be very difficult to
read. In general, I recommend that you
use a laptop or desktop computer and not
a a phone to take this course. You
should read the syllabus carefully and
make sure you understand it. Let me know
if you have any questions. And you
should you should log into the system
called CARAP for the first time using
the link in D2L. Carnap is where a lot
of our practice exercises, you can think
of them as homework assignments. Uh as
well as some of our exams will be used
and you'll need to you'll need to access
that through D2L. So it syncs with your
D2L account. And once you feel
comfortable with all of that and if
you've you've asked me any questions if
you have them, you should go ahead and
take the practice exam. One of the last
things I want to do is just mention
briefly that occasionally you'll find in
the video lectures in this course
references to philosophy 320, a class
called deductive logic. That is that is
the old number and title for this class.
So I originally taught this class under
that number. Some of the slides uh in
the video lectures will have that course
number on it. But don't worry, the
content is exactly the same. This is not
a 300level class masquerading as a 200LE
class. This always should have been a
200 level class and it's been corrected.
Now, so just if you ever see references
to to Phil 320 deductive logic, just
know that that that's this class. In the
unusual case that you took that class
already, um you should not be taking
this class. Okay? There shouldn't be any
overlap. Okay. Next, what I'm going to
do is give a little guided tour of the
D2L setup for this class. I have logged
into D2L and clicked on our course. And
here's the basics that you see. When you
log in, you'll see the welcome to class
announcement here. It hasn't posted yet
cuz the class hasn't started. But most
of what you'll find that you need to
access in the course is under content
which you can view here or or down here.
So I'll click up here. And I've gone
through everything before. So you'll it
will look a little different because not
everything here on the left will be
unlocked when you first come in. You'll
also see the video lecture that I'm
recording now will be posted there. But
you'll see the course introduction gives
you some basic information about what
you need to do in this unit. The link to
the textbook is here, which you can
download or print. You'll also see
there's a link to order it print on
demand um from Lulu. I think it's $7 and
change plus shipping cost. The class
syllabus is here, which has all the
basic information about the class, what
the different units consist of, and how
the grading works. You'll need to click
on Carnapp login to set up your account
in Carnapp, which I mentioned just a
minute ago. So, make sure you do that.
And you'll come back to this page often
to do your practice exercises and also
some of your exams. And then once you've
clicked on everything else, the practice
exam will open up and you'll need to
complete this in order to unlock unit
one. And generally this is how all the
course components are going to work. All
the different units are going to work.
You'll unlock the unit. You'll get some
basic information and you'll go through
activities like the lectures, like the
practice exercises one by one. And once
you've done a sufficient amount of work
of that material, not necessarily all of
it, it'll unlock the exam for that unit
which you can take. And once you receive
a satisfactory score on that exam, it'll
unlock the next unit. Finally, I just
want to mention that although this is an
online asynchronous self-paced course,
there are lots of ways that you can get
help and you can get in touch with me.
I'm always available uh for you to reach
out and I will do my best to get back to
you quickly. I do have office hours uh
that are listed on the course website on
D2L and you can come see me in person in
my office in Feainer, but you can also
uh reach me on teams, email and by phone
during that time. All that information
is available on D2L. If that time is not
a good one for you, you can reach out
and I will respond promptly. If you
don't hear back from me uh within 24
hours, please send me a note unless it's
the weekend. So, you should hear back by
the next business day from me. So,
that's the basics of this class. As I
said, feel free to reach out if you have
any questions and best of luck with it.