Understanding Assertions, Propositions, and the Gettier Problem

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Feb 27, 2026

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Assertion: A linguistic act (spoken or written) that carries a truth value—true, false, or indeterminate.
Example: “This cat will pee on my desk before the end of the show.” The truth value is indeterminate until the show ends.
Question: A linguistic act that does not assert anything and therefore has no truth value.
Proposition: The content or meaning of an assertion, independent of the language used.
“This is a cat” (English) and “Este es un gato” (Spanish) assert the same proposition.
A proposition is true when it corresponds to reality (e.g., the object referred to as “this” is in fact a cat).

Propositional Attitudes and Belief

Propositional attitude: The speaker’s mental state toward a proposition.
If the speaker believes the proposition is true, the attitude is belief.
If the speaker pretends the proposition is true while actually disbelieving it, the attitude is disbelief.
Belief: Holding a propositional attitude of truth.
One can believe “This is a cat” even if it is false; the belief is still a belief because the attitude is that the proposition is true.
Consequently, false beliefs are possible.

Justification

Justification: Evidence or support for a belief.
Testimony: Accepting another’s word, especially from an expert, as reliable evidence.
First‑person observation: Information acquired through the senses (e.g., directly seeing a cat and identifying it as a cat).
Most everyday knowledge is justified by testimony (teachers, books, news), but justification can also arise from personal observation.

Traditional Definition of Knowledge

Knowledge is traditionally defined as justified true belief.
True: The belief corresponds to reality.
Belief: The subject holds a propositional attitude that the proposition is true.
Justified: The belief is supported by evidence (testimony, observation, etc.).

The Gettier Problem

In the 1960s, Edmund Gettier presented cases where someone has a justified true belief but, intuitively, does not have knowledge.
Gettier argued that “justified true belief” is insufficient because luck can make a justified true belief true without it being knowledge.

Gettier Cases

Smith–Jones Job Case (Gettier’s original)
Smith is told by the reliable company president that Jones will get the job.
Smith counts ten coins in Jones’s pocket.
Smith forms the belief: “The person who gets the job has ten coins in his pocket.”
Unbeknownst to Smith, the president’s testimony is false; Smith, not Jones, gets the job, and Smith also has ten coins.
Smith’s belief is justified (testimony + observation) and true (the job‑holder has ten coins), yet his justification does not actually point to the truth.
Chisholm’s Sheep/Dog Case
Looking across a field, one sees an object that looks like a sheep and believes “There is a sheep in the field.”
The object is actually a dog, but a real sheep is hidden behind a hill.
The belief is justified (the visual appearance) and true (a sheep exists), but the justification is based on a misidentification.
Both cases illustrate that a justified true belief can arise from faulty justification, suggesting that knowledge requires something beyond JTB.

Ongoing Philosophical Debate

Many philosophers view Gettier’s examples as having undermined the justified true belief definition of knowledge.
The debate continues: if knowledge is not JTB, what additional condition(s) are required?
Contemporary discussions still explore possible solutions and alternative definitions.

Takeaways

An assertion is a linguistic act that carries a truth value, while a question does not assert anything and has no truth value.
A proposition is the content of an assertion independent of language, and it is true when it corresponds to reality.
Propositional attitudes describe a speaker’s mental state toward a proposition, with belief being the attitude that the proposition is true, allowing for false beliefs.
Knowledge has traditionally been defined as justified true belief, where justification can come from testimony or first‑person observation.
Gettier cases show that having a justified true belief does not guarantee knowledge because the justification may be faulty or involve luck.
Philosophers continue to debate what additional conditions beyond justified true belief are needed for knowledge.

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Epistemology Textbook Recommended

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Full Transcript YouTube

Crash Course Philosophy is brought to you
by Squarespace.
Squarespace: Share your passion with the world.
You probably think you know a lot of things.
But do you know what it means to know something?
We’ve spent quite a bit of time discussing
beliefs and knowledge, but we haven’t really
been specific about what we mean when we talk
about those things.
Thankfully, philosophers love a good definition.
They have very specific and lucid ideas in
mind when they use terms like know or believe
or proposition or justification.
And, about ten minutes from now, you too will know what you’re really saying when you use those words.
But, just because these terms have been defined, doesn’t mean that philosophers aren’t still arguing over them.
Because you know, that’s how philosophers
do.
Their definitions might seem kind of obvious
at first, but the more you think about them,
the more nuanced they turn out to be.
Like, is having knowledge of something the
same thing as being correct?
Or, if you believe something to be true, and
it is true, does it matter if your belief in it is justified?
And can you be right about something without
really trying?
Answers to these questions and more await
you, as well as
cats!
[Theme Music]
So you’ve heard this already: Philosophers
love a good argument.
But you’ve figured out by now that philosophers
argue in a different way than, like, kindergarten
kids, or Internet trolls, or other people
who confuse “arguing” with sniping back
and forth or just thinking up witty comebacks.
Nope. Philosophers have all kinds of rhetorical
devices at their disposal that they can use
to advance an idea, or call into question
the ideas of their interlocutors.
So in order to hold your own in a philosophical
debate, you’re gonna have to know the difference
between two things that sound like exactly
the same thing: an assertion, and a proposition.
And you’ll need to be able to tell whether
someone actually knows what they’re talking
about, or if they just believe what they’re
saying might be true.
For example: The sentence I’m saying right
now is an assertion. An assertion is a linguistic
act – either spoken or written – that
has a truth value. And despite what it might
sound like, truth value isn’t a measure
of how right something is. It’s just the
state of being either true, or false, or indeterminate.
All declarative sentences have truth values.
Declarations that assert something about the
past or present are either true or false.
And assertions about the future are indeterminate,
at least when they’re expressed, because
no one knows if they’re right or not yet.
For example, I’m gonna assert that “This cat will pee on my desk before the end of the show.”
That assertion has a truth value, but it’s
indeterminate, because the show’s not over yet.
We’re just gonna have to wait and see.
Now, all of this contrasts with other kinds of linguistic acts, like questions, which don’t assert anything.
“This is a cat” is an assertion, as opposed
to “Is that a cat?,” which is a linguistic
act, but not an assertion.
But the substance of what you assert has a
name, too.
The content of your assertion is your proposition.
It’s the underlying meaning of what you’re saying.
So even though an assertion itself can change,
depending on say, what language it’s spoken
in, its meaning doesn’t change just because
its outer packaging does.
Like, “This is a cat” and “Este es un
gato,” both assert the same proposition.
And a proposition is true if it asserts a
claim that corresponds to reality.
The proposition when I assert “This is a
cat,” is true if the object of the “this”
is in fact a cat, and false if it is anything
other than a cat. Like, “This is a cat.”
It’s worth pointing out that attitude counts,
too, when you’re asserting something.
A speaker’s mental state toward the proposition
they’re making is their propositional attitude.
If I say, like, “This is a cat,” but I
actually believe it to be a rat and I’m
trying to fool you, then philosophers would
say that I have a propositional attitude of disbelief.
Whereas, if I think I’m speaking truthfully,
I have a propositional attitude of belief.
And of course, you’re not going to get very
far as a philosopher unless you understand
the classic definition of belief itself. Based
on the lingo you’ve learned so far today,
belief is just when you take a propositional
attitude of truth.
I believe that this is a cat, if I think it’s
true – that is, if my attitude is that the
assertion corresponds to reality. And even
if I’m wrong -- even if there were an aardvark
on my desk, or if there weren’t a cat on
my desk at all, which there isn’t anymore
-- if I really thought there was a cat on
my desk, that would just be my belief.
My propositional attitude, in other words,
is what determines if I have a belief.
What all this means is that I, like everyone
else, can have false beliefs. Simply thinking
something doesn’t make it correspond to
reality, which is what’s needed for truth.
But of course, the fun of arguing is showing
off what you know to other people, or at least
producing really clever evidence to support
your case.
So, this raises the question of what it means to actually know something, in the philosophical sense.
The traditional definition of knowledge is
that it’s a justified true belief.
Note that there are three separate components here.
So, I have knowledge that this is a cat if:
I first believe i’s a cat
And also that it is in fact a cat – that
is, my belief corresponds to reality and is
therefore true. And finally, I can be said
to have knowledge about this cat if my belief
is justified – meaning, I have some sort
of legitimate evidence to support my belief.
Now, we’ve already defined truth and belief.
Justification is simply evidence, or other
support, for your belief. If you remember
back to episode 2, you’ll recall that premises
offer justification for conclusions. And justification
can come in a variety of forms. Most often,
it comes about through testimony – just
taking someone’s word for it. Not all testimony
is strong, or trustworthy, of course. But
if it comes from someone who’s an expert
on the topic in question, you might consider
the testimony to be reliable.
And the fact is, most of what you know about
the world, you learned through testimony.
You took your teachers’ word for it when
they were teaching you stuff, and the same
goes for every book you’ve ever read and
every news report you’ve ever seen. They’re
all just forms of testimony, which you accepted as justification for your knowledge, and your beliefs.
But justification can come in other forms,
too. Another common type is first person observation
– information you acquire through your senses.
If I believe that a cat is a cat, because
I already have robust and well-informed beliefs
about cats, then, having had extensive experience
with them in the past, I’m identifying the
cat as a cat through my direct contact with
it
It looks, feels, acts like a cat. Ergo: cat!
But! Philosophy wouldn’t be any fun if the
key to knowledge were that easy, right?
Until American philosopher Edmund Gettier
came along in the 1960s, philosophers were
in pretty widespread agreement about the definition
of knowledge -- that it’s justified true belief.
Because, you can believe any old thing, but
in order to know something, it just makes
sense that you must also have evidence for
your belief, and it must be true. In other
words, you can have a false belief, but you
can’t have false knowledge. And if something
you thought you knew turns out not to be true, then the fact is, you never actually knew it, you just believed it.
And likewise, you might happen to hold a true belief, but if you don’t have any justification for it, if you
just accidentally happened to be right, which happens sometimes – that doesn’t count as knowledge, either.
Enter Edmund Gettier. Gettier wrote a short
but fabulously influential paper that turned
the standard understanding of knowledge upside
down.
He did this by proposing what came to be known
as Gettier cases – situations in which one
can have justified true belief, but not knowledge.
Which brings us to this week’s Flash Philosophy!
Let’s go to the Thought Bubble.
Here’s one of Gettier’s original cases.
Smith and Jones have both applied for the same job.
The president of the company told Smith that Jones will get the job. This counts as evidence;
the president of the company would seem to be a reliable source of this information.
Meanwhile, Smith counts the coins
in Jones’ pocket and sees that there are
ten coins in there. Smith then forms a belief,
based on his first person observational evidence
of the coins, as well as the testimony of
the company president.
He comes to believe that: The person who gets
the job has 10 coins in his pocket.
But, it turns out, the testimony of the president
was false, and it’s Smith, not Jones, who gets the job.
AND, it just so happens, unbeknownst to Smith,
that he also has 10 coins in his own pocket.
So, Smith has a belief – that the person
who gets the job has 10 coins in his pocket.
And that is justified – because he counted
Jones’ coins, and the president told him
Jones was getting the job. And his belief
also turns out to be true – the person who
got the job did have 10 coins in his pocket.
However, neither pieces of justification actually
pointed Smith to the right answer. The president’s
testimony was wrong, and the 10 coins that
he saw were in Jones’ pocket, not his own.
So it seems Smith simply lucked into being
right.
Gettier argued that we now have a case of
justified true belief that is not knowledge.
As he pointed out, you don’t KNOW something
if you simply stumbled into the right answer.
Thanks Thought Bubble, the philosophical world
was turned upside down by this idea, and philosophers
– loving a good counterexample – began
generating their own Gettier cases.
American philosopher Roderick Chisholm proposed
this one:
Looking across a field, you see an object
that looks like a sheep, and you form the
belief that “there is a sheep in the field.”
It turns out that the object you see is actually
a dog.
Yet, there is also a sheep, obscured from
your vision by a hill.
So, you have a justified true belief, but
the justification for your belief -- the object
that you saw – is not a sheep. You just
lucked into being right.
Once you understand how it works, it’s pretty
easy to generate Gettier cases of your own.
And many philosophers today think that Gettier successfully destroyed the “justified true belief” definition of knowledge.
But even though the 1960s might seem long
ago to you, remember: philosophers are in
the business of having millennia-long debates
about stuff. So it shouldn’t surprise you
that the philosophical debate about this is
still a-raging.
But if knowledge is not justified true belief,
then…whaaat is it?
Next time, we will look at one possible answer.
In the meantime, you learned about some of
the key concepts we use when discussing belief
and knowledge. You learned what defines an
assertion and a proposition, and that belief
is a kind of propositional attitude. We also
learned about forms of justification and the
traditional definition of knowledge, which Edmund Gettier just totally messed with, using his Gettier cases.
And the cat did not pee on my desk! Because
the cat was unable to spend any time at all
on my desk. So it turns out the assertion
that I made was false.
But it is a true assertion that this episode
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