(intro music)
Hi! My name is Julianne Chung,
and I am a graduate student at Yale University.
Today, I am going to talk about truth and validity.
There are many different good qualities
that arguments can have.
For example, they can be clear,
they can be interesting,
they can be persuasive, and so on.
In this video, however, we are going to discuss
just two good qualities that arguments can have
that are particularly important for determining
whether we should accept their conclusions.
The first is this: the premises of an argument may be true,
that is, they may be in agreement with the facts.
In philosophy, truth and falsity are held to be
properties of statements, but not arguments.
Second, an argument may be valid.
An argument is valid when its conclusion
follows logically from its premises.
In other words, an argument is valid
just in case the truth of its premises
guarantees the truth of its conclusion.
In philosophy, validity and invalidity
are held to be properties of arguments,
but not statements.
To see the difference between these properties,
it will be helpful to look at some examples,
all of which involve my good friend Julia's dog, Split.
This is an example of an argument
that has true premises and is valid.
Premise (1): All Australian Shepherds are dogs.
Premise (2): Split is an Australian Shepherd.
Conclusion: Therefore, Split is a dog.
In this argument, not only are the premises true,
but the conclusion follows logically from them.
Next is an example of an argument that has true premises
but is not valid.
Premise (1): All dogs are animals.
Premise (2): All cats are animals.
Conclusion: Therefore, all cats are dogs.
Here, the premises are obviously true,
but the conclusion does not follow logically from them.
Of course, this argument is clearly unacceptable,
because its conclusion is obviously false.
However, sometimes arguments can have true premises,
as well as true conclusions,
but still be invalid because the conclusions
do not follow logically from them.
Here is an example of such a case.
Premise (1): All dogs are animals.
Premise (2): All Australian Shepherds are animals.
Conclusion: Therefore, all Australian Shepherds are dogs.
Because of this, it is important
that we are careful to ensure
that the conclusion really does follow
from the premises under consideration
when we are evaluating an argument.
We are now going to look at an argument
with at least one false premise that is valid.
Premise (1): You can't teach an old dog new tricks.
Premise (2): Split is an old dog.
Conclusion: Therefore, you can't teach Split new tricks.
Here, the first premise is false,
but the reasoning is valid, because the conclusion
follows logically from the premises.
Notice, too, that just as in the last example,
the conclusion of this argument may happen to be true,
although the argument does not establish that it is.
Alright, just one more example.
This argument has at least one false premise and is invalid.
Premise (1): I like Split.
Premise (2): Training dogs is easy.
Conclusion: Therefore, I'll win a lot of awards
for teaching Split how to roll over.
In this example, not only is premise two false,
but the conclusion does not follow logically
from the premises.
You've probably already noticed that truth and falsity,
as well as validity and invalidity,
can appear in various combinations in an argument,
giving rise to four possibilities.
Let's take a moment to review them together.
Possibility one: we may have our facts right,
our premises are true, and we may use them properly.
Our reasoning is valid.
Possibility two: we may have our facts right,
our premises are true, and we may use them improperly.
Our reasoning is invalid.
Possibility three:
we may have our facts wrong,
some of our premises are false,
and we may use them properly.
Our reasoning is valid.
And finally, possibility four:
we may have our facts wrong,
some of our premises are false,
and we may use them improperly.
Our reasoning is invalid.
When we are evaluating an argument,
we should only accept its conclusions
if the first possibility obtains.
Philosophers call such arguments "sound arguments."
Because of this, you might be wondering
why we should be at all interested
in arguments that are valid, but whose premises are false?
One answer is that we are often not
in a position to know whether our premises are true.
But being able to validly infer the conclusions
that would follow from such premises if they were true
sometimes enables us to judge whether they are true.
This is because validly inferring a conclusion
that we know to be false from a given set of premises
will tell us that one of our premises must be false too.
After all, a false conclusion cannot validly
be deduced from true premises.
Consider the following example.
Say that John calls his boss at work one day,
and tells her that he is in bed
with a terrible case of the flu.
His boss, it seems, could use that information
to construct the following argument.
Premise (1): John is in bed with a terrible case of the flu.
Premise (2): If john is in bed
with a terrible case of the flu,
then he is not bowling.
Conclusion: Therefore, John is not bowling.
This argument is valid.
Its conclusion follows logically from its premises.
So, if John's boss were to see him bowling,
what could she conclude?
Premise (2) seems untouched by this bit of evidence.
Premise (1), however, is in danger.
She could conclude that John is not in bed
with a terrible case of the flu.
It seems he lied.
This is, of course, just a very simple example.
That said, hopefully it suffices to show
that we often use reasoning like this
to figure out whether claims are true or false.
Thus, it is indeed often very useful for us to know
whether an argument is valid,
even if we don't know whether its premises are true.
For more information about truth, validity, and soundness,
I highly recommend checking out Paul's video on validity
and Aaron's video on soundness.
Subtitles by the Amara.org community