It's been a long and winding road as the Beatles used to say, but we're finally at
the last stages of reconstructing arguments.
We've looked at stage one, which is close analysis. Stage two which is get down to
basics. Stage three which is sharpen edges, stage four is organize parts, and
we are doing stage five which is fill in gaps and we'll also get to stage six
which is conclude. Stage five really consists of four
separate steps. First we need to assess the argument for
validity. Then we need to add suppressed premises.
Enough of them to make it valid. Then we need to assess those suppressed
premises for truth or falsehood. And then we need to qualify the
suppressed premises in order to make them true.
The whole goal is to make the suppressed premises both plausible for their truth,
and enough to make the argument valid. So, these steps within the stage really
do work in tandem together to try and make the argument good.
We already learned how to assess validity.
You simply ask, "Is it possible for the premises to be true and the conclusion
false, and if so, the argument is not valid and if not, the argument is valid."
And the way you figure out whether it's possible is you try to tell a story or
describe a situation and if you can describe a coherent situation where the
premises are true and the conclusion is false, then that show that the argument
is not really valid. The main topic for today is, what do you
do when you assess the argument for validity and you find out it's not
valid?" And the answer is, you add suppressed premises, enough of them to
make the argument valid. But that might seem like cheating.
I mean, you start with an argument that's no good, it's not valid,
and then you just throw in some extra premises in order to make it valid.
Why is it that's just distorting the argument and making up something that
wasn't there? The answer is that it's not really bad.
And if it were bad, we'd all be in bad shape because in everyday life, people
always take things for granted. They make assumptions.
We do it too, and if we didn't, boy, our arguments
would be really long and boring. So there's something to be said in favor
of suppressing premises, at least, the obvious ones that people really do take
for granted. But we can also get tricked.
People can suppress premises that really are questionable, and they just don't
want us to see that they're making that assumption.
So, it's useful to fill out the argument with suppressed premises to make sure it
really is valid, because that brings those assumptions out in the open, where
we can assess whether or not they're true or false.
Another reason to fill in suppressed premises is to understand the argument
better. Because if people suppress premises, then
they're showing us some of their footprints along the path.
But if we really want to know the full path that their reasoning followed, we've
got to see every single footprint. So,
the goal of bringing up the suppressed premises is to let us trace exactly where
the reasoning is from one step to another.
So there are two goals: One is to trace the full path every step and the other
goal is to see if there are any miss-steps or they are trying to hid
something from us by getting rid of one of their footsteps, so that's the point
of bringing up suppressed premises. To accomplish these goals is tricky.
You have to find suppressed premises that are just strong enough to make the
argument valid but not so strong that there going to be implausible.
because you don't want to ascribe all kinds of suppressed premises to the
person that they didn't really believe, and they didn't really need for their
argument. So it's kind of like Goldilocks and the
Three Bears. You want suppressed premises to be not
too hot and not too cold, but just right. Here's an example from a previous
lecture. My wife always gives me either a sweater
or a board game. This box does not contain a sweater
because it rattles when it's shaken so this time she must have given me a board
game. We put this in standard form this way.
First premise: This box rattles when I shake it and that shows you it doesn't
contain a sweater. Third, she always gives me either a
sweater or a board game. Conclusion, this time she must have given
me a board game. Now the first step in this argument is,
this box rattles when I shake it. And the conclusion there is it doesn't
contain a sweater. That's the part of the argument we want
to focus on here and ask whether that argument is valid.
The argument is not valid, because it's possible for the premise to be true and
the conclusion false. How can that happen?
Well, my wife might be fooling me. She might know that I expect either a
sweater or a board game, so she puts a sweater in the box.
And then she puts little rocks around the outside so when I shake it, I'll hear
something. So that's possible, and that shows that
the argument's not valid. Well, how can we make the argument valid?
The question here is, can we add a suppressed premise that will turn this
invalid argument into a valid argument? Here's one that will do the trick.
A box that contains a sweater doesn't rattle when shaken.
Now the argument looks like this. This box rattles when I shake it.
The box that contains a sweater doesn't rattle when shaken, so this box doesn't
contain a sweater. The explicit premise is that this box
rattles when I shake it. The suppressed premise is that a box that
contains a sweater doesn't rattle when shaken and together they are suppose
support the conclusion that this box doesn't contain a sweater, but do they
really support that conclusion? Is the argument valid?
Well, it's valid only if there's no possibility that the premises are true
and the conclusions false. Without the suppressed premise we saw
this might be possible, because my wife might be fooling me and putting rocks
around the sweater. So let's see if that's going to ruin the
validity of this argument. No!
Because if the sweater has got rocks around it so it makes noise when I shake
it, then the premise that says a box that contains a sweater doesn't rattle when
shaken turns out to be false. So that's not a case where the premises
are true and the conclusions false because the premise is false in that
case. So, by adding this premise, we actually succeeded in making the argument
valid. The problem of course is that validity is
not enough for a good argument, as we saw several lectures ago.
You can have an argument that's very bad, when the argument is not sound. What we
want really is soundness. So, that's why we need the next step,
mainly, check the supressed premises for truth.
Assess whether they're true or false. And, if they're not true, then you need
to qualify them, in order to make them true.
because you don't want to claim that the person giving the argument was assuming
this falsehood, when the didn't have to. So let's see if there's some way to
qualify this suppressed premise in order to make it true.
How can we qualify this premise to make it true?
How are we going to do that? Let me think.
Oh. What about that little word only.
You could add that. You could say, a box that contains only a
sweater doesn't rattle when shaken. But the word only, what exactly does that
mean? We need to clarify that.
What exactly is the word only exclude? It excludes something, that's the
function of the word only, but what does it exclude?
Well. It probably excludes other things that
might make the rattling sound like if my wife put rocks in the box.
So we can clarify this premise by saying a box that contains only a sweater and
not anything else that might make a rattling sound when shaken, won't rattle
when shaken. Well, is that premise true?
Well, you might quibble about details but it's close enough for now.
What we need to do though is to go back and determine whether, when we put that
suppressed premise in, the argument's valid.
And the argument now looks like this. This box does rattle when shaken, and a
box doesn't rattle when shaken if it contains only a sweater and not anything
else that makes a rattling sound. So this box doesn't contain a sweater.
Is that valid? Well, no,
for the same reason we saw before, because my wife might be a trickster who
puts rocks around my sweater in the birthday present box in order to fool me.
Then, the premises can be true, and the conclusion false.
It's possible that, the first premise is true.
This box rattles when I shake it. And the second premise is true,
a box doesn't rattle when shaken if it contains only a sweater and nothing else
that makes a rattling sound. But it's false that this box doesn't
contain a sweater, because it still does contain a sweater,
and it contains a sweater in addition to those pesky little rocks that make all
that rattling noise. Well, if your argument's not valid, we've
got to go back to that other step and add another suppressed premise.
Remember how I told you how these different steps within this stage work in
tandem and what's happening is you've got to check it for validity, add a
suppressed premise, recheck for validity, maybe add another suppressed premise, and
that's what we're doing now. So what kind of suppressed premised can
we add. Well, we could add my wife is not a
trickster but basically that amounts to she wouldn't put rocks in a birthday
present with a sweater in order to fool me.
So we could make that a little more explicit by making the suppressed premise
something like this. If this box contains a sweater, then it
only contains a sweater and it doesn't include anything else that would make a
rattling sound when shaken. And now we can stick that as an extra
suppressed premise into the argument. Now the argument looks like this.
This box rattles when I shake it. A box doesn't rattle when shaken, if it
contains only a sweater and not anything else that makes a rattling noise when
shaken. If this box contains a sweater, then it
contains only a sweater and doesn't contain anything that rattles when
shaken. So this box does not contain a sweater.
Now we have an argument that's valid. And the suppressed premises are true, at
least given our life's not a trickster, which she's not, I assure you.
And it looks like we have a sound reconstruction,
just what we were looking for. Admittedly,
this argument is a lot longer and more convoluted than the original,
and that shows why people suppress premises instead of talking the way this
argument goes. And of course, many people would be
perfectly well convinced by the original argument because they share the
assumptions that are in the suppressed premises.
So why do we go through all the trouble to go through this process and add the
suppressed premises? Remember, the reason is that we want to
understand the pathway between the premises and conclusion.
We want to understand how the reasoning works step by step by step.
And we want to do that because sometimes people are going to include suppressed
premises that aren't true, and we want to bring them out and make
those assumptions explicit so that we can assess them for truth and falsehood.
And when you're talking to somebody you trust, you might not have to do that and
it's okay to suppress premises. But when you really want to know whether
the argument's any good, that's when you want to fill it out with the suppressed
premises. The point of going into detail on this
example is to illustrate this stage of reconstruction.
You want to assess the argument for validity,
add suppressed premises that make it valid.
Check them for truth. If they're not true, you qualify them,
and then you go back and see whether that qualification made the argument not valid
anymore. And you go back and forth and back and
forth until you've got a sound reconstruction.
The same steps are going to apply to all kinds of suppressed premises.
And sure enough, there are all kinds of suppressed premises.
So let's go through a few examples a lot more quickly in order to show the variety
of suppressed premises that are assumed in arguments.
Here's one example. Abraham Lincoln turned 40.
On February 12th, 1849. Therefore, Charles Darwin also turned 40
on February 12th, 1849. Now, is that argument valid?
No chance. Of course it's possible for the premise
to be true and the conclusion false. So we have to add a suppressed premise.
The suppressed premise is, that Abraham Lincoln and Charles Darwin were born on
the same day. And they were, it happened to be February
twelfth, 1809. So now, we've filled out the argument.
Abraham Lincoln turned 40 on February 12th, 1849.
Abraham Lincoln and Charles Darwin were born on the same day, therefore Charles
Darwin also turned 40 on February 12th, 1849.
Now is the argument valid? No.
It's still [LAUGH] not valid. because Darwin might have died before
1849. So we have to add another suppressed
premise. Mainly, that both Abraham Lincoln and
Charles Darwin lived beyond 40. So now we have a fuller argument.
Abraham Lincoln turned 40 on February 12th, 1849.
Abraham Lincoln and Charles Darwin were born on the same day.
Both of them lived beyond the age of 40. Therefore, Charles Darwin also turned 40
on February twelve, 1849. Now the argument looks pretty good.
We had to have two suppressed premises but we finally have a valid argument.
And what this shows is that sometimes the suppressed premises are purely factual
matters. In this case that they were born on the
same day and that they both lived beyond 40.
So sometimes we have factual suppressed premises.
Here's another quick example. You ought to obey her because she's your
mother. Here, the premise is that she's your
mother and the conclusion is that you ought to obey her.
Well, is that argument valid? No way cause it's possible that she's
your mother but it's false that you ought to obey her.
When could that happen? Maybe, she was like abusive or stupid or
whatever. Then maybe you ought not to obey her even
though she is your mother. So we have to add a premise, namely, you
ought to obey your mother. Now we can say she's your mother, you
ought to obey your mother therefore you ought to obey her, but of course that a
supressed premise you ought to obey your mother is questionable because maybe she
was abusive or stupid. So let's add another supressed premise
that your mother was not abusive or stupid, of course we also have to qualify
that moral premise that you ought to obey your mother if she's not abusive or
stupid. And now the argument looks like this -
she's your mother, you ought to obey your mother if she's not abusive or stupid.
Your mother was not abusive or stupid. Therefore, you ought to obey her.
An notice that here, we added a moral premise about the fact that you ought to
obey your mother under certain conditions.
Namely, she's not abusive or stupid. And the second premise is she was not
abusive or stupid. So, we have a moral premise and a factual
premise, both being suppressed in the argument that you ought to obey her
because she's your mother. Here's another .
It's the Sabbath, so you ought to go to synagogue.
Well, that's clearly not valid. One suppressed premise is that you're
Jewish. The other suppressed premise is you
haven't been to synagogue already today, on this Sabbath.
And the third suppressed premise is a religious norm,
mainly Jews ought to go to the synagogue on the Sabbath.
And you need that whole bunch of suppressed premises in order to get from
the premise, that it's the Sabbath, to the conclusion, that you ought to go to
synagogue. And of course all of those premises might
be questionable. Some people would question them.
Some people would deny them, but the point here is to figure out what's being
assumed by someone who gave the original argument.
And anybody who says it's the Sabbath, so you ought to go to synagogue, seems to be
assuming you're Jewish, you haven't been already, and Jews ought to go to the
synagogue on the Sabbath. So what these suppressed premises do is
they bring out the assumptions that somebody who gave that argument must have
had in mind. The last case is a little bit trickier.
It has to do with linguistic suppressed premises.
Jen and Bob are first cousins, therefore they share a grandparent.
Now, in order to understand that argument, you
have to know that first cousins always share a grandparent. That just follows
from the definition of what a first cousin is.
But it's not quite so obvious, is that biological sisters are female.
And so, there's even more need to bring out that linguistics suppressed premise
in this case. But it's still not necessary to make the
argument valid. It's just not possible that Janet and Bob
are first cousins, and they don't share a grandparent.
Because the suppressed premise is purely linguistic, so it's necessarily true, so
you can't possibly be first cousins without sharing a grandparent.
Still, the point of bringing out linguistic suppressed premises is to show
every little step along the way. The argument might be valid without those
suppressed linguistic premises, but we won't understand why it's valid and why
the reasoning goes through unless we add the linguistics suppressed premise.
So it's worth doing that. Shh.
Here's a trick. Don't tell anybody.
Okay? It's just between me and you.
You can always make any argument valid just by adding a suppressed premise that
says if the premises are true, then the conclusion is true.
But don't tell anybody, because if people start doing that, and
they start making the argument valid that way, with that suppressed premise, we're
never going to understand the pathway of reasoning.
It makes the argument valid, but it doesn't serve the real purpose of adding
suppressed premises which is to understand the pathway of reasoning.
So you can do that. It's a trick.
It makes that argument valid but it doesn't achieve our goal because our goal
is not just to make the argument valid, it's to make the argument valid so that
we can understand the pathway of reasoning.
So it's important to know that trick, but don't use it unless you have to.
The examples so far have been pretty trivial, I admit it.
But the same points apply in very important context such as politic
debates, politician can suppress premises in perfectly legitimate ways.
They're just trying to save time and make their arguments more efficient, maybe
even sometimes clearer because you don't have to add all those little details.
But sometimes politicians abuse suppressed premises.
They take things for granted that they shouldn't be taking for granted.
Here's an example. A politician might argue, my opponent is
soft on crime because he's opposed to the death penalty.
Well, that assumes, as a suppressed premise, that anyone who's opposed to the
death penalty must be soft on crime. And if the politician were to come out
and say that, it would seem pretty questionable,
and that's probably why he suppresses it. And then another politician might say, my
opponent is in favor of the death penalty,
so he must not have read all the recent studies that show that the death penalty
doesn't deter. Well that argument assumes the suppressed
premise that if you've read those studies you'ld be convinced by them,
and that the only point of the death penalty is deterrence.
But the point is that politicians talking about extremely important issues can take
things for granted, that if they were brought into the light of day will be
questionable, and that's why they hide them.
So when you're listening to people give arguments on important issues in your
life, then you ought to be looking for these
suppressed premises and asking yourself whether or not you really ought to be
agreeing with them about that assumption. Finally, we finished reconstruction.
Yipee, right? Oh, no, not quite,
because there's one more stage, and that stage is drawing a conclusion.
Of course, if we've come up with a sound reconstruction, then we know that the
argument is sound, and we know that the conclusion is true,
because every sound argument has a true conclusion.
But if we don't come up with a sound reconstruction, then what do we say?
Well, you've got to ask, whose fault is it?
It might be the fault of the argument. Maybe we couldn't come up with a sound
reconstruction because there just is no sound reconstruction.
But maybe we couldn't come up with a sound reconstruction because we just
weren't imaginative enough, or try hard enough.
Still, if we try really long an hard, and charitably interpret the argument as
best we can to make it, look as good as we can, and we still can't make it sound.
Then, we've at least got reason to believe that the argument's not sound.
Of course, that doesn't mean that the conclusion's not true,
because unsound arguments can still have true conclusions.
But at least we know that this argument doesn't prove that the conclusion is
true. And so, this method of reconstruction can
lead us either to the belief that the argument is sound, because we found the
sound reconstruction, or to the conclusion is not sound,
because we tried long and hard to find a sound reconstruction that didn't, but
that's still not going to show us that the conclusion of the argument is false.
The point of reconstruction then is to reach a conclusion on this issue of is
the argument sound or not. And if we try our best and do it as well
as we can and charitably, then we can be justified in believing that the argument
is sound or not.