Lecture 3-6 - Fill in Gaps and Conclude

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 gonna be implausible.
Cuz you don't wanna 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 wh en 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 fal se.

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. Cuz 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 s

aw 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, cuz 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 rec
onstruction, 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 twelfth, 1849. Therefore, Charles
Darwin also turned 40 on February twelfth,

1849. Now, is that argument valid? No
chance. Of course it's possible for the

premise to be true and the conclus ion
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

twelfth, 1849. Abraham Lincoln and Charles
Darwin were born on the same day,

therefore Charles Darwin also turned 40 on
February twelfth, 1849. Now is the

argument valid? No. It's still not valid.
Cuz 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 twelfth, 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 a

lso 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
i t'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 politicia ns 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 a rgument 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.