Soundness and Validity 1

[ Music ]>>All right, we’ve got some new
vocabulary for deductive arguments. Hooray. I’ll bet you couldn’t wait. Validity, soundness, where an
argument is valid or sound. We need some new vocabulary to help describe
the things that we’re seeing in sentences. Remember that having the vocabulary for
something helps you describe it, see it, and know it, and that’s why we do this at all. You all said you wanted new vocabulary,
and so here comes some for you. If we take a look at deductive arguments,
you’ll have seen lots of different kinds by now. The etymology of deductive, of course, means
to lead away, and then the idea here is that you’re leading away from a premise
as if you’re leading your logic, the process of your thinking away from
some principal belief, abstraction, definition, rule, gray area even. The definition of horses is listed right here, though that’s not a complete
definition obviously. All horses are mammals. All mammals are animals. Therefore, all horses are animals. The idea is that you apply the
minor premise to the major premise and then you have a new conclusion. There’s nothing too spectacular about this,
but when we do get deductive arguments that are spectacular, they
really hit home for us. I don’t know what your reaction is to
the video that I had our class watch, but to my mind it’s one of those key deductive
arguments that people out there accept or they reject and then they
feel the consequences of. Remember Alan from the video? In the video, the rule was be nice. Work hard. You will do fine. Alan is nice, and Alan works hard. Alan will do fine. The idea is that we’re taking a close
look at that rule, see how the specifics of that rule play out and what conclusions
can follow from that rule or led away from that rule once we start applying them
to actual specific circumstances and people. Logic in deductive argument has to be
tested and work in order for it to work. That seems self evident,
like it has to be sensitive. You know what it means here. If you take a look at these fairly plain Jane
arguments, which really hinge on definitions of things like horses, and
look down at the bottom. It says if the logical premises follow
one right after another in logical order, the argument is said to be valid. All horses are mammals. Next step, all mammals are animals. Next step, therefore, all horses are animals. Step, step, step. Now, of course, arguments can
get a lot longer than this. We see it actually in the one
we’ve already taken a look at. Be nice, and then we had to add that
second major premise, work hard, and then the third part of that
sentence, you will do fine. The idea that [inaudible] has communicated to
his students is that those three are connected, and that’s part of the major premise. That can be quite complex indeed. It even can be as complex as a student slapping
other students and still having him be nice and working hard, which we will have
talked about in class by this time. That’s validity. Step by step. One step follow right from another, and since
the premise itself can be kind of nuance for tricky, that’s why we slow it down, take a
close look at it and see whether it’s something that can allow minor premises
to follow straight from it. Next bullet point, if a major premise
is untrue in a deductive argument and the reasoning is invalid, the
whole argument is said to be unsound. There’s that soundness. If we don’t accept a definition of a horse as
being a mammal, all right, or if the validity of the argument won’t go step by step, then
we’ve got a problem with the soundness. The soundness has a lot more
to do with that premise and whether we accept it
[inaudible] taking a look at this. If at any point we didn’t accept the
connection between being nice and working hard and you will do fine for yourself,
then we’d be really examining with careful eyes the soundness
of that first premise. Okay, so let’s see if I can
sum these up for you. Let me see if I can sum up this
business about validity and soundness. Validity has to do with how the logical premises of a deductive argument follow one
right after another in logical order. They seem to make sense because as if
you’re walking up a flight of steps, one step naturally leads to the next, the foundation of those steps
being the major premises. The validity has to do with how
those statements fit together. Step, step, step. How do they go? Soundness has to with whether the major
premise is true or warranted or accepted and how the reasoning is also valid. So in that sense, it encompasses validity,
and that’s a kind of unique definition or a definition that people won’t
have heard of and won’t remember from a previous class, so I
have to spell it out here. That means if we’re thinking
about it, that soundness and sound arguments are a
subset of valid arguments. You can have valid but un-sound arguments,
which is not meant to throw you or confuse you. It’s meant actually to say that sometimes
people will accept as a major premise something that is not quite accepted or warranted
at the time to see how the logic of an argument will play itself out. They’ll try to test out the validity of
an argument even though they may know that the major premise is
not universally accepted. That’s the way it was, in fact,
with the Declaration of Independence and some other major documents where
they were testing out the soundness and then the validity of their arguments. So all sound arguments are valid. Not all valid arguments are sound. By the way, since I’m using [inaudible] and
the example of Alan and that rule, be nice, work hard, good things will follow, I realize
that are a lot more deductive arguments in the video that for the purpose
of this video I’m ignoring. There are arguments made about why the
students should be these things even if other people aren’t being these things
and how this work will pay off in the future, how it creates a culture of excellence. You might notice that all of these
definition or premise arguments are arguments that are deductive in nature, really
focus on how the students should behave, and he’s trying to inculcate
lots of values through them. Are there shortcuts in this class? Of course not. You shouldn’t take shortcuts. “You kids are American,” he says,
and, of course, each kid will define that during the course of his or her experience
in class and really throughout their lives. He goes back to Atticus who, to him, represents
a deductive argument, or he gives examples or an instruction of delayed gratification so
students don’t try to take the candy right now. They can wait until after dinner. Or that they can do this, that they
are able instead of being unable. Okay, and my last question
there, can you think of others? I bet you can actually, especially
from that video. Just because it’s a fifth and
sixth grade class does not mean that the lessons they learned are elementary. Sometimes it actually helps to look back at the
deductive arguments that you recognize going on in the videos for fifth and sixth graders
because you can see how they have played out in relief for your own
colleagues and for yourself. All right, here’s some questions for you that
we return to class and talk about more detail. Logic has to be tested and
work in order for it to work. Have the argument over on the left hand side or,
excuse me, on the right hand side of the slide. All right, so let’s see if we can figure out two
questions which we’ll try and answer in class. Here is the statement about
logic has to be tested and work in order for the whole argument to work. Over on the right hand side we have the
old argument that we looked at before. Be nice. Work hard. You will do fine. Alan is nice. Alan works hard. Alan will do fine. What can we conclude about this sentence? Alan did fine. Does that mean that Alan was nice? Think about that for a minute. We take a look at the argument up on the right. We see down below that Alan did fine. Does that mean necessarily that Alan was nice? If you have an answer, jot it down now. Keep yourself honest. If you know why you have your
answer, you might even add that because you have an explanation
already in mind, which is good. Actually it allows you to be
precise with your description. The answer here is no, and the explanation
why will be what we try to tackle in the next video but also in class. This particular argument has
a problem with its validity, and we will take a look at that more in detail. Why is there a problem with
validity in this argument? Second case example. Logic has to be tested and
work in order for it to work, in order for the argument to work itself. We have the same argument
over on the right hand side. Here we have the statement,
“Alan did not do fine.” Does that mean that Alan did not work hard? Hmm, okay, different kind of question,
and we’re thinking about this. I want you to think about your answer, even
jot it down on that same sheet of paper. Alan did not do fine. Does that mean that Alan did not work hard? Let me think about that. If we can compare this argument
to the original argument, what do you think about what this says? You have your answer? Do you know why you have your answer? Yes, it does mean that actually. Can you explain why? Again, this is an issue that hinges
on the validity of an argument. This will work in part because
of the validity of the argument. We’re not trying to be purposefully tricky here. Alan did not do fine. Therefore, it cannot follow that he worked
hard based on this rule that we have above. Now in class we’ll answer some
of these and compare our answers, but take a look at these two examples. “Alan did not do fine” and
what can be concluded, and “Alan did fine” and what can be concluded. I’ve given you the answers for them
and asked you to think about them. If you don’t understand them or if you want
to have more further discussion about them, let’s look at them right in class
and try to work [background music] through the logic of the statements. [ Music ]

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