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In this video on categorical arguments and reasoning I'm going to show you how to diagram
And in particular, I'm going to show you how to diagram the A-claim.
I'll do some upcoming videos on the other three
but for now I just want to get a handle on this one here.
So let's start with this:
Here's our categories of S&P and we have this overlapping segment as well
A good way to think about this is to
divide this Venn diagram into three parts
Part 1 - which represents
this region here (outlined in pink or red).
Part 2: which represents this middle region here, this overlapping segment...
of S&P (outlined in blue).
And then lastly,
region 3 which represents
this region here (outlined in green).
Now another anything about this
is you can think about it in terms of inclusion and exclusion
of members have one class in another. And so this first region here
the region in the pink (or the red) is the the region
of S and not P
the bar over the P stands for the "not." That's where there's members of the S-class
but not the P-class
because it's outside at that P circle - that P category.
So the middle section here represented by the 2
is overlapping, so it represents both
S&P - we have both members that the S&P class
in region 2. And so in region
3 we have the
P-class but not the S-class...
because this is the area were members the P class are but they're not
...not in the
area where the S-class is, so it excludes the S-class but includes the P-class.
So let's look at an A-claim here: here's the
A-claim, claims of the form
"All S are P"
So for example, "All uncles are males" is an A-claim.
It's of the form "All S are P" where "uncles"
is the subject of the claim
the claim is about "uncles"
and then, "males" is the predicate
...is the predicate
term of the claim... meaning that
the predicate says something about the uncle, it's a characteristic of uncles.
So we're saying here is that
in saying "All uncles are males" - this is the diagram.
So let's see how we get to it. Well, the way we get to it
is by shading out that particular region
that doesn't apply. The particular region.
doesn't apply is the region where S
is and not P, so the shading of this region
stands for the region that doesn't apply to the claim.
If "All S are P" then we can't have
members at the S-class that are not P - they have to be included in it.
So the A-claim is the claim that talks about the inclusion
of the members have one class in another class. In particular
the inclusion of the S-class in the P-class.
Every member at the S-class - all
"S" are members of the P-class, so the shading in the region here
means that this region doesn't apply to the claim -
it's the empty set or the null set
such that if we had a jig-saw
we could simply cut this region out that I'm shading here
pull it out and it would accurately represent the truth
of the A-claim such that
if they're is an S it exist also as a member
of the P-class. And that's how you diagram the A-claim.