The Art of Economic Argument Going Beyond Aristotelian Logic
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Aristotelian Logic
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Aristotle’s syllogisms emphasize the central concept of validity. Visualizing
syllogisms in terms of the three-circle Venn diagrams gives us a picture of validity
in the strongest Aristotelian sense: airtight, ironclad validity.
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In this talk, we will go beyond Aristotle to look at validity much more broadly.
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In general, validity refers to the degree of support between premises and
conclusion.
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Does this fact support this claim? Do these premises render the conclusion highly
plausible?
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Does this evidence give us good reason to believe the conclusion? The reasoning
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may not be airtight, but is it solid enough to act upon?
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Aristotle’s Square of Opposition
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Beyond the Syllogism
1. Spending $50 billion in annual economic aid to foreign
countries would be justified only if we knew that either they
would genuinely benefit from the exchange or we would.
2. We don’t know that we would benefit from the exchange.
3. It might further weaken our already vulnerable economy.
4. We don’t know that they would genuinely benefit.
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Beyond the Syllogism
5. The track record of foreign aid that has been misdirected,
misappropriated, or lost in foreign corruption is all too
familiar.
6. With $50 billion a year, we could offer college scholarships
to every high school graduate and major health benefits for
every man, woman, and child in the United States.79
7. Our obligations are first and foremost to our fellow citizens.
8. We should spend the $50 billion here rather than in foreign
aid.
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How Good is the Argument?
There are lots of premises in that argument, far more than in
Aristotle’s syllogisms, and lots of transition steps. Together, they
are intended to drive us toward the conclusion. But how good is the
argument? And how should we analyze an argument such as this?
Trying to deconstruct it into syllogisms is nearly impossible. We
will see how to analyze it later.
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Flow Diagram
The best way to analyze complex arguments is
with a simple visualization: a flow diagram. Such
a diagram will help us see the validity of a
complex argument. Breaks, disconnects, and
weak logical links can show us invalidity in an
argument.
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The Basic Rule
The basic rule is simple: When one claim is
intended to support another, we put an arrow
from the first to the second. The problem,
however, is that propositions don’t come
labeled as premises or conclusions. They can
function in either role. It all depends on the
context, on the structure of the argument.
Another difficulty is that the first sentence you
hear doesn’t always come first logically.
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Example
Consider this argument, for example: (1) If the
governor is impeached, we might be no better
off. (2) Impeaching the governor would require
another election. (3) But there is always the
chance that people would then vote for
someone equally corrupt.
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Ordering the Propositions
The propositions are numbered in the order of
presentation, but what we want to know is
something different. We want to know where
the reasoning flows from and where it flows to.
It will help if we can identify the conclusion.
Which is the conclusion: (1), (2), or (3)?
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Reordering
It’s proposition (1) that is the conclusion, right at
the beginning. Everything else is offered in
support of that conclusion. The logic of
the argument starts from (2), which leads to (3).
And that leads to the conclusion: If the governor
is impeached, we might be no better off.
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Branching Flow Diagrams
Of course, arguments get more complicated
than that, so we need to add complications in
the flow diagrams. First of all, arrows can
branch. A set of propositions can lead to
multiple conclusions or parallel conclusions.
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Example
Think about how to graph the following: (1) We
can get only so much money from taxes;
taxation resources have to be balanced among
different social needs. (2) Taxation for prisons
must, therefore, be balanced against taxation for
education. (3) If we build more prisons, we’ll
have less for education. (4) If we spend more on
education, we’ll have less for the prisons we
may need.
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Branching Conclusions
That argument has branching conclusions. The
first proposition leads directly to the second.
From (1) we graph an arrow to (2), but at that
point, our arrows branch.
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Branching In
Further, just as arrows can branch out, they can
branch in. Sometimes several propositions lead
to the same place.
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Example
Consider this example: (1) We are dangerously
reliant on foreign energy sources. (2) Our oil
comes primarily from the Middle East. (3) Most
of our natural gas does, as well. (4) Even the
elements in our batteries come from such places
as Zambia, Nairobi, and China.
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Convergence
First, find the conclusion. The conclusion is the
first sentence. Each of the other propositions is
an argument for that conclusion in its own right.
We graph it by having arrows converge on a
single conclusion.
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Independent and Dependent Reasons
Independent reasons function independently.
But sometimes reasons have to function
together in order to lead to a conclusion.
Dependent reasons only function together. In a
case where all three propositions work together
as dependent reasons, we can mark them like
this:
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Stress Testing
How do we know whether propositions are working
independently or dependently toward a
conclusion? The answer is argument stress testing.
If we have independent reasons and one of them
fails, the argument should still go through. If we
knock out a reason and the argument is still
standing, it must be an independent reason.
However, that won’t hold for dependent reasons.
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Graphing Complex Arguments
We now have the basic elements of any
argument flow diagram. But when we start to
graph real arguments, we can see how those
elements can combine into an immense variety
of structures.
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Revisiting Previous Argument
Consider the argument we started with above,
about spending $50 billion in foreign aid or for
college scholarships here. The conclusion is (8).
How are the rest of the propositions meant to
support that conclusion? Here’s a sketch of that
argument:
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Argument Clusters
The argument uses two dependent clusters, functioning
independently of each other. One cluster uses (1), (2), and (4):
Together, they offer an independent argument. If a stress test
showed that the information about the college education in (6) and
(7) was false, then (1), (2), and (3) together would still stand as an
independent argument for the conclusion. Propositions (3) and (5)
are backups for (2) and (4). All those together make one argument
for the conclusion. Another argument comes from (6) and (7)
working together.
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Data and Warrants
We can expand on flow diagrams for arguments
using the work of the philosopher Stephen
Toulmin. We have talked about premises that
function together, representing them as
numbers
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Data and Warrants
What Toulmin points out is that there is often
more structure just beneath that plus sign.
Some of those numbers may stand for premises
that function as what he calls data. Some
function instead as what he calls warrants. They
function together but in a very specific way.
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From Data to Warrant to Conclusion
Any argument starts with some kind of data. But
an argument often doesn’t just go from data to
conclusion. It has a middle step—a step that
says how the data are supposed to lead to the
conclusion. Thus, instead of a plus sign between
premises (1) and (2), it might be better to
represent them like this:
Example
The total revenue test can help policymakers
determine which tax is best in terms of being
able to raise as much revenue as possible with
the least deadweight loss. If a good is price
inelastic it might be a good candidate for a tax.
Therefore, it might be a good idea for
policymakers to try to use the total revenue test
when choosing which goods to tax.
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A Global Carbon Tax or Cap-and Trade?
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