The document provides an overview of the categorical syllogism, including its components and rules. It defines a syllogism as having three propositions: two premises and a conclusion, where the premises make the conclusion true. It outlines the key components of a syllogism, including the middle term that links the premises to the conclusion. The document also lists rules for valid syllogisms, such as requiring the middle term to be distributed in at least one premise and prohibiting two negative premises.

1. The Categorical
Syllogism (I)
How to Think:
An Introduction to Logic
with David Gordon

2. Inference is the process of passing
to a new truth.
Inference is the third act of the mind
The other two are Conception ---
forming an idea of something---and
Judgment---connecting two
concepts, or denying that there is a
connection
Deduction moves from general to
particular. Induction moves from
particular to general.

3. Deductive Inference is called a Syllogism
In a Syllogism, there are three propositions:
Two Premises and a Conclusion
The premises make the conclusion true. If the
Premises are true, the conclusion is true.
Be careful about saying the conclusion “must”
be true. What is necessary is the whole
statement, “If the premises are true, then the
conclusion is true”. Don’t detach the
conclusion and say that it is necessary.

4. All Keynesians are opponents of the
free market
Krugman is a Keynesian
Therefore, Krugman is an opponent
of the free market
The conclusion is true but not
necessary---Krugman could change
his mind.

5. How can you get to a new truth?
Through a Middle Term
The Middle Term is found in both
premises. It is combined with the
Predicate of the Conclusion in the
Major Premise. It is combined with
the Subject of the Conclusion in the
Minor Premise
In the Conclusion, the Middle Term
(the connection) drops out.

6. Example: All giraffes are married
All men are giraffes
All men are married
The Middle Term is giraffes. This is the
term that does not appear in the
conclusion
The Major Premise is “All giraffes are
married” because it contains the
Predicate of the conclusion
The Minor Premise is “All men are
giraffes” because it contains the
Subject of the Conclusion

7. Why does the connection enable us to
arrive at a new truth?
The Subject is included in the class of
the Middle Term. The Middle Term is
included in the class of the Predicate.
In the example, “giraffes” are in the
class “entities that are married”. “Men”
are included in the class of “giraffes”.
Thus, “men”, the subject term of the
conclusion, is included in the class
“entities that are married”, the
predicate of the conclusion.

8. If one of the premises is negative
(an E or O proposition) the
explanation is different
No hippopotamus is a goalie
Some men are hippopotamuses
Some men are not goalies
Here the middle term is
“hippopotamus”. The Major Premise
excludes hippopotamuses from the
class of “goalies”
The Minor Premise includes “some
men” within the class of
“hippopotamuses”

9. Thus, the conclusion says that
“some men”, i.e., the ones who are
hippopotamuses, are excluded from
the class of “goalies”.
Note that this syllogism leaves open
whether there are men who are not
hippos and, if there are men who
aren’t hippos, whether these men
are goalies.

10. Rules for the Syllogism.
The middle term must be distributed
in at least one of the premises.
With a distributed term, you know
how much of the class the term
applies to.
In our example, “giraffes” is
distributed in the Major Premise, “All
giraffes are married.” It is not
distributed in the Minor Premise,
“Some men are giraffes”. We don’t
know how much of the class of
“giraffes” is covered by “some
men”.

11. If you violate this rule, you commit
the fallacy of the undistributed
middle.
All men are married
Some married people are divorced
All men are divorced.
“Married people”, the middle term,
is undistributed in both premises.
Thus, the argument isn’t valid.

12. If a term is distributed in the
conclusion, it must be distributed in
a premise.
All mortals are crazy
Some men are mortals
All men are crazy
Here, “mortals’ is the middle term. It
is distributed, but this reasoning is
still invalid. “Men” is distributed in
the conclusion, “all men”, but is not
distributed in the premise that
mentions it, “some men”.

13. A syllogism must have at least one
general premise
(an A or an E proposition)
Otherwise, there would be no
movement from general to particular.
Some men are crazy
Some crazy people are Keynesians
Some men are Keynesians
This also commits the fallacy of
undistributed middle.

14. A syllogism cannot have two
negative premises.
(E or O propositions)
No Misesians are Keynesians
No Keynesians are Marxists
No Misesians are Marxists.
Even though the conclusion is true,
it doesn’t follow from the premises.
The premises just exclude Misesians
and Marxists from the class of
“Keynesians”. They don’t tell us how
Misesians and Marxists are related.

15. A syllogism cannot contain an
equivocal term.
All heavy objects are objects that
weigh at least ten pounds
Human Action is a heavy book.
Human Action is an object that
weighs more than ten pounds.
“Heavy” is used equivocally, to
mean both “having a big weight”
and “dealing with difficult subject
matter.”

16. We will not go into the details, but
“Figure” refers to where the middle
term is placed in each premise.
For example, in the first figure, the
middle term is the subject of the
major premise and the predicate of
the minor premise.
All mortals are men
All crazy beings are mortal
All crazy beings are men.

17. “Mood” refers to the type of
propositions in the syllogism (A, E, I,
or O). The example is a valid mood:
A, A, A. It is in the first figure.
Aristotle thought that it was the
most evident form of the syllogism.
There are four figures. Syllogisms
not in the first figure can be reduced,
i.e., changed to the first figure, but
we won’t go into details.

18. “Sir Karl Popper has pointed out that
the idea that one could predict one’s
future knowledge. . .is
philosophically incoherent: if one
could predict one’s future
knowledge, then one would already
know it.”
Tom Palmer, Realizing Freedom,
(Cato Institute, 2009), p.444.

19. “Sir Karl Popper has pointed out that the
idea that one could predict one’s future
knowledge. . .is philosophically incoherent:
if one could predict one’s future
knowledge, then one would already know
it.”
Tom Palmer, Realizing Freedom, (Cato Institute, 2009), p.444.
This argument relies on an
ambiguity in “future knowledge”.
This can mean either “knowledge
we don’t have now but will have in
the future” It can also mean
“knowledge we have now but will
continue to have in the future.” If
you can predict what you will know
in future, then what you predict
won’t be future knowledge in the
first sense. It will be future
knowledge in the second sense. All

20. The states of the Middle East
“had all been conjured into existence less
than one hundred years ago out of the ruins
of the defeated Ottoman empire in World
War I…. This being the case, there was
nothing "utopian" about the idea that such
regimes — which had been planted with
shallow roots by two Western powers
[Britain and France] and whose legitimacy
was constantly challenged by internal
forces both religious and secular — could
be uprooted with the help of a third Western
power and that a better political system
could be put in their place.”
Norman Podhoretz, World War IV,
(Doubleday, 2007), pp.144-145.

21. The states of the Middle East
“had all been conjured into existence less
than one hundred years ago out of the
ruins of the defeated Ottoman empire in
World War I…. This being the case, there
was nothing "utopian" about the idea that
such regimes — which had been planted
with shallow roots by two Western powers
[Britain and France] and whose legitimacy
was constantly challenged by internal
forces both religious and secular — could
be uprooted with the help of a third
Western power and that a better political
system could be put in their place.” Norman
Podhoretz, World War IV, (Doubleday, 2007), pp.144-145.
This is non sequitur. It doesn’t follow from
the fact that it state doesn’t have deep
roots that it is realistic to try to replace it
with something better.

22. An argument often given against
anarchism is this:
Every conflict between protection
agencies requires some other
agency to settle it.
Therefore, there must be a central
agency that is the ultimate agency
to settle disputes.

23. This is a quantifier shift fallacy.
It moves from, “Every dispute
requires some agency to settle
it” to “There is some agency
that must settle all disputes.”
This doesn’t follow.
Compare, “Everyone has a
father” does not imply
“Someone is everyone’s father.’