How to Think: Introduction to Logic, Lecture 4 with David Gordon - Mises Academy
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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.
![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.](https://image.slidesharecdn.com/logiclecture4-130626141954-phpapp02/85/How-to-Think-Introduction-to-Logic-Lecture-4-with-David-Gordon-Mises-Academy-20-320.jpg)
![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.](https://image.slidesharecdn.com/logiclecture4-130626141954-phpapp02/85/How-to-Think-Introduction-to-Logic-Lecture-4-with-David-Gordon-Mises-Academy-21-320.jpg)
How to Think: Introduction to Logic, Lecture 4 with David Gordon - Mises Academy
- 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.’