| I. Logic is the study of the methods and principles used in distinguishing
correct from incorrect reasoning. |
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B. Logic differs from psychology in being a
normative or a prescriptive discipline rather than a descriptive discipline. |
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1. I.e., it prescribes how one ought to
reason; it's not concerned with how one actually does reason. |
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2. Logic is concerned with laying down the rules
for correct reasoning. |
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3. Consequently, logic seeks to distinguish good
arguments from poor ones. |
| II. How Logic helps reasoning: |
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A. "Practice makes better."
Some examples of how this course can help reasoning about the world
are as follows. |
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1. Consider this syllogism: |
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All followers of Senator Jones are in favor of
higher taxes.
All communists are in favor of higher taxes.
All followers of Senator Jones are communists. |
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It will become easy for us to recognize the
fallacy in this argument as the fallacy of the undistributed middle term. |
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2. Consider this informal argument: |
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In spite of the large number of UFO spottings
that can be attributed to weather conditions and known aircraft and other factors, there
are hundreds of sightings that cannot be accounted for. Hence, we can safely conclude that
UFO's exit. |
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Consider this counter-example: |
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In spite of the large number of quarters put
under kid's pillows which can be attributed to sneaky parents, brothers, sisters, and so
forth, there are hundreds of cases which cannot be accounted for. Therefore, the tooth
fairy exits. |
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B. As well, this course can help with
"the negative approach"—that we
avoid errors by being aware of them, e.g., being aware of common
formal and informal fallacies. |
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1. Consider the passage, "Napoleon became a
great emperor because he was so short." In this short argument, the fallacy of false cause
(or non causa pro causa) occurs. If this
argument were good, all or most short persons would become great emperors. |
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2. Consider the passage, "People in
developing countries get old as an earlier age, because the average life expectancy is so
short in those countries." Due to infant mortality, people do not get older more
quickly; the fallacy of division occurs. |
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C. Methods, criteria, and techniques, all are
given as methods of testing correctness. These are some of the
techniques we will be learning and using in this class. These
methods are shown here merely
for purposes of illustration.. |
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1. For example, we can draw Venn Diagrams to
show the fallacy of the undistributed middle term in problem I, A
discussed above. |
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2. Or we can show the fallacy in I, A
by appealing to
specific rules. |
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All P is Mu.
All S is Mu.
All S is P.
The term shared by both premisses is said to be undistributed because
it does not refer to each and every persons in favor of higher taxes. |
| III. There are several kinds of logic which exhibit a kind
of family relation: dialectic, multivalued logic, logic of commands, fuzzy logic, etc. |
| IV. In this course, basically, we will use just two kinds of
logic: deductive and inductive. |
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A. Deductive
Logic: concerned with
determining when an argument is valid (i.e., deals with conclusive inferences). |
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1. A deductive argument is one which claims
that its conclusion follows with necessity. |
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2. If that claim is not met, then the argument
is said to be invalid. |
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3. Consider this example from Time
magazine about the Kennedy assassination: |
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"Since tests proved that it took at least
2.3 seconds to operate the bolt on Oswald's rifle, Oswald obviously could not have fired
three times--hitting Kennedy twice and Conally once--in 5.6 second or less." |
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2.3 |
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The first load
ned not be counted. |
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2.3 |
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verses |
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2.3 |
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+ 2.3 |
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+ 2.3 |
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6.9 sec. |
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4.6 sec. |
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The response by Frederick T. Wehr:
"Sir…This argument, which has appeared in many publications since the
assassination, is faulty, and I am surprised that I haven't seen it refuted before this.
Assuming that the bolt of Oswald's rifle can, in fact, be operated in 2.3 seconds, then
Oswald definitely could fire 3 shots in less than 5.6 seconds, for a stop watch would be
started when the first shot was fired; the second shot would be fired when the stop watch
read 2.3 seconds, and the third shot would be fired when the stop watch read 4.6 seconds.
You have apparently overlooked the fact that, in the time it takes to fire 3 shots, it is
only necessary to operate the bolt twice." |
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B. Inductive Logic is concerned with the
correctness of inferences for which the evidence is not conclusive (i.e., probable
inferences). |
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1. Hence, an inductive argument is one whose
conclusion is claimed to follow with probability. |
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2. Consider the example from Mark Twain's Notebook:
"…at bottom I did not believe I had touched that man. The law of probabilities
decreed me guiltless of his blood, for in all my small experience with guns I had never
hit anything I had tried to hit and I knew I had done my best to hit him." |
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3. Or consider extrapolation techniques used in
stock market prediction, e.g., the wedge formation. |
| V. What logic is not: |
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A. Logic is not the science of the laws of
thought--in which case it would be a descriptive science like psychology. |
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1. Sometimes people can come to conclusions
reliably without being able to know or explain how the conclusion was reached. E.g.,
the so-called intuitive type of personality. |
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2. Often people can come to the right conclusion
for the wrong reasons. Logic is the study of the modes of correct reasoning as shown in an
interpersonal manner. |
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B. Logic is not really the science of reasoning
either because the logician is not interested in the psychological processes of reasoning. |
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1. The logician is interested in the structure
of arguments. |
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2. People infer
statements and statements entail
other statements. |
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3. We want to say that the entailment is there
even though someone does not at this time understand it. |
