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Philosophy 103: Introduction to Logic
The Nature of Logic

Abstract: Some of the uses of logic are illustrated, and deductive arguments are briefly distinguished from inductive arguments.

I. Logic is the study of the methods and principles used in distinguishing correct from incorrect reasoning.
B. Logic differs from psychology in being a normative or a prescriptive discipline rather than a descriptive discipline.
1. I.e., it prescribes how one ought to reason; it's not concerned with how one actually does reason.[1]
2. Logic is concerned with laying down the rules for correct reasoning.
3. Consequently, logic seeks to distinguish good arguments from poor ones.
II. How Logic helps reasoning:
A. "Practice makes better."  Some examples of how this course can help reasoning about the world are as follows.
1. Consider this syllogism:
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.
It will become easy for us to recognize the fallacy in this argument as the fallacy of the undistributed middle term.
2. Consider this informal argument:
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.
Consider this counter-example:
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.
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.
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.
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.
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..
1. For example, we can draw Venn Diagrams to show the fallacy of the undistributed middle term in problem I, A discussed above.

2. Or we can show the fallacy in I, A by appealing to specific rules.
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.
A. Deductive Logic: concerned with determining when an argument is valid (i.e., deals with conclusive inferences).
1. A deductive argument is one which claims that its conclusion follows with necessity.
2. If that claim is not met, then the argument is said to be invalid.
3. Consider this example from Time magazine about the Kennedy assassination:
"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."

The first load ned not be counted.
2.3 verses 2.3
2.3 2.3
6.9 sec. 4.6 sec.
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."
B. Inductive Logic is concerned with the correctness of inferences for which the evidence is not conclusive (i.e., probable inferences).
1. Hence, an inductive argument is one whose conclusion is claimed to follow with probability.
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."
3. Or consider extrapolation techniques used in stock market prediction, e.g., the wedge formation.
V. What logic is not:
A. Logic is not the science of the laws of thought--in which case it would be a descriptive science like psychology.
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.
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.
B. Logic is not really the science of reasoning either because the logician is not interested in the psychological processes of reasoning.
1. The logician is interested in the structure of arguments.
2. People infer statements and statements entail other statements.
3. We want to say that the entailment is there even though someone does not at this time understand it. Logic Homepage


1. E.g. Immanuel Kant writes, “Logic does not really contain the rules in accordance with which man actually thinks but the rules for how man ought to think. For man often uses his understanding and thinks otherwise than he ought to think and use his understanding. Immanuel Kant, The Bloomberg Logic in Lectures on Logic trans. J. Michael Young (Cambridge: Cambridge University Press, 1992), [26] 13.

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