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Summary Notes

These are summary notes so that you can really listen in class and not spend the entire time copying notes. These notes will not substitute for reading the chapters in the text, nor can they replace the text as there are many subtleties we will discuss in class that are also presented in the text. Use these as a supplement.

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Section 5.1| Section 5.2 | Section 5.3

Smartboard notes


5.1 Standard Form, Mood and Figure

Syllogism: deductive argument consisting of two premises and a conclusion.

Categorical syllogism: 

deductive argument consisting of three categorical propositions that is capable of being translated into standard form.

Parts of a Categorical Syllogism:

Terms:

Major Term: predicate of conclusion

Minor Term: subject of the conclusion

Middle Term: occurs once in each premise and does not occur in the conclusion

Premise Names:

Major Premise: top; one that contains the major term

Minor Premise: listed second; one that contains the minor term

Standard Form Rules

Note the need to rearrange arguments that are not in standard form.

Mood: letter names of proposition that make it up (A, E, I & O)

Figure: determined by the location of the middle term in the two premises that make it up

Unconditionally Valid Categorical Syllogisms

Explain what "unconditionally valid" means. This should be a review of Chapter 4 in that we also dealt with unconditionally valid syllogisms there also.

Aristotelian Additions

Backwards Reconstruction of Arguments Given Mood & Figure

 

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5.2 Venn Diagrams

 

Venn Diagrams are on every major graduate school test known to man. Many of them have more than three variables, but we'll learn tricks to solve the most complicated of puzzles.

Review the method for drawing a basic Venn Diagram; note the seven areas that have to be visible.

The Diagram:

The Rules:
  1. Mark premises only.
  2. Universal premises are entered first.
  3. Focus on the two areas (variables) addressed in the premise you are graphing and give only minimal attention (i.e., ignore) the third circle.(See my note below about particular propositions [I & O statements] requiring an X.)
  4. Particular conclusions assert existence (i.e., are Aristotelian) and therefore should be evaluated for both conditions.
  5. Shade all of the area in question.
  6. Note the process summarized below for entering particular propositions.

All arguments containing premises that require us to place an 'x' on the line between two sections are invalid!!!

    1. The 'X' cannot dangle on the outside of a diagram, and also cannot be placed on the intersection of two lines. (This one is a bit obscure until you start doing the problems.)
    2. Process for determining where to place the 'X': When you have a particular proposition that requires an X be placed in the diagram do the following:
    3. Isolate the two diagram areas (S & P, P & M, or S & M) where the X will be placed. 
    4. If one of the areas is already shaded, then the X should be placed in the other half of the area. If neither area is shaded, then the X should be placed on the boundary line between the two areas.

Examples:

Aristotelian Diagrams

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5.3 Rules and Fallacies

These five rules may be used as a convenient cross-check against the method of Venn Diagrams.The first two are dependent on distribution.

Rule 1: Middle term must be distributed at least once. Rule 2: All terms distributed in the conclusion must be distributed in one of the premises. Rule 3: Two negative premises are not allowed. Rule 4: A negative premise requires a negative conclusion, and a negative conclusion requires a negative premise. Rule 5: If both premises are universal, the conclusion cannot be particular.

 

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Smartboard Notes from Chapter 5 Lectures:

Smartboard Notes from Chapter 5 Lectures:

5.1 Mood and Figure

 

 

 

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5.2 Venn Diagrams

 

Section 5.3: Rules for Checking Validity

 

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