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MLS 570 Critical Thinking Reading Notes for Fogelin:. Categorical Syllogisms We will go over diagramming Arguments in class . Fall Term 2006 North Central College. The difference …. All squares are rectangles All rectangles have parallel sides All squares have parallel sides

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## MLS 570 Critical Thinking Reading Notes for Fogelin:

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**MLS 570Critical ThinkingReading Notes for Fogelin:**Categorical Syllogisms We will go over diagramming Arguments in class. Fall Term 2006 North Central College**The difference …**• All squares are rectanglesAll rectangles have parallel sides All squares have parallel sides • This argument cannot be written as p qq r . p r • This is because the premises in the argument are not compound, nor do they contain an “if … then” construction. [needed in order to use the conditional connective.]**Categorical Propositions**• All squares are rectanglesAll rectangles have parallel sides All squares have parallel sides • Each premise asserts a relationshipbetween the two terms. To understand this relationship we use a diagram of two overlapping circles. • This way of showing how Categorical Syllogisms work are called VennDiagrams**Diagramming propositions:All A are B**• All squares are rectangles – this says that there is nothing that is a square that is not a rectangle. • So we shade out the part of the diagram where nothing exists. [the pink in this diagram] Squares Rectangles**Diagramming propositions:No A are B**• Two groups or “classes” that have nothing in common would be diagrammed like this. Again you shade in the area where there is nothing. TrianglesSquares**Diagramming propositions:Some A are B**• How do we handle “some”? • For example: Some aliens are spies . We don’t want to shade in a whole area as that would mean “all”-- so we put an asteriskin the middle – this means that there is “at least one person who is an alien is also a spy” aliens spies**Diagramming propositions:Some A are not B**• Some aliens are not spies. aliens spies**Diagramming the propositions:Some B are not A**• Some spies are not aliens. aliens spies**The 4 Basic Categorical Forms I**A: All S is P E:No S is P I: Some S is P O: Some S is not P. • These are not propositions, but patterns for whole groups of propositions. • “Some spies are not aliens” is a substitution instance of the O propositional form.**The 4 Basic Categorical Forms II**One more wrinkle ;) A: Universal Affirmative E. Universal Negative All S is P No S is P I:Particular Affirmative O: Particular Negative Some S is P Some S is not P**The 4 Basic Categorical Forms II**How this looks in a table. Affirmative Negative. UniversalAll S is P No S is P ParticularSome S is P Some S is not P**The four basic categorical forms**• All S is P [S=subject term, P=predicate term] S P**The four basic categorical forms**• No S is P [S=subject term, P=predicate term] S P**The four basic categorical forms**• Some S is P [S=subject term, P=predicate term] S P**The four basic categorical forms**• Some S is not P [S=subject term, P=predicate term] S P**Exercise 1- #4:Indicate the information given in the diagram**using the 4 basic propositions. Some S is not P Some S is P Some P is not S [this is not one of S P the four forms, But is readable From the diagram]**Exercise 1- #8:Indicate the information given in the diagram**using the 4 basic propositions. Some S is P All P is S [this is not one of the four forms, S P but is readable From the diagram]**“Contradictories”: E & I propositions**• These are pairs among the basic propositions that can’t be true at the same time. • Example: The E proposition says that there is nothing that is both S & P, while the I proposition says that there is at least one thing that is both S & P . E: No S is P I: Some S is P**“Contradictories”: A & O propositions**• These are pairs among the basic propositions that can’t be true at the same time. • Example: The E proposition says that there is nothing that is both S & P, while the I proposition says that there is at least one thing that is both S & P . A: All S is P O: Some S is not P**Validity for Arguments containing Categorical Propositions**An argument is valid if all the information contained in the diagram for the conclusion is included in the diagram for the premises. [be sure to label the subject and predicate terms correctly.] Some whales are mammals Some mammals are whales**Validity for Arguments containing Categorical Propositions**You can [and should] generalize this to: Some S is P This argument is Some P is S valid because the diagram for the conclusion is contained in the diagram for the premises.**Immediate Inferences**These are arguments with a single premise constructed from the A, E, I and O propositions. • The simplest is conversion. I and E easily convert. • From an I proposition “Some S is P” you can infer its converse, which is “Some P is S” • From an E proposition “No S is P” you can infer its converse, which is “No S is P” • Neither of the O or A propositions can be automatically converted. • “Some S is not P” does not infer “Some P is not S” • “All S is P” does not infer “All P is S.”**The Theory of the Syllogism**• The argument has exactly two premises and one conclusion. • The argument contains only basic A, E, I, and O propositions. • Exactly one premise contains the predicate term. • Exactly one premise contains the subject term. • Each premise contains the middle term. • The predicate term is the term in the predicate location in the conclusion. • The premise that contains the predicate term is called the major premise**The Theory of the Syllogism**• The predicate term is the term in the predicate location in the conclusion. • The premise that contains the predicate term is called the major premise • The subject term is the subject of the conclusion. • The premises that contains the subject term is called the minor premise . All rectangles are things with 4 sides (Major premise) All squares are rectangles (Minor premise) All squares are things with 4 sides (Conclusion) Subject term = “Squares”; Predicate term = “Things with 4 sides” Middle term = “Rectangles”**Venn Diagrams for determining the validity of a Categorical**Syllogism All rectangles have four sides All squares are rectangles All squares have four sides Squares Things having 4 sides Notice that all the things that are squares are corralled into the region of all things that have 4 sides. This shows that this Rectangles syllogism is valid**No ellipses have sides**All circles are ellipses No circles have sides Circles Sides Conclusion Ellipses You can see that the diagram for the conclusion is already present in the diagram for the premises.**Strategy:diagram a UNIVERSAL premise before a Particular one**as it may tell you where the*should go. All squares have equal sides Some squares are rectangles Some rectangles have equal sides. The conclusion -- that there is something that is a Rectangle -- already appears in the diagram.**An Invalid argument**All pediatricians are doctors All pediatricians like children All doctors like children Below:The diagram for the conclusion is not contained in the diagram for the premises Above: The diagram for the premises[ask: why ispart of the diagram darker?]**Diagramming “some”: when does the asterisk go on the**line? Some doctors are golfers Some fathers are doctors Some fathers are golfers . • The asterisk goes on the line when you have no information about the relationship. • For example in the above argument “Some doctors are golfers” the premise says nothing about the relation of doctors to fathers. Thus the blue asterisk is on the line between D & F. • Likewise in the second premise nothing is said about golfers. So the red asterisk is on the line between F & G.**Diagramming “some”: Is the argument valid?**Some doctors are golfers Some fathers are doctors Some fathers are golfers . The argumentis invalid becausethe diagram for the conclusion is not already contained in the diagram for in the premises.

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