4.4, 4.5, and 4.6 Notes PDF

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4.4, 4.5, and 4.6 Notes...

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4.4, 4.5, 4.6 4.4 ●

Conversion ○ Switching the subject term with the predicate term ○ ex) All A are B → All B are A ● Illicit conversion ○ fallacy ○ ex) all A are B ○ Therefore all B are A ■ Fallacy bc ● All cats are animals (true) ● Therefore, all animals are cats (false) ● Obversion ○ If you obvert something twice you get the original statement ■ Aka it doesnt change the truth values (as seen in venn diagrams) ○ All the venn diagrams are the same (logically equivalent) 1. Changing the quality (without changing the quantity) 2. Replacing the predicate with its term complement a. No S are P → All S are P // Some S are P → some S are not P b. Term complement: word or group of words that denotes the class complement (everything outside the class) i. Dog → non dog ((for the predicate one!!!!!)) ● ex) All A are B → No A are non B ● Contraposition ○ Switching the subject and the predicate terms ○ Replacing the subject and predicate terms with their term complements ■ ex) All A are B → All non-B are non-A ● Illicit contraposition ○ Fallacy ○ ex) Some A are B ○ Therefore, some non-B are non-A ■ Some animals are non-cats (true) ■ Therefore, some cats are non-animals (false) ● Logically equivalent ((same venn diagrams)) ○ CONVERSION ○ CONTRAPOSITION ■ Most of the time if you switch subject and predicate it will switch the diagram but not in these cases *****learn the diagrams a bit better they are kind of confusing

4.5 ●

Traditional square of opposition ○ An arrangement of lines that illustrates logically necessary relations among the four kinds of categorical propositions

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Contradictory = opposite truth value Contrary = at least one is false (not both true) ■ Expresses only partial opposition ● One Given as true, other has to be false ● One Given as false, other could be either true or false (logically undetermined truth value) ● A/E ○ Subcontrary = at lease one is true (not both false) ■ Expresses a kind of partial opposition ■ One Given as false, other has to be true ■ One given as true, other could be true or false (logicallyundetermined truth value) ■ I/O ○ Subalternation = truth flows downward, falsity flows upward ■ Truth trickles down, false flows up ■ If it is the opposite direction you would have logically undetermined truth value Illicit subcontrary ○ Illicit application of subcontrary ○ Formal fallacy ■ ex) some A are B\\ Therefore, it is false that some A are not B ● Question: do you still prove invalid by counterexample????? Illicit contrary ○ Inference that depends on incorrect application of the contrary relation ○ Formal fallacy ■ ex) it is false that all A are B\\ Therefore, no A are B Illicit subalternation ○ Inference that depends on incorrect application of the subalternation relation ■ ex) some A are not B\\\ Therefore, no A are B ● Question: just form, how do you know if it given as true or false?

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Existential fallacy ○ Committed from the Aristotelian standpoint when and only when contrary, subcontrary, and subalternation are used (in an otherwise correct way) to draw a conclusion from a premise about things that do not exist Conditionally valid ○ Applies to an inference after the Aristotelian standpoint has been adopted and we are not certain if the subject term of the premise denotes actually existing things ○ Validity rests on if there anything/one in that term actually exists → once you know it does exist, you can assert the inference is valid from Aristotelian standpoint ■ Sometimes you dont know if they letters denote existing things valid/soundness also applies

4.6 Boolean vs Aristotelian ● Venn diagrams are different (E/A [I/O are the same]) ○ X in a circle = signifies that something exists in the area in which it is placed ■ Represents an implication of existence made by universal propositions about actually existing things ● Same idea as contrary, subcontrary, subalternation ○ True or false depending on (whether the overlap is empty, something exists in a certain spot...etc) ● How to test an immediate inference from the Aristotelian standpoint ○ Reduce the inference to its form (venn diagram) from the Boolean standpoint If the form is valid, proceed no further. The inference is valid from both standpoints ○ If the inference form is invalid from the Boolean standpoint and has a particular conclusion, then adopt the Aristotelian standpoint ● If it has a circled x where there is an x then it is conditionally valid → is denoted in the conclusion even if it is condtional ■ Conditionally valid, check to see if term denotes something that actually exists ● Yes = valid ● No = invalid A logic “cares about” whether the predicate term refers to existing things whereas B logic does not...