Business:
1. Exam 1 is next Wednesday. Review will be Monday at the end of class. It will be on everything up to and including today.
2. Don't wait too long to do the podcast/blog article reviews.
Homework 4B Review
3D & 3M
Logical Force, Validity, Soundness, and Inductive vs Deductive Arguments
Definitions:
1. Logical force is the degree to which a conclusion follows logically from the premise(s).
2. Validity is the logical relation between the aggregate of the premises and the conclusion: If an argument is valid, then if the premises are assumed to be true, the conclusion must also be true. Otherwise stated: If the premises are assumed to be true it's logically impossible for the conclusion to be false. By definition, all deductive arguments are valid and all inductive arguments are invalid.
3. Soundness refers to the truth value of a valid (deductive) argument. If an argument is valid and the premises are true (not just assumed to be true) then the argument is sound. An argument can be valid but not sound. An argument cannot be sound but not valid. A sound argument is always valid.
4. A deductive argument is one in which if we assume the premises to be true then the conclusion must also be true. Otherwise stated, if we assume the premises to be true, it's impossible for the conclusion to be false. The premises of a deductive argument are always both relevant and sufficient.
5. An inductive argument is one in which if we assume the premises to be true it's possible for the conclusion to be false. Inductive arguments are probabilistic arguments. A strong inductive argument will mean that, if we assume the premises to be true, it's improbable that the conclusion is false (or very likely that it's true). A weak inductive argument will mean that, even if we assume the premises to be true, the conclusion isn't likely to be true. A cogent inductive argument is one that is strong and the premises are true. An uncogent inductive argument is one that is either weak or strong and one or more premises are false. (see examples below). The premises of a cogent inductive argument are always relevant but not sufficient. Inductive arguments are never 100% sufficient...if they were, they'd be deductive arguments!
6. Identifying an argument as deductive vs inductive: (a) Assume the premises to be true; (b) evaluate whether it's possible for the conclusion to be false (no matter how improbable); (c) if yes, then the argument is inductive, if no, then the argument is deductive. Otherwise stated: if we assume the premises to be true, a deductive argument's premises will always be relevant and sufficient; an inductive arguments premises might be relevant (to varying degrees) but never sufficient.
7. Internal/Premise Relevance: If we assume all premises to be true, premise relevance is the degree to which a premise increases the likelihood that a conclusion is true.
8. Sufficiency: An argument is sufficient if, assuming the premises to be true, the conclusion is also guaranteed to be true. If an argument's premises are sufficient then it is a deductive argument. If not, then it is an inductive argument.
Examples: Strong and Weak Inductive Arguments
(P1) An opaque jar contains exactly 100 marbles.
(P2) There are 99 blue marbles in the jar.
(P3) There is 1 red marble in the jar.
(C) The marble picked is blue.
(P1) An opaque jar contains exactly 100 marbles.
(P2) There are 99 blue marbles in the jar.
(P3) There is 1 red marble in the jar.
(C) The marble picked is red.
E.g., paranormal
Examples: Deductive Vs Inductive + check for relevance and sufficiency
(P1) Every raven I've ever seen is black.
(C) Therefore, the next raven I see will also be black.
(P1) Every person who has had a bacterial lung infection was cured with anti-biotics.
(C) Tomorrow, a person with a lung infection will be cured by ant-biotics.
(P1) All ravens are black.
(P2) I see a raven.
(C) The raven is black.
(P1) Most NFL players weigh over 200lbs.
(C) The next NFL player I meet will weigh over 200lbs.
(P1) Killing humans is wrong.
(P2) Abortion is killing a human.
(C) Abortion is wrong.
(P1) We are morally obligated to help others when the value to them would be great and the cost to us would be little.
(P2) A starving child would benefit greatly from a $20/month donation and the cost to us is little.
(C) We are morally obligated to donate a small amount every month to starving children.
(P1) A watch has a high degree of complexity and so could not have been designed and assembled by chance and must have been assembled and designed by an intelligent being.
(P2) Life also has a high degree of complexity and so could not have been designed and assembled by chance.
(C) Therefore, life must also have been assembled and designed by an intelligent being.
(P1) All cats are mammals.
(P2) All mammals are lions.
(C) All cats are lions.
(P1) If my dog is left alone he will pee on the floor.
(P2) I left my dog alone.
(C) My dog peed on the floor.
Some Standard Deductive Forms
Universal to instance; modus ponens, disjunctive syllogism
Some Standard Inductive Forms
Generalization, statistical syllogism, argument from analogy, induction by enumeration, slippery slope, argument from ignorance,
Order of Operations for Evaluating Arguments (See Flow Chart PDF via email).
Homework 5A:
p. 64 Ex. 3C Also evaluate for premise acceptability after evaluating for sufficiency (i.e., follow the flow chart I sent you).
p. 78 Ex. 3M Question 4 a-e
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