Chapter 1 Notes: Logic and Deduction

logic

-science of argument
-all about distinguishing good arguments from bad arguments

argument

a set of statements along with an explicit or implicit inferential claim

1. At least 2 statements (a conclusion and at least 1 premise)

2. An inference

Conclusion indicator word is the best clue that condition 2 is satisfied

What must an argument have?

inferential claim

the idea that one of the statements (the conclusion) can be INFERRED from the other statements

premise

statements that are SUPPOSED TO support the conclusion

conclusion

statement the arguer seeks to support

fallacious argument

an argument where the premise doesn’t support the conclusion

statements

sentences that take on a truth value

truth value

whether the sentence is true or false

question

What is an example of a sentence that doesn’t have a truth value?

simple statement

assertion of an affirmative state of affairs

conjunction

an “and” type statement

disjunction

an “either… or” statement
-at least one of the simple statements is true, but both may be true as well

conditional

an “if… then” statement

antecedent

part that follows “if” in a conditional statement

consequent

part that follows “then” in a conditional statement
should NEVER be confused with conclusion

categorical

a statement that relates two classes of things

truth conditions

circumstances under which the statements are true

whether premises provide the conclusion with the INTENDED type of support

What do logicians mainly focus on?

symbolic logic

translating arguments into symbols and applying rigorous techniques to evaluate them

categorical logic

logic of classes

propositional logic

logic of truth-functional statements

predicate logic

a hybrid of categorical and propositional

1. Identify the parts of the argument

2. Translate argument into symbolic form

3. Apply a technique to determine whether the premises support the conclusion

Steps of Argument Evaluation Process

1. therefore

2. consequently

3. hence

4. we may conclude that

5. so

6. thus

7. reasonable to infer

8. it follows that

common conclusion indicator words

1. since

2. given that

3. because

4. assuming

5. as

6. moreover

7. seeing that

8. may be inferred from

common premise indicator words

enthymeme

an argument with at least one unstated/left out premise

deductive argument

an argument where the premises are supposed to make the conclusion necessary

if the premises were true, then the conclusion would HAVE to be true as well

inductive reasoning

an argument in which the premises are supposed to make the conclusion probable

if the premises were true, then PROBABLY the conclusion would also be true

the author’s intention

What do we evaluate arguments based on?

1. It’s reasonable to infer

2. Probably

3. It seems likely that

4. It’s safe to conclude

5. It’s a good bet that

6. It’s plausible that

inductive argument indicator words

Deduction Indicators

1. It necessarily follows

2. Entails

3. Necessitates

4. We can only conclude

5. It must be that

6. It’s certain that

1. indicator words/phrases (especially before conclusion)

2. subject matter of argument

3. actual amount of support the premises give to the conclusion

How to decide deductive vs. inductive?

1. have PREDICTIONS as their conclusions

2. based on expert testimony

3. generalize to a whole group

4. argue by analogy

5. about cause and effect

6. have scientific theories as conclusions

Common Characteristics of Induction Arguments (6)

1. Reach conclusions by MATHEMATICAL calculation

2. Categorical arguments

3. Based on the DEFINITION of a word

4. employ the REDUCTIO method

Common Characteristics of Deduction Arguments (4)

reductio method

proving something is false by showing that it has the characteristics of something false