Logic Week 1 Notes - Prof. Matthew Congdon PDF

Preview

Summary

Prof. Matthew Congdon...

Description

Black text = lecture video info Red text = textbook info

1/25/21 Introduction Lecture What is logic - John Locke: logic = anatomy of thinking - Anatomy → understanding how something functions by examining its parts and how those work together to make a unified whole -

-

Logic = anatomy of arguments - Arguments = set of statements or propositions leading up to a conclusion (statements and propositions build support for the conclusion) Logic = systematic use of methods and principles to analyze, evaluate, and construct arguments - Investigates the level of correctness of the reasoning found in arguments

What is an argument A group of statements in which the conclusion is claimed to follow from the premises → separate premise from conclusion w/ a line

Types of Logic - Propositional logic (weeks 2-6) - Simple statements → represented by letters; indicate a proposition -

Logical operators (aka: connectives) → represented by symbols; logically connect simple sentences together to isolate the logical relationships between propositions

-

Categorical logic (weeks 7-10) - Older logical language; developed by Aristotle - Uses venn diagrams and the square of oppositions to represent logical relationships between statements

-

Informal logic (weeks 11-13) - Think about the context in which arguments are made; specific relationships between people that influence whether or not an argument is convincing - Examples: op-ed pieces, political debates

-

Philosophy of logic (week 14) - Logical paradoxes

Black text = lecture video info Red text = textbook info

Basic Terminology of Logic -

Statement: sentence that can be assessed as true or false - Declarative sentence → claim that something is true -

Attempt to convey information Every statement has a truth value (either true or false) Ex: All mammals are warm-blooded

-

Truth value: every statement is either true or false

-

Argument: collections of statements in which the conclusion is claimed to follow from the premise(s) - Consists of premises and a conclusion - Can have unlimited premises but only one conclusion - Logical analysis of argument → rational use of language and reasoning skills; organized; appeals to relevant reasons and justification

-

Premise: a statement intended to provide support for a conclusion - Premise indicator: words or phrases that help us recognize arguments by indicating the presence of premises - Example: because, since, given that

-

Conclusion: the statement that is claimed to follow from the premise(s) of an argument - Conclusion indicators: words or phrases that indicate the presence of a conclusion - Example: therefore, consequently

-

Proposition: the meaning of a statement; the information content imparted by a statement

-

Inference: the reasoning process that is expressed by an argument - Inferential claim: expresses a reasoning process; objective; can be explicit or implicit - If you accept this premises then these conclusions follow - Explicit → use premise and conclusion indicators -

Implicit → no premise and conclusion indicator but still has inferential relationship between premise and conclusion

-

Non-Inferential passage examples: advice, warnings, unsupported statements, explanations

Black text = lecture video info Red text = textbook info

Truth Value Analysis vs. Logical Analysis -

Truth value analysis: process of determining whether the premises are true or false

-

Logical analysis: process of determine whether the premises (assuming they are true) support the conclusion - Determines the strength of an inferential claim - Will focus on this in class (rather than truth value analysis) - Deductive argument: an argument claiming that the conclusion follows necessarily from the premises Deductive vs. Inductive Arguments

-

Deductive & inductive = 2 main classes of arguments

-

Deductive argument: inferential claim of the argument is that the conclusion follows necessarily from the premises - Mathematical precision - Under the assumption that the premises are true → impossible for conclusion to be false -

-

Indicator word examples: necessarily, certainty, definitely, absolutely Strong inferential connection between premises and conclusion

Inductive argument: inferential claim of the argument is that the conclusion probably follows from the premises - Under the assumption that the premises are true → improbable for conclusion to be false -

Indicator word examples: probably, likely, unlikely, improbable, plausible, implausible Weak inferential connection between premises and conclusion Types of inductive arguments: analogical, statistical, causal, legal, moral, scientific

Black text = lecture video info Red text = textbook info

1/27/21 Validity Validity - Valid vs. Invalid → Primary terms used to assess deductive arguments -

Deductive argument is valid if (assuming premises are true) it is impossible for conclusion to be false - Valid arguments are considered as “truth preserving” → truth of the premises is preserved/kept throughout the argument to the conclusion

-

Deductive argument is invalid if (assuming premises are true) it is possible for the conclusion to be false

-

Counterexample - To a statement: evidence that shows the statement is false; concerns truth value analysis - Absolute terms are often subject to simple counterexamples - To an argument: evidence that the premises assumed to be true do not make the conclusion necessarily true - One counterexample is enough to make argument invalid - Argument is valid if no counterexamples exist

-

Determining if an argument is valid is a matter of formal logical analysis NOT truth value analysis

Black text = lecture video info Red text = textbook info

-

Must ask yourself if the form of the argument is truth preserving; not if the content is true

Formal Logic - Disregards or abstracts from the content of an argument to get the pure logical structure of the argument - Isolate the logic from the content by using letters like “x, y, z”

Form Argument Form - (in categorical logic) An arrangement of logical vocab and letters that stand for class terms, such that a uniform substitution of class terms for the letters results in an argument - Logical vocabulary → terms like “all” and “are” -

Nonlogical vocabulary → the content; class terms (ex: “dogs” or “cats”)

-

Types of argument forms - Fallacy of affirming the consequent - Modus ponens - Fallacy of denying the antecedent - Modus tollens - Hypothetical syllogism - Disjunctive syllogism

Conditional Statement “If...then..” - Antecedent = simple statement following “if” - Consequent = simple statement following “then” Formal Fallacy - Logical error that occurs in the form of an argument - Can only occur in deductive arguments Statement Form - (in categorical logic) An arrangement of logical vocab and letters that stand for class terms, such that a uniform substitution of class terms for the letters results in a statement - Example: D = dogs; C = cat; S = snakes

Black text = lecture video info Red text = textbook info

Soundness Soundness - Argument is sound if it meets BOTH of these 2 conditions 1) It is valid (uses logical analysis) 2) All premises are true (uses truth analysis) - Sound argument is about as good as an argument can get

Week 1 Recap

Table 1: All the logical possibilities available in deductive argument Premises

Conclusion

Validity

Soundness

1. True

True

Valid or Invalid

Sound or Unsound

2. True

False

Invalid

Unsound

3. At least one is false

True

Valid or Unvalid

Unsound

4. At least one is false

False

Valid or Unvalid

Unsound

Black text = lecture video info Red text = textbook info

Table 2: Types of argument forms Argument Form Name

Example

Form

Validity

Fallacy of affirming the consequent

1. If Sherry lives in LA, then she lives in CA 2. Sherry lives in CA

1. If L, then C 2. C

Invalid

C: Sherry lives in LA

C: L

1. If Sherry lives in LA, then she lives in CA 2. Sherry lives in CA

1. If L, then C 2. L

C: Sherry lives in CA

C: C

1. If Sherry lives in LA, then she lives in CA 2. Sherry does not live in LA

1. If L, then C 2. It is not the case that L

C: Sherry does not live in CA

C: It is not the case that C

1. If Sherry lives in LA, then she lives in CA 2. Sherry does not live in CA

1. If L, then C 2. It is not the case that C

C: Sherry does not live in LA

C: It is not the case that L

1. If Sherry lives in LA, then she lives in CA 2. If Sherry lives in CA, then she lives in the U.S

1. If L, then C 2. If C, then U

C: If Sherry lives in LA, then she lives in the U.S

C: If L, then U

1. Sherry lives in LA or San Fran. 2. Sherry does not live in LA

1. L or S 2. It is not the case that L

C: Sherry lives in San Fran

C: S

Modus ponens

Fallacy of denying the antecedent

Modus tollens

Hypothetical syllogism

Disjunctive syllogism

Friday Discussion (1/29) -

-

All arguments can be broken down into 2 forms - Deductive - Inductive One difference to remember btwn the 2 forms - Deductive → conclusion follows necessarily from the premises -

-

Inductive → conclusion follows probably from the premises

We hold deductive and inductive arguments to different standards - Deductive standard → validity -

Evaluated as “either/or”

Valid

Invalid

Valid

Valid

Valid

Black text = lecture video info Red text = textbook info

-

- Either valid or invalid Inductive standard → strength/weakness -

Evaluated on a degree scale of strength Friday Discussion...