Philosophy 120 - PowerPoint Presentation

Slide1

Philosophy 120

Symbolic Logic I

H. Hamner HillSlide2

Logic is the science of

arguments

Separate good arguments from bad ones

Identify the characteristics of good arguments (validity and soundness)

Produce good arguments of our ownSlide3

Student Objectives

learn the vocabulary of logic

master methods and principles

explain important concepts in logic

improve communication skills

symbolize arguments using logical notation

test arguments for validity

evaluate reasoning using the tools of logicSlide4

Requirements

3 in class examinations

10 routine graded homework assignments

a comprehensive final examinationSlide5

Cell Phones, Tablets, etc.

Turn them off. We are in class, your calls and web surfing can wait. Do not text message during class.

Cell phones and logic do not mix.

Hang up and derive!

Read

this column

from the New York Times.Slide6

Textbook and Associated Computer Program

The Power of Logic, 5

th

edition, available at the Textbook Services.

Slide7

Logic is the science of arguments

All rational inquiry turns on the ideal of a logical consequence, the idea that some claim must necessarily follow from others.

Arguments are designed to show that one claim logically follows from others.

Logic allows one to determine whether the arguments succeed.Slide8

What is an argument?

An argument is not a disagreement or a form of verbal battle.

An argument is a set of statements, one of which (the conclusion) is supposed to follow from the others (the premises).Slide9

Statement

A sentence that has a truth value, i.e., a sentence that is either true or false (but never both).

Statements are true when what they assert about the world is the case.

Can you think of a sentence that is not a statement?Slide10

Can you think of a sentence that is not a a statement?

OK, this is the sort of question logicians love to ask, because the question itself is a legitimate answer! The sentence “Can you think of a sentence that is not a statement?” is itself a sentence that is not a statement. Questions are neither true nor false. Commands, exclamations, and exhortations (Let’s . . .) are other sentences that do not express statements.Slide11

Types of statements

Simple--A simple statement asserts exactly one fact about the world

Compound--A compound statement is one or more simple statements plus logical connectives.

5 logical connectives: not, and, or, if-then, if and only ifSlide12

NOTE:

TRUTH

is a property of statements.

VALIDITY

is a property of argumentsSlide13

Conclusion

A statement one is urged to accept on the basis of reasons given.Slide14

Premise

A statement given as a reason for believing some other statement.Slide15

Identifying premises and the conclusion

Correctly identifying the premises and conclusion of an argument are essential if we are to evaluate it.

English uses many discrete premise and conclusion indicators (review your handout) that serve as guideposts in arguments.Slide16

Deductive Validity

A characteristic of arguments in which the truth of the premises guarantees the truth of the conclusion. It is impossible for both the premises of a valid argument to be true and the conclusion to be false.

Any argument that is not valid is

invalid

or

non-validSlide17

Validity does NOT guarantee the truth of the conclusion

It is possible for the conclusion of a valid argument to be false. If this is the case, then at least one premise must be false

.Slide18

The following argument is VALID:

All trout are mammals

All mammals have wings

SO, all trout have wings

This argument is valid because IF the premises are true THEN the conclusion MUST be true. This holds even though the premises are in fact false.Slide19

Soundness

A characteristic of valid arguments whose premises are in fact true. It is impossible for the conclusion of a sound argument to be false.

It is irrational to reject the conclusion of an argument one admits to be sound.Slide20

Logical Form and Grammatical Form

Logic is not a matter of grammar. “Following logically’ is not a matter of grammatical placement.Slide21

Logic is a matter of form

Logic is a

formal

discipline. It is concerned with the formal or structural properties (patterns) and relations in statements and arguments.Slide22

Argument Forms

An

argument form

is a pattern of argument, the logical structure of an argument. Argument forms are either valid or non-valid.

Valid arguments have valid argument forms.Slide23

Consistency

Consistency is a property of sets of statements

A set of statements is

consistent

if, but only if, it is possible for all of the statements in the set to be true.

A set of statements is

inconsistent

if, but only if, it is impossible for all of the statements in the set to be true.Slide24

Consistency and Validity

We can use the concept of consistency to test an argument for validity.

How? Suppose I gave you a consistency checking machine (a machine that tests a set of statements for consistency). How could you use that machine to determine whether an argument is

valid

?Slide25

Hamner’s Helpful Home Consistency Checker

Input Output

(set of statements) (verdict)

Consistent

Not ConsistentSlide26

Using the Consistency Checker

Negate the conclusion of the argument and then ask whether the set of statements consisting of the premises and the negation of the conclusion is consistent. If yes, then the argument is NON-VALID. If no, if that set is inconsistent, then the argument is VALID.Slide27

Historical Significance

Indirect Proof (Reductio ad Absurdum)

Euclidean and Non-Euclidean Geometry

Lobachevsky ReimannSlide28

Indirect Proof

Both Lobachevsky and Reimann tried to establish the truth of all 5 of the core postulates of Euclidian geometry using indirect proof. They succeeded in proving 4 out of 5, but efforts to prove the parallel postulate by indirect proof never led to a contradiction.

In fact, the failure to prove the parallel postulate led to the development of Non-Euclidian geometry.Slide29

Logic and Psychology

Contexts of DISCOVERY and contexts of JUSTIFICATION are different.

LOGIC is concerned with the context of justification, the business of defending beliefs.

The "logic" of discovery is a matter for the discipline of psychology

.Slide30

Justification and Discovery

Ramanujan and the difference between justification and discovery.Slide31

Justification and Discovery

Ramanujan was one of the greatest mathematicians of the 20

th

Century. Today’s mathematicians are still trying to prove some of his theorems.

He insisted that his ideas came to him in dreams, presented by the Goddess Namakaal. Even if this is true, it doesn’t concern the logician.

Logicians are interested in the justification of the theorems (How they are proved), not how the are discovered.Slide32

Arguments are often confused with explanations

Sometimes the language of arguments is used when one is not arguing for a conclusion but rather trying to explain a phenomenon.Slide33

Arguments:

Answer the question "Why should I believe this?“

Give reasons for believing that something is the case.Slide34

Explanations:

Answer the question "Why is this the case?“

Give an account of something already believed to be the case (the facts are not in dispute).Slide35

Key Ideas

Definition of “argument”

Validity is a matter of form

Validity does not guarantee the truth of the conclusion

Consistency as a test for validity

Contexts of discovery and justification

Arguments and explanations