UNIT 1 - Basic Concepts in Logic-1

7/28/2019 UNIT 1 - Basic Concepts in Logic-1

1/18

BASIC CONCEPTSIN LOGIC

Engineering a culture of

ReasoningUNIT 1


2/18

LOGIC

The following are two (2) definitions of logic:

1. Logic is the study of methods for evaluating

whether the premises of an argument

adequately support (or provide good evidence

for) its conclusion (Howard-Snyder and

Wasserman, 2009).

2. The paraphrased version of this definition says

that; logic is roughly the study of methods for

evaluating arguments (Howard-Snyder and

Wasserman, 2009). 2


3/18


4/18

Dissecting Definition of Logic

ArgumentAn argument is a set of statement s where some of thestatement s are intended to support another.

An argument may be split into two (2) main areas:

1. Premises

2. Conclusion

Argument

An argument is a set of statement s where some ofthe statement s, called the premises, are intended tosupport another, called the conclusion.

4


5/18


Example of an argument:

Every logic book has at least one sensible

example. The power of logic is a logic book, so,

The Power of Logic contains at least one (1)

sensible example.

1. This argument has two (2) premisesi.e., the

two (2) 1st sentences.

2. The sentence that follows the word so is the

conclusion.5


6/18

Propositions & Sentences

Proposition-A proposition is a truth or falsehoodthat may or may not be expressed in a sentence

(Howard-Snyder and Wasserman). In other words,

propositions are expressions that are bearers of truth

value; the things that are really true or false. Proposition-A statement expressing a judgement or

opinion (Pocket Oxford English Dictionary).

EXAMPLE

1. The car is blue

2. The grass is green

3. You are kind 6


7/18


What is a Statement?A statement is a declarative sentence which is

either true (describing things as they are) or false

(describing things in ways other than they are).Example:

1. Some people are smart

2. No one is smart

3. Some people weigh up to 400 pounds.

NB: none of the sentences are suggestions,

commands nor questions. 7


8/18

Deductive and Inductive Arguments

Since there are two (2) ways that the premisesof an argument can support the conclusion, wecan distinguish between two (2) kinds of

arguments. These are deductive and inductivearguments.

Deductive ArgumentA deductive argumentis one in which the premises are intended toguarantee the conclusion.

Example - All philosophers like logic. Ned is aphilosopher. So, Ned likes logic.

8


9/18

Deductive and Inductive Arguments

Inductive Argument

An inductive argumentis one in which the premises are intended tomake the conclusion probable, withoutguaranteeing it.

Examples

- Most philosophers like logic. Ned is aphilosopher. So, Ned likes logic.

- Some Americans work in business. DonaldTrump is an American. So, Donald Trumpworks in business.

9


10/18

Valid and Invalid Arguments Valid Arguments A valid argument is one in which it is

necessary that, if the premises are true, then the conclusion istrue.

Valid Arguments A valid argument is a deductive

argument in which the premises succeed in guaranteeing theconclusion. There are three (3) things to note about these

concepts are:

1. There is a necessaryconnection between the

premises and the conclusion.2. The truth of the conclusion is absolutelyguaranteed by the

truth of the premises.

3. It does not say that the premises and conclusion of a valid argument are

in fact true or are necessarily true. Rather, it says, if the premises are true, thenthe conclusion is necessarily true.

10


11/18

Valid and Invalid Arguments

Valid - If an argument is either Sound or logical

it is valid:

1. Soundness means; that both premise and

conclusion are in fact true = Valid

2. Logical means; the premise is true or false

but it still guarantees the conclusion (that is,

conclusion still follows from premise) = valid

11


12/18


Argument valid with true premise and true

conclusion.

- Example - If Harry loved Dumbledore, then

Harry was sad when Dumbledore died. So,

Harry was sad when Dumbledore died.

Argument is valid with false premise and false

conclusion.

- Example - All sharks are birds. All birds are

politicians. So, all sharks are politicians

(conclusion guaranteed by premises). 12


13/18


Invalid Arguments An invalid argument is

one in which it is not necessary that, if the

premises are true, then the conclusion is true.

Invalid Argument with true premises and true

conclusion

Example - Some Americans work in business.

Donald Trump is an American. So, Donald

Trump works in business (conclusion true but

not guaranteed by premises).

13


14/18

Valid, Invalid Arguments & TruthValid Argument(Premises guaranteeing

conclusion)

Invalid Argument(Premises do not guarantee

conclusion)True premises

True conclusion

If Harry loved Dumbledore,

then Harry was sad when

Dumbledore died. So, Harry

was sad when Dumbledore

died.

Some Americans work in business.

Donald Trump is an American. So,

Donald Trump works in business.

False premises

False conclusion

All sharks are birds. All birds

are politicians. So, all sharks

are politicians.

Every genius is a philosopher.

Homestar Runner is a philosopher.

So, Homestar Runner is a genius.

False premises

True conclusion

All dogs are ants. All ants are

mammals. So, all dogs aremammals.

Everything coloured is red.

Stephen Colbert is a mortician. So,Stephen Colbert is hilarious.

True premises

False conclusion

All dogs are animals. All cats are

animals. Hence, all dogs are cats.

Unknown

truth value

All of the Cappadocians

accepted perichoresis.Basilwas a Ca adocians. So, Basil

Some hylidae are heterophoric.

Maggie is heterophoric. So, Maggieis a h lidae.

14


15/18


16/18

Arguments Summary

16

Arguments

Valid Arguments Invalid Arguments

Valid

argument

With all

premises

true are

sound

All invalid

arguments

are unsound

Valid

argument

With at least

one false

premises

are unsound


17/18

Categories of Unsound

Arguments

There are three categories:

Category 1 - it is valid but it has at least one

false premise

Category 2 - it is invalid, but all of its premises

are true.

Category 3 - it is invalid and it has at least onefalse premise

An unsound argument is one that either is

invalid or has at least one false premise.17


18/18

Conclusion We want deductive arguments to be valid and have all

true premises (sound argument). Arguments are neither true nor false only statements can

be.

Arguments can be valid, invalid, sound or unsound.

Statements cannot be valid, invalid, sound or unsound.

Premises and conclusion (statements) can either be true

or false.

Premises and conclusions (statements) cannot be valid,invalid, sound or unsound.

Validity makes no reference necessarily to truth or

falsehood. Rather, its focus is whether the conclusion islinked to the remise18

UNIT 1 - Basic Concepts in Logic-1

Documents

Transcript of UNIT 1 - Basic Concepts in Logic-1