Logic & Critical Thinking - Exam 1

Contraries

-A & E -BOTH CANT BE TRUE BUT BOTH CAN BE FALSE -Differ in quality but NOT in quantity (both universal)

Subalterns

-A & I (Affirmative) -E & O (Negative) -Same quality, different quantity -Vertical pairs -If the A is TRUE, the I MUST BE TRUE -If the E is TRUE, the O MUST BE TRUE -If the I is FALSE, the A MUST BE FALSE -If the O is FALSE, the E MUST BE FALSE *Truth comes DOWN, Falsity comes UP

What is a proposition?

-A declarative statement that makes an assertion about what is or isn't the case -It has to be either true or false -It has to have enough information to stand alone as a complete though Ex: Grass is green OR Denver is in the state of Colorado Ex of a NON preposition: Close the door

Rule 1 (Categorical syllogisms)

-A syllogism must contain three and only three terms -Associated fallacy: FALLACY OF 4 TERMS

A form

-All S are P -What gets distributed: Subject -Quantity: Universal -Quality: Affirmative

What makes a syllogism CONDITIONALLY VALID?

-Both premises are UNIVERSAL (A or E) -The conclusion is PARTICULAR (I or O)

What makes a syllogism UNCONDITIONALLY VALID?

-Does not draw a particular conclusion from two universal premises

Contradictories

-E & I -A & O -Diagonal on the square -Logical opposites (they necessarily have OPPOSITE truth values) -Differ in BOTH quantity and quality Ex: All poodles are dogs, some poodles are not dogs

Copula

-Has to be in the form 'to be' -Function: to join things together -Examples: is, am, are, was, were, be, being, been, will be, have been

Subcontraries

-I & O -Differ in quality but NOT in quantity (both particular) -Both can be true, but both CANT be false

Rule 5 (Categorical syllogisms)

-If a term is distributed in the conclusion, it has to be distributed in the premises also -Associated fallacy: Fallacy of illicit major(p)/illicit minor (s)

Rule 3 (Categorical syllogisms)

-If the conclusion is affirmative, both premises have to be affirmative -Associated fallacy: Fallacy of drawing an affirmative conclusion from negative premises

Rule 2 (Categorical syllogisms)

-If the conclusion is negative, EXACTLY one premise must be negative -Associated fallacy: Fallacy of drawing a negative conclusion from affirmative premises

E form

-No S are P -What gets distributed: Subject and Predicate -Quantity: Universal -Quality: Negative

Examples of PREMISE indicators

-Since -Because -For -As -Follows from... -As shown by... -Inasmuch as... -As indicated by... -The reason is that... -For the reason that... -May be inferred from... -May be derived from... -May be deduced from... -In view of the fact that...

I form

-Some S are P -What gets distributed: Nothing -Quantity: Particular -Quality: Affirmative

O form

-Some S are not P -What gets distributed: Predicate -Quantity: Particular -Quality: Negative

Rule 4 (Categorical syllogisms)

-The middle term must be distributed at least once -Associated fallacy: Fallacy of the undistributed middle

Special words

-The only -Only -If/Then -Wherever (where) -Whenever (when) -Never

Examples of CONCLUSION indicators

-Therefore -Hence -So -Accordingly -In consequence that -Consequently -Proves that -As a result -For this reason -Thus -It follows that -For these reasons -I conclude that -Which shows that -Which means that -Which entails that -Which implies that -Which allows us to infer that -We may infer

'If/Then'

-Whatever follows 'if' immediately becomes the subject of an A

'Never'

-Whatever follows 'never' immediately becomes the subject of an E Ex: She never sleeps with the light on --> No times she sleeps are instances when the light is on

'Only'

-Whatever follows 'only' becomes the PREDICATE of an A Ex: Only humans have rational thought --> All beings with rational thought are humans

'The only'

-Whatever follows 'the only' immediately becomes the subject of an A Ex: The only people who pass are those who study --> All people who pass are people who study

'Whenever' (when)

-Whatever follows 'whenever' immediately becomes the subject of an A -Location, place Ex: Whenever it rains, it pours --> All days it rains are days it pours

'Wherever' (where)

-Whatever follows 'wherever' immediately becomes the subject of an A -Time, day Ex: Wherever it rains, it pours --> All places it rains are places it pours

Guidelines for translation

1. Categorical propositions in standard form begin with 'all', 'no', or 'some' 2. S & P must be nouns or noun-phrases 3. The copula must be some form of the verb 'to be' 4. Singular nouns (nouns that pick out specific individuals) DO NOT REQUIRE A QUANTIFIER; these will be understood to be UNIVERSAL 5. In general, S & P should not contain negatives

Definition of a syllogism

A deductive argument with EXACTLY TWO premises and one conclusion

Which forms can NEVER have a negative copula?

A & E

Validity and soundness apply to only what?

ONLY ARGUMENTS

Truth and falsity apply to ONLY what?

ONLY PROPOSITIONS

Quantifier

All, No or Some

What is soundness?

An argument is sound if and only if it is valid and all the premises are TRUE

What is validity?

An argument is valid if and only if it is such that if the premises are all true, it is not possible for the conclusion to be false (the truth of its premises guarantees the truth of its conclusion--it is IMPOSSIBLE for the premises to be true and the conclusion to be false--an argument is valid if the truth of the premises logically guarantees the truth of the conclusion)

Rules for standard form categorical syllogisms

1. Every proposition has to be in standard form (A, E, I, O) 2. It has to be exactly the same terms used 3. The terms used must be used in the same sense

Definition of opposition

2 standard form categorical propositions stand in a relationship of opposition when they have the same subject and predicate, but differ in terms of quantity, quality or BOTH

Definition of a categorical syllogism

A syllogism with EXACTLY THREE categories that are related to each other and each category appears EXACTLY TWO TIMES

What form is ALWAYS valid?

EVERY EIO

A valid argument must have a true conclusion (T/F)

FALSE

Contraries cannot both be false (T/F)

FALSE

If an A proposition is false, then its subaltern must be false

FALSE

Figure 3

Major premise: MP Minor premise: MS Conclusion: SP

Figure 1

Major premise: MP Minor premise: SM Conclusion: SP

Figure 4

Major premise: PM Minor premise: MS Conclusion: SP

Figure 2

Major premise: PM Minor premise: SM Conclusion: SP

What are truth values?

Properties of propositions (which can be true or false) that are binary and correspond to reality.

What are conclusions?

Proposition, the truth of which is meant to be demonstrated by a premise (A proposition whose truth has been inferred on the basis of other propositions assembled with it in a logical argument.)

What are premises?

Propositions offered as evidence for a conclusion. It should be able to stand alone as a complete thought

A deductive argument's conclusion is meant to be proven with absolute certainty (T/F)

TRUE

An argument that is sound cannot have a false conclusion (T/F)

TRUE

Propositions make a claim about what is (or is not) the case (T/F)

TRUE

What arguments can be considered valid?

TT, FF, FT

Inductive reasoning

The intent is to give good reasons to believe the conclusion is probably true

Deductive reasoning

The intent is to give reasons whose truth logically necessitates the truth of the conclusion (CERTAINTY)

Major premise

The premise that contains the major term (always the first premise)

Minor premise

The premise that contains the minor term (always the second premise)

Middle term (M)

The term that appears in both premises

Major term (P)

The term that appears in the PREDICATE of a conclusion

Minor term (S)

The term that appears in the SUBJECT of a conclusion