Logic Reading 1: From Thales to Aristotle

Argument

composed of 2+ statements, in which a conclusion follows from a premise; valid or invalid; either deductive or nondeductive

Deductive Argument

conclusion CLAIMED to follow necessarily from its premises

Valid Deductive Argument

conclusion DOES follow necessarily from its premises

Sound Argument

true premises and validity

Logic’s Greek term is “logos”. What does it mean?

It’s the meaning of uncovering concerns. it refers to speech (meaningful utterances).

Term

verbal utterance that signifies idea; can’t be true or false/ clear or unclear

Clarity

clear or unclear meaning

Statement

true or false utterance

Philosophy

activity of clarifying ideas of nature of reality, value, knowledge, reason

Syllogism

arguments with 2 premises and a conclusion

Deductive Syllogism

deductive argument with 2 premises and a conclusion (mediate and immediate inferences)

Inference

synonym for argument

Categorical Proposition

statement that relates 2 classes or categories, denoted by a subject term and predicate term (either/part is ex/included)

Quantifier

specifies ex/inclusion (all, no, some)

Copula

links subject with predicate (are, are not)

In “All S are P”, what is the quantifier?

All

In “All S are P”, what is the copula?

are

In “All S are P”, what is the subject?

S

In “All S are P”, what is the predicate?

P

Quantity

either universal (all, no) or particular (some); whether there’s a claim about every member or some member

Quality

either affirmative (all, some are) or negative (no, some are not); whether it affirms or denies membership

Distribution

if a statement makes an assertion about every member of the class denoted by that term; is distributed if statement assigns attribute to every member

Which proposition is an “A”?

All S are P

Which proposition is an “E”?

No S are P

What proposition is an “I”?

Some S are P

What proposition is an “O”?

Some S are not P

What’s the quantity of an A-proposition?

Universal

What’s the quantity of an E-proposition?

Universal

What’s the quantity of an I-proposition?

Particular

What’s the quantity of an O-proposition?

Particular

What’s the quality of an A-proposition?

affirmative

What’s the quality of an E-proposition?

negative

What’s the quality of an I-proposition?

affirmative

What’s the quality of an O-proposition?

negative

What’s distributed in an A-proposition?

the subject (one)

What’s distributed in an E-proposition?

the subject and the predicate (both)

What’s distributed in an I-proposition?

nothing

What’s distributed in an O-proposition?

the predicate (one)

Complement (of a class)

a class containing all the things that aren’t a member of another class

Term-Complement

word or phrase the denotes the class complement

Conversion

interchanging subject and predicate terms (No S are P= No P are S)

Which propositions work with conversion?

E and I

Conversion by Limitation

switching subject and predicate in an A-statement and making quantity particular (All S are P, so Some P are S)

Obversion

switching the quality and replacing predicate with its term-complement (All S are P = No S are non-P)

Which propositions work with obversion?

A, E, I, and O

Contraposition

replacing subject with term-complement of its predicate and replacing predicate with term complement of its subject

Which propositions work with contraposition?

A and O

Contraposition by Limitation

contraposition + making quality particular (No S are P, so some non-P are not non-S)

What are the Conditions for Contradiction?

the truth of either proposition necessarily means the falsity of the other/ the falsity of either proposition necessarily means the truth of the other. This is only between propositions that have the same subject and predicate, and they differ in quality and quantity (A and O; E and I).

Where are the propositions located on the Square of Opposition?

A: top left; E: top right; I: bottom left; O: bottom right

Contradiction

relation between the opposed A and O propositions or E and I propositions (if one is true, the other is false; vice versa)

On the Square of Opposition, where is contradiction located?

the center

Contrariety

can both be false, but both can’t be true

On the square of opposition, what propositions do contrariety relate with?

A and E

Subcontrariety

can both be true, but can’t both be false

On the Square of Opposition, what propositions do subcontrariety relate with?

I and O

Subalternation

if the universal is true, then the particular under it is true

On the Square of Opposition, what propositions do subalternation relate with?

A to I; E to O

Superalternation

If a particular is false, then the universal over it is false

On the Square of Opposition, what propositions do superalternation relate with?

I to A; O to E

What does the Square of Opposition tell you about propositions?

what proposition contradicts any given proposition; arrows tell which inferences are valid and how to complete a valid inference from one opposed proposition to another

If an A-proposition is true, then an E-proposition is:

false

If an A-proposition is true, then an I-proposition is:

true

If an A-proposition is true, then an O-proposition is:

false

If an E-proposition is true, then an A-proposition is:

false

If an E-proposition is true, then an I-proposition is:

false

If an E-proposition is true, then an O-proposition is:

true

If an I-proposition is true, then an A-proposition is:

unknown

If an I-proposition is true, then an E-proposition is:

false

If an I-proposition is true, then an O-proposition is:

unknown

If an O-proposition is true, then an A-proposition is:

false

If an O-proposition is true, then an E-proposition is:

unknown

If an O-proposition is true, then an I-proposition is:

unknown

If an A-proposition is false, then an E-proposition is:

unknown

If an A-proposition is false, then an I-proposition is:

unknown

If an A-proposition is false, then an O-proposition is:

true

If an E-proposition is false, then an A-proposition is:

unknown

If an E-proposition is false, then an I-proposition is:

true

If an E-proposition is false, then an O-proposition is:

unknown

If an I-proposition is false, then an A-proposition is:

false

If an I-proposition is false, then an E-proposition is:

true

If an I-proposition is false, then an O-proposition is:

true

If an O-proposition is false, then an A-proposition is:

true

If an O-proposition is false, then an E-proposition is:

false

If an O-proposition is false, then an I-proposition is:

true

What syllogistic structure is Figure 1?

MP

SM

:.SP

What syllogistic structure is Figure 2?

PM

SM

:.SP

What syllogistic structure is Figure 3?

MP

MS

:.SP

What syllogistic structure is Figure 4?

PM

MS

:.SP

Enthymeme

one premise is not explicitly stated

Conclusion Indicator

A word or phrase appearing in an argument and usually indicating that what follows is the conclusion of an argument

What’s a partial list of common conclusion indicators?

therefore, hence, so, accordingly, in consequence, consequently, proves that, as a result, for this reason, thus, for these reasons, it follows that, I conclude that, which shows that, which means that, which entails that, which implies that, which allows us to infer that, which points to the conclusion that, we may infer

Premise Indicator

In an argument, a word or phrase that normally signals that what follows it are statements serving as premises

What’s a partial list of common 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 deducted from, in view of the fact that

What’s the first piece you find in translating categorical syllogisms into standard form?

the conclusion

How do you find the conclusion in an improperly formed syllogism?

indicator words

What’s the second piece you find in translating categorical syllogisms into standard form?

the major premise

How do you find the major premise in an improperly formed syllogism?

if it includes the predicate of the conclusion

What’s the third piece you find in translating categorical syllogisms into standard form?

the minor premise

How do you find the minor premise in an improperly formed syllogism?

if it includes the subject of the conclusion