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Formal Aristotelian Logic > Basic Formal Logic > Flashcards

Basic Formal Logic Flashcards

1
Q

Truth

A

Statement describing reality

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2
Q

Validity

A

When the conclusion logically follows the premises

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3
Q

Sound

A

When an argument is both true and valid

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4
Q

Simple Apprehension

A

The act by which the mind grasps the concept or general meaning of an object without affirming or denying anything about it.

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5
Q

Term

A

The verbal expression of a simple apprehension, usually just one word; terms are divided into univocal, equivocal, and analogous.

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6
Q

The three stages of Simple Apprehension

A

Sense perception, mental image, concept through abstraction (simple apprehension)

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7
Q

Comprehension

A

The completely articulated sum of the intelligible aspects or elements (notes of Porphyrian Tree) represented by a concept.

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8
Q

Notes of the Porphyrian Tree

A

Substance (non-material existence)
Body (material existence)
Organism (living existence)
Animal (sentient existence)
Man (rational existence)

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9
Q

Extension

A

What the concept refers to; what tells us the things to which that essence applies.
i.e the term Man refers to all men that live, have lived, or ever will live. When the comprehension gets smaller, the extension extends to a larger group.

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10
Q

Significance of a term

A

Univocal, equivocal, analogous

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11
Q

Supposition of a term

A

Verbal (referring to the term as it exists in a grammatical form. i.e Man is a noun), Logical (when a term refers to something that exists logically. i.e Man has five notes), Real (when the term refers to the object as it exists in the real world. i.e Man was created by God)

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12
Q

Judgement

A

The act by which the intellect unites by affirming, or separates by denying. The second stage of reasoning.

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13
Q

Proposition

A

The verbal expression of Judgement, usually in the form of sentences. It expresses truth or falsity. In correct logical form, it requires a quantifier, subject, predicate, and copula.

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14
Q

A statement

A

All S is P. Affirmative and universal.

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15
Q

I statement

A

Some S is P. Affirmative and particular.

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16
Q

E statement

A

No S is P. Negative and universal.

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17
Q

O statement

A

Some S is not P. Negative and particular.

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18
Q

Quantifiers

A

All, some, no, some…not

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19
Q

Copula

A

Any form of the verb “to be”- am, is, are, was, were, etc.

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20
Q

Quality

A

When a proposition is affirmative or negative.

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21
Q

Quantity

A

Whether a proposition is universal or particular

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22
Q

Rule of Contradiction

A

Statements differing in both quality and quantity. A,O; E,I

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23
Q

Rule of Contraries

A

When universal statements differ in quality. A,E.

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24
Q

Rule of Subcontraries

A

When two particular statements differ in quality. I,O

25
Q

Rule of Subalterns

A

When two statement have the same quality, but differ in quantity. A,I; E,O

26
Q

1st Law of Opposition

A

Contradictories cannot at the same time be true nor at the same time be false.

27
Q

2nd Law of Opposition

A

Contraries cannot at the same time both be true, but can at the same time be false.

28
Q

3rd Law of Opposition

A

Subcontraries may at the same time both be true, but cannot at the same time both be false.

29
Q

4th Law of Opposition

A

Subalterns may both at the same time both be true or both be false. If the particular is false, then the universal is false, if the universal is true, the particular is also true.

30
Q

Distribution

A

The status of a terms in regard to its extension.

31
Q

Distributed

A

When a term refers to all the members of the class of things denoted by that term.

32
Q

Undistibuted

A

When a term refers only to some of the member of the class of things denoted by that term.

33
Q

Distribution of A statement

A

Subject: distributed
Predicate: undistributed

34
Q

Distribution of I statement

A

Subject: undistributed
Predicate: undistributed

35
Q

Distribution of E statement

A

Subject: Distributed
Predicate: distributed

36
Q

Distribution of O statement

A

Subject: undistributed
Predicate: distributed

37
Q

Steps For Obversion

A
  1. Change the quality of the sentence
  2. Negate the predicate (add not in front of predicate)
38
Q

Standard Example of Obversion (affirmative and negative, universal and particular)

A

All s is p-> No s is not p; no s is p-> All s is not p; Some s is p-> Some s is not p; Some S is not P-> Some s is not p.

39
Q

Steps for Conversion

A
  1. Interchange subject and predicate
40
Q

Conversion valid types of propositions

A

E and I

41
Q

Steps for partial conversion of a statement

A
  1. Interchange subject and predicate
  2. Change quantity
    I.e: all s is p -> some p is s
42
Q

Steps for Contraposition

A
  1. Obvert the statement
  2. Convert the statement
  3. Obvert the statement again
43
Q

Contraposition valid types of propositions

A

A and O

44
Q

Example of contraposition (both A and O)

A

All s is p-> all non not p is non not s; some s is not p-> some non not p is s

45
Q

Deductive inference

A

The act by which the mind establishes a connection between the antecedent and the consequent,
where the 1st and 2nd premise are the antecedent and the conclusion is the consequent of the reasoning.

46
Q

Reasoning

A

The act by which the mind acquires new knowledge by means of what it already knows.

47
Q

Two types of reasoning

A

Deductive and inductive

48
Q

Syllogism

A

A group of propositions in orderly sequence, one of which( the consequent) is said to be necessarily inferred from the the others( the antecedent).

49
Q

The Essential law of argumentation

A

If the antecedent is true, the consequent must also be true.

Cor.1. If the syllogism is valid and the consequent is false, then the antecedent(one or both of the premises) must be false
Cor.2. In a valid syllogism with a true consequent, the antecedent is not necessarily true( one or both of the premises may still be false)

50
Q

The three terms in a syllogism

A

Major- predicate of conclusion
Minor- subject of conclusion
Middle- the term that logically links the two, appears in both premises, but does not appear in the conclusion

51
Q

Major and minor premise (in a categorical syllogism)

A

Major premise- the premise with the major term, always first in the syllogism
Minor premise-the premise with the minor term

52
Q

Principle of reciprocal identity

A

Two terms that are identical with a third term are identical with each other. ( if a is b, and b is c, then a is c)

53
Q

Principle of reciprocal non-identity

A

Two terms, one of which is identical with a third term and the other of which is non-identical with that third term, are non-identical with each other. ( if a is c, and b is d, b is not c)

54
Q

Dictum de Omni

A

What is affirmed universally of a certain term is affirmed of every term that comes under that term.
(Dogs-> terriers, retrievers, pit bulls, etc.)

55
Q

Dictum de Nullo

A

What is denied universally of a certain term is denied of every term that comes under that term

56
Q

Terminological Rules for categorical syllogisms and corresponding fallacies

A
  1. There must be three and only three terms
    -The fallacy of four terms
  2. The middle term must not occur in the conclusion
    If middle term is used equivocally,
    - fallacy of equivocation
57
Q

Quantitative rules for categorical syllogisms and corresponding fallacies

A
  1. If a term is distributed in the conclusion, then it must be distributed in the premises
    - Fallacy of illicit major/minor depending on the term not distributed
  2. The middle term must be distributed at least once
    -fallacy of the undistributed middle
58
Q

Terminological rules for categorical syllogisms and corresponding fallacies

A
  1. no conclusion can follow from two negative premises
    - fallacy of exclusive premises
  2. If the two premises are affirmative, the conclusion must also be affirmative
    -fallacy of drawing a negative conclusion from affirmative premises
  3. If either premise is negative, the conclusion must also be negative
    - fallacy of drawing an affirmative conclusion from a negative premise
59
Q

The seven rules of validity for categorical syllogisms

A
  1. There must be three and only three terms
  2. The middle term must not occur in the conclusion
  3. If a term is distributed in the conclusion, it must be distributed in the premises
  4. The middle term must be distributed at least once
  5. No conclusion can follow from two negative premises
  6. If the two premises are affirmative, the conclusion must be affirmative
  7. If either premise is negative, the conclusion must also be negative.

Formal Aristotelian Logic (2 decks)

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