Basic Formal Logic Flashcards
Truth
Statement describing reality
Validity
When the conclusion logically follows the premises
Sound
When an argument is both true and valid
Simple Apprehension
The act by which the mind grasps the concept or general meaning of an object without affirming or denying anything about it.
Term
The verbal expression of a simple apprehension, usually just one word; terms are divided into univocal, equivocal, and analogous.
The three stages of Simple Apprehension
Sense perception, mental image, concept through abstraction (simple apprehension)
Comprehension
The completely articulated sum of the intelligible aspects or elements (notes of Porphyrian Tree) represented by a concept.
Notes of the Porphyrian Tree
Substance (non-material existence)
Body (material existence)
Organism (living existence)
Animal (sentient existence)
Man (rational existence)
Extension
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.
Significance of a term
Univocal, equivocal, analogous
Supposition of a term
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)
Judgement
The act by which the intellect unites by affirming, or separates by denying. The second stage of reasoning.
Proposition
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.
A statement
All S is P. Affirmative and universal.
I statement
Some S is P. Affirmative and particular.
E statement
No S is P. Negative and universal.
O statement
Some S is not P. Negative and particular.
Quantifiers
All, some, no, some…not
Copula
Any form of the verb “to be”- am, is, are, was, were, etc.
Quality
When a proposition is affirmative or negative.
Quantity
Whether a proposition is universal or particular
Rule of Contradiction
Statements differing in both quality and quantity. A,O; E,I
Rule of Contraries
When universal statements differ in quality. A,E.
Rule of Subcontraries
When two particular statements differ in quality. I,O
Rule of Subalterns
When two statement have the same quality, but differ in quantity. A,I; E,O
1st Law of Opposition
Contradictories cannot at the same time be true nor at the same time be false.
2nd Law of Opposition
Contraries cannot at the same time both be true, but can at the same time be false.
3rd Law of Opposition
Subcontraries may at the same time both be true, but cannot at the same time both be false.
4th Law of Opposition
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.
Distribution
The status of a terms in regard to its extension.
Distributed
When a term refers to all the members of the class of things denoted by that term.
Undistibuted
When a term refers only to some of the member of the class of things denoted by that term.
Distribution of A statement
Subject: distributed
Predicate: undistributed
Distribution of I statement
Subject: undistributed
Predicate: undistributed
Distribution of E statement
Subject: Distributed
Predicate: distributed
Distribution of O statement
Subject: undistributed
Predicate: distributed
Steps For Obversion
- Change the quality of the sentence
- Negate the predicate (add not in front of predicate)
Standard Example of Obversion (affirmative and negative, universal and particular)
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.
Steps for Conversion
- Interchange subject and predicate
Conversion valid types of propositions
E and I
Steps for partial conversion of a statement
- Interchange subject and predicate
- Change quantity
I.e: all s is p -> some p is s
Steps for Contraposition
- Obvert the statement
- Convert the statement
- Obvert the statement again
Contraposition valid types of propositions
A and O
Example of contraposition (both A and O)
All s is p-> all non not p is non not s; some s is not p-> some non not p is s
Deductive inference
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.
Reasoning
The act by which the mind acquires new knowledge by means of what it already knows.
Two types of reasoning
Deductive and inductive
Syllogism
A group of propositions in orderly sequence, one of which( the consequent) is said to be necessarily inferred from the the others( the antecedent).
The Essential law of argumentation
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)
The three terms in a syllogism
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
Major and minor premise (in a categorical syllogism)
Major premise- the premise with the major term, always first in the syllogism
Minor premise-the premise with the minor term
Principle of reciprocal identity
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)
Principle of reciprocal non-identity
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)
Dictum de Omni
What is affirmed universally of a certain term is affirmed of every term that comes under that term.
(Dogs-> terriers, retrievers, pit bulls, etc.)
Dictum de Nullo
What is denied universally of a certain term is denied of every term that comes under that term
Terminological Rules for categorical syllogisms and corresponding fallacies
- There must be three and only three terms
-The fallacy of four terms - The middle term must not occur in the conclusion
If middle term is used equivocally,
- fallacy of equivocation
Quantitative rules for categorical syllogisms and corresponding fallacies
- 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 - The middle term must be distributed at least once
-fallacy of the undistributed middle
Terminological rules for categorical syllogisms and corresponding fallacies
- no conclusion can follow from two negative premises
- fallacy of exclusive premises - If the two premises are affirmative, the conclusion must also be affirmative
-fallacy of drawing a negative conclusion from affirmative premises - If either premise is negative, the conclusion must also be negative
- fallacy of drawing an affirmative conclusion from a negative premise
The seven rules of validity for categorical syllogisms
- There must be three and only three terms
- The middle term must not occur in the conclusion
- If a term is distributed in the conclusion, it must be distributed in the premises
- The middle term must be distributed at least once
- No conclusion can follow from two negative premises
- If the two premises are affirmative, the conclusion must be affirmative
- If either premise is negative, the conclusion must also be negative.
