Logic 2 Flashcards
What is the definition of Universal?
A concept that is not prevented from being shared or applied to many individuals
What is the definition of Singular?
A concept that is prevented from being shared or applied to many individuals
What is an Essential Univeral?
Says something about what a thing is
What is a Non-Essential Universal?
Says something about what belongs to a thing
What are the 5 Universals?
- Genus
- Species
- Specific Difference
- Property
- Accident
What are the 3 Essential Universals?
- Genus
- Species
- Specific Difference
What are the 2 Non-Essential Universals?
- Property
- Accident
What is a Genus?
That which can be said of many things differing in their realities, or it is a relation of universality by which something one can be said of many that differ specifically
What is a Species?
That which is said of many things that differ by their individuals (real species) or it is a relation of universality by which something one can be said of many that differ only in number (individuals)
What is a Specific Difference?
A relation of universality of which something is predicated in a way that sets one thing apart from another, not just as distinct in number but as different in kind
Porphyrian Tree
What is a Property?
A relation of universality in virtue of which something is said of a species as belonging only, necessarily, and always to that species and to every individual of that species
What is an Accident?
The accident is defined as a universal relation implied when something is attributed to a species as that which belongs contingently (not necessary) to that species and to the individuals of that species. They do not necessarily apply to a single species but can be applied to many.
What is the difference between Properties and Accidents?
Properties are specific, accidents are general
What are the 10 Categories?
- Substance
- Quantity
- Quality
- Relation
- Action
- Being Passive (passivity)
- When
- Where
- Position
- Habit
What is the Subject?
The substratum/locus/location of accidents or attributes. It is also called a “substance.”
What is the Existence in a Subject?
Something that requires a subject in order to be at all i.e., an accident
What is Does not exist in a subject?
The subject itself or the ‘substance’
What is Predicable of a Subject?
Signifies that something we know can be said of or predicated of a subject. These are the five universals we covered earlier: genus, species, specific difference, property, and accident
What is Not Predicable of a Subject?
A singular
What is Negation?
The denial of something
What are the 4 types of Opposition?
- Contradictory Opposition
- Privative Opposition
- Contrary Opposition
- Relative Opposition
What is Contradictory Opposition?
The most fundamental and exhaustive opposition. It is a simple and perfect negation between being and non-being
What are the qualities of Contradictory Opposition?
-The positive is an existing thing
- The negative does not exist
- You cannot remove both of these categories
together from a single thing (one of them
applies to every individual in existence)
- You cannot join these categories together in a
single thing (a single thing must be one or the
other)
Table from reading (contradiction)
What is Privative Opposition?
Similar to contradictory opposition in that we have a relationship between being and non-being. The difference is that being and non-being here are IN A SUBJECT.
-Example: Ear-Hearing-Deafness
Qualities of Privative Opposition?
- the positive (faculty) exists
- The negative does not exist (absence of
faculty) - You can remove these categories together
from a single thing that does not have the
faculty (one’s nose is neither hearing nor deaf)
-You cannot join these categories together in a
single aspect of a subject (you can’t be deaf
and hearing in the same ear, but someone i.e.,
subject, should be deaf in their right ear and
hearing in their left ear)
Table from reading (privative)
What is Contrary Opposition?
A relation between two terms existing as opposites
- Hot/Cold
-White/Black
What are the Qualities of Contrary Opposition?
- Both opposites exist
- You can remove these categories from
subjects (they do not apply to everything in
existence) - If one applies to something, the other cannot
be joined with it in the same aspect. (my cup of coffee is hot, which means it cannot be cold.) They can be brought together in the same subject, but not in the same aspect. For instance, a black and white striped shirt
Table from reading (contrary)
What is Relative Opposition?
A relation of being and being in which both opposites refer to one another
-father/son
What are the Qualities of Relative Opposition?
- Both the negative and the positive exist
- We cannot join them in the same subject from
the same respect. Someone cannot be a father
to the person they are a son to - You can remove them from a thing (a boy
cannot be a sister)
What is the goal of conceptualization?
Definition because a definition tells us what a specific concept is
What is Definition?
Definition is an art, and its aim is to try and say what a thing is i.e., its quidditty.
What are the 2 parts of The Definition?
- The definitum
- The definiens
What is a Definitum?
The thing we are defining
What is the Definiens?
The definition itself, the phrase or sentance that tells us what a thing is
Important things about the Definition
- The definition must not be too general or too
specific - The definition must be inclusive and exclusive
What are the rules of definition?
- The definition and definitum are convertible
a. This means that we can switch the
definitum with the definition in a sentence
and it would still make sense - The definition is clearer that the definitum
- The definition must be inclusive and exclusive
What is Inclusive?
The definition includes all of the individuals of a thing. We defined a tree as a plant with bark, branches, leaves, and roots, usually tall with apples, we have excluded other types of trees that fit under the term tree
What is Exclusive?
The definition excludes all of the individuals that do not fit into the thing. If we defined tree as “a plant” that would include more things than simply trees
What is a Complete Real Definition?
Composed of the proximate genus and the proximate specific difference of a thing. This is the best type of definition.
- Example: Man is a rational animal
What is a Deficient Real Definition?
Composed of a far (medial or supreme) genus and a proximate specific difference of a thing. Or, at least, just a proximate specific difference. It is called a “deficient real definition” because it only has one part of a complete real definition, the proximate specific difference
- Example: Man is a rational living thing
What is a Complete Description?
A composition of proximate genus and property
- Example: Man is an animal capable of
grammar
What is a Deficient Description?
A composition of accidents, or property. It is deficient because it has only one of the elements of a complete description: the property
What is the debated definition and why is it debated?
A bunch of accidents. It is debated because a bunch of accidents doesn’t tell you the quiddity of a thing
Terms:
- Complete: Proximate genus
- Real Definition: Proximate Specific Difference
- Deficient: Lacking a Proximate Genus
- Description: Property
What is a Definition by Example?
Used in teaching to help students understand the meaning of a word. It does not actually define the term; it merely points to what it is with an example
- Example: Timid: When a mouse sees a lion
What is Definition By Comparison/Resemblance?
When you define a thing by giving something else that is similar to it in some quality
- Example: A bird is like a plane (they both fly)
What is Definition by Name?
- Etymology
- Common/general meaning
- A lexical definition
- A technical definition
What is Etymology?
Explains a word’s etymologysuch as defining “philosphy” as “love of wisdom from the Greek PHILO + SOPHIA”
What is Common/general Meaning?
Gives a common meaning for a word. For instance, defining “sky” as “the blue thing above us”
What is a Lexical Definition?
Giving the definition of a thing that is used in normal speech,
What is a Technical Definition?
A definition that is used in a particular science
What are the Fallacious Definitions?
- Circular Definition
- Infinite Regress Definition:
What is a Proposition?
A complete composite expression that has the capacity for truth or falsity in and of itself
What is the Subject?
The thing that one makes a judgment on, the thing being judged
What is the Predicate?
The judgment made on the subject
What is the Verb Copula?
A sign that joins the subject and predicate
What is a Judgment?
The mental decision of whether a proposition is true or false
What type of sentence is a proposition?
A declarative sentence
What type of sentence is not a proposition?
Commands, Requests, or Questions
What are the parts of a proposition?
- Subject
- Verb Copula
- Predicate
What are the divisions of a proposition?
- Unity
- Quality
- Quantity
- Matter
- Modes
What is Unity?
By what way a proposition is one.
What are the two general types of propositions based on unity?
- Categorical proposition
- Compound/hypothetical proposition
What is a Categorical Proposition?
A proposition that can be broken up into two parts, a subject and a predicate. Categorical propositions say one thing of another and are thus ABSOLUTELY one.
-Example: Zaid is a writer
What is a Compound/hypothetical proposition?
These propositions do not join two single parts together, rather they join two or more propositions together
-Example: If it is daytime, then the sun has risen
- The verb copula of these propositions is no longer a single word. They are connectives such as If-then or Either-or
What are the 2 types of propositions according to quality?
- Affirmative
- Negative
What is an Affirmative Proposition?
When the predicate is joined with the subject i.e., composition
- Example: Zaid is a writer
What is a Negative Proposition?
When the predicate is separated from the subject i.e., division
-Example: Zaid is not a writer
What is the quantity of a proposition based on?
Based on the quantity of the subject
What are the 2 types of propositions according to Quantity?
- Singular Proposition
- Universal Proposition
What is a Singular Proposition?
If the subject is an individual, such as “Zaid is a writer”
What is a Universal Proposition?
Universal means that which can be predicated of many individuals. A universal proposition is universal if the subject is universal.
What are the 3 types of Universal Propositions?
- Indefinite
- Universal
- Particular
What is a Particular Proposition?
Indicates that the predicate is of the subject for some of the individuals or some individual
What is a Universal Proposition?
The predicate is being predicated of the subject in a universal way, i.e., it is said of every individual
What is an Indefinite Proposition?
It does not specify whether it is a particular or a universal
Table from reading (universals)
What is the division of the proposition, matter, based on?
Based on the relation between the subject and the predicate
What are the 3 types of Matter?
- Necessary Matter
- Impossible Matter
- Contingent Matter
What is Necessary Matter?
Found in a proposition when the predicate is in the subject i.e., belongs to the essence or quiddity of the subject. If the predicate of a proposition has a genus, species, specific difference, or property of a subject the proposition has necessary matter.
What is Impossible Matter?
When the predicate does not belong to the subject. The predicate and subject cannot be joined in our minds
What is Contingent Matter?
When the predicate is neither in the subject (in the essence or quiddity) nor does not belong to the subject. Basically not necessary or impossible.
Table from reading (Predicates)
What are the 2 propositions based on Modes?
- Simple Proposition
- Modal Proposition
What is Mode?
Indicates how the predicate belongs or does not belong to the subject
What is a Simple Proposition?
A simple proposition does not express its mode
What is a Modal Proposition?
A proposition that has its verb copula modified explicitly by a mode
What are the 4 possible Modes?
- Necessary
- Impossible
- Possible
- Contingent
What is Distribution?
The status of a term in regard to its extension. A term is Distributed if it stands for all of its individuals. A term is Undistributed if it stands for only some of its individuals
What is Extension?
What the concept applies to
Distribution of Propositions
A - Every A (All individuals of A) is B (some individuals)
E - No A (all individuals of A) is B (all individuals of B)
I - Some A (some individuals of A) is B (some individuals of B)
O - Some A (some individuals of A) is not B (all individuals of B)
Table from reading (Distribution)
What are the Rules for Distribution?
- Every universal proposition distributes the
subject - Every particular proposition had an
undistributed subject - Every negative proposition distributes its
predicate - Every affirmative proposition has an
undistributed predicate
What are the 4 relations in the square of opposition?
- Contradiction
- Contrariety
- Sub-contrariety
- Sub-alternation
What is the mnemonic poem for the square of opposition?
In the heavens, truth never fails
It descends to the earth where falsity prevails.
And with its descent, falsity flies,
Destroying universals with particular lies.
What is Contradiction (in the square of opposition)?
If one is true, the other is false. If one is false, the other is true.
What is Contrary (in the square of opposition)?
If one is true, the other is false. If one is false, the other is unknown.
What is Sub-contrary (in the square of opposition)?
If one is false, the other is true. If one is true, the other is unknown.
What is Subalternation (in the square of opposition)?
If the universal is true, the particular is true. If the universal is false the particular is unknown. If the particular is false, the universal is false. If the particular is true, then the universal is unknown.
Square of Opposition Rules:
- Contradictory opposition: two propositions cannot be true or false at the same
time. - Contrary opposition: two propositions cannot be true at the same time.
- Sub-contrary opposition: two propositions cannot be false at the same time.
- Subalternation: Whenever the universal is true, the particular is true. Whenever
the particular is false, the universal is false - Contradiction: if one is true, the other is false. If one is false, the other is true.
- Contrary: if one is true, the other is false. If one is false, the other is unknown.
- Sub-contrary: if one is false, the other is true. If one is true, the other is unknown.
- Subalternation: if the universal is true, the particular is true. If the universal is
false, the particular is unknown. - If the particular is false, the universal is false. If the particular is true, then the
universal unknown
The square of opposition:
What is Obversion?
Change the quality of the proposition and negate the predicate term. We travel across the top or bottom of the square.
What are the Rules of Obversion?
- Change the quality of the proposition
- Negate the prediacte term
Image from reading (obversion)
What propositions are you allowed to use Obversion on?
A to E
E to A
I to O
O to I
What is Conversion?
Exchanging the subject and predicate while maintaining quality and truth
What are the 2 types of Conversion?
- Accidental Conversion
- Simple Conversion
What is Accidental Conversion?
You switch the subject and predicate and change the quantity.
What is Simple Conversion?
You switch the subject and predicate of the proposition.
What propositions can you Accidentally Convert?
A and E
What propositions can you Simply Convert?
I and E
Image from reading (conversion)
What are the 3 Operations we can perform in Propositions?
- Obversion
- Conversion
a. Simple
b. Accidental - Contraposition
a. Complex way
b. Simple way
What is Contraposition?
A combination of obversion and conversion. Switch the subject and the predicate. Then negate both the subject and predicate terms.
What are the 2 types of Contraposition?
- Complex way
- Simple Way
What are the rules for Contraposition in the Complex Way?
- Obversion
- Simple Conversion
- Obversion
What are the rules for Contraposition in the Simple Way?
- Switch the subject and predicate
- Negate both the subject and predicate
Table of Operations for Propositions: (Very Important)
What are the different types of Compound/Hypothetical Propositions?
There is a total of 5 which are divided into 2 major groups which are:
1. Explicit
2. Implicit
What is an Explicit Proposition?
A proposition that has its complex composition fully revealed in the expression of the proposition. It has all of its parts fully said in its expression.
What are the 3 types of Explicit Propositions?
- Conditional
- Disjunctive
- Copulative
What is a Conditional Proposition?
Joins two categorical propositions with the connectives “if…then.”
What is the Antecedent?
The proposition that comes after the “if” in a categorical proposition.
What is the Consequent?
The proposition that comes after the “then” in a categorical proposition.
What is the relation between the Antecedant and the Consequent called?
The sequence
Important information about Conditional Propositions:
For a conditional proposition to be true, the second part, the consequent must follow the antecedent necessarily; otherwise, the proposition is invalid.
What are Disjunctive Propositions?
Join two categorical propositions with the non-verbal connective copula “either…or”
Important information about Disjunctive Propositions:
One side of the proposition is true and the other side is false. Both cannot be true at the same time, and both cannot be false at the same time.
What are the 3 Relations of Disjunctive Propositions?
- 2 terms cannot be brought together, but
they can be removed. (example: A body
is either white or it is black) - 2 terms cannot be removed but they can
be brought together. (example: Zaid is
either in the sea or he is not drowning
(this means: he can be in the sea and
not drowning at the same time)) - 2 terms cannot be joined or removed.
(example: A number is either even or it
is odd)
What are Copulative Propositions?
Propositions that join 2 categorical propositions with a connective such as “and”
What is the condition for Copulative Propositions?
For this proposition to be true, both categorical propositions must be true by themselves.
What is an Implicit Compound Proposition?
A proposition that does not have its complex composition fully revealed in the expression of the proposition.
What are the 2 types of Implicit Propositions?
- Exclusive Proposition
- Exceptive Proposition
What is an Exclusive Proposition?
A proposition that contains words like “only” and “alone.”
What is an Exceptive Proposition?
A proposition that uses words like “except.” In these propositions, something within the subject is removed from the predicate.
How to derive the 2 propositions from an Exceptive Proposition?
- Create a proposition with the “exceptive” and then with the contradiction of that “exceptive” that is derived from the original subject.
(non + exceptive + subject)
Table from reading (Compound Propositions)
