Terms: Verbal/Real Disputes and Definition
Language is the means by which we communicate with each other and when words are used mistakenly or carelessly, then our attempt to communicate with each other fails. Disagreements with other persons can be genuine or not genuine disagreements. The disagreements are genuine disagreement results from differences of attitudes about facts (but agreement on the facts) or differences of beliefs about the facts. The disagreement is not a genuine disagreement when the disagreement with any person we are attempting to communicate with is the result of the misuse of words.
Different
Kinds of Disputes
- Disagreement
in attitude. “A cheers while B sulks when
- Disagreement
about the facts: A maintains that the Pacific entrance to the
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Mary and John are both chemistry students presently enrolled at Murray State University. Mary claims that all chemistry students at MSU have to take Chemistry 305 before they can graduate from MSU with a major in chemistry. John, on the other hand, maintains that Chemistry 305 is only an elective course that is not required for graduation with a major in chemistry at MSU . |
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This disagreement between Mary and John is a genuine dispute
that cannot be resolved by defining the key terms in the dispute. Whether
Mary or John is right depends on how the world is and not on how she or he is
using the English language. The |
A second kind of dispute or quarrel is a verbal dispute. When there is a merely verbal dispute between two speakers, there is no disagreement in attitude about the facts or disagreement about the facts. Verbal disputes arise when the key terms the speakers are using to communicate with each other are ambiguous. The absence of disagreement is hidden from the speaker because the terms they use to communicate with each other are ambiguous. Some word or phrase central to their dispute often has different senses that should not be confused and the dispute arises because the parties to the dispute do not realize the word or phrase has different but equally legitimate meanings. Disagreements of this kind can be resolved by specifying the different senses of the key words or phrases in their dispute. See pp. 100-101 for William James famous example of verbal disagreement based upon the ambiguous verb ‘go around.’
The third kind of dispute is the apparently verbal but really genuine dispute. When the quarrel goes beyond the differ use of key terms and phrases, some genuine disagreement (either attitude or belief) remains. Consider the case that two parties have seen the same film and are discussing the part of the movie with the most explicit sexual activity. One party thinks the part with the explicit sexual activity makes the movie a porn movie. One part says the explicit sexual activity make the movie porn and wicked while the other party says treatment of explicit sex in the movie has aesthetic merit and the movie is true art not pornography. Even if we defined the words “porn” and “pornography”, the two parties would still likely disagree. The disagreement is not about words but about the nature of a film and what makes a film a good film and what makes a film a bad film. We call this kind of disagreement conceptual disagreement The parties to the dispute have different criteria for the application of some key term – in say the same thing differently, the parties have different conception of what it is that is named by that term.
Example of an apparently verbal but really genuine dispute: Mary believes that to abort a fetus is always morally wrong, whereas Ann believes that there are situations in which it is morally acceptable to abort a fetus. Mary and Ann have different understandings of what is meant by the term "fetus." On the one hand, Mary believes that a fetus is "a child" and thus should have all the legal rights that other children do have, including the right to life. Ann believes, on the other hand, that a fetus is merely a small piece of human tissue of the mother's body and therefore the only right is the mother's right to do with her body as she pleases.This is an apparently verbal disagreement that turns out to be a really genuine dispute. Even if Mary and Ann were to clarify by giving definitions what each understood by the term "fetus," they not resolve their dispute. Each would probably insist on her own criteria for applying the term "child."
flowchart to determine if a dispute is real:
1.) Ask if there is some ambiguity of key terms or phrases used by the speakers in the dispute?
If the answer to the question “Is there is some ambiguity of key terms or phrases used by the speakers in the dispute?” is NO then we have a genuine dispute or disagreement.
If the answer is Yes “to
the question Is there is some ambiguity of key terms or phrases used by the
speakers in the dispute?”, then we see if see if getting
rid the ambiguity (of the key term or phrases by giving definitions of these
key terms in the dispute) eliminates the disagreement? If the answer to this
question is Yes, then we have a verbal disagreement. If the answer to
this question is NO then we have an apparently verbal disagreement but
really a genuine disagreement.
Definition: Lets us address two questions today:
1.) what is the purpose of providing the reader with a definition (What are
definitions for) and 2.) how can we avoid ambiguity and/or equivocation in our
use of words?
What are definitions for?
Definitions are used to make communication between the writer and his audience
clear. Let us assume you are writing an essay about twins. In the essay you
plan to use the terms “identical twins” and “fraternal
twins.” You have to consider whether your reader will know what these
terms mean in genetics. If you think the persons to whom you want to
communication your argument do not have knowledge of genetics, then you know
the distinction that you plan to make between “identical twins: and
“fraternal twins” will not be understood by your readers: they may think
identical twins must be of the same sex and fraternal twins must be brothers.
Thus you should define the terms “identical twins” and
“fraternal twins” in your essay. Thus, a definition gives the reader
the meaning of a term that the reader may not, without your definition,
understand.
How can we avoid ambiguity and/or
equivocation?
Definitions are a way of restricting the meaning of a term that has several
meanings: without restricting the term’s meaning, the term is ambiguous.
What is a definition? Definitions are statements about the meaning of a
term. A definition does not give you all the meanings of a term in all the
contexts that it might be used. A definition specifies one of the connotations
of the term or specifies the designation of the term. “Identical twins”
are “twins that develop from the same egg.” This means that
“twins that develop from the same egg” and identical twins has
the same designation. In a definition there are two terms: the “term to be
defined” and the defining term (the term used to define “the term to
be defined.” A definition is a statement that these two terms have the
same designation. In everyday language we say: A person who uses the word
“X” is referring to the act “Y” or “X” means
“Y”. Thus we will begin our discussion of definition by
suggesting that the proper form for a definition is: “X” (term to be
defined) has the same designation as “Y” (the defining term). We need
to add a reference to the scope of “the term to be defined”
and “the defining term”. The scope specifies the context in which the
term is used. For example, the terms bonnet and hood do not always have the
same designation but bonnet (used in British conversations or writings about
cars) has the same designation as hood (used in American conversations about
cars). Thus the definition of the British word “bonnet” when used in
conversations about cars is:
“Bonnet” (in British writings about cars) has the same designation as “Hood” (used in American conversation about cars). This account of definition is a paraphrase of Beardsley’s discussion of definition in Practical Logic
Copi distinguishes between five kinds of definitions and he discusses the uses of each kind, techniques for constructing definitions, and rules for applying these techniques.
The five kinds of definition are: stipulative, lexical, précising, theoretical definitions, and persuasive definitions. Two of these five kinds of definitions – namely stipulative and lexical definitions -are used to eliminate ambiguity (a term is ambiguous in a particular context if the term can have more than one meaning). Précising definitions are used to reduce vagueness (a term is vague when there exists borderline cases and we can not be sure it the term should apply to these borderline cases or not should not apply).
A working definition of each of the five kinds of definition is:
1.) Stipulative definitions assign a meaning to some symbol. A Stipulative definition is a proposal or a resolution to use the “term to be defined” [or definiendum] to mean the same as “the defining term” [or definiens].
2.) Lexical definitions are also used to eliminate ambiguity. In addition lexical definitions in an English Dictionary are used to increase the vocabulary of persons not familiar with standard usage of English Words. A lexical definition does not give its definiendum a new meaning as stipulative definitions do; lexical definitions report the meaning term already has.
3.) Precising definitions, the third kind of definition that Copi discusses, are used to make commonly used terms more precise or to reduce excessive vagueness.
4.) Theoretical definitions are used to state a comprehensive understanding of the objects to which the term applies. Theoretical definitions attempt to give a scientifically useful description of the objects to which the term applies.
5.) The fifth kind of definition that Copi discusses is called Persuasive definition. Persuasive definitions are used to influence the attitudes or stir the emotions of an audience and thus indirectly to alter conduct.
A definition states
the literal (as opposed to the expressive) meaning of a class or general term.
Every class term has both an extensional meaning and an intentional meaning.
The extensional meaning of a class term is all the objects denoted by the term.
All the objects within the extension of the term or denoted by the term have
some common characteristics or attributes: the
general term "planet" for example applies equally to Venus, Mars,
Jupiter, and Earth. The intentional meaning of a term is the set of
characteristics shared by all objects to which the general term refers and only
shared by those objects: the set of
charachteristics shared by all the objects to which the general term refers provides
the criterion for deciding whether an object falls within the extension of the
term.We should note that the extension of some terms is empty: in other
words, there may be no actual objects to which the term applies. This is the
case, for example, for imaginary creatures like angels, pixies, and dragons. We
know what they are-we know their attributes ( intensional meaning) even if they
don't exist.
How does one define a (class or general) term? Some
definitions approach defining a general term through its extension, or
denotation (example and pointing); others approach defining a general term
through its intension (synonymous, operational, genus-species). Each approach
has its advantages and disadvantages.
The methods of constructing different kinds of
intentional definitions are: synonymous definitions, operational definitions,
definitions by genus and specific difference. Copi’s rules for
constructing real definitions (or definitions by genus and difference) are
helpful: 1.) A definition should state the essential attributes of the species;
2.) A definition must not be circular (A circular definition is one in which
the definiendum itself appears as part of the definiens.); 3.) A
definition must be neither too broad nor too narrow (The definiens
should not denote moreor fewer things than are denoted by the definiendum.);
4.) A definition must not be expressed in ambiguous, obscure, or figurative
language; and 5.) A definition should not be negative where it can be
affirmative.
Term - Robinson's power-point presentation on constructing a definition by genus and specific difference.
Proposition
Definition
Four parts
Two essential attritubes
Distribution (of logical subject term and predicate term)
Venn Diagrams and the Modern
Translation of categorical proposition into standard form
4.1 Definition:
A proposition is a sentence that is either true or false. There are conditional
propositions, disjunctive propositions, and categorical propositions. The
conditional proposition if A then B does not assert that B is true or that A is
true: the conditional proposition if A then B claims that if A is true then B
is true. The disjunctive proposition A or B does not assert that A is true or
that B is true; however it does claim that they are not both false. In contrast
the categorical proposition does assert that some fact or state of affairs is
true. Copi/Cohen and Hurley interpret the categorical proposition as being a
claim about the relation of two classes of objects: the relation of inclusion
or exclusion of the class named by the subject of the proposition in or from
the class named by the predicate of the categorical proposition.
Thus let us briefly state the class interpretation of a
categorical proposition: A categorical proposition is a proposition that
relates two classes denoted or named by the subject term and the predicate
term. The categorical proposition asserts that either all (universal
proposition) or part (particular proposition) of the class denoted by the
subject term is either included in or excluded from the class denoted by the
predicate term: thus, there are four basic types of categorical proposition,
and the standard forms of these four types are as follows:
Standard form Categorical Propositions Class
interpretation of categorical Propositions
All S are P asserts that the whole subject class is contain
in the predicate class
No S are P asserts that the whole subject class is excluded
from the predicate class
Some S are P asserts that part of the subject class is
contained in the predicate class.
Some S are not P asserts that part of the subject class is
excluded from the predicate class.
In these standard forms, S stands for the subject term and P for the predicate
term. The words "all," "no," and "some"
("some" is understood to mean "at least one”) are called
logical quantifiers: all, no, and some indicate how much of the subject class
claimed to be included in or excluded from the predicate class. The words
"are" and "are not" are called copulas: a copula does the
work or function of expressing the fact that the speaker is asserting or
claiming the inclusion in or the exclusion of subject term from the predicate
class is true. A categorical proposition is in standard form if it is a
substitution instance of one of these four standard forms. The categorical
proposition “Light rays travel at a fixed speed” has the standard
form of “All S are P” and is in standard form when rewritten as
“All <light rays> are <things that travel at a fixed
speed>.”
4.2 Two essential attributes or properties of every categorical proposition
are Quality and Quantity.
Quality
Every categorical proposition either affirms (then we say the proposition is
affirmative) or denies (then we say the proposition is negative) the subject
class is included in the predicate class. Thus the quality of a proposition is
either affirmative or negative depending on whether it affirms or denies the
subject class is included in the predicate class. “All S are P” and
“Some S are P” are affirmative propositions, and “No S are
P” and “Some S are not P” are negative propositions. We can
determine the quality of universal categorical proposition by looking at the
universal quantifier: “All S are P” propositions are affirmative and
“No S are P” are negative; we can determine the quality of particular
propositions by looking at the copula: “Some S are P” is affirmative
and “Some S are not P” is negative.
Quantity
Depending on whether a proposition is asserting something about the entire
class of its logical subject (each and every member of the class) or merely
asserting something about some one or few members of its subject class, the
proposition is universal or particular. “All S are P” and “No S
are P” are universal propositions and “Some S are P” and
“Some S are not P” are particular propositions. Thus, all categorical
propositions have a quantity and each one is either universal or particular.
The logical quantifier (all, no, or some) indicates the quantity of the
categorical proposition. “All” and “No” indicates the
proposition is universal and “some” indicates the categorical
proposition is particular.
Distribution is the attribute of a term when the term occurs as
the logical subject or predicate of a categorical proposition. A term is
distributed if the categorical proposition (as a whole) makes an assertion
about every member of the class denoted by the term. Thus if the categorical
proposition asserts something (inclusion in or exclusion from another class)
about every member of the subject class or predicate class then the term is
distributed; however if the proposition does not make an assertion about every
member of a subject class or the predicate then subject term or the predicate
term is undistributed.
Universal Affirmative
The proposition “All S are P” does assert something about the entire
subject class so the subject term is distributed but it does not assert
anything about all members of the predicate class so the predicate term is
undistributed.
Universal Negative
The proposition “No S are P” does assert something about every member
of the subject class and also about every member of the predicate class: so
both terms (subject term and predicate term) are distributed in a universal
negative proposition.
Particular Affirmative
“Some S are P” or a particular affirmative proposition asserts
something about only one member of the subject class: it says that at least one
member of the subject class is included in the predicate class or that a member
of the S class is also a member of the P class. Thus a particular says
something about one member of the subject class and one member of the predicate
class but it does not say or make an assertion about either the entire subject
or the entire predicate class. Thus the subject and the predicate terms of a
particular affirmative proposition are undistributed.
Particular Negative
A particular negative proposition has a subject term that is undistributed and
a predicate term that is distributed. Something is said about one member of the
subject class but not about all member of the subject class: thus the subject
term is undistributed. But the particular negative proposition does assert that
the entire predicate class is separated from at least one member of the subject
class: thus the predicate term is distributed.
Summary of distribution of subject and predicate terms as they occur in a
categorical proposition.
The Subject term in an A proposition is distributed. The Predicate term in an A
proposition is undistributed. In an E proposition both the Subject term and the
Predicate terms are distributed. In an I proposition both the Subject term and
the Predicate term are undistributed. In an O proposition the Subject term is
undistributed, but the Predicate term is distributed. Thus, the subject terms
of universal propositions are distributed and the subject terms in particular
propositions are not distributed. The predicate terms in affirmative
propositions are not distributed and the predicate terms in negative
propositions are distributed.
4.3 Venn Diagrams And The Modern Square Of Opposition
According to the modern interpretation of the square of opposition, an
ambiguity exists in the meaning of the A proposition "All S are P,"
and in the meaning of the E proposition "No S are P." If these
propositions are taken to imply the existence of at least one member of the
class denoted by their subject term "S " and also taken to imply the
existence of at least one member of the class denoted by their predicate term
"P," then the propositions are being understood in the traditional or
Aristotelian sense. But if these propositions are not taken to imply the existence
of at least one member of the class denoted by their subject term "S"
or of the class denoted by their predicate term "P," then the A and E
propositions are being understood in the modern or Boolean sense. Thus, the
modern interpretation of the A proposition "All S are P " is
"There does not exist an S that fails to be a P." And we can see by
looking at the Venn diagram of an A proposition: “if there is no S at all,
then there is no S that fails to be P” and therefore the A proposition is
true. Likewise, on the modern or Boolean interpretation, the E proposition
"No S are P" means "There does not exist an S that is a P."
The Venn diagram of an E proposition makes it clear that “if there
is no S at all, then there is no S that is a P, so that the E-proposition is
true. Thus, on the modern or Boolean interpretation of the A-type categorical
proposition and of the E-type categorical proposition, if there is no S at all,
then both the A-type and the E-type propositions are true.
The following summarizes the modern or Boolean interpretation of all four types
of categorical propositions:
A =
"All S are P"
= There
does not exist an S that fails to be a P.
E =
“All S are P”
= There does not exist an S that
is a P.
I =
"Some S are P"
= There
does exist an S that is a P.
O =
"Some S are not P"
= There
does exist an S that fails to be a P.
Thus, the modern or Boolean interpretation and the traditional or Aristotelian
interpretation have quite different interpretations of the universal
propositions (A and E).
In the nineteenth century, the John Venn invented a manner of representing the
four categorical propositions in their modern interpretation by drawing circles
to representing the meaning of the logical subject class and the logical
predicate class of each categorical proposition. The basic conventions for such
diagrams are as follows:
1. Each term is represented by a circle. (Each categorical
proposition has two terms so the diagram representing a categorical proposition
contains two overlapping circles, one representing the logical subject and one
predicate of the categorical proposition.)
2. The area inside the circle for a term represents the
extension of that term, and the area outside the circle represents everything
not in the extension of that term.
3. Shading of an area means that the class of things in that
area is empty and placing an "X" in an area indicates that the class
represented by that area is not empty--that is, that there is at least one
thing in it.
4. If a given area is neither shaded out nor filled in with
an "X," nothing is said about that the class represented by that
area.
Using Venn diagrams, we may represent all four of the categorical propositions
in their modern interpretations:
The diagrams show that the A and E propositions in
their modern interpretations say nothing about existence. The
diagrams also show that the A-type and the O-type propositions assert the exact
opposite of each other: The logical relation between the A and the O type of
propositions is the relation of contradiction. "A and the O are
contradictory" means that it can not be the case that both
propositions are true at the same time and it cannot be the case that both
propositions are false at the same time. The E-type and the I-type propositions
also assert the exact opposite of each other; thus, they also are related to
each other as contradictories.
The relation of contradiction between the A and the O and between the E and the
I can be represented as follows:
Thus, the modern square represents the modern or Boolean interpretation of
categorical propositions: from the truth of an A-type proposition we may immediately
infer the falsity of the corresponding O-type proposition, but we may not
immediately infer either the truth or falsity of the corresponding E-type
proposition or the truth or falsity of the corresponding I-type
proposition. From the falsity of an A proposition we can immediately
infer the true of an O proposition but we may not immediately infer either the
truth or falsity of the corresponding E-type proposition or the truth or
falsity of the corresponding I-type proposition. In short, only the truth or
falsity of the contraditory p can be immediately inferred: it will have the
opposite truth value of its contradictory.
Translating Categorical Propositions into Standard Form (Summary of Copi and Cohen’s 9 rules or guidelines for translating non-standard statements into categorical propositions.
Translating propositions in nonstandard form into standard form categorical propositions requires us to reformulate them as A, E, I, or O propositions without changing their meanings. No hard and fast rules dictate how to do this in all cases, but the following nine rules suggest guidelines for reformulating nonstandard propositions.
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1.) Singular Propositions firm or deny that a specific individual belongs to a certain class. "Socrates is a philosopher" and " My house is not red" are examples. Although singular propositions refer to a specific individual, we can also interpret singular propositions as referring to a class with only one member. Thus, an affirmative singular proposition like "Socrates is a philosopher" can be understood as the standard A proposition "All people who are Socrates are philosophers." Similarly, a negative singular proposition such as "My house is not red" can be understood as the standard E proposition "No thing that is my house is red." Thus, affirmative singular propositions are understood to be A propositions, and negative singular propositions are understood to be E propositions. 2.) Categorical propositions with adjectives or adjectival phrases as predicates: we can reformulate such propositions into standard form propositions by replacing the adjective (or adjectival phrase) with a term designating the class of all objects to which the adjective (or adjectival phrase) applies. 3.) Categorical propositions with verbs other than the standard-form copula "to be." Propositions with a main verb other than "are or are not" can be translated into standard form by treating the verb or verb phrase as a class-defining characteristic. 4.) Categorical propositions in nonstandard order. In ordinary language some statements have all the parts of a standard-form categorical propositions but are arranged in a nonstandard order. To reformulate one of these statement you must first decide which is the subject term (What is being talked about) and then rearrange the words to express a standard-from categorical proposition. 5.) Categorical propositions with nonstandard quantifiers. “Negative quantifiers like "not every" and "not any" are trickier than affirmative quantifiers and require care to reformulate Thus, for example, "Not every S is P" reformulates as "Some S is not P," whereas "Not any S is P" reformulates as "No S is P." 6.) Exclusive propositions. Categorical propositions that involve the words "only" "or" "none but" are called exclusive propositions. Exclusive propositions translate into A propositions following this general rule: reverse the subject and predicate, and replace the "only" with "all." Thus "Only S is P" and "None but S’s are P’s" are understood to express "All P is S." 7.) Propositions without quantifiers. 8.) Propositions not in standard form that have logically equivalent standard-form alternatives. 9.) Exceptive propositions are propositions that assert that all members of some class are members of some other class, with the exception of the members of one of its subclasses. Exceptive propositions thus make a compound claim: 1.) first that all members of the subject class that are not in the excepted subclass are members of the predicate class, and 2.) second that no members of the subclass are members of the predicate class. |
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Additional comments on Translation of
sentences in English into standard form categorical propositons:
1. Subject and Predicate terms (a term denotes a class of things –
therefore subject term and predicate term must be a noun)
2. Non-standard verbs (chance non-standard verbs to standard copula -
either are or are not)
3. Singular propositions (translated as universal statement by means
of parameter - persons or things) Example. socrates is a man. All persons
identical to Socrates are men.
4. Adverbs and pronouns
adverbs refering to position in
space (everywhere, nowhere) translated as "places"
adverbs refering to time (never,
always, when) translated as "times"
pronouns (who, anyone) translated as
"persons"
5. Unexpressed quantifiers
6. Non-standard quantifiers (few, a few, not every)
A few=Some <logical subject>are
<logical predicate>.
Few or almost all or not quite All= Some
are and Some are not. (compound I and O)
Not everyone= Some are not.
All are not= depending on
meaning either an E or an O.
7. Conditional statements (translated as universals and/or use of
transposition)
Transposition: the antecedent
and the consequent of a conditional statement can exchange places if both are
negated.
Unless means "if
not"
8. Exclusive propositions (only, none but, none except and no
…except at the beginning of sentence) reverse terms: if in the middle of
the sentence then term that preceded only is subject.
9. The only (different from statements beginning with Only) what follows
the only is subject
10. Exceptive (All except or all but) translated as two statements.
Principle of the syllogism:
All <middle term> are (included in ) <major term>. (Major
Premise)
All<minor term> are (included in) < middle term>.
(Minor Premise)
All <minor term> are (included in) <major term >.
(Conclusion)
Steps to put syllogism
into standard form:
1. use premise and conclusion indicators to identify the conclusion:
2. predicate of conclusion is the major term and subject of the
conclusion is the minor term.
3. major premise will contain the major term (predicate of
conclusion) and the middle term.
4. minor premise will contain the minor term (subject of the
conclusion) and the middle term.
5. put the statements in the following order: Major premise, Minor Premise,
and Conclusion.
We will be mainly concerned with deductive arguments. A deductive
argument is an argument whose premisses claim to provide conclusive grounds
for the truth of its conclusion. In a deductive argument, if in fact the
premisses do not provide conclusive grounds (impossible for the premisses to be
true and the conclusion false) for the conclusion, then the argument is
invalid; it the premisses do provide conclusions grounds for the conclusion,
then the argurment is valid. Every deductive argument is either valid or
invalid.
We will study two theories of deduction: Aristotle's theory
and modern symbolic logic's theory of deduction. The purpose of a theory of
deduction is to explain or give an account of the relationship between the
premisses and the conclusion of a valid deductive argument. We will
particularly be concerned with different methods for evaluating deductive
arguments: namely, distingushing between valid and invalid
arguments.
Translating ordinary
language into categorical form
In translating ordinary language into categorical form, one must
consider what is being talked about (the logical subject) and what is being
asserted about it (the logical predicate). For example: "Banks that make
too many risky loans will fail." In this English sentence, the noun
“banks” is the what is being talked about – thus the logical
subject. The author limits the class being talked about by adding the
clause “that make too many risky loans.” The author is
asserting that “banks that make to many risky loans” are banks that
fall into the class (logical predicate) of “institutions that
will not succeed.” She expresses this logical assertion by using the
English verb “will fail.”
To put all of this information into a categorical proposition:
1.
Identify the logical subject and logical predicate. In this
example, “banks that make too many risky loans” is the logical
subject , and, since the logical subject and the logical predicate must
be a noun, “institutions that will fail” is the logical
predicate. NOTE: The predicate must be a broader class than the
subject in an affirmative proposition.
2.
Determine the quantifier based on the logical schema of the four categorical
propositions. In this example, ask yourself if the author is concerned
about all “banks that make risky loans” or only some “banks that
make to many risky loans.”
3. Determine the quality of the statement
– either affirmative or negative. In the example, the author makes a
positive assertion concerning the inclusion of the subject class in the
predicate class.
The result of applying these three
guidelines is:
All (banks that make too many risky loans) are (institutions that will fail).
All (B) are (I).
Translating Categorical Propositions into Standard Form (Summary of Copi and Cohen’s 9 rules or guidelines for translating non-standard statements into categorical propositions.
Translating propositions in nonstandard form into standard form categorical propositions requires us to reformulate them as A, E, I, or O propositions without changing their meanings. No hard and fast rules dictate how to do this in all cases, but the following nine rules suggest guidelines for reformulating nonstandard propositions.
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1.) Singular Propositions firm or deny that a specific individual belongs to a certain class. "Socrates is a philosopher" and " My house is not red" are examples. Although singular propositions refer to a specific individual, we can also interpret singular propositions as referring to a class with only one member. Thus, an affirmative singular proposition like "Socrates is a philosopher" can be understood as the standard A proposition "All people who are Socrates are philosophers." Similarly, a negative singular proposition such as "My house is not red" can be understood as the standard E proposition "No thing that is my house is red." Thus, affirmative singular propositions are understood to be A propositions, and negative singular propositions are understood to be E propositions. 2.) Categorical propositions with adjectives or adjectival phrases as predicates: we can reformulate such propositions into standard form propositions by replacing the adjective (or adjectival phrase) with a term designating the class of all objects to which the adjective (or adjectival phrase) applies. 3.) Categorical propositions with verbs other than the standard-form copula "to be." Propositions with a main verb other than "are or are not" can be translated into standard form by treating the verb or verb phrase as a class-defining characteristic. 4.) Categorical propositions in nonstandard order. In ordinary language some statements have all the parts of a standard-form categorical propositions but are arranged in a nonstandard order. To reformulate one of these statement you must first decide which is the subject term (What is being talked about) and then rearrange the words to express a standard-from categorical proposition. 5.) Categorical propositions with nonstandard quantifiers. “Negative quantifiers like "not every" and "not any" are trickier than affirmative quantifiers and require care to reformulate Thus, for example, "Not every S is P" reformulates as "Some S is not P," whereas "Not any S is P" reformulates as "No S is P." 6.) Exclusive propositions. Categorical propositions that involve the words "only" "or" "none but" are called exclusive propositions. Exclusive propositions translate into A propositions following this general rule: reverse the subject and predicate, and replace the "only" with "all." Thus "Only S is P" and "None but S’s are P’s" are understood to express "All P is S." 7.) Propositions without quantifiers. 8.) Propositions not in standard form that have logically equivalent standard-form alternatives. 9.) Exceptive propositions are propositions that assert that all members of some class are members of some other class, with the exception of the members of one of its subclasses. Exceptive propositions thus make a compound claim: 1.) first that all members of the subject class that are not in the excepted subclass are members of the predicate class, and 2.) second that no members of the subclass are members of the predicate class. |
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Additional comments on Translation of
sentences in English into standard form categorical propositions:
1. Subject and Predicate terms (a term denotes a class of things –
therefore subject term and predicate term must be a noun)
2. Non-standard verbs (chance non-standard verbs to standard copula -
either are or are not)
3. Singular propositions (translated as universal statement by means
of parameter - persons or things) Example. Socrates is a man. All persons
identical to Socrates are men.
4. Adverbs and pronouns
adverbs referring to position in
space (everywhere, nowhere) translated as "places"
adverbs referring to time (never,
always, when) translated as "times"
pronouns (who, anyone) translated as
"persons"
5. Unexpressed quantifiers
6. Non-standard quantifiers (few, a few, not every)
A few=Some <logical
subject>are <logical predicate>.
Few or almost all or not quite All= Some
are and Some are not. (compound I and O)
Not everyone= Some are not.
All are not= depending on
meaning either an E or an O.
7. Conditional statements (translated as universals and/or use of
transposition)
Transposition: the antecedent
and the consequent of a conditional statement can exchange places if both are
negated.
Unless means "if
not"
8. Exclusive propositions (only, none but, none except and no
…except at the beginning of sentence) reverse terms: if in the middle of
the sentence then term that preceded only is subject.
9. The only (different from statements beginning with Only) what follows
the only is subject
10. Exceptive (All except or all but) translated as two statements.
Proposition (Robinson's power-point
presentation) Definition: statement or proposition is a sentence
that asserts or claims that something is the case or is not the case: a
statement is either true or false.
argument
premise
conclusion
premise indicators
conclusion indicators
Copi has a good list of premise and conclusion indicators in his textbook. Please read this list carefully and then look for them as you read argumentative essays. The most common premise indicators are because, since, and for. The most common conclusion indicators are therefore, thus, and consequently. Other premises indicators are “in support of this statement we can say that…” and “relevant data are …”. Other conclusion indicators are “The implication is that…” and "The point of all of this is …”
Conclusion indicators
Premises indicators
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thus |
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