CONTENTS

CTP Index

CTP List (1)

█ Logical possibility

Consider the law of non-contradiction: Nothing can both have a property and lack it at the same time. For example, one cannot be a bachelor and married at the same time. A binary state cannot be both 1 and 0 at the same time. Note that this principle applies to the macrocosmic world of human experience, and not necessarily at the quantum scale.

█ Physical possibility

As our knowledge of the physical world increases, our understanding of the limits of physical possibility expands. For example, Einstein believed that quantum entanglement of particles—"spooky action at a distance," as he called it—is not physically possible. But we now know that this seemingly impossible phenomenon is real. 

Possibility does not imply actuality. To establish that something is real, we need reliable evidence that it actually exists. Pictures used to be reliable visual evidence of some state of affairs in the world. Now we must be able to determine the integrity, source, and context for an image before we can give it the status of "evidence."

█ Personal experience

We can’t infer what is from what seems. It is an error in reasoning to conclude that an event or phenomenon (X) is real because it seems real. Questions to ask: Is my experience of X corroborated or shared by others? Does my experience of or conclusion about X contradict all known previous experience? Is it possible that a peculiarity of human perception / cognition (eg: color constancy), could be operative?

Reasons for doubting include: perceptual construction, memory construction, effects of stress, effects of expectancy and belief, selective attention, misjudgments of probabilities, subjective validation, altered states of consciousness, poor observational conditions, sensory impairments or limitations, and conflicts with other observations / knowledge that we have good reason to believe.

█ Belief vs Knowledge

As an extension of individual subjectivism, social relativism holds that society, not the individual, determines what is true. But, society used to believe that the Earth was flat, that the sun orbited the Earth, etc. The same problems and contradictions that plague individual subjectivism also aflict social relativism.

Neither knowledge nor reasonable belief requires certainty. Practical wisdom takes note of probabilities. A proposition is beyond a reasonable doubt when it provides the best explanation of something. But being justified in believing a proposition is no guarantee of its truth.

█ Background information

The quest for knowledge involves eliminating inconsistencies and contradictions among our beliefs. Sometimes we observe or learn about things that conflict with our background knowledge—that vast system of well-supported beliefs that we habitually use to guide our thoughts and actions (much of it referred to as "common sense"). Background knowledge includes both "street smarts" and "school smarts."

The structure of background information can be compared to the structure of a large tree. Bigger branches (beliefs) support smaller ones, which in turn support even smaller ones. Accepting some claims is analogous to pruning small branches—giving up only peripheral beliefs. Accepting others is akin to cutting large branches.

█ Evidence / experts for claims

The truth of a claim is established by the amount and type of evidence in its favor—not by the lack of evidence against it. Also, attempting to place the burden of proof on the nonbeliever is asking for the impossible. To prove a universal negative statement (eg: No X things exist.), you would have to exhaustively investigate all of time and space.

This is the "flip side" of the preceding principle. Here again, the error in reasoning is an appeal to ignorance as in this example: "No one has ever proven that alternate universes exist; therefore they don’t".

The more evidence we have for a proposition, the more credence we should give it. The probability of the truth of a contingent or scientific proposition can range from close to 0 (eg: Someday, humans will travel faster than the speed of light.), to close to 1 (eg: E = mc 2). It is generally held that only logical truths warrant such strong belief that their probability values equal 1 (eg: "The bar is either one meter long or it isn’t.")

The opinions of experts are superior to our own, but only in their fields of expertise. Just because someone is an expert in one field doesn’t mean that he or she is an expert in another. For example, being an accomplished actor or skillful athlete does not make a person qualified to offer medical opinions.

█ Objective reality

Only if we have good reason for believing that they are not functioning properly should we doubt the traditional sources of knowledge: perception (the physical senses), introspection (witnessing dispositional mental states), memory, and reason.

When there is disagreement about a particular state of affairs, the objectivist (moderate realist), believes that it is at least theoretically possible to determine truths through rational discourse. Humans syndicate confidence in their common beliefs through ongoing dialogue with each other, and through the methods of logic and science.

• Mysticism is just tomorrow’s science dreamed today. –Marshall McLuhan
• Not I, but the whole world says it: everything is one. –Heraclitus
• When one sees that everything exists as an illusion, one can live in a higher sphere than ordinary man. –The Buddha
• …often my body would become so light that it lost all weight. –St. Theresa

█ Scientific method / hypotheses

The scientific method is our most reliable means of establishing the truth of an empirical proposition beyond a reasonable doubt. Science seeks to understand the world by identifying general principles that are both explanatory and predictive. To minimize the potential for error, inadequacy, or fraud, the scientific method requires repeatable results. In general, any procedure that serves to systematically eliminate reasonable grounds for doubt can be considered scientific. For example, consider this general method:

1. Observe.
2. Construct general hypotheses (possible explanations) for what was observed.
3. Deduce a specific state of affairs that must also be true if a particular hypothesis is true.
4. Test each hypothesis by checking out the deduced consequences.

The process of creating hypotheses (possible explanations) is just as open-ended as the process of artistic creation. Although inductive reasoning can lead to the formulation of a hypothesis, other processes—like direct insight, and imaginative construction—are also sources of useful hypotheses. A good hypothesis must account for all the evidence it is intended to explain.

If a hypothesis cannot be tested, there is no way to determine whether it is true or false. Hypotheses have observable consequences only in the context of a background theory. So, to be testable, a hypothesis must predict something more than what is already assumed by the background theory.

█ Criteria of adequacy for hypotheses

Some hypotheses are attractive because they promise to open new lines of research by making the most novel predictions. For example, Einstein’s theory of relativity predicts that light waves travelling near massive objects will appear to be bent because space-time around these bodies is curved. Before Einstein, the common belief was that light traveled in Euclidean straight lines since photons had no mass.

The more a hypothesis explains and predicts, the more it systematizes and unifies our knowledge. For example, Einstein’s theory of relativity came to be preferred over Newtonian theories of gravity and motion because the theory of relativity explained and predicted everything that Newton’s theories could, plus some things that it couldn’t (like variations in Mercury’s orbit).

Although not simple to define, scientific simplicity can be understood as the fewest number of assumptions required by a hypothesis. The simpler the hypothesis, the more it unifies and systematizes our knowledge, and the less likely it is to be false since there are fewer ways for it to go wrong. Hence, Copernicus’s heliocentric theory of planetary motion was considered preferable to Ptolemy’s geocentric theory. This principle is often referred to as Occam’s Razor: Do not multiply entities beyond necessity.

The hypothesis that fits best with established beliefs is to be preferred. It might be reasonable to accept a hypothesis that is not conservative if it possesses other criteria of adequacy. There are borderline cases where reasonable people can disagree, and clear-cut cases where disagreement would be irrational. Although it may not be clear at what point a person becomes bald, it's irrational to consider a person with a full head of living hair as bald.

The criteria of simplicity and conservatism should lead you to prefer ordinary explanations over unusual and ad hoc (created after the emergence of the phenomena) explanations. You should always reject any explanation for which no possible evidence could count against it—where every apparent counterexample is explained away or not allowed to count.

SKILL Dimension: Consensus List of Core CT Cognitive Skills and Sub-Skills (2)

1. INTERPRETATION

Sub Skills: Categorization, Decoding Significance, Clarifying Meaning
To comprehend and express the meaning or significance of a wide variety of experiences, situations, data, events, judgments, conventions, beliefs, rules, procedures, or criteria.

2. ANALYSIS

To identify the intended and actual inferential relationships among statements, questions, concepts, descriptions, or other forms of representation intended to express beliefs, judgments, experiences, reasons, information, or opinions.

3. EVALUATION

Sub Skills: Assessing Claims, Assessing Arguments
To assess the credibility of statements or other representations which are accounts or descriptions of a person's perception, experience, situation, judgment, belief, or opinion; and to assess the logical strength of the actual or intended inferential relationships among statements, descriptions, questions, or other forms of representation.

4. INFERENCE

To identify and secure elements needed to draw reasonable conclusions; to form conjectures and hypotheses; to consider relevant information and to educe the consequences flowing from data, statements, principles, evidence, judgments, beliefs, opinions, concepts, descriptions, questions, or other forms of representation.

5. EXPLANATION

Sub Skills: Stating Results, Justifying Procedures, Presenting Arguments
To state the results of one's reasoning; to justify that reasoning in terms of the evidential, conceptual, methodological, criteriological, and contextual considerations upon which one's results were based; and to present one's reasoning in the form of sound and cogent arguments.

6. SELF-REGULATION

Self-consciously to monitor one's cognitive activities, the elements used in those activities, and the results educed—particularly by applying skills in analysis and evaluation to one's own inferential judgments with a view toward questioning, confirming, validating, or correcting either one's reasoning or one's results.

DISPOSITIONAL Dimension: Consensus List of Core CT Affective Dispositions (2)

APPROACHES TO LIFE AND LIVING IN GENERAL

• ■ inquisitiveness with regard to a wide range of issues
• ■ concern to become and remain generally well-informed
• ■ alertness to opportunities to use CT
• ■ trust in the processes of reasoned inquiry
• ■ open-mindedness regarding divergent world views
• ■ flexibility in considering alternatives and opinions
• ■ understanding of the opinions of other people
• ■ fair-mindedness in appraising reasoning
• ■ honesty in facing one's own biases, prejudices, stereotypes, egocentric, or socio-centric tendencies
• ■ prudence in suspending, making, or altering judgments
• ■ willingness to reconsider and revise views where honest reflection suggests that change is warranted.

APPROACHES TO SPECIFIC ISSUES, QUESTIONS OR PROBLEMS

■ clarity in stating the question or concern

■ orderliness in working with complexity

■ diligence in seeking relevant information

■ reasonableness in selecting and applying criteria

■ care in focusing attention on the concern at hand

■ persistence though difficulties are encountered

■ precision to the degree permitted by the subject and the circumstance

This is the "intake" cycle. Some of this input, or claims, might be stated in vague or incomplete ways. So the first step is to formulate all claims so that they are as clear and specific as possible. Note: Although not all claims are hypotheses, any unusual claim can be considered a hypothesis—a provisional explanation for a particular phenomenon.or state of affairs.

■ Determine the exact nature and limitations of the empirical evidence.
Assess the evidence and determine whether there are or could be any reasonable doubts about the "evidence." Use CTP #1-15.  For example, Clive Backster, a FBI lie detector expert, claimed that when he attached his lie detector to a philodendron in his office, he was able to detect that the plant was aware of his thoughts. Subsequent experiments by biologists, botanists, and other scientists could not reproduce Backster's reported results. So, a theory of plant sentience that cites Backster’s experiments as "evidence" should be disqualified according to CTP #15 (Backster is not an expert in botany), and  CTP #19 (the scientific method requires repeatable results).

System 1 is FAST, automatic, frequent, emotional, stereotypic, unconscious. Examples of System 1's abilities include:

• ■ localize the source of a specific sound
• ■ complete the phrase "war and ..."
• ■ display disgust when seeing a gruesome image
• ■ solve 2+2=?
• ■ read text on a billboard
• ■ drive a car on an empty road
• ■ come up with a good chess move (if you're a chess master)
• ■ understand simple sentences
• ■ connect the description "quiet and structured person with an eye for details" to a specific job

System 2 is SLOW, effortful, infrequent, logical, calculating, conscious. Examples of System 2's abilities include:

• ■ direct your attention towards the clowns at the circus
• ■ direct your attention towards someone at a loud party
• ■ look out for the woman with the grey hair
• ■ dig into your memory to recognize a sound
• ■ sustain a higher than normal walking rate
• ■ determine the appropriateness of a particular behavior in a social setting
• ■ count the number of A's in a certain text
• ■ give someone your phone number
• ■ park into a tight parking space
• ■ determine the price/quality ratio of two washing machines
• ■ solve 17 × 24
• ■ determine the validity of complex logical arguments

argument

A group of statements, one or more of which (the premises) are claimed to provide support for, or reasons to believe, one of the others (the conclusion). Every argument may be placed in either of two basic groups: those in which the premises really do support the conclusion (good arguments), and those in which they do not, even though they are claimed to (bad arguments).

statement

A sentence that is either true or false, typically a declarative sentence or a sentence component that could stand as a declarative sentence. The following sentences are statements:

In this guide, proposition and statement are used synonymously.

proposition

In the narrow sense, the meaning or information content of a statement. Technically, the three statements: "The pig is big." | "Le cochon est gros." | "El cerdo es grande." express a single proposition. In this guide, proposition and statement are used synonymously.

truth values

Truth (T) and falsity (F) are called the two possible truth values of a statement.

premise(s)

The statement(s) that set forth the reasons or evidence for the conclusion.

conclusion

The statement that is claimed to follow from (supported by or inferred from) the premises.

inference

In the narrow sense of the term, the reasoning process expressed by an argument. In the broad sense of the term, “inference” is used interchangeably with “argument.”

deductive argument

An argument incorporating the claim that it is impossible for the conclusion to be false given that the premises are true.

inductive argument

An argument incorporating the claim that it is improbable that the conclusion is false given that the premises are true.

simple non-inferential passages

Passages (texts) that lack a claim that anything is being proved. Such passages contain statements that could be premises or conclusions (or both), but what is missing is a claim that any potential premise supports a conclusion or that any potential conclusion is supported by premises. Passages of this sort include:

• • warnings
• • pieces of advice
• • statements of belief or opinion
• • loosely associated statements
• • reports

expository passage

A kind of discourse that begins with a topic sentence followed by one or more sentences that develop the topic sentence. If the objective is not to prove the topic sentence but only to expand it or elaborate it, then there is no argument

illustration

An expression involving one or more examples that is intended to show what something means or how it is done. Often confused with arguments because many illustrations contain indicator words such as “thus".

explanation

An expression that purports to shed light on some event or phenomenon. The event or phenomenon in question is usually accepted as a matter of fact. Every explanation is composed of two distinct components: the explanandum and explanans. The explanandum (accepted fact) is the statement that describes the event or phenomenon to be explained, and the explanans (the account of reasons) is the statement or group of statements that purports to describe the causes for the occurance of the event or phenomenon.

1. Eliminate extraneous textual material. Extended arguments are often mixed together with fragments of reports, pieces of expository writing, illustrations, explanations, and statements of opinion.
2. Assign numbers to all statements.
3. Identify premises and conclusions using arrows to represent the inferential links.
4. Identify sub-arguments and separate strands of argumentation that lead to separate conclusions.
5. Take note of common patterns. A vertical pattern consists of a series of arguments in which a conclusion of a logically prior argument becomes a premise of a subsequent argument. A horizontal pattern consists of a single argument in which two or more premises provide independent support for a single conclusion. If one of the premises were omitted, the other(s) would continue to support the conclusion in the same way.

conditional statement

an “if… then…” statement; for example:

• If professional football games incite violence in the home, then the widespread approval given to this sport should be reconsidered.
• If Roger Federer has won more Grand Slams than any other contender, then he rightfully deserves the title of world’s greatest tennis player.

• Some conditional statements are similar to arguments in that they express the outcome of a reasoning process. As such, they may be said to have a certain inferential content. Conditional statements are especially important in logic (and many other fields), because they express the relationship between necessary and sufficient conditions.

antecedent

The component statement immediately following the “if”.

consequent

The component statement immediately following the “then”. The link between the antecedent and consequent resembles the inferential link between the premises and conclusion of an argument. Yet there is a difference because the premises of an argument are claimed to be true, whereas no such claim is made for the antecedent of a conditional statement. Accordingly, conditional statements are not arguments.

necessary condition

If A then B. B is said to be a necessary condition for A. Thus, being an animal is a necessary condition for being a dog.

sufficient condition

If A then B. A is said to be a sufficient condition for B. For example, being a dog is a sufficient condition for being an animal.

Argument based on mathematics

An argument based on mathematics is an argument in which the conclusion depends on some purely arithmetic or geometric computation or measurement. For example, a shopper might place two apples and three oranges into a paper bag and then conclude that the bag contains five pieces of fruit. Or a surveyor might measure a square piece of land and, after determining that it is on each side, conclude that it contains . Since all arguments in pure mathematics are deductive, we can usually consider arguments that depend on mathematics to be deductive as well. However, arguments that depend on statistics are a noteworthy exception and are usually best interpreted as inductive.

argument from definition

an argument in which the conclusion is claimed to depend merely on the definition of some word or phrase used in the premise or conclusion. For example, someone might argue that because Claudia is mendacious, it follows that she tells lies, or that because a certain paragraph is prolix, it follows that it is excessively wordy. These arguments are deductive because their conclusions follow with necessity from the definitions of “mendacious” and “prolix.”

syllogism

In general, an argument consisting of exactly two premises and one conclusion.

categorical syllogism

Each statement in a categorical syllogism begins with one of the words “all,” “no,” or “some.”

All As are Bs.
All Bs are Cs
Therefore, all As are Cs.

hypothetical syllogism

A syllogism having a conditional (“if… then”) statement for one or both of its premises.

If p then q.
p.
Therefore, q.

disjunctive syllogism

A syllogism having a disjunctive (“either… or…”) statement.

Either p or q.
Not p.
Therefore, q.

categorical proposition

A proposition that relates two classes, or categories. The classes are denoted respectively by the Subject (S) term and the Predicate (P) term. The proposition asserts that either all or part of the class denoted by S is included in or excluded from the class denoted by P.

standard form

The standard-form of a categorical proposition is:

Eg: All S are P

A, E, I, and O propositions

The names of the four types of categorical propositions:

distribution

Universal (A and E) statements distribute their subject terms. Negative (E and O) statements distribute their predicate terms. Briefly: Universals distribute Subjects, and Negatives distribute Predicates. So, A statements distribute the Subject, E statements distribute both terms, I statements distribute neither term, and O statements distribute the Predicate.

Venn diagram

An arrangement of overlapping circles in which each circle represents the class denoted by a term in a categorical proposition. Every categorical proposition has exactly two terms (S and P), so the Venn diagram for a single categorical proposition consists of two overlapping circles.

Each circle is labeled so that it represents one of the terms in the proposition. In general, the left-hand circle represents the subject (S) term, and the right-hand circle the predicate (P) term.

• If an area is shaded, there are no items in it.
• If an area contains an " x" there is at least one item in it.

Aristotelian standpoint

From the Aristotelian standpoint the first two universal propositions (A and E) can convey evidence about existence. When things exist, the Aristotelian standpoint recognizes their existence, and universal statements about those things have existential import.

Boolean standpoint

From the Boolean standpoint, the first two universal propositions (A and E) imply nothing about the existence of the things denoted by S. When things exist, the Boolean standpoint does not recognize their existence, and universal statements about those things have no existential import.

interpreting universal propositions

The Aristotelian and Boolean standpoints are alternative sets of "ground rules" for interpreting the meaning of universal propositions. Either standpoint can be adopted for any categorical proposition or any argument composed of categorical propositions.

Venn Diagrams: Shading = emptiness | X = existence

All S are P (universal)

No members of S are outside P.

Aristotelian Standpoint: Existence implied if referring to actually existing things (real beings).

Boolean Standpoint: Existence not implied.

No S are P (universal)

No members of S are inside P.

Aristotelian Standpoint: Existence implied if referring to actually existing things (real beings).

Boolean Standpoint: Existence not implied.

Some S are P (particular)

At least one S exists that is a P.

The word “some” implies existence.

Eg: “Some mammals are zebras” asserts that at least one mammal exists that is a zebra.

Some S are not P (particular)

At least one S exists that is not a P.

The word “some” implies existence.

Eg: “Some mammals are not zebras” asserts that at least one mammal exists that is not a zebra.

categorical syllogism

A deductive argument that has three categorical propositions and is able to be translated into standard syllogistic form.

class complement | term complement

The complement of a class is the group consisting of everything outside the class. For example, the complement of the class of dogs is the group that includes everything that is not a dog (cats, fish, trees, and so on). The term complement is the word or group of words that denotes the class complement. For terms consisting of a single word, the term complement is usually formed by simply attaching the prefix “non” to the term. Thus, the complement of the term “dog” is “non-dog,” the complement of the term “book” is “non-book,” and so on.

form of a syllogism

The form of a syllogism is determined by its mood and figure. After a categorical syllogism has been put into standard form, its validity or invalidity can be determined by merely inspecting its form.

mood

Denoted by the letter names (A, E, I, O), of its constituent propositions. The letter for the major premise is listed first, then the letter for the minor premise, and finally the letter for the conclusion.

figure

Determined by the position of the occurrences of the middle term in the premises. There are four figures:
.

To symbolize the four syllogistic figures:

1. Put the syllogism in standard form (major premise followed by minor premise and conclusion).
2. Drop the quantifiers and copulas.
3. Determine the figure of the syllogism (positions of the three terms in the syllogism).
4. Determine the mood of the syllogism (the pattern of the A, E, I, O propositions).

Determining the figure (positions of the three terms):

Determining the mood (pattern of the A, E, I, O propositions):

Syllogisms with these figures and corresponding moods are all valid:

For example:

In this example, the term Earthlings is the middle term. So, this syllogism is in Figure 4.

An EIO-4 categorical argument is always valid. See section 5.2 below for more information.

Opposite truth value
(the same as in the Modern Square of Opposition)

At least one is false
(not both true)

At least one is true
(not both false)

• Truth flows downward
• Falsity flows upward

valid deductive argument

An argument in which it is impossible for the conclusion to be false given that the premises are true. In these arguments the conclusion follows with strict necessity from the premises.

invalid deductive argument

A deductive argument in which it is possible for the conclusion to be false given that the premises are true. In these arguments the conclusion does not follow with strict necessity from the premises, even though it is claimed to.

test for validity

To test an argument for validity we begin by assuming that all the premises are true, and then we determine if it is possible, in light of that assumption, for the conclusion to be false.

sound argument

A deductive argument that is valid and has all true premises. Both conditions must be met for an argument to be sound; if either is missing the argument is unsound. A sound argument, therefore, is what is meant by a good, or successful, deductive argument in the fullest sense of the term.

It is not always possible to determine the soundness of a deductive argument. But that does not mean that soundness is unimportant in logic. It is crucially important that soundness be recognized as a criterion of evaluation that is distinct from validity.

unsound argument

A deductive argument that is invalid, has one or more false premises, or both.

No cyborgs are Earthlings.
major term: cyborgs

Some Earthlings are Martians.
minor term: Martians

Therefore, some Martians are not cyborgs.

strong inductive argument

An inductive argument in which it is improbable that the conclusion be false given that the premises are true. In such arguments, the conclusion does in fact follow probably from the premises.

weak inductive argument

An inductive argument in which the conclusion does not follow probably from the premises, even though it is claimed to.

uniformity of nature

All inductive arguments depend on the principle that the future tends to replicate the past, and regularities that prevail in one spatial region tend to prevail in other regions. Good inductive arguments are those that accord with the uniformity of nature. They have conclusions that we naturally expect to turn out true.

test for strength

To test an inductive argument for strength we begin by assuming that all the premises are true, and then we determine whether, based on that assumption, the conclusion is probably true. This determination is accomplished by linking up the premises with regularities that exist in our experiential background. All of these regularities are instances of the uniformity of nature.

cogent argument

A is an inductive argument that is strong and has all true premises. Also, the premises must be true in the sense of meeting the total evidence requirement. If any one of these conditions is missing, the argument is uncogent.

A cogent argument is the inductive analogue of a sound deductive argument and is what is meant by a good, or successful, inductive argument without qualification.

uncogent argument

An inductive argument that is weak, has one or more false premises, fails to meet the total evidence requirement, or any combination of these defects.

types of meaning

Linguistic expressions can have different kinds of meaning:

• • Emotive meaning : Expresses or evokes feelings
• • Cognitive meaning: Conveys information

emotive meaning

Statements having emotive meaning often make value claims. When such statements occur in arguments, the value claims should be disengaged from the emotive terminology and expressed as separate premises.

value claim

A claim that something is good, bad, right, wrong, better, worse, more important, or less important than some other thing. Such value claims are often the most important part of the cognitive meaning of emotive statements.

cognitive meaning

Cognitive meanings can be defective in two ways:

1. Vagueness : The meaning is blurred.
2. Ambiguity : More than one clearly distinct meaning is possible.

Ambiguity and vagueness are important in logic because there are countless occasions in which the evaluation of an argument leads to the observation, “Well, that depends on what you mean by …” If phraseology in an argument is vague or ambiguous, its meaning must be clarified before any evaluation can proceed.

vague expression

An expression that allows for borderline cases in which it is impossible to tell if the expression applies or does not apply. Vague expressions often allow for a continuous range of interpretations. The meaning is hazy, obscure, and imprecise. How fresh does something have to be in order to be called “fresh”?

ambiguous expression

An expression that can be interpreted as having more than one clearly distinct meaning in a given context. For example, if one were to describe a beer as a light pilsner, does this mean that the beer is light in color, light in calories, or light in taste?

term

A word or phrase that can serve as the subject of a statement. Terms include:

• • Proper names (Napoleon, North Dakota, etc.)
• • Common names (animal, house, etc.)
• • Descriptive phrases (author of Hamlet, books in my library, etc.)

intension
(connation)

Intensional meaning of a term refers to the attributes that the term connotes. For example, the intensional meaning of the term “cat” consists of the attributes of being furry, of having four legs, of moving in a certain way, of emitting certain sounds, etc.

conventional connotation

The conventional connotation of a term includes the attributes that the term commonly calls forth in the minds of competent speakers of the language. The connotation of a term remains more or less the same from person to person and from time to time.

extension
(denotation)

Extensional meaning of a term refers to the members of the class that the term denotes. The extensional meaning of the term “cat” consists of cats themselves—all the cats in the universe.

„

empty extension

Terms with empty extension denote the empty (or “null”) class, the class that has no members. For example, “unicorn,” “leprechaun,” “gnome,” “elf,” and “griffin.”

mention (of a word)

"Wherever" is an eight-letter word.” In this statement, it is not the word itself that is the subject but rather the quoted word. In this statement, “wherever” is mentioned.

use (of a word)

“I will follow you wherever you go.” In this statement, “wherever” is used.

definition

A word or group of words that assigns a meaning to a word or group of words:

• Definiendum : The word or group of words being defined
• Definiens : The word or group of words that does the defining

Definitions can serve different purposes, so there are different kinds of definitions

Stipulative definitions

Assign a meaning to a word when it first comes into use. This may involve either coining a new word or giving a new meaning to an old word. The purpose of a stipulative definition is usually to replace a more complex expression with a simpler one. Because a stipulative definition is a completely arbitrary assignment of a meaning to a word for the first time, there can be no such thing as a “true” or “false” stipulative definition.

Lexical definitions

Report the meaning a word has within a community of users. Dictionary definitions are all instances of lexical definitions. In contrast with a stipulative definition, which assigns a meaning to a word for the first time, a lexical definition may be true or false depending on whether it does or does not report the way a word is actually used. Also, lexical definitions are useful for eliminating ambiguity.

Precising definitions

Reduce the vagueness of a word. The definition “‘Poor’ means having an annual income of less than $10,000 and a net worth of less than $20,000” is an example of a precising definition. Whenever words are taken from ordinary usage and used in a highly systematic context such as science, mathematics, medicine, or law, they must always be clarified by means of a precising definition.

Theoretical definitions

Appeal to a theory to characterize whatever the term denotes. Such a definition provides a way of viewing or conceiving these entities that suggests deductive consequences, further investigation (experimental or otherwise), and whatever else would be entailed by the acceptance of a theory governing these entities. The definition of the term “heat” found in texts dealing with the kinetic theory of heat is a good example: “‘Heat’ means the energy associated with the random motion of the molecules of a substance.” Many terms in philosophy, such as “substance,” “form,” “cause,” “change,” “idea,” “good,” “mind,” and “God,” have been given theoretical definitions.

Persuasive definitions

Influence the attitudes of the community of users regarding whatever the word denotes. Persuasive definitions amount to a certain synthesis of stipulative, lexical, and, possibly, theoretical definitions backed by the rhetorical motive to engender a certain attitude. As a result of this synthesis, a persuasive definition masquerades as an honest assignment of meaning to a term while condemning or blessing with approval the subject matter of the definiendum. For example:

• “Abortion” means the ruthless murdering of innocent children.
• “Abortion” means a safe and established surgical procedure whereby a woman is relieved of an unwanted burden.

definition by genus and difference

Fallacies of Relevance

The premises are not relevant to the conclusion.

Fallacies of Weak Induction:

The premises may be relevant to the conclusion, but they supply insufficient support for the conclusion.

Fallacies of Presumption:

The premises presume what they purport to prove.

Fallacies of Ambiguity:

The conclusion depends on some kind of linguistic ambiguity.

Fallacies of Illicit Transference:

An attribute is incorrectly transferred from the parts of something onto the whole or from the whole onto the parts.

Accident

A general rule is applied to a specific case it was not intended to cover.

Appeal to force

Arguer threatens the reader/listener.

Appeal to pity

Arguer elicits pity from the reader/listener.

Appeal to the people

Arguer incites a mob mentality (direct form) or appeals to our desire for security, love, or respect (indirect form). This fallacy includes appeal to fear, the bandwagon argument, appeal to vanity, appeal to snobbery, and appeal to tradition.

Argument against the person

Arguer personally attacks an opposing arguer by:

• • verbally abusing the opponent (ad hominem abusive),
• • presenting the opponent as predisposed to argue as he or she does (ad hominen circumstantial), or
• • presenting the opponent as a hypocrite (tu quoque).
  Note: For this fallacy to occur, there must be two arguers.

Missing the point

Arguer draws a conclusion different from the one supported by the premises.
Note: Do not cite this fallacy if another fallacy fits.

Red herring

Arguer leads the reader / listener off the track (with a misleading scent).

Straw man

Arguer distorts an opponent’s argument and then attacks the distorted argument.
Note: For this fallacy to occur, there must be two arguers.

Appeal to ignorance

Premises report that nothing is known or proved about some subject, and then a conclusion is drawn about that subject.

Appeal to unqualified authority

Arguer cites an untrustworthy authority.

False cause

Conclusion depends on a nonexistent or minor causal connection. This fallacy has four forms:

• • post hoc ergo propter hoc
• • non causa pro causa
• • oversimplified cause
• • gambler’s fallacy.

Hasty generalization

A general conclusion is drawn from an atypical sample.

Slippery slope

Conclusion depends on an unlikely chain reaction of causes.

Weak analogy

Conclusion depends on a defective analogy (similarity).

Begging the question

Arguer creates the illusion that inadequate premises are adequate by leaving out a key premise, restating the conclusion as a premise, or reasoning in a circle.

Complex question

Multiple questions are concealed in a single question.

False dichotomy

An “either … or …” (disjunctive) premise hides additional alternatives.

Suppressed evidence

Arguer ignores important evidence that requires a different conclusion.

Equivocation

Conclusion depends on a shift in meaning of a word or phrase.

Amphiboly

Conclusion depends on an incorrect interpretation of an ambiguous statement made by someone other than the arguer.

Composition

An attribute is incorrectly transferred from the parts to the whole.

Division

An attribute is incorrectly transferred from the whole to the parts.