| Rhetoric to Logic |
KInds of Statements |
Arguments vs Nonarguments |
Meaning |
| Definitions |
Necessary & Sufficient |
Linguistic Pitfalls |
Logical Concepts |
| Validity Soundness |
Valid Arguments | Causation |
Morality |
Logic and Structure
Introduction
Human beings love order, and we will try to impose order in almost every situation. That includes reading. Clearly, most reading relies on understanding words in the order they appear in a sentence. Even beyond that, we anticipate patterns and shapes that particular types of writing will take, and we build expectations based on the first few sentences that we read.
This section will help you understand what you can learn from a piece of reading based on the shape it takes, in addition to what the words themselves convey.
Rhetorical Modes
We’ve been focusing on broad categories of reading materials so far: literature, journalism, textbooks, and academic writing. Since most of the reading (and writing!) you’ll do throughout your college career falls into the “academic writing” category, this is a good point to slow down and examine the building blocks of academic writing more closely.
Rhetoric is the study of writing, so the basic types of academic writing are referred to as rhetorical modes. Let’s look at 10 of the most common types.
1. Narration
The purpose of narration is to tell a story or relate an event. Narration is an especially useful tool for sequencing or putting details and information into some kind of logical order, usually chronological.
Literature uses narration heavily, but it also can be useful in academic writing for strong impact.
An academic essay about the impact of lead in the drinking water in Flint, Michigan, for instance, might include a narrative section that tells the story of one particular family that’s been impacted. This will help illustrate the broader impacts on the community.
2. Description
The purpose of description is to re-create, invent, or visually present a person, place, event, or action so that the reader can picture that which is being described. It is heavily based on sensory details: what we experience through our five senses.
Description is very useful in writing of all types.
3. Example
We’ve been looking at examples so far, with the lead in the water of Flint, Michigan. An exemplification essay extends this idea even further: it carries one or more examples into great detail, in order to show the details of a complex problem in a way that’s easy for readers to understand.
4. Definition
In the vocabulary section we talked about word definitions in great detail. A definition essay takes the concept of “definition” more broadly, moving beyond a dictionary definition to examine a word or concept as we actually use and understand it.
5. Process Analysis
Analyzing a process can also be thought of as a “how-to” essay. Technical writing includes a lot of process analysis, for instance. Academic writing can incorporate process analysis to show how an existing problem came to be, or how it might be solved, by following a clear series of steps.
6. Division/Classification
A classification essay takes one large concept, and divides it into individual pieces. A nice result from this type of writing is that it helps the reader to understand a complex topic by focusing on its smaller parts. This is particularly useful when an author has a unique way of dividing up the concepts, to provide new insight into the ways it might be viewed.
7. Comparison/Contrast
Comparison focuses on similarities between things, and contrast focuses on their differences. We innately make comparisons all the time, and they appear in many kinds of writings. The goal of comparison and contrast in academic essays is generally to show that one item is superior to another, based on a set of evaluations included as part of the writing.
8. Cause/Effect
If narration offers a sequence of events, cause/effect essays offer an explanation about why that sequence matters. Cause/effect writing is particularly powerful when the author can provide a cause/effect relationship that the reader wasn’t expecting, and as a result see the situation in a new light.
9. Problem/Solution
This type of academic writing has two equally important tasks: clearly identifying a problem, and then providing a logical, practical solution for that problem. Establishing that a particular situation IS a problem can sometimes be a challenge–many readers might assume that a given situation is “just the way it is,” for instance.
10. Argument & Persuasion
The purpose of argumentation (also called persuasive writing) is to prove the validity of a point of view, by presenting sound reasoning to thoroughly convince the reader. These assume that the reader is initially uninformed about the topic, or holds a viewpoint that differs from the author’s. The author’s goal is to bring the reader around to his or her way of thinking on the matter.
As the examples of the Flint, Michigan drinking water situation show, there is a lot of overlap between the different rhetorical modes. Many academic essays combine two or more different rhetorical modes in one finished product. This leads to a rich reading experience.
Logical Arguments
Anything you read that includes an attempt to persuade you to think a certain way is likely to include logical argument as part of that persuasion.
The text below introduces the idea of premises and conclusions. As you view this, think about the relationship of premises and conclusions as they align with main ideas and supporting evidence in paragraphs that we explored earlier in this module.
Elements of an Argument
ARGUMENTATION VOCABULARY
Claim: a statement or opinion that is either true or false
Argument: a claim supported by premises
Conclusion: the main claim in an argument
Premises: claims that support and argument’s conclusion
Claim: a statement or opinion that is either true or false
Argument: a claim supported by premises
Conclusion: the main claim in an argument
Premises: claims that support and argument’s conclusion
A claim is an assertion about the truth, existence, or value of something that is either true or false. Claims are also called statements or propositions.
When supported by premises, a claim becomes a conclusion. For example:
- This class is easy.
- The Detroit Lions have the potential to make the NFL playoffs.
- This chemical structure is unstable.
- Democratic socialism is superior to a pure democracy.
An argument is an assertion that contains both a conclusion and premises. It is a statement of fact or opinion that is based on evidence. Keep in mind that not all statements are arguments, and some statements may contain multiple arguments.
A conclusion is the main claim of an argument that is supported by a premise. It is the logical result of the relationship between the premises. Identifying the conclusion is the first step in understanding the argument.
But how do you identify the conclusion? Follow these steps:
- Ask, “Is the statement the main point, or is it a claim given to support another statement in the argument?
- Identify the indicator word that often precedes the conclusion, such as
| Therefore | Thus | As a result | That’s why | Consequently | So |
| This Means | This shows | It follows that | This suggests | Hence | Accordingly |
| Because | For | As |
| Since | Inasmuch as | As shown by |
| Given that | As indicated by | The reason is that |
| Premise | Today’s freshmen cannot write very well |
| Premise | Joe is a freshman, |
| Conclusion | so he must be a poor writer. |
Practice identifying the premises and conclusions
In order to identify the premises and conclusion, you should first rewrite the argument in standard form. You do this by identifying which claim is the conclusion, then working backwards to identify which claims are premises that support the conclusion. It should look like this:
| Standard Form | |
| Premise 1: | |
| Premise 2: | |
| Conclusion: | |
Deductive and Inductive Arguments
Deduction
In the process of deduction, you begin with some statements, called “premises,” that are assumed to be true, you then determine what else would have to be true if the premises are true.
For example, you can begin by assuming that God exists, and is good, and then determine what would logically follow from such an assumption. You can begin by assuming that if you think, then you must exist, and work from there.
With deduction you can provide absolute proof of your conclusions, given that your premises are correct. The premises themselves, however, remain unproven and unprovable.[1]
Examples of deductive logic:
-
All men are mortal. Joe is a man. Therefore Joe is mortal. If the first
two statements are true, then the conclusion must be true.[2]
-
Bachelors are unmarried men. Bill is unmarried. Therefore, Bill is a
bachelor.[3]
-
To get a Bachelor’s degree at Utah Sate University, a student must have
120 credits. Sally has more than 130 credits. Therefore, Sally has a
bachelor’s degree.
Induction
In the process of induction, you begin with some data, and then determine what general conclusion(s) can logically be derived from those data. In other words, you determine what theory or theories could explain the data.
For example, you note that the probability of becoming schizophrenic is greatly increased if at least one parent is schizophrenic, and from that you conclude that schizophrenia may be inherited. That is certainly a reasonable hypothesis given the data.
However, induction does not prove that the theory is correct. There are often alternative theories that are also supported by the data. For example, the behavior of the schizophrenic parent may cause the child to be schizophrenic, not the genes.
What is important in induction is that the theory does indeed offer a logical explanation of the data. To conclude that the parents have no effect on the schizophrenia of the children is not supportable given the data, and would not be a logical conclusion.[4]
Examples of inductive logic:
-
This cat is black. That cat is black. A third cat is black. Therefore all
cats are are black.[5]
-
This marble from the bag is black. That marble from the bag is black. A
third marble from the bag is black. Therefore all the marbles in the bag
black.[6]
-
Two-thirds of my latino neighbors are illegal immigrants. Therefore,
two-thirds of latino immigrants come illegally.
-
Most universities and colleges in Utah ban alcohol from campus. That most
universities and colleges in the U.S. ban alcohol from campus.
Deduction and induction by themselves are inadequate to make a compelling argument. While deduction gives absolute proof, it never makes contact with the real world, there is no place for observation or experimentation, and no way to test the validity of the premises. And, while induction is driven by observation, it never approaches actual proof of a theory. Therefore an effective paper will include both types of logic.[7]
Critical Thinking and Logical Fallacies
Many of the texts you’ll read in college will rely heavily on logical arguments. Logic is highly valued as a way of persuading readers, since it can be confirmed to be true.
However, logic can be used badly. When you’re reading, you’ll want to be able to pick out bad logic as well as good logic. This video series helps us identify different types of “bad logic” in reading we might encounter.
https://quillbot.com/courses/basic-reading-and-writing/chapter/outcome-logic-and-structure/
Kinds of Statements
There are three main sentence types in English:
- Declarative sentences are used for assertions, e.g. "He is here."
- Interrogative sentences are used to ask questions, e.g. "Is he here?"
- Imperative sentences are used for making requests or issuing commands, e.g. "Come here!"
For present purposes, we shall take a statement to be any declarative sentence. A declarative sentence is a complete and grammatical sentence that makes a claim. So here are some examples of statements in English :
- Snow is white.
- The moon is made of green cheese.
- Everyone is here.
- Whatever will be, will be.
- The data and information provided on this web page is for informational purposes only, and is not intended for trading or commercial purposes, unless written prior permission is obtained by the user from the author, though the author will not be liable for any errors or delays in the content, or for any actions taken in reliance thereon.
As you can see, statements can be true or false, and they can be simple or complex. But they must be grammatical and complete sentences. So these are not statements :
- The United Nations [ A proper name, but not a sentence ]
- Bridge over troubled waters. [ Not a complete sentence ]
- Come here right now! [ A command that is not a complete sentence making a claim ]
- Will you be available on tuesday or wednesday? [ A question ]
- HJGAS&*^@#JHGKJAS*&^*!@GJHGAA*&S [ Ungrammatical ]
There is an easy test to decide whether something is a statement in English. Suppose you have a sentence φ and you add "it is true that" to the front. If the resulting expression is grammatical, then φ is a statement. Otherwise it is not.
So for example, φ might be "bridge over troubled waters". We append "it is true that" to the front, and end up with "it is true that bridge over troubled waters." But this expression is not grammatical. So "bridge over troubled waters" is not a statement. However, "I am like a bridge over troubled waters" is a statement, because "it is true that I am like a bridge over troubled waters" is grammatical.
https://philosophy.hku.hk/think/logic/statements.php
Distinguishing Arguments - from Nonarguments and Explanations
Abstract: Arguments are distinguished from nonarguments and explanations: Several kinds of nonargumentative discourse are characterized, illustrated, and distinguished from argumentative discourse.
| I. We said last period that every argument in logic has a structure — every argument in logic can be described in terms of this structure. | |||||||||
| A. Premisses: statements which give evidence for, or reasons for, accepting the conclusion. | |||||||||
| B. Conclusion: statement which is purported to be established or affirmed on the basis of other statements (the premisses). | |||||||||
| II. Recognizing Arguments: Given these characterizations, then, how do we sort out arguments from the rest of the kinds of linguistic behavior? | |||||||||
| In effect, what we are doing is separating the territory of logic from the rest of the world. | |||||||||
| In order to know to what we can apply our powerful methods of analysis, we need to learn how to separate argumentative discourse from non-argumentative discourse. | |||||||||
| A. Typical argumentative "look-a-likes" fall into four main categories. | |||||||||
| 1. Fiction, poetry, emotional discourse: the purpose is not factual truth. | |||||||||
| 2. Commands: they are not statements because they have no truth value. (However, they can be subjected to a "logic of commands" as noted later.) | |||||||||
| 3. Conditional statements (by themselves) are not arguments.: "If ... then ..." statements, sometimes called "hypotheticals," although many logicians distinguish different various forms of conditionals. | |||||||||
| 4. Explanations: their purpose is usually not to prove, but to provide understanding. In general, explanations are not arguments. (Some good explanations have a deductive character, as discussed below.) | |||||||||
| B. Fiction, poetry, emotional discourse are to be distinguished as well. | |||||||||
| 1. Even though good fiction has a good internal logic, there is usually no proof involved. | |||||||||
| a. The truth in a story is like the “ah-ha”; experience of an insightful explanation. | |||||||||
| b. Our learning is indirect — i.e., we perceive or understand the truth. | |||||||||
| c. The investigation of the status of fictional statements is an area in active present inquiry. | |||||||||
| d. The work of fiction, as a whole, can be thought of as a very large conditional statement: | |||||||||
| If {we assume characters, plot, etc.} then {such and such statements consistently follow}. | |||||||||
| e. This proceeding is the sort of thing that is done in thought-experiments. E.g., consider the main point of W. Somerset Maugham's Of Human Bondage as represented by the Persian rug. With its intricate design, the rug has no purpose other than itself and so becomes a metaphor of life itself. | |||||||||
| 2. Poetry's purpose is not to prove or demonstrate logically, but to appeal to our emotions or insight. | |||||||||
| a. Often these insights are alogical — hyperbole, contrast, contradiction, analogy, etc., flash insight, evoke sentiment, and blaze awareness. | |||||||||
| b. E.g., consider Stephen Vincent Benét's “The Ballad of William Sycamore“: | |||||||||
|
"So I saddled a red unbroken colt And I rode him into the day there, And he threw me down like a thunderbolt And rolled on me as I lay there. |
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|
The hunter's whistle hummed in my ear As the city men tried to move me, But I died in my boots like a pioneer With the whole wide sky above me." |
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| To raise the question of how a dead man can write a poem is to miss the point. | |||||||||
| 3. Emotional Discourse: in common parlance, everyday “heated arguments” are alogical — the standards of formal logic are not meant to apply. | |||||||||
| a. E.g., as in a newspaper description of heated discourse: “one man was shot, one man was injured after a heated argument in a bar.” | |||||||||
| b. From a logical point of view, the heated exchange of views is often resolved by the doctrine that “might makes right” rather than by logical reasoning. | |||||||||
| C. Commands, especially those put as imperative statements are not arguments. | |||||||||
| 1. Again, we could evaluate a series of commands for logical consistency (as when we are told to do different things by the same authority), but commands, strictly speaking, are neither true nor false, so they are not normally part of arguments. | |||||||||
| 2. As we will see later, imperatives can function as directive (e.g., "Study hard"), expressive (e.g., "Have a nice day), or informative (e.g., "Study pages 25-140 for the test"). | |||||||||
| 3. Sometimes we need to understand the context use of imperatives in order to understand their function —although imperatives are used, the passage might be intended to be argumentative. | |||||||||
4. Consider the following quotation:
“Be careful who you pretend to be, for that you will surely become.”Is the author explaining how pretense can be harmful? Is the author trying to prove it?, or is the author warning us not to pretend? One could only tell by looking at the context in which this sentence was used. |
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| D. Conditionals look very much like arguments and intuitively "feel" very much like arguments, but their antecedents are not asserted to be true. They are no more than complex statements. (Often, we will analyze an argument with conditional statements — e.g., as in the statement, “If the premisses are true, then the conclusion will follow.”) | |||||||||
|
1. The parts of a conditional:
If {antecedent} then {consequent} |
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| 2. If I say, "If someone fails this class, then I will eat the textbook," I haven't proved anything. | |||||||||
| 3. A conditional can be thought of as conditionally being an argument if the antecedent is true, but this is not at all what is being asserted. However, in an argument the premisses are asserted as true. | |||||||||
| 4. Since conditionals are statements, then, of course, they can be part of arguments: | |||||||||
| Consider, the hypothetical syllogism | |||||||||
| If I drop this book, then it will fall to the floor. | |||||||||
| If it falls to the floor, then it is heavier than air. | |||||||||
| Therefore, if I drop this book, then it is heavier than air. | |||||||||
| Or an argument form called modus ponens | |||||||||
| If you study hard, then you make an A in logic. | |||||||||
| You study hard. | |||||||||
| Therefore, you make an A. | |||||||||
| D. How to distinguish arguments from explanations. | |||||||||
| 1. By carefully reading the text, you can discern several important differences between an argument and an explanation. | |||||||||
| a. Do a group of statements give evidence, grounds, or reasons for some other statement? | |||||||||
| b. Is the purported conclusion better known than the purported premisses? | |||||||||
| c. Is a causal connection asserted or implied? | |||||||||
| d. What is the author's purpose in offering the passage? | |||||||||
|
e. What is the context of the passage? |
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|
Argument |
Explanation |
||||||||
| (1) expresses an inference | does not usually express an inference | ||||||||
| (2) offers evidence, grounds or reasons | offers an account why | ||||||||
| (3) goes from well known statements to statements less well known | gives less well known statements why a better known statement is true | ||||||||
| (4) draws a logical connection between statements | describes a causal connection | ||||||||
| (5) has the purpose to establish the truth of a statement | has the purpose to give an account of something | ||||||||
|
2. In general, these questions point to some of the difference between arguments and explanations. However, reasoning does sometimes have an explanatory function which is neither intended to be persuasive or probative in character but is intended to facilitate understanding. Consequently, sometimes arguments are used for explanatory purposes. In other words, the distinction between arguments and explanation cannot always be maintained and can often be determined by the context in which the relevant passage occurs. |
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|
3. Consider the following passage drawn from Ludwig von Mises (q.v., image above) in an edition of I.M. Copi's Introduction to Logic [(New York: Macmillan, 1978), 24-25.]: |
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“(1) The Roman Empire crumbled to dust because (2) it lacked the spirit of liberalism and free enterprise.” |
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| Which statement is better known (1) or (2)? Since the first statement is better known, we would say that this is an explanation which shows a causal connection rather than an argument with a logical implication. | |||||||||
|
a. If the author were advancing the general thesis "All countries that
lack these attributes crumble to dust," therefore the Roman Empire did,
then a Deductive Nomological Explanation is being
given. In point of fact, this is precisely the argument which von Mises
gives in the original passage from which this passage was excerpted:
"The Roman Empire crumbled to dust because it lacked the spirit of liberalism and free enterprise. The policy of interventionism and its political corollary, the Fuhrer principle, decomposed the mighty empire as they will by necessity always disintegrate and destroy any social entity." Ludwig von Mises, Human Action (Auburn: Mises,1949), 763. |
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| With some thought, we can see that the last sentence in the quoted passage above is in the context of the passage the tacit missing premise: “All countries that lack the spirit of liberalism and free enterprise crumble to dust.” (I.e., it's a translation of the contraposition of the last sentence in the quotation above). So we have the following argument: | |||||||||
|
[All countries that lack the spirit of liberalism and free enterprise
crumble to dust.] The Roman Empire lacked the spirit of liberalism and free enterprise. |
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| Therefore, the Roman Empire crumbled to dust. | |||||||||
|
b. Very often, the Deductive Nomological Method of Explanation is given
as a method of ordering science into a deductive system. |
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| Explanans: | L1, L2, ... , Lk General Laws | ||||||||
| [Logical Deduction] | C1, C2, ... , Ck Statements of Antecedent Conditions | ||||||||
| Explanandum: | Description of the empirical phenomenon to be explained. | ||||||||
|
E. The statements in an explanation “move” from well known to less well known statements. For example, the answer to why rainbows form on gasoline-station driveways is expressed in terms of layers of different density fluids with different optical properties. The index of refraction, reflection, wavelengths of light, and the electromagnetic spectrum are all mentioned. https://philosophy.lander.edu/logic/nonarg.html |
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A Miniguide to Critical Thinking
1.2: Meaning
Literal meaning is a property of linguistic expressions. The literal meaning of a sentence is determined by its syntax and the conventional meaning of the words in the sentence. The literal meaning of a sentence should be distinguished from its conversational implicature the information that is implicitly conveyed in a particular conversational context, distinct from the literal meaning.
For example, suppose we ask Amie whether she wants to go hiking and she replies, “I am verytired”. Naturally we would infer that Amie does not want to go hiking. But this is not part of the literal meaning of her reply. Rather, the information that she does not want to go is inferred indirectly. Similarly, suppose Lala says, “Po likes books”. We might take Lala to be saying that Po likes to read. But this is at most the conversational implicature, and not part of the literal meaning of what Lala said. It might turn out that Po hates reading and she likes books only because she uses them to decorate her house. But even if this is the case, Lalas assertion is stilltrue.
These examples show that when we want to find out whether a statement is true, we should consider its literal meaning, and not the conversational implicature. This is particularly important in the legal context. The content of a contract is typically determined by the literal meaning of the terms of the contract. If there is a dispute about the contract, ultimately it is settled by looking at the literal meaning of the terms, and not by what one or the other party thinks was implied implicitly.
Meaningless vs. empty statements
In ordinary usage, the adjective meaningless is sometimes used rather indiscriminately. Very often, claims that are pointless or empty are also described as meaningless. For example, suppose Peter is asked whether he will go to the party, and he replies “if I come, I will come”. Strictly speaking, this is an empty statement as it does not provide any useful information. But the statement is perfectly grammatical and meaningful. To be accurate one should not describe such statements as meaningless.
1.3: Definitions
Lack of clarity in meaning can hinder good reasoning and obstruct communication. One way to make meaning clearer is to use definitions. A definition is made up of two parts: the definiendum and the definiens. The definiendum is the term that is to be defined, whereas the definiens is the group of words or concepts used in the definition that is supposed to have the same meaning as the definiendum. For example, bachelor is defined as an unmarried man. The word “bachelor” is the definiendum, and “an unmarried man” is the definiens. We now look at four main kinds of definitions.
Reportive definition
A reportive definition is also known as a lexical definition. It reports the existing meaning of a term. This includes the bachelor example above, or the definition of prime number as any integer greater than one and divisible only by one and itself. A reportive definition should capture the correct usage of the term that is defined.
Stipulative definition
A stipulative definition is not used to explain the existing meaning of a term. It assigns a new meaning to a term, whether or not the term has already got a meaning. If the stipulative definition is accepted, then the term is used in the new way that is prescribed. For example, we might stipulate “KFC” to mean “Korean-style Fried Chicken”. Once the definition is accepted,we can then say things like, “We are going to cook KFC for dinner tonight”.
Precising definition
A precising definition is used to make the meaning of a term more precise for some specific purpose. For example, a bus company might want to give discounts to elderly passengers. But simply declaring that the elderly can pay a reduced fare will lead to many disputes, since it isnot clear how old one should be to qualify as an elderly person. So one might define “an elderlyperson” to mean any person of age 65 or above. This is of course one among many possible definitions. A precising definition might be seen as a combination of reportive and stipulative definition.
Precising definitions are very important in drawing up laws and regulations. We might want to eliminate or punish sexual harassment, but we need a good definition of sexual harassment to clarify what is appropriate and what is not. A biology professor who makes his students unhappy by giving a surprise exam on sexual reproduction should better not be counted as sexual harassment under any such definition.
Precising definitions can also be used to resolve disputes that involve some key concepts whose meanings might not be clear enough. Suppose two people are arguing whether animals such as birds or apes possess language. To resolve this dispute, we need to be more precise as to what is meant by language. If by language we refer to any system of communication, then obviously birds and other animals do make use of languages. On the other hand, “language” might be used in a different sense, referring to more sophisticated communication systems with a recursive syntax. If this is what is meant, the communication systems of many animals would not qualify as language.
Persuasive definition
A persuasive definition is any definition that attaches an emotive connotation to a term when it actually none. The connotation can be either positive or derogatory. For example, someone against abortion might define “abortion” as the murder of an innocent child inside the womb.This definition carries a negative connotation, as the term murder suggests that abortion is wrongful killing, and it also assumes that the aborted fetus is already a person. This definition might make a useful rhetorical tool, but it is a biased and inappropriate definition. Whether abortion is wrong should be determined by careful analysis and argument, and not to be stipulated by a definition.
Evaluating definitions
The criteria for evaluating definitions depend on the kind of definition we are considering. With reportive definition, it is important that the definition correctly captures the usage of the term that is defined. In particular, the definition should be neither too wide nor too narrow.
- A definition is too wide (or too broad) if the definiens applies to things that the definiendum does not apply to. For example, defining an airplane as a flying machine is too wide since helicopters are also flying machines but they are not airplanes.
- A definition is too narrow if the definiens fails to apply to things to which the definiendum applies, e.g. defining a triangle as a plane figure with three equal straight sides.
- Notice that a definition may be both too wide and too narrow at the same time. Consider the definition of a chair as a piece of furniture with four legs for people to sit on. The definition is too narrow as some chairs might not have four legs. It is also too wide because a sofa with four legs might still not be a chair.
The question of whether a definition is too broad or too narrow does not arise with stipulative definitions, since the definition is not meant to capture existing usage. But it is important that the definition should avoid circularity, inconsistency and obscurity.
1.4: Necessary and Sufficient Conditions
The concepts of necessary and sufficient conditions help us understand and explain the different kinds of connections between concepts, and how different states of affairs are related to each other.
To say that X is a necessary condition for Y is to say that it is impossible to have Y without X. In other words, the absence of X guarantees the absence of Y. A necessary condition is sometimes also called an essential condition. Some examples:
- Having four sides is necessary for being a square.
- Being brave is a necessary condition for being a good soldier.
To show that X is not a necessary condition for Y, we simply find a situation where Y is present but X is not. Examples:
- Being rich is not necessary for being well-respected, since a well-respected teacher might in fact be quite poor.
- Living on the land is not necessary for being a mammal. Dolphins are mammals, but they live in the sea.
We use the notion of a necessary condition very often in daily life, even though we might be using different terms. For example, life requires oxygen is equivalent to saying that the presence of oxygen is a necessary condition for the existence of life.
A state of affairs can have more than one necessary condition. For example, to be a good concert pianist, it is necessary to have good finger technique. But this is not enough. Being good at interpreting piano pieces is another necessary condition.
Next, we turn to sufficient conditions. To say that X is a sufficient condition for Y is to say that the presence of X guarantees the presence of Y. In other words, it is impossible to have X without Y. If X is present, then Y must also be present. Some examples:
- Being a square is sufficient for having four sides.
- Being divisible by 42 is sufficient for being an even number.
To show that X is not sufficient for Y, we come up with cases where X is present but Y is not,such as:
- Having a large market share is not sufficient for making a profit. The company might be dominating the market by selling at a loss.
- Loyalty is not sufficient for honesty because one might have to lie in order to protect the person one is loyal to.
Expressions such as If X then Y, or X is enough for Y, can also be understood as saying that X is a sufficient condition for Y. Note that some state of affairs can have more than one sufficient condition. Being blue is sufficient for being colored, but being green, being red are also sufficient for being coloured.
Given any two conditions X and Y, there are at least four ways in which they might be related to each other:
- X is necessary but not sufficient for Y.
- X is sufficient but not necessary for Y.
- X is both necessary and sufficient for Y. (or jointly necessary and sufficient)
- X is neither necessary nor sufficient for Y.
This classification is very useful when we want to clarify how two concepts are related to each other, especially when it comes to more abstract concepts. For example, in explaining the nature of democracy we might say that the rule-of-law is necessary but not sufficient for democracy.
1.5: Linguistic Pitfalls
Linguistic pitfalls are misuses of language where language is used in an inappropriate way toobscure, distort, or mislead.
Ambiguity
A word, phrase, or sentence is ambiguous when it has more than one meaning. There are different kinds of ambiguity.
- Lexical ambiguity refers to cases where a single term has more than one meaning in the language. For example, the word deep can mean profundity (What you have said is very deep.), or it can be used to describe physical depth (This hole is very deep). Similarly for words like young (inexperienced or young of age), or bank (river bank or financial institution).
- Referential ambiguity arises when the context does not make it clear what a pronoun or quantifier is referring to, e.g. Ally hit Georgia and then she started bleeding. In the preceding sentence, it is not clear whether it was Ally, Georgia, or some other person who was bleeding.
- Syntactic ambiguity are cases of ambiguity that comes about because there is more than one way to interpret the grammatical structure. This can happen even when there is no lexical ambiguity. Consider the sentence “we shall be discussing violence on TV”. It might mean the discussion will be conducted during a television program, or it might mean violence on TV is the topic to be discussed.
When dealing with ambiguity we should ensure that the context makes it clear to the audience what the correct interpretation should be. We can also try to clarify meaning explicitly by listing out all the different possible interpretations. This process of removing ambiguity is known as disambiguation. Naturally, avoiding ambiguity applies only to situations where we want to communicate precisely and accurately.
Vagueness
A term is vague if it lacks a precise boundary. When the sun sets it becomes dark, but there is no sharp boundary where it abruptly switches from bright to dark. So “dark” and “bright” are vague terms.
“Tall” is also vague since sometimes we are not sure if a person is tall or not, even when we know the person’s exact height. This is because the meaning of “tall” is not precise enough. The same applies to words like “mountain”, “clever”, “cheap”, etc. In fact, probably most words in natural languages are vague.
Notice that vagueness is not the same as ambiguity. A word can be vague even though it is not ambiguous, and an ambiguous term can have two meanings which are both very precise.
When we need to be precise and informative, we should avoid vagueness. Vague claims are frequent in horoscope predictions. Here is one:
- Be prepared for a change of direction this week as something unexpected comes up.
What counts as a change of direction is very vague. Does it count if someone blocks your way so you cannot walk in a straight line? Without a precise explanation it is too easily to find one event or another as evidence that confirms the prediction.
Instructions that are vague offer little concrete guidance. Someone being told to try harder might not really know what to do, and setting more precise goals are often more useful.
However, it would be a mistake to say that critical thinking requires the elimination of all vagueness. Vague terms are useful in everyday life because we do not always have to be precise. It is also difficult if not impossible to be precise about when we have to be precise. It all depends on the situation.
Incomplete Meaning
A term has an incomplete meaning if the property or relation it expresses depends on some further parameter to be specified by the context, either explicitly or implicitly. This includes terms such as “useful”, “important”, “similar”, and “better”. Practically all objects are useful and important only in some respects but not others. For example, is a life buoy more important than a million dollars? Well, it depends. If you are about to drown, then yes. But not if you never go near water.
Distortion
Distortion is a matter of using words with inappropriate semantic associations, or to use words in a way that deviates from its standard meaning without clear indications.
The use of inappropriate emotive expressions is one typical example of distortion. Many expressions in the language are not purely descriptive but carry positive or negative connotations.
Sometimes people define “democracy” as dictatorship of the majority. The word “dictatorship”carries a negative connotation, so this description implicitly assumes that democracy is bad.This distorts the meaning of “democracy”. Democracy as a system of government might not be perfect, but we should justify our criticisms more carefully and clearly.
Reification
The word “reify” came from the Latin word res, which means thing. Reification is treating an abstract idea or property as if it were a concrete physical object. Consider the popular claim that “History is just”. A person or a system of rules or laws can be just or unjust, but justice is not really a property of history, taken as a body of facts about what has happened in the past. But of course we can guess what the speaker might have in mind when the statement is made. Perhaps the intended meaning is something like Eventually people will make the correct and fair judgment about what has happened.
Reification in itself need not be objectionable. It increases dramatic impact and is often used in poetry and metaphors. The test is whether the original claim can be translated into a sentence without reification. If not, this is a sign that the original claim does not have a clear meaning.
1.6: Basic Logical Concepts
Consistency
Two (or more) statements are inconsistent with each other when it is logically impossible for all of them to be true at the same time. For example: The earth is flat, and The earth is spherical are inconsistent statements since nothing can be both flat and spherical. On the other hand, if you have any two statements that are both true, they are certainly consistent.
Entailment
A sentence X entails Y if Y follows logically from X. In other words, if X is true then Y must also be true, e.g. 30 people have died in the riots entails more than 20 people died in the riots,but not vice-versa.
If X entails Y and we find out that Y is false, then we should conclude that X is also false. But of course, if X entails Y and we find out that X is false, it does not follow that Y is also false.
If X entails Y but Y does not entail X, then we say that X is a stronger claim than Y (or Y is weaker than X). For example, all birds can fly is stronger than most birds can fly, which is still stronger than some birds can fly.
A stronger claim is of course more likely to be wrong. To use a typical example, suppose we want to praise a person X but are not sure whether X is the best or not, we might use the weaker claim “X is one of the best” rather than the stronger “X is the best”. So we need not be accused of speaking falsely even if it turns out that X is not the best.
Logical Equivalence
If two statements entail each other then they are logically equivalent. For example, everyone is ill is equivalent to nobody is not ill, and cheap things are no good is actually equivalent to good things are not cheap. If two statements are logically equivalent, then necessarily they must always have the same truth value.
Arguments
In ordinary usage, the word “argument” is often used to refer to a heated dispute between two or more parties. But in logic and critical thinking, the term has a different meaning. Here,an argument is taken to be a list of statements, one of which is the conclusion and the others are the premises (assumptions) of the argument. To give an argument is to provide a set of premises as reasons for accepting the conclusion. The ability to construct, identify and evaluate arguments is a crucial part of critical thinking. We all have lots of opinions on lots of things,but most people are not good at giving arguments in support of their opinions.
Here is an example of a short argument made up of three statements. The first two statements are the premises, and the last one is the conclusion:
- Every star produces radiation.
- The Sun is a star.
- Therefore, the Sun produces radiation.
Arguments in real life often are not presented in such a neat manner, with the premises and conclusions clearly laid out. So how do we identify them? There are no easy mechanical rules,and we usually have to rely on the context in order to determine which are the premises and the conclusions. But sometimes the job can be made easier by the presence of certain premise or conclusion indicators. For example, if a person makes a statement, and then adds “this is because ...”, then it is quite likely that the first statement is presented as a conclusion, supported by the statements that come afterwards. Words like “after all”, “suppose” and “since” are also often used to precede premises. Conclusions, on the other hand, are often preceded by words like “therefore”, “so”, “it follows that”.
The secret to good reading and writing skill is to develop the ability to construct and summarize arguments, and to present arguments clearly and systematically. The same goes for giving good presentations.
1.7: Validity and Soundness
The idea of a valid argument is one of the most important concepts in critical thinking, so you should make sure you fully understand this topic. Basically, a valid argument is one where the premises entail the conclusion. What this means is that if the premises are true, the conclusion must also be true. So here is a valid argument with two premises and a conclusion:
- Moby Dick is a whale.
- All whales have fins.
- So, Moby Dick has fins.
This is another argument with just one premise and a conclusion:
- Barbie is 90 years old.
- So Barbie is older than 20.
In both of these arguments, if the premises are all true, there is no way that the conclusion will be false. So the arguments are indeed valid. Notice that the validity of the argument does not depend on whether the premise is in fact true. Consider the second argument above. Even if Barbie is actually only a ten-year-old, the argument is still valid. Validity only requires that when the premises are true, so is the conclusion. It depends only on the logical connection between the premises and the conclusion. It does not depend on their actual truth or falsity. A valid argument can have false premises and a false conclusion. A valid argument can also have a false premise but a true conclusion, as when Barbie is 30 years old.
This, however, is not a valid argument. It is invalid:
- Barbie is older than 20.
- So, Barbie is over 90 years old.
The argument is not valid because it is possible that the premise is true and the conclusion is false. For example, Barbie could be 21. Or she could be 80. These situations are counterexamples to the argument. Basically, a valid argument is an argument with no possible counterexamples.To sharpen your skills in evaluating arguments, it is important that you are able to discover and construct counterexamples. Giving a counterexample can help you convince other people that a certain argument is mistaken.
There are a few important points worth remembering:
- An invalid argument can have true premises and a true conclusion. In the previous argument, both the premise and the conclusion are true if Barbie is 99 years old. But remember that true premises and a true conclusion are not sufficient for validity, because the logical connection between them is missing. This means that an argument with true premises and conclusion can still be a bad argument.
- Notice that we are making a distinction between truth and validity. Statements (the premises and the conclusion) can be true or false, but they are not valid or invalid. Arguments might be valid or invalid, but they should never be described as true or false.
- It is possible to have a valid argument where the premises are false but the conclusion is true. Validity only guarantees that when you start with true premises, you end up with a conclusion that is true. So we should never say things like your assumptions are false, so even if you reasoning is logical your conclusion cannot be true.
Soundness
Given a valid argument, all we know is that if the premises are true, so is the conclusion. But validity does not tell us whether the premises or the conclusion are true or not. If an argument is valid, and all the premises are true, then it is a sound argument. Of course, it follows from such a definition that a sound argument must also have a true conclusion.
In discussion, it would be nice if we can provide sound arguments to support an opinion. This means showing that our argument is valid, and that all the premises are true. Anyone who disagree would have to show that not all the premises are true, or the argument is not valid, or both.
To improve critical thinking, these are good habits to cultivate when it comes to argument analysis:
- Identify clearly the premises of an argument. Can we state the assumptions clearly?
- Check whether the assumptions are true or not.
- Evaluate the validity of the argument. Even if the premises are true, the logical reasoning of the argument can still be quite bad. The evaluation of the premises and the reasoning are two separate tasks.
- When arguing for a certain conclusion, always see if you can find more than one argument to support it. This would make your case more convincing. Being able to count the number of arguments in support of a position is an important thinking skill.
Hidden assumptions
When people give arguments sometimes certain assumptions are left implicit. Example:
- It is wrong to create animals with human DNA because it is unnatural.
This argument as it stands is not valid. Someone who gives such an argument presumably has in mind the hidden assumption that whatever that is unnatural is wrong. It is only when this assumption is added that the argument becomes valid.
Once this is pointed out, we can ask whether it is justified. We might argue for example,that there are plenty of things that are unnatural but are not usually regarded as wrong (e.g.cosmetic surgery, going to the Moon, contraception, etc). Pointing out the hidden assumption in an argument can help resolve or clarify the issues involved in a dispute.
In everyday life, many arguments have important hidden assumptions which have not been made explicit. It is part of good critical thinking to be able to identify these assumptions. One way to do this is to see what additional premises are needed to add to an argument to make it valid.
1.8: Patterns of Valid Arguments
Obviously, valid arguments play a very important role in reasoning, because if we start with true assumptions, and use only valid arguments to establish new conclusions, then our conclusions must also be true. But how do we determine whether an argument is valid? This is where formal logic comes in. By using special symbols we can describe patterns of valid argument, and formulate rules for evaluating the validity of an argument. Below we introduce a few patterns of valid arguments. You should make sure that you can recognize these patterns and make use of them in reasoning.
Modus ponens
Consider this argument:
- If copper is a metal, then it conducts electricity.
- Copper is a metal.
- So, copper conducts electricity.
Notice that it has a similar structure compared with this one:
- If there is a storm tomorrow, the park will close.
- There will be a storm tomorrow.
- So the park will close.
Both arguments are of course valid. What is common between them is that they have the same structure or form:
- If P then Q.
- P.
- Therefore Q.
Here, the letters P and Q are sentence letters. They are used to translate or represent statements.
By replacing P and Q with appropriate sentences, we can generate the original valid arguments.
This shows that the two arguments have a common form. It is also in virtue of this form that the arguments are valid, for we can see that any argument of the same form is a valid argument.
Because this particular pattern of argument is quite common, it has been given a name. It is known as modus ponens.
However, don’t confuse modus ponens with the following form of argument, affirming the consequent, which is not valid!
- If P then Q.
- Q.
- Therefore, P.
It is often a mistake to reason with an argument of this form. This is not valid:
- If Jane lives in London, then Jane lives in England.
- Jane lives in England.
- Therefore Jane lives in London.
Here are some other patterns of valid argument.
Modus tollens
- If P then Q.
- Not-Q.
- Therefore, not-P.
Here, not-Q simply means the denial of Q. So if Q means Today is hot., then not-Q can be used to translate It is not the case that today is hot, or Today is not hot.
- If there was a major earthquake, we would have felt it.
- We did not feel anything.
- So, there was no major earthquake.
But do distinguish modus tollens from the following fallacious pattern of argument, Denying the antecedent:
- If P then Q.
- Not-P.
- Therefore, not-Q.
An example:
- If Elsie is competent, she will get a promotion.
- But Elsie is not competent.
- So she will not get a promotion.
Hypothetical syllogism
- If P then Q.
- If Q then R.
- Therefore, if P then R.
Example: If God created the universe, then the universe will be perfect. If the universe is perfect, then there will be no evil. So if God created the universe, there will be no evil.
Disjunctive syllogism
- P or Q.
- Not-P.
- Therefore, Q.
Example: Either the government brings about more sensible educational reforms, or the only good schools left will be private ones for rich kids. The government is not going to carry out sensible educational reforms. So the only good schools left will be private ones for rich kids.
Dilemma
- P or Q.
- If P then R.
- If Q then S.
- Therefore, R or S.
When R is the same as S, we have a simpler form:
- P or Q.
- If P then R.
- If Q then R.
- Therefore, R.
Example: Either we increase the tax rate or we don’t. If we do, the people will be unhappy.If we don’t, the people will also be unhappy. (Because the government will not have enough money to provide for public services.) So the people are going to be unhappy anyway.
Arguing by Reductio ad Absurdum
The Latin name here simply means reduced to absurdity. It is actually an application of modus tollens. It is a method to prove that a certain statement S is false:
- First assume that S is true.
- From the assumption that it is true, prove that it would lead to a contradiction or some other claim that is false or absurd.
- Conclude that S must be false.
For example, suppose someone claims that the right to life is absolute and it is always wrong to kill a life, no matter what. Assume that this is true. We would then have to conclude that killing for self-defence is also wrong. But surely this is not acceptable. If killing an attacker is the only way to save your own life, then most people would agree that this is morally permissible. Since the original claim leads to an unacceptable consequence, we should conclude that the right to life is not absolute. This kind of reductio method is used in many famous mathematical proofs.
Other Patterns
There are of course many other patterns of deductively valid arguments. It is understandable that you might not remember the names of all these patterns. What is important is that you can distinguish the valid ones from the invalid ones, and construct examples of your own.
1.9: Causation
Causation is about how one event brings about another event. The most important point to remember about causation is probably the advice that one should not confuse correlation with causation. Suppose events of type A are positively correlated with events of type B. One common mistake in causal reasoning is to jump to the conclusion that A is therefore the cause of B. This is bad reasoning because we have not ruled out other possible explanations, such as:
- The order of causation is reversed– Suppose people who like to play violent video games are more likely to engage in violent behaviour. Does it mean those games make people violent? Maybe. But it could also be the other way round. Perhaps people who are predisposed to violence are more likely to enjoy and play violent video games, but the games themselves do not make people more violent.
- The correlated events have a common cause– It is said that when ice-cream sale increases,so does the number of shark attacks on swimmers. Does eating ice-cream make sharks attack people? Of course not. There is a correlation only because when the weather is hot, more people go swimming and more people eat ice-cream. Hot weather is the underlying causal factor that links the two factors but there is no direct causal connection between them.
- The correlation is an accident– A correlation provides evidence for causation only if the correlation is robust and can be observed repeatedly. If you manage to lose weight after eating less carbohydrates for a few weeks, this might just be a coincidence. Perhaps it is just because you ended up eating less when you are more aware of your diet. We need more evidence to decide whether eating less carbohydrates is a good way to control one’s weight.
Some common mistakes in causal reasoning
- Genetic fallacy– Thinking that if some item X comes from a source with a certain property,then X must have the same property as well. But the conclusion does not follow, e.g.Eugenics was practised by the Nazis so it is obviously disgusting and unacceptable.
- Fallacy of the single cause– Wrongly presupposing that an event has a single cause when there are many causally relevant factors involved. This is a fallacy where causal interactions are being over-simplified. For example, when a student committed suicide, the public and the media might start looking for the cause, and blame the tragedy on either the parents,the school work, the society, etc. But there need not be a single cause that led to the suicide. Many factors might be at work.
- Confusing good causal consequences with reasons for belief– Thinking that a claim must be true because believing in it brings about some benefit. Examples: God exists because after I have become a believer I am now happier and a better person. I don’t think my girlfriend is cheating on me because otherwise it is the end of my world and I cannot accept that. These examples might seem unrealistic because people often do not state their reasons so explicitly, but we should not underestimate how emotions can bias our reasoning in more subtle ways.
1.10: Morality
Morality is about what is right or wrong, what should or should not be done, and what rights or duties we might have. As such morality is normative and not purely descriptive. Descriptive statements describe facts without any value judgments. John hit Billy is a purely descriptive claim about a physical action. No value judgment is involved since the statement says nothing as to whether what is described is good or bad. But if we say it was wrong for John to hit Billy, then we have made a value judgment. Similarly, the following claims are all normative claims:
- We should not torture babies for fun.
- Age discrimination is wrong.
Notice that descriptive claims about moral beliefs in themselves are not normative. The statement Peter thinks that abortion is wrong is a descriptive statement about one of Peters beliefs.There is not judgment of whether Peter is right or wrong so this is not a normative claim.
Given that descriptive statements do not involve any moral judgments, we should be careful of arguments that rely on purely descriptive assumptions to derive a normative conclusion. One argument we discussed earlier is that it is wrong to create animals with human DNA because it is unnatural. But what counts as unnatural is unclear. If it is a matter of whether something occurs in the environment without human intervention, then the claim that something is or is not natural is a descriptive claim. This by itself has no normative consequences. To derive the conclusion that cloning is wrong, we need a normative assumption like unnatural things are wrong. But of course, such an assumption is questionable if not false.
Similarly, many people often argue it is OK to kill animals and eat meat, because animals eat each other anyway, or that evolution is a matter of survival of the fittest. Again these arguments jump from purely descriptive claims to normative conclusions. Just because something happened quite a lot does not mean that it should be done. Some animals kill the weak and the old, or sometimes even eat their own offspring, but this does not mean we should do the same thing.To infer a normative claim, you need to make assumptions about values or about what is right and wrong. It is a mistake to try to derive normative claims solely on the basis of descriptive claims. Such a mistake is known as the naturalistic fallacy.
https://human.libretexts.org/Bookshelves/Philosophy/A_Miniguide_to_Critical_Thinking
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