It is important for people to think critically so that they can make good choices. People often don't realize how irrational some of the decisions they make are. Critical thinking is thinking that criticizes. Critical thinking is to evaluate something against a certain standard. One of the most important things anyone can criticize is reasoning. Reasoning comes into play when people:
Logic is used to determine whether a statement is true, whether the reasoning is correct, and whether we can draw a connection. In this case, it is not about making up statements, but about evaluating (the correctness of) statements that have been made in order to ultimately form the correct conclusions.
To achieve this, people evaluate their thinking on the basis of rationality. When they understand how to think critically, they can use this knowledge to be critical of multiple topics that are important in everyday life. It is also important to remember that criticizing other people's ideas does not mean that they are attacked, but that the logic is sought in something. In addition, criticizing someone is not always an example of critical thinking. One can criticize without thinking about it.
When someone comes to a conclusion, they have a belief. A belief is propositional. That means it is either true or false. A belief is the same as a judgment and an opinion. When a belief is used in an explanatory sense, it produces an assertion as a result. Claims can be considered critically.
A distinction must be made between objective claims and subjective judgments. An objective claim has the following characteristic: whether something is true or false is independent of a person's belief as to whether it is true or false. Objective claims are true or false, but this is not always known. A subjective judgment, on the other hand, is not independent of whether someone thinks it is true or false. Many statements contain both objective and non-objective elements.
A subjective judgment is always true. For this reason, it does not make sense to label subjective judgments in terms of probability. In addition, it cannot be seen as something that can be supported by evidence. Evidence is something that increases the likelihood of an assertion. Many objective claims cannot be supported with evidence either.
Some opinions are not subjective judgments because their truth or falsehood is independent of what people think is true or false. Objective opinions can also be called factual opinions. However, this does not mean that factual opinions are always true.
Relativism is the idea that the "truth" of things is related to culture.
Moral subjectivism takes as its starting point that the moral assessment of something as right or wrong is entirely subjective.
Issues are questions. One issue is whether a statement is true or false. Some issues are objective and some are subjective. The first thing that comes with critical thinking is determining what the issue actually is. Sometimes it is difficult to determine exactly what the claim is (and what the associated issue is). This could be because someone is using difficult terms or someone is deliberately not wanting to clarify his or her claim.
An argument is a reason presented to prove that a statement is true. A statement that is used as a reason to prove that another statement is true is called a premise. The statement that a premise provides evidence for is called the conclusion of an argument.
Whether an argument is good depends on whether a premise actually supports the conclusion of the argument. This is only possible if the premise is true. A second criterion is therefore that the premise must be relevant to the conclusion. This means that the premise must be related to the conclusion in such a way that the premise increases the chance that the conclusion is correct. It's important to remember that sometimes it may seem like someone is making an argument when they aren't. An argument is not a summary of facts. You can recognize an argument if it is used to prove or support a claim.
Belief formation is also influenced by unconscious features of human psychology, so-called cognitive biases. These biases influence the way information is processed. A few of these biases are:
Critical thinking helps to spot substandard substantiation or cover up mistakes. It doesn't say what the truth is.
This chapter discusses two ways of reasoning.
An argument is used to prove or support a theorem. An argument always has two parts: a premise and a conclusion. If a claim does not consist of these two parts, it is not an argument. "God exists" is not an argument, and "God exists, and if you don't believe that you're going to hell," neither.
"Something had to create the universe, so God exists" is an argument. The premise supports the conclusion that is drawn. A premise aims to provide reasons for accepting the conclusion.
The same statement can be the conclusion of one argument and the premise of another argument. An example:
The statement "The car is no longer usable" is the conclusion that follows from premise 1, but also forms the premise for the conclusion that a new car must be bought. Conclusion 1 is therefore, in addition to a conclusion, also a premise for Conclusion 2.
It often happens that arguments contain unspoken premises or conclusions. An example of an unspoken premise:
You cannot borrow books without a library card.
Jan cannot borrow books from the library.
The unspoken premise here is that Jan does not have a library card. This explains that he cannot borrow books from the library.
In addition, conclusions can also be unspoken. For example: "The political party most commonly seen as the vote of the people will win the elections. So the SP will win the elections. " The unspoken conclusion here is that the SP is seen most as the voice of the people.
There are deductive and inductive arguments.
Words like "because", "since" or "this is explained by" often follow a premise. Such a premise then comes after the conclusion. For example, you can claim that you are sad because your partner forgot your birthday. The premise in a good deductive argument proves the conclusion drawn from a logical standpoint
In deductive reasoning, validity is very important. An argument is called valid when it is not possible for the premise to be true and the conclusion to be false.
An example:
Premise: "Jan was chairman before Piet was chairman and Klaas was chairman after Piet.
Conclusion: "Jan was chairman before Piet was chairman".
In this example it is impossible that the premise is correct and that the conclusion drawn is not true. So the premise of a good deductive argument proves the conclusion. There is therefore a valid argument. If the premise of a valid argument is true, the argument is called sound.
There are two kinds of deductive arguments:
The premise of an inductive argument does not prove the conclusion, but supports the conclusion. An inductive argument is therefore not an all-or-nothing principle, as with a deductive argument. Support for a conclusion is provided in degrees by inductive argument. An example is that the perpetrator of a murder is being sought. A woman has been murdered and her husband is known to have threatened her repeatedly. This is certainly not evidence that he killed her, nor does it support the claim that he killed her. If his fingerprints are found on the murder weapon, this still doesn't support the claim that he killed her, but this does lend more support to the claim that he killed her.
A good inductive claim thus indicates that the conclusion is most likely to be true. Two points are important here:
There are four types of inductive arguments:
To find out whether an argument is deductive or inductive, it is important to read or listen carefully. The difference between a deductive and an inductive argument is that in induction there is a most likely possibility and in deduction there is no other way than the conclusion.
Inductive arguments are often used in legal proceedings, for example to convict suspects. A person is found guilty when the claim is highly supported (beyond reasonable doubt) that he or she has committed a crime. This evidence is less strong than deductive evidence. This is because deductive arguments do not support gradations. There is an all-or-nothing principle: a conclusion must be true if the premises are correct.
It is not difficult to turn an inductive argument into a deductive argument. To do this, a universal premise must be added. This is a premise that serves as a rule to which there are no exceptions. Suppose someone says, "Jan and Marieke are about to divorce. They are constantly arguing." This statement can be made into a deductive argument when a universal rule is added, namely that all couples who argue constantly are about to get divorced. Sometimes it happens that a conclusion is based on a stated and an unspoken premise. An example: Imagine hearing two professors talking and one saying "Give him a 1, this is the second time you've caught cheating!"
In everyday life, people often make use of unspoken premises. However, we notice an unspoken premise due to the context and content of the subject.
Reasoning in daily life often has to do with weighing considerations against each other. This process is also called balance of considerations reasoning. It contains both deductive and inductive elements. When you make a trade-off, you look at induction at how strong or weak an argument is and at deduction at how valid and correct the argument is.
Argument identification is the recognition of arguments. An argument consists of two elements: (1) a premise (or several premises) that supports (2) the conclusion. In this way arguments can be recognized. There are words or phrases that are often used to show that a conclusion will follow. Examples are: "therefore", "so", "the conclusion is" and "this shows that". There are also words used to show that a premise will follow. Examples are: "given that", because "and" because ".
There are three levels of persuasion (modes of persuasion). Sometimes external factors influence judgments. For example, if your mother finds something, it will count more heavily in your own judgment than the judgment of a stranger. This is called ethos.
In addition to using rhetoric, the use of photos or images can have a powerful influence on viewers' emotions. Thus their judgments can be influenced. This is called pathos.
The speaker can also convince through the use of information and arguments. This is called logos. Unfortunately, logos (rational argument) is the least effective way of persuasion.
Many arguments are difficult to understand because they are not on paper and because they pass quickly in a conversation. Premises and conclusions are therefore not easy to distinguish. When understanding an argument, it is important to first establish the conclusion. The next step is to find the premise (s) on which the conclusion is based. Next, the examples on which the premise (s) is or are based on should be considered, in the event that examples are given. These steps can be used to understand spoken arguments and written arguments.
When the relationship between premises and conclusions is understood, the structure of an argument is understood. In establishing the premises, it is important to pay attention to words such as "because", "therefore", and "since". When arguments in a written story need to be analyzed, it is smart to break the story down into premises and link numbers to these premises. Subsequently, the numbers can be processed in a diagram, using arrows, so that causes (premises) and consequences (conclusions) can be better distinguished.
It is important to distinguish between an argument on the one hand and a description, statement or summary on the other. This is not always easy. The question is whether someone uses reasons to support or prove his or her conclusion. If so, then there must be arguments in the story he or she tells. When evaluating an argument, there are two things to consider:
Not everything is an argument. An argument always consists of two parts. Phrases containing "if" and "then" are not arguments. A list of facts is also not an argument. Phrases containing "because" may or may not be an argument depending on what is followed. If it provides proof, then it is an argument. If it indicates a cause, it is not an argument.
Example: "Pete is wearing swimming trunks because he was swimming" is not an argument. This is where it explains the cause.
"Piet was swimming because he was wearing his swimming trunks" is an argument, because it provides a reason. So it is important to read carefully and understand what is in the sentence.
This chapter is about writing a good text.
Sometimes written documents are difficult to understand. This is often because vague language is used in the text. A term is called vague when it is not clear where the boundary is drawn in relation to the term. An example of such a term is "bald". There are people who are completely bald, but also people who are semi-bald due to their hair loss. It is not clear to what extent the term "bald" applies to them.
Ambiguity occurs when a word or phrase has more than one meaning and can therefore be interpreted in different ways. Three types of ambiguity are distinguished:
1. Semantic ambiguity
Semantic ambiguity occurs when a word or phrase is used that is accompanied by ambiguity. This ambiguity can be avoided by replacing the relevant words or phrases with a clearer description.
2. Grouping ambiguity
Group-related ambiguity occurs when a word is used to talk about an entire group when it is not true for the individual members of a group. There are two fallacies based on this form of ambiguity.
3. Syntactic ambiguity
Syntactic ambiguity occurs when a statement can be interpreted in multiple ways due to the structure (syntax) of the statement.
Ambiguous pronoun references are when it is not clear what a pronoun refers to.
Context often clarifies what the sentence means, but this is not always easy to read. However, it is more important that there is ambiguity in a statement than what kind of ambiguity it is.
Generalization, just like vagueness and ambiguity, can lead to confusion or misunderstanding. The less detail a statement provides, the more general it becomes. When events are described too broadly, this leads to ambiguity. Often, politicians will use generic terms so that if they cannot deliver on their promises, they may indicate that their claims have been interpreted too specifically.
It is important to define terms well so that terms and phrases are clear. Some terms are easier to define than others. Definitions can vary between languages and cultures, and it is important to make a definition as clear as possible to avoid misunderstandings.
There are several reasons why definitions are used:
It can also happen that people make a definition that is not so much based on facts. When these kinds of belief-oriented definitions are devised, they respond to emotions (emotive meaning / rhetorical force). The next time someone hears a word, the new definition immediately accompanies an emotion.
In practice there are three types of definitions:
It is important for all types of definitions that they:
An essay that mainly revolves around belief should contain at least four parts:
The best thing is to start with an introduction that explains why a topic is interesting to write about at all. Then you can discuss your own opinion. This must be clearly formulated, so that the reader immediately understands what the writer thinks of the subject. The arguments used must also be clear and reliable
Four tips that can be used to write an essay:
The following four tips can also help you write properly:
It is advisable to pay attention to the following writing errors when writing a piece:
In addition, here are a few final tips for your essay:
Sometimes an essay is written to convince readers of something. It is then important to pay attention to the following five points:
When writing an essay, it is important not to make assumptions about:
Writing in a sexist or racist way immediately gives the impression that you are not objective. For example, it is striking that when people differ in skin color or ethnic origin, this is explicitly stated, while this is often not the case when people are white. Women are also seldom referred to when "man" is spoken of, it is only about the man. It is important to keep this in mind when writing.
One can look at the credibility of an claim itself, but also at the credibility of the source from which an claim comes. It's important to know that credibility comes in degrees. Credibility is therefore not an all-or-nothing principle. Sources are not all equally credible. Someone's credibility can decrease, for example when you hear that someone has a criminal record, or increase because you hear that someone has a master's degree in neuropsychology.
In general, the following can be said about a claim: a claim may be considered implausible if it contradicts the content of the claim is with what we already know is already known (background knowledge), or if the source of the claim has an interest in you others believe the claim.
So people pay attention to these factors when trying to determine whether someone is credible. Often people base their judgment also on characteristics that do not matter, such as age, gender, origin, accent, clothing and height. In fact, we should not base our judgment on someone's credibility on these factors. It's important to remember a few rules of thumb when it comes to credibility:
Our own observations are our most reliable source of information about the world. People distrust statements that do not agree with their observations. For example, if we just saw Mr. X's red car and Mr. Y tells that Mr. X has a blue car, we don't think Mr. Y is credible. Our observations are influenced by many factors:
Our observations are also influenced by our personal interests and cognitive biases. There are also factors in the outside world that can influence our observations: amount of light, amount of sound and the speed of events. In addition, our observations are also influenced by our expectations and fears. If you hear that mice have been seen in the flat in which you live, you quickly think that you have mice in your house yourself (for example, if you quickly see something moving in the corner of your eye while you are sitting on the couch). Our observations are also influenced by personal interests and thinking errors. Finally, wishful thinking also influences our observations. Wishful thinking happens when a person's hopes and desires color his or her ratings and beliefs.
Critical thinkers are always on the lookout for the possibility that what they remember perceiving is not what they did perceive. But even though first-hand observations are not foolproof, they are still the best source of information. Claims contrary to one's own direct perception must be seriously questioned.
Background knowledge is about the beliefs that someone has that consist of facts that they have observed and learned.
Much of our background knowledge is corroborated by multiple sources. People don't believe statements that contradict their background knowledge. When we first hear a claim, we first try to find out how credible it is. This is called initial plausibility. If it turns out that a claim does not contradict our background knowledge, then the claim has average credibility to us. However, if it turns out that the claim contradicts our background knowledge, then we assign low credibility to the claim. Only when very strong evidence is given for the claim will we believe that the claim is correct.
There will be discussed here several factors that influence the degree of credibility of a source.
First, it is important to distinguish between interested parties and uninterested parties. An interested party is made up of people who benefit from their claims being believed by others. A disinterested party is made up of people who do not necessarily benefit from their claims being believed by others.
People also pay attention to the physical appearance of the other party. People are more likely to believe that someone is lying when he or she is nervous or looks away. In contrast, people are more likely to believe someone if he or she is confident and / or attractive
It is wise to be suspicious of the claim made by an interested party.
Yet it can also happen that such a statement is correct. When we talk about the credibility of a source, we can talk about two things:
Whether someone has enough knowledge about a topic depends on someone's expertise and experience. Expertise is assessed on the basis of a person's education, experience, performance, reputation and position. A person's performance is only important if it is related in a relevant way to what he or she claims. This also applies to experience. Remember, being an expert in one area does not mean he or she is an expert in another.
The news comes to us in different ways. Each way has its pros and cons. It concerns the following ways:
Advertising is made to sell all kinds of products. Today this is done in an increasingly sophisticated way. Advertisers know how the human mind works and use this knowledge to create commercials. They know what people are sensitive to and how to get people to buy their product anyway. Often people even buy things they don't even need because of this.
There are two types of commercials:
The commercials from the second category can be divided into three categories:
Of course it is also possible to combine two or all of these options.
Advertisements try to persuade people to adopt all kinds of behaviors: buying a new TV cabinet, voting for a local politician, quitting a bad habit, etcetera. Advertisers know our fears and are happy to use them against us, they know our needs and respond to them.
There are two types of advertisements:
The latter category often responds to feelings, uses people we dread to advertise the product or shows situations in which we would like to find ourselves. Sometimes all three elements are wrapped up in an ad.
Advertisers who give us reasons to buy a product often tell us something about the product, but not much. The promises made by the seller in many cases offer no guarantee and remain a bit vague. In some cases the message with which the advertiser wants to convince us can even be called misleading.
Ads that give reasons to buy never justify the purchase - they are not arguments. They can influence our choice and adjust our reasoning for whether or not to buy a product.
This chapter will further examine the effect of persuasion.
Words can be persuasive (rhetorical force / emotive meaning). They can evoke images, feelings and emotions in us. Good speakers apply a number of techniques that appeal and convince us with the help of rhetoric.
Rhetoric is about the investigation of persuasive writing. For example, we can write a piece in various ways that portrays Hamas members as freedom fighters or as terrorists. Of course there is nothing wrong with someone trying to convince others of something. However, it is important to think critically and thus distinguish between arguments and rhetoric. Rhetoric should not add to the credibility of a claim, because rhetoric is not about substantive arguments. Rhetoric often uses rhetorical methods. These are methods of persuasion that are sometimes used through rhetoric.
Rhetorical methods can be divided into different groups of methods. The first group usually consists of single words or short sentences that are positive or negative. They are also called slanters. Examples are euphemism, dysphemism and weaselers. The second group of methods depends on unjustified assumptions. Examples are stereotypes, innuendo and loaded questions. The third group consists of methods related to humor. The fourth group consists of methods using definitions, explanations and analogies. Examples are rhetorical analogies and rhetorical definitions.
Here are some rhetorical methods that belong to the first group of rhetorical methods:
Example:
Piet: Did Hans tell the truth?
Jan: Yes, this time.
In this case, Jan does not say that Hans often lies at other times, but he did mean it. We can determine that by the choice of words.
Two forms of innuendos are paralipsis and loaded questions.
With analogies you should always ask yourself whether the comparison is logical and why someone would contrast things in such a way. Analogies are super subjective, if you compare a cat with a mouse, the cat seems very dangerous, if you then compare a cat with a tiger, the cat seems very sweet. It is very easy to be misled by an analogy.
Nowadays it is possible to change photos by using all kinds of computer programs. By manipulating facial expressions and lighting in photos, photos can evoke certain feelings. Misleading images and photos can result from the following:
Demagogues use extreme rhetoric to spread false ideas and gain power over people. Four rhetorical techniques that are used here are:
This chapter examines relevance and thinking errors related to relevance.
A fallacy is a reasoning error. It's an argument that the content doesn't support. In the case of a relevance fallacy, the premise is not relevant to the conclusion or point in the question. The thinking errors discussed in this chapter are all relevant thinking errors. Such thinking errors are also called red herrings. This is because if you pull a herring around on the floor, it becomes impossible for a dog to smell anything but the herring, and therefore gets lost - just like thinking errors can lose track.
The ad hominem fallacy (also called argumentum ad hominem) is the most common fallacy. Here, a claim someone makes is judged by the source of the claim rather than the caim itself. An example is that something a professor says must be true, since he or she has a lot of knowledge. A distinction is made between four types of ad hominem thinking errors:
In a false dilemma, someone pretends that there are only two options, when in reality there are more than two options.
With a perfectionist fallacy, someone says that something must be perfect (for example, a policy form). If not, this policy will be rejected. This person actually acts as if there are only two options: something has to be perfect and if not, it is no longer taken seriously.
With a line-drawing fallacy, one draws a clear line to make a certain statement, while this does not have to be the case at all.
There is a question of misplacing the burden of proof when the next conversation occurs, for example. A says, "God exists." B says, "How do you know?" A says, "Prove He doesn't exist." This is a fallacy, since it is up to A to prove that God exists (and not B), after all, he is the one who says that God exists. One form of misplacing the burden of proof is:
The begging the question is a fallacy where one uses an argument for a statement in which one says that the premises are accepted and as a result automatically the conclusion too.
There are several thinking errors in which emotions play an important role:
Common other thinking errors are:
Inductive fallacies are intended to support the likelihood of their conclusions, but are in reality too weak to do so. Chapter 11 will provide further information on inductive reasoning. However, this information is not necessary to understand this chapter. This chapter is devoted to inductive thinking errors.
Two fallacies are common in inductive generalizations: (1) generalizing too quickly (hasty generalizing) and (2) incorrectly generalizing (biased generalizing). Below is an overview of the thinking errors that are made in inductive generalizations:
Generalizing from exceptional cases means making a claim based on a rare or biased sample. The latter is also called the fallacy or biased sample. Another form of generalizing from exceptional cases is self-selection fallacy. This is an overestimation of the correctness of a conclusion derived from a relatively large but self-selected sample. An example is an online poll - people often forget that only a very specific group will find the poll at all.
The fallacy of misfortune is the reverse of the generalization of special cases. It occurs when a speaker or writer assumes that a general statement automatically holds for a specific case that is exceptional.
The fallacy weak analogy (also called false analogy) is a weak argument based on insignificant similarities between two or more things. Often this agreement has been completely taken out of context in order to make the analogy. An example is: "If you kill someone with a knife, it is murder, so if a surgeon kills someone on the operating table, it is also murder."
A common fallacy is the mistaken appeal to authority. In this fallacy, a writer or speaker tries to support the content of a statement by providing as evidence the opinion of someone who has absolutely no authority in the matter. An example is: "My father says the president is lying about the test, so it must be that he is indeed not telling the truth."
Mistaken appeal to popularity (sometimes called fallacious appeal to common belief): this fallacy occurs when a writer or speaker makes a statement and emphasizes that "everyone knows" or that it is "common knowledge." Often this is not the case, and claiming that everyone knows something does not immediately make your statement correct or true.
Mistaken appeal to common practice: this fallacy occurs when a writer or speaker uses as an argument that something is more common, or that it is tradition. If this were really a correct argument, slavery and stoning people would also be justified because people had been doing that for years.
Bandwagon fallacy: Here a writer or speaker uses the phrase "everyone thinks" (and other phrases similar to this).
The following two fallacies have in common that they create an incorrect cause-and-effect relationship between two variables.
Post Hoc, Ergo Propter Hoc: This literally means "after this, therefore because of this". That still sounds very complicated, but it simply boils down to the fact that a writer or speaker is mistakenly assuming that when one event occurs after another, that event is caused by the other. This fallacy is often shortened to "post hoc".
There are different variants for post hoc:
Cum Hoc, Ergo Propter Hoc: This literally means "with this, therefore because of this". A speaker or writer makes this mistake when he or she assumes that the fact that two events are occurring at the same time, one of these events caused the other event.
There are also different variants here:
The slippery slope fallacy is an argument based on an unsupported warning that is controversial. It is suggested here that there will be an extremely undesirable outcome if one takes one (1) particular step now. Example: "No, we should not lower the alcohol limit, because that will be back to 16 that morning, to 11 next year, and in five years babies will be drinking beer in the crib!"
When someone gives a claim that cannot be tested, then there is an untestable explanation. Since this useless, vague, untestable claim does not ultimately prove anything, it cannot be seen as arguments.
This chapter discusses formal thinking errors.
The three formal fallacies that will be discussed are affirmation of consistency, antecedent negation, and undivided middle.
In this chapter, examples are given each time involving two premises and one conclusion. An erroneous example is given below:
If P, then Q.
Q.
Therefore P.
In this example, the first part of the premise after "if" is the antecedent of the statement (sentence 1). The part after "then" forms the consequent (sentence 2). The example constitutes the fallacy confirming the consequent. One premise incorrectly confirms the consistency of the other. When P and Q are reversed in (2) and (3), the argument is valid.
An example of this is:
In negating the antecedent, one premise negates the antecedent of the other. An example of this is:
Another example is:
The undivided middle fallacy occurs when the speaker or writer assumes that two things related to a third thing are also related to each other. An example is:
An example of such a schedule is:
This is erroneous reasoning.
Ambiguous claims can produce fallacy. This is the case, for example, with the fallacy of equivocation. This is related to semantic ambiguity. This fallacy uses statements such as premises and / or conclusions that contain words or phrases that can be interpreted in more than one way, thereby misinterpreting a premise.
The ambipholy also uses semantic ambiguity. This fallacy uses assertions such as premises and / or conclusions that are ambiguous because of their grammatical structure.
The composition fallacy occurs when a feature of parts of something is incorrectly assigned to the whole. The opposite of this is the fallacy division: assuming that something that is true for the whole is also true for parts of the whole.
If anything can be said of every member of the class / group, the reasoning error is accident. If something can only be said of the class / group as a whole (and so it would not make sense to apply the statement to all individual members of the class), then we speak of division:
There are even more fallacies:
This chapter discusses deductive arguments.
There are two techniques for creating and evaluating deductive arguments. This chapter is mainly about categorical logic. This is logic based on the relationships of inclusion and exclusion between categories in categorical statements. Categorical logic is useful in clarifying and analyzing deductive arguments. Understanding how this works allows us to be more critical and precise about propositions and arguments and avoid ambiguity.
A categorical claim says something about categories of objects. A standard form categorical claim is a claim that arises when names or descriptions are added to categories. Here are four types of it:
By "some" we mean "at least one".
The words appearing on the dotted lines above are called terms. The word that appears in the first dotted line is a claim and is called the subject term. The word that appears on the second dotted line is called the predicate term.
The words that serve as subject term and predicate term in a sentence are together also called classes. The above claims can also be processed and displayed in Venn diagrams. Such a Venn diagram is a graphical representation of all possible hypothetical logical relationships between a finite set of statements. Visually, this is a circle for each category, which overlap when they have a community. The overlap between some of the statements allows you to draw conclusions from the statements; this is because relationships are visible.
Thus, the "biting some dogs" claim would be represented by two overlapping circles - one circle for "dogs", and one circle for "bite". The overlap is then "dogs that bite". Because this claim is all dogs, but some dogs you put a cross in the overlapping piece to indicate that at least one dog is biting.
The A and I claims are called affirmative claims because they include part of another class. The E and O claims are called negative claims because they exclude part of one class from another.
It is important to be able to convert (or translate) a claim into a standard form categorical claim that means the same thing. Two claims are the same (equivalent claims), when they are both the same in exactly every situation. This conversion must be done precisely so that the meaning of the claim is not changed. For some claims this is easy. The claim "every rose is a flower" can easily be transformed into an A claim, namely: "All roses are flowers". However, it is sometimes more difficult to convert a claim into one of the four standard form categorical claims. It is therefore important to be the first to identify the terms that appear in a claim.
Because converting claims can sometimes be difficult, a number of rules of thumb can be used:
Two categorical claims correspond when they have the same subject term and the same predicate term. So the claim "All Protestants are Christians" corresponds to "Some Protestants are Christians." In both claims, "Protestants" is the subject term, while "Christians" is the predicate term. The claim "Some Christians are not Protestant" does not correspond to the above two claims, because the places of the subject term and the predicate term are interchanged in this claim. Logical relationships between A, E, I, and O claims can be explained in one figure: the square of opposition.
With the help of the square of opposition we can often read the truth values of the claims. There are a number of limitations to this:
The following categorical actions can be done:
Examples are:
- E-Claim: "No Chinese are Africans" and "No Africans are Chinese". These claims are therefore equal to each other.
- I claim: "Some capitals are major cities" and "Some major cities are capitals".
- Universe of discourse: the claims we make are context bound. When a teacher walks into the class and says everyone has passed, students know that it's not about everyone in the whole world, but about people in the class itself. In principle, the context of the claim determines the population of the claim.
- Complementary class: for each category within a universe or discourse there is a complementary category, for example "students" and "non-students". These are called complementary terms. Often this is simple enough to do by pasting awful "not-", although in some cases there are specific words for it.
There are two ways to find the reverse of a claim:
Schematically: ~ P = Q, P = ~ Q
Example:
All categorical claims, whether they belong to the A, E, I or O category, are equal to their opposite form.
A third categorical performance is called contraposition. To find the contraposition of a categorical claim, (1) the subject term has to be put in place of the predicate term, while the predicate term has to be put in place of the subject term. In addition, (2) both terms should be replaced by complementary terms. From a schematic point of view; P = Q, ~ P = ~ Q
Example:
Only A and O claims are equal to their counter position.
A syllogism is a deductive argument that consists of two premises. A categorical syllogism is a syllogism consisting of standard form categorical claims, where three terms of each claim must appear exactly twice in two of the claims.
An example:
All terms ("Americans", "consumers" and "Democrats") appear exactly twice in two different claims.
The terms of a syllogism are labeled as follows:
When S and P are connected by means of M, an argument is valid. An argument is called valid if it is not possible for the premises to be true, while the conclusion is false. With a Venn diagram it is possible to find out what the relationship between S, P and M is so that it can be seen whether an argument is valid.
A Venn diagram consists of three circles: on the left is the minor term, on the right is the major term and below in the middle is the middle term. When one of the premises is an I or O premise, there can be confusion about where to place the “X”. Sometimes a decision can be made using the following rules:
Categorical syllogisms can also be hidden in unspoken premises. It is then important to identify the unspoken premises and to write out the categorical syllogisms step by step.
In addition to drawing a Venn diagram, there is an easier method to test the validity. This method is based on three simple rules. These rules are based on two concepts: (1) affirmative and negative categorical claims and (2) the concept of distribution. Distribution is when a claim says something about every member of a category. There is no distribution when a claim does not say something about every member of a category.
A syllogism is valid if the following three rules are met:
An example is:
The term "people" is the M and is not distributed in either premise. The first premise is an A claim and is not distributed in terms of predicate term and the second premise (an O claim) is not distributed in terms of subject term. This syllogism therefore does not meet the criteria of rule two. This means that this argument is not valid.
This chapter discusses other deductive arguments.
This chapter is about truth-functional logic (also called propositional / sentential logic). Specifically, this involves applying principles of logic to assertions and analogies. Truth tables are often used in this context. These tables often contain two letters: P and Q. These are also called claim variables and are a symbolic representation of premises and conclusions.
A claim, P, is true (T) or false (F). This is indicated by noting down the letter P, putting a dash under it and then noting the letter T and F below each other. Noting it like this shows the possible truth values for P. Sometimes numbers are used, where: true = 1 and false = 0.
There are different types of truth tables:
The truth table for the conjunction NOT (truth table for negation) shows that whatever value P may have, its negation (~ P) is always the opposite:
Truth table of the conjunction NOT:
P | ~P |
1 | 0 |
0 | 1 |
Conjunction (&): this is a claim consisting of two claims. These claims are called conjunctions. A conjunction is true only if the two claims that make up the general claim are true (that is, if P and Q are true). An example of a conjunction is: Jamie is at home and Sophie is at work. Jamie is P and Sophie is Q.
Truth table of the conjunction EN:
P | Q | P & Q |
1 | 1 | 1 |
1 | 0 | 0 |
0 | 1 | 0 |
0 | 0 | 0 |
Truth table of the conjunction OR:
P | Q | P ∨ Q |
1 | 1 | 1 |
1 | 0 | 1 |
0 | 1 | 1 |
0 | 0 | 0 |
Truth table for 'if ... then ...':
P | Q | P → Q |
1 | 1 | 1 |
1 | 0 | 0 |
0 | 1 | 1 |
0 | 0 | 1 |
When we add an extra letter, for example "P, Q and R", the number of possible combinations of T and F are doubled, and thus the number of rows in the truth table is also doubled.
The columns of the letters (example: P, Q and R) used when filling in the column of a general claim (example: Q & R) are called reference columns.
A table provides us with a truth-functional analysis of the original claim. It displays the truth values of a general claim, based on the truth values of smaller parts of the claim.
Two claims are the same (truth-functionally equivalent) when they have exactly the same truth table. In that case, the T's and F's in the column under one claim are ordered in the same way as the T's and F's in the other column.
The main goal here is to produce a claim that is equal to the original claim, but in which the truth-functional structure is displayed. A number of problems can also arise here. The most important thing in symbolizing is that the claim is well read and understood.
What does the word 'if' introduce?
The word "if" introduces the antecedent of a conditional claim. The phrase "only if" introduces the effect of a conditional claim.
Example;
IF: If I buy you lunch it's because you won the bet. "
ONLY IF: I'll buy you lunch, but only if you win the bet.
Conditional claims are sometimes described on the basis of necessary conditions and conditions that are sufficient.
An example is: "For example, the presence of oxygen is necessary to be able to breathe. If we can breathe (A), then we must have oxygen (Z). The necessary condition then becomes the result of a conditional claim: A → Z.
A sufficient condition guarantees that something can exist if only a specific condition is met. Being born in America, for example, is enough to get an American passport. You don't have to do anything else for that. Sufficient conditions are described, such as the antecedents of conditional claims. If Pete was born in America (A), then Pete has an American passport (B): A → B.
Also under necessary and sufficient conditions, attention must be paid to the difference between "if" and "only if". The word "if" introduces the sufficient condition. The phrase "only if" introduces the necessary condition.
The word "unless" equals the (v) used in disjunction. To know where a disjunction begins, we can look at where the word "of" or "if" occurs in the sentence.
A truth-functional argument can be valid and not valid. An argument is invalid when the premises are true, but the conclusion is false. An argument is valid when the premises on which the conclusion is based are true. A distinction is made between three valid argument patterns and the corresponding three invalid argument patterns. Important terms for the valid argument patterns are:
If P, then Q
P.
So Q
If P, then Q
Not Q
So not P
If P, then Q
If Q, then R.
So, if P, then R.
Important concepts in the invalid argument patterns are those discussed earlier: affirming the consequence (affirming the consequent), denying the antecedent and the undivided middle
A truth-functional argument can take countless forms. Nevertheless, we can test the validity of such an argument. This is done by means of truth tables.
Deduction is a useful means to mainly prove that an argument is valid instead of that an argument is not valid. There are four sets of rules in this regard.
Group 1: Basic valid argument patterns:
If P, then Q
P.
So Q
If P, then Q
Not Q
So not P
If P, then Q
If Q, then R.
So, if P, then R.
P or Q
Not P
So Q
P & Q → P P
& Q → Q.
P.
Q
So P & Q.
P, conclusion: P \ / Q.
Q, conclusion: P \ / Q.
P → Q.
R → S.
P \ / R. Conclusion: Q \ / S.
1) P → Q. 2) R → S. 3) ~ Q \ / ~ S. Conclusion: ~ P \ / ~ R.
Group 2: Truth functional equivalents:
P → (Q \ / R),
P → ~~ (Q \ / R).
P → (Q \ / R),
P → (R \ / Q).
(P → Q) ~ (P \ / Q).
(P → Q) (~ Q → ~ P).
~ (P&Q) (~ P \ / ~ Q),
~ (P \ / Q) (~ P & ~ Q).
[P → (Q → R)] [(P&Q) → R].
[P & (Q&R)] [(P&Q) & R],
[P \ / (Q \ / R)] [(P \ / Q) \ / R].
[P & (Q \ / R)] [(P&Q) \ / (P&R)],
[P \ / (Q & R)] [(P \ / Q) & (P \ / R)].
P ∨ ~ P. A tautology is a sentence that is always true: it is raining or it is not raining.
Conditional evidence is both a rule and a strategy to form a deduction. This proof is based on the following idea: suppose we try to make a deduction for a conditional claim: P → Q. If we formed this deduction, what have we actually proven? We have proven that if P is true, then Q will be true. In this case we can assume that P is true and try to prove that Q must also be true based on that. If we can, so if we can prove Q after assuming that P is true, then we have proved that if P occurs, then Q must also occur. There are, however, a number of important rules when it comes to conditional evidence. For example, conditional evidence can only be used to make a conditional claim and not to prove another claim. Also, if conditional evidence is used more than once in claims, they should be approached in exactly the opposite order.
This chapter discusses what inductive reasoning is.
Inductive reasoning is reasoning to support a conclusion rather than to demonstrate it.
An argument based on analogy is an argument that something has a certain property, because an equal thing has the same property. An example of this is:
Jan likes to fish.
That is why his brother Piet likes to fish.
The analogues in the example above are Jan and Piet. The conclusion-analogue (Piet) is attributed a certain trait (likes to fish), because the premise-analogue (Jan) likes fish. The conclusion-analogue is also called target analogue and the premise-analogue is also called the sample analogue.
Here are some guidelines for evaluating arguments based on analogy:
When an argument based on analogy is proven to be false, it is attacking analogy. Weak analogy (also called false analogy) is a weak argument based on insignificant similarities between two or more things.
Evaluating arguments based on analogy is actually a matter of comparing and contrasting the analogues. It requires us to rely primarily on our experience of how similar two or more things are.
Analogues are also used for other purposes:
A person generalizes from a sample when he or she attributes a certain trait to members of a certain population, because this has been proven in a small group. The most important principles for evaluating such arguments are:
The sampling frame is a definition of the population and the attribute. It helps us determine whether an individual belongs in the population and whether they possess the attribute. So it is a part of the population (or: a sample) that we have been able to determine for study. However, we are not sure if the values resulting from the sample are exactly the same in the population. For example, which party people vote for also depends on sex, age, religion and income. A sample represents a population if the variables linked to the attribute are present in the sample in the same proportion as in the population.
A sample is biased when the variable is not present in the same proportion in the sample as it is in the population.
The spread that is calculated differs from sample to sample, because of this a random variation arises. This is also called the error margin. The error margin can be calculated on the basis of (1) the sample size and (2) the confidence level. The confidence level shows the probability that the proportion found in a sample falls within the error margin. A sample can be enlarged to reduce an error margin. In colloquial terms, we use informal terms to indicate the probability that a conclusion is correct, for example by using terms such as "likely" and "it is almost certain that ...".
A random sample is therefore not completely free of biases, because the variables are nevertheless vulnerable to random variation.
Statistical syllogism is the type of argument that is the opposite of generalization from a sample. When someone de-generalizes, you conclude that certain members of a population have an attribute, because a large proportion of all members of the population have that attribute.
Reasoning from general to specific takes the following form:
An example is:
In the example above, there is an inductive syllogism (also called statistical syllogism). The strength of an inductive syllogism depends on the general statement, namely, "Most X's are Y's." If it is incorrect, then the conclusions that follow from the claim are also incorrect. The more often the most X and a Y are (for example, the more often it happens that teachers vote for the SP), the stronger the argument is that someone who is a teacher should be an SP voter.
The principle of total evidence is the idea that when estimating the probability of something, you have to take into account all available relevant information. Schematically, the argument takes this form:
The strength of such arguments depends on the parts of X that are also Y. The larger the portion, the stronger the argument. Don't confuse the general probability that the conclusion is true with the strength of the argument.
A causal statement describes the cause of a particular event. A causal hypothesis is a statement that describes that X causes another variable (Y). It is important not to incorrectly describe a certain causal pattern. Three principles apply here:
In a randomized experiment, subjects are randomly assigned to one of the conditions: the experimental condition or the control condition.
Observational studies are not experiments. The researcher does not manipulate people's assignment to a particular group. The groups are merely observed. A distinction is made between a prospective (something that has yet to take place) and a retrospective (something that has already taken place is being investigated).
Observational studies provide weaker confirmation of causal hypotheses, as confounding variables may not be evenly distributed in the groups.
Inferences to the best explanation are arguments that conclude that a particular outcome was caused by another event or condition. The conclusion sets out the most likely cause of the result: of the things that could have caused it, the conclusion tells us what is most likely.
The strength of such arguments depends on how likely it is that alternative, equally plausible explanations of the outcome are true: how likely it is that something else that could have caused the outcome actually happened.
To criticize an inference to the best explanation, one has to try to think of other possible explanations, other possible things that could plausibly cause the outcome, that are as likely to have happened as X.
If we want to calculate the probability that two independent events occur together (X and Y), we have to multiply the probability of X and the probability of Y. Many people make a mistake and add up the odds. However, if we want to calculate the probability of one of these two events (X or Y), then we add the probabilities of X and Y together.
The estimated value is the result of how much you expect to win combined with the amount you can win. When the estimated value is greater than 0 then it makes sense to take the guess.
This chapter further examines moral, legal and ethical reasoning.
A value judgment is a term for an assertion in which a judgment emerges. A value judgment assesses the value or desirability of something or someone. An example is a teacher who says about a student who has committed fraud: "He deserves a 3 for his report". The teacher does not describe the student, but expresses an opinion about the student.
In moral reasoning, an attempt is made to establish moral value judgments. Not every value judgment expresses a moral value judgment. When it is said, "our queen dresses well," it is a value judgment, but not moral. A moral value judgment often includes words such as right, wrong, and bad. An example of a moral value judgment is: "It was the teacher's mistake to withhold information."
There are the following two principles of moral reasoning:
Consequentialism is based on the premise that the consequences of a decision or action determine the moral value. If an action produces more happiness than the alternatives, then it is the right action to take. Here we speak of utilitarianism. This involves weighing up the various consequences of alternatives and then choosing the action that brings the best happiness. This perspective is problematic. When we consider whether we should do something or not, we take into account several things, such as the rights of others and our own duties. Another consequentialist theory is ethical egoism. It is assumed here that if an action brings more happiness to yourself than the alternatives, then it is correct to perform it, and if it brings less happiness to yourself than the alternatives, then it is wrong to perform it. And as a last perspective, there is also ethical altruism, in which one's own happiness and the happiness of others are seen as equal, and therefore equally important.
In duty theory (deontologism), value is attached to moral duties. We should or should not do things not to achieve something, but simply because it is right or wrong. Only then can we speak of moral imperative. When we try to keep a promise, we should do it because we should. A moral imperative is categorical: it describes an action that is performed, not in order to achieve a certain result, but because the action is our moral duty. But how can we determine what our moral duty is? Two things need to be considered here:
1) The principle of action relates to what you want to do
2) Determine if you wish the principle were universal and that everyone could follow it when they were in the same situation as you were.
Moral relativism takes as its starting point that what is right and wrong is dependent on and determined by someone's group or culture. This is not about what is believed to be right and wrong. After all, this can differ from group to group. This is really about right and wrong. Moral relativism has three complications:
In moral subjectivism, the starting point is that the idea of what is right and wrong is a subjective opinion. Just thinking that something is right or wrong makes it so for that particular person.
Religious relativism assumes that what is right and wrong is determined by the religion of a culture or society. The same three complications discussed in moral relativism can reappear here. When do you belong to a certain religion, even within a certain culture or religion, conflicting principles often apply and people who adhere to one religion / culture may think that people who adhere to another religion / culture are doing something wrong.
Religious absolutism assumes that the correct moral principles are accepted by the right religion. One problem with this is that opinions on what the correct religion is vary.
Virtue ethics does not focus on what should be done, but on how someone should be. A person does not try to figure out what should or should not be done to achieve a certain result, but rather focuses on what kind of person he wants to be, for example reliable and friendly.
Legal reasoning is deductive and inductive. If it is deductive, the reasoning can be sound, valid or invalid. Deductive reasoning also contains categorical and hypothetical reasoning. When it is inductive it can range from strong to weak. Inductive reasoning includes generalizations, analogical reasoning, and cause and effect reasoning.
In case of appeal to precedent or stare decisis, use is made of a case that is used as a guideline in a similar new case. Appeal to precedent is an analogical argument. If a previously resolved case (A) is the same as a similar new case (B), then decisions can be made by B in the same way as decisions were made at A. The principle of consistency is also used here: matters that do not differ must be treated in the same way.
The same perspectives discussed in moral reasoning apply here again.
The claim that the laws should make anything that is immoral as illegal serves as the basis for legal moralism. This is used, for example, to prohibit murder or sexual abuse.
In the damage principle, the point is that the prohibition of X has the reason that X can harm others.
Legal paternalism is based on the premise that laws can be justified if they prevent someone from harming themselves. So laws forbidding X can be done can be justified, if X is causing major problems with other people.
The insult principle is based on the assumption that a law prohibiting X can be justified if X can offend others. An example is the burning of a flag.
Eight aesthetic principles that support and influence the most artistic creations and critical judgments about art are:
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