Formal Logic Midterm Exam

Example of Expressing the Same Proposition

"My father hasn't any reason to become querulous in that manner." "My Dad doesn't have any cause to complain like that."

Using an example, explain what is wrong with saying the following: "Proposition P is true for me." Make sure you explain why people are tempted to say such things.

"People who go out every weekend perform worse in school than people who do not." "I go out every weekend so that is true for me." It is meaningless to say something is "true for me" because it only matters if the proposition is true or false when describing the state of affairs. When people say "true for me" they really mean that they believe that proposition, and that they believe it passionately or dogmatically.

Using an example, explain how a deductive argument can have true premises and a true conclusion and still not be valid.

(1) If Mary likes dogs, she will go to the dog show in Canada. (2) Mary does not like dogs. Therefore, (3) she will not go to the dog show in Canada. The proposition in this argument is all presumed to be true; however, just because Mary does not like dogs does not mean she will not go to Canada for another reason. It also does not mean she will not go to a dog show because people do things they do not like.

State and explain the six standards for a legitimate appeal to authority.

(1) The person cited as an authority has sufficient expertise in the subject matter in question. We should be careful to sort out whether the person's expertise is genuine. We will have to determine what sort of education and experience a supposed expert has and whether they are sufficient to count as a reliable authority in the matter in question. (2) The proposition justified by appealing to the expertise of the person cited as an authority is a proposition about matters within that person's area of expertise. It is important to determine what subject matter a proposition is about and to check to see whether the person cited as an authority is an authority concerning the subject matter. (3) There is agreement—for good reason—among the experts in that area about the truth or falsity of the proposition in question. When we appeal to authority, we rely on the authorities to whom we appeal to have good argument to support their conclusions. The appeal to authority is only as good as the argument the experts have accepted for the truth of their conclusions. (4) The area of expertise is a legitimate area or discipline. We need to examine and assess the actual arguments about the subject matter. (5) The person cited as an authority is not significantly biased. The more important it is that we arrive at the truth, the less we should rely on appealing to authority and the more we should turn to examining the actual arguments about the subject matter. (6) The person cited as the relevant authority is identified. When the authority is not named or identified, it is impossible for us or our audience to be in a position to examine and evaluate arguments, or to tell if our source is actually an expert in the appropriate field.

Name and state the first two laws of logic.

1. Law of bivalence: Each proposition is either true or false. 2. Law of truth values: No propositions is both true or false.

Standard-Form Categorical Proposition

A categorical proposition that expresses these relations with complete clarity

Fallacy

A common mistake in reasoning that leads you to accept a bad argument as a good one.

Law of Logic

A condition that must hold before any proposition could possibly have a truth value.

Give the definition of an invalid argument. Give both a paraphrase in your own words and the formal definition as given in the text. Give an example of an invalid argument (other than the examples given in the text).

A deductive argument is invalid if and only if it is possible for the premises to be true and the conclusion false. So with no exceptions, both premises have to be true and the conclusion false for it to be an invalid deductive argument. (1) If there is good luck ahead, a black cat will cross me. (2) A black cat crossed me. Therefore, (3) there will be good luck ahead.

Give the definition of a sound argument. Give both a paraphrase in your own words and the formal definition as given in the text. Give an example of a sound argument (other than the examples given in the text).

A deductive argument is sound if and only if it is both valid and all its premises are actually true. So every premise must be valid and true for a deductive argument to be sound. (1) Comedians are funny (2) Mike is a comedian Therefore, (3) Mike is funny.

What is the confusion involved in saying that an attitude is true or false?

A person's attitude is not a proposition. Only propositions are true and false. Therefore, an attitude cannot be true or false.

1) Using examples, explain the difference between dependent and independent premises.

A premise is dependent if and only if they are supposed to be taken together in support of the conclusion. A premise is independent if and only if each premise (or set of premises) is supposed to support the conclusion regardless of whether the other premise (or other set of premises) is supposed to support the conclusion. A dependent premise looks like "If it storms outside, I will wear my rainboots. It is storming out. Therefore, I will wear my rainboots." An independent premise looks like "The child will receive no help because no one volunteers. The child will fail because there are no resources for them to use."

1) What is an intermediate conclusion?

A proposition if and only if it functions both as the conclusion of one argument and the premise of another argument.

Categorical Proposition

A proposition that relates two classes or categories

What is prudential reason?

A prudential reason is a reason to accept a proposition as true because of fear or harm or hope of a benefit that may be an effect of holding the proposition to be true: a factor other than the proposition's actual truth value.

Define rhetorically effective argument.

A rhetorically effective argument is rhetorically effective if and only if it is successful in persuading its audience of the truth of its conclusion.

In what circumstances should we say "true proposition" or "statement of fact" rather than "fact"? Why?

A statement of fact is a proposition that is describing a state of affairs.

State of Affairs

An arrangement of things in the world.

What does it mean for someone to have an opinion? How do opinions differ from other propositional attitudes?

An attitude of belief directed towards a proposition that describes a state of affairs. A person has an opinion if and only if that person believes some proposition to be true.

Give definitions of a bad inductive argument. Give both a paraphrase in your own words and the formal definition as given in the text. Give an example of a bad inductive argument (other than the examples given in the text).

An inductive argument is bad if and only if it is either weak or has at least one false premise. So if there is one false premise or just weak in general, it is automatically a bad inductive argument. (1) There are 21 red cards in a deck. (2) There are 27 black cards in a deck. (3) The red and black cards are mixed in the deck Therefore, (4) the first card picked randomly from the deck will be red.

Give the definition of a weak inductive argument. Give both a paraphrase in your own words and the formal definition as given in the text. Give an example of a weak inductive argument (other than the examples given in the text).

An inductive argument is weak if and only if the argument is such that if the premises of the argument were true, then the conclusion would be less likely (or no more likely) to be true than to be false. So since there is only a possibility the premises are true, it is not unlikely for the conclusion to be more false than true, thus leading to a weak inductive argument. (1) There are 5 black cats in a litter. (2) There are 9 orange cats in a litter. (3) The cats will be adopted by random. Therefore, (4) the first cat to be adopted will be a black cat.

What is wrong with promoting dogmatism and skepticism?

Both shun the use of reason.

Subject and Predicate Term

Classes or categories that go into a categorical proposition

Using examples, explain why contingent conditional propositions should not be confused with arguments.

Contingent conditionals do not suppose their antecedents are logically implied to their consequents. Only conditional propositions that are necessarily true are logical implications. "If the sea levels begin to rise, then there will be fewer land."

What, in general, is the problem with appealing to people's motives or emotions?

Critical thinking can be difficult and time consuming, while people are more readily motivated by their emotions than reason. This can lead to confusion with support for the truth of propositions.

How do logic and critical thinking help us resist force?

Do the premises support the conclusion? Are the premises actually true? Doing this allows us to think for ourselves

What are dogmatism and skepticism?

Dogmatism is about someone accepting a proposition as true (or false) regardless of reasons for and against, whereas skepticism is about someone rejecting a proposition as true (or false) regardless of reasons for and against. So, the difference isn't about truth and falsity, but an attitude of either unconditional acceptance (i.e., belief) of truth value (either true or false) or rejection (i.e., doubt) of truth value (either true or false).

Truth Values

Form/Content of a single proposition

If a deductive argument is invalid, what does that indicate about the truth or falsity of its premises? Why?

If a deductive argument is invalid it does not indicate anything about the truth or falsity of its premises because an argument with two true premises can still be invalid if its premises do not support its conclusion.

Why are logic and critical thinking important?

If we do not think for ourselves someone else will think for us. Reason helps us defend ourselves against the force of rhetoric

Explain the function of premise and conclusion indicator words and phrases. Explain why such indicators do not always serve to indicate premises or conclusions.

Indicators indicate casual relations between events. When there are no indicators for the premise of conclusion, we must consider the possibility that there is no argument present. We should still try to look for the proposition that best expresses the main point.

Explain why (give the argument that) fact and opinion do not constitute genuine alternatives to one another.

Is that a square root or a carburetor? The terms fact or opinion don't pose a genuine alternative because they do not pick out comparable things.

If an argument is sound, what does that indicate about its validity? Why?

It indicates that the argument is valid because for an argument to be sound it must also have to be valid.

If an argument is a good inductive argument, what does that indicate about the truth or falsity of its conclusion? Why?

It indicates that the conclusion is more likely to be true than false, but it does not indicate with certainty that the conclusion is true. It must be strong a strong argument to be a good argument.

How is the fifth standard for a legitimate appeal to authority related to ad hominem circumstantial fallacies?

It is important we arrive at the truth more than relying on appealing to authority and we should turn to examining the actual arguments about the subject matter. We have to exercise good judgement about whether some expert's bias is of a degree significant enough to undermine their authority. For example, if a researcher has shared economic interest with an unethical company, biasing factors may affect them and we should use caution when looking for evidence that bias is in their results by using good judgement.

If an inductive argument is weak, what does that indicate about the truth or falsity of its premises? Why?

It says nothing about the truth or falsity of its premises because the definition of a weak inductive argument says that if the premises were true then the conclusion would no more likely to be true than false, but it does not say anything about the truth of premise.

How does knowledge differ from a fact in the most basic sense?

Knowledge is an attitude of justified belief that is directed towards true propositions.

Explain the difference between a (casual) law of nature and a law of logic.

Laws of nature regulate casual relations between actual events in the world, while laws of logic are necessary conditions for the possibility of there being any proposition whatsoever.

Vocab Propaganda

Messing with the meanings of words

Why must we say that a deductive argument only supposes that its premises support its conclusion? In other words, why must the definition of deductive argument include the word "supposes" or its equivalent?

Not all deductive arguments are good arguments, in a bad deductive argument the premises may not support the conclusion, a deductive argument that does not support the conclusion is still considered an argument, so we say supposes.

Why must we say that an inductive argument only supposes that its premises support its conclusion? In other words, why must the definition of inductive argument include the word "supposes" or its equivalent?

Not all inductive arguments are good arguments, in a bad inductive argument the premises may not support the conclusion's truth. An inductive argument that does not support the conclusion is still considered an argument, so we say suppose.

What should we look for to determine whether a text contains an argument?

Note the main assertion, make a note of the first reason support their conclusion, write down every other reason, and underline the most important reasons.

Compare and contrast the content of rhetoric with the content of logic and critical thinking.

People and their attitudes is what is important to rhetoric. Critical thinking is concerned with propositions

What are people usually asking when they ask the question "Is that a fact or an opinion?" What confusions are involved in asking this question in this way?

People are usually asking about authority of the person who are making the claim that they are making. They are looking for reliability from an authority figure.

Why does the question "Is that a fact or an opinion?" promote dogmatism and skepticism?

Promoting dogmatism: can affirm truth just based on authority without reason. Promoting Skepticism: that the person asked the question has no authority to affirm the proposition. "just their opinion.

Using the distinction (make the distinction before using it) between propositions and states of affairs, explain what "true" and "false" mean. In what way are truth values relations?

Propositions are the basic unit of meaning in language. State of affairs are the arrangements of things in the worlds. So, a proposition is "true" if it correctly describes a state of affairs. Truth values are relations between a proposition and state of affairs.

Explain why a proposition can never be valid or invalid, and why an argument can never be true or false.

Propositions can never be valid or invalid because no single proposition by itself can express an argument. Arguments require at least two propositions—one to serve as a conclusion and one to serve as a premise. Valid or invalid express the relationship between the premises and conclusions in a deductive argument. An argument can never be true or false because arguments cannot have truth values. Arguments consist of the assertion of a relationship between several propositions. The relationship between propositions are not, themselves, a proposition and cannot have a truth value.

Using an example, explain why people's psychological states are irrelevant to consideration of logic.

Psychological states or no concern of logic. Sue believes God exists. A psychological explanation of her belief would refer to some psychological influences. Casual explanations would be used to explain her belief. Logic would use whether her statement is a proposition and whether it is true or false. Logic would look at the arguments that give reasons and premises that are supposed to support the conclusion that God exists.

Compare and contrast the form of rhetoric with the form of logic and critical thinking.

Rhetoric proceeds by assertion of the opinions the rhetorician wants the audience to believe. Critical thinking evaluates arguments to see if the premises support the conclusion.

Compare and contrast the aim of rhetoric with the aim of logic and critical thinking.

Rhetoric tries to persuade people to coerce them to believe something; to seek power over others. Critical thinking aims at good reasoning

Compare and contrast the means of rhetoric with the means of logic and critical thinking.

Rhetoric uses appealing forms of speech, flattery of the audience, and tricks. Critical thinking tries to find the strongest version

What are the different meanings of the word "fact"? Which meaning is most basic? Why?

Something is a fact if and only if it is a state of affairs. A true proposition which describes a state of affair is a statement of fact. Knowledge comes from having both.

Proposition

That aspect of Language that can be true or false

Why is the appeal to what most people believe, do, or approve of an illegitimate appeal to authority?

The appeal to what most people do is illegitimate because it does not appeal to any divided intellectual labor or specialized expertise.

Rhetoric

The art (technique of persuasion). An act of using language is a form of rhetoric if and only if the use of language attempts to influence people by affecting their attitudes and actions.

Distinguish between content propaganda and vocabulary propaganda.

The difference between Content Propaganda and Vocabulary Propaganda is the difference between the truth and meaning. Content propaganda tries to deceive us that false propositions are true and that true propositions are false. Vocabulary Propaganda tries to deceive us by distorting the meanings of words or phrases to make it unclear which propositions sentences are expressing.

What distinctions should we use instead of the bogus one between fact and opinion?

The distinction between proposition and state of affairs. And the distinction between knowledge and proposition.

What are the elements of making a clear distinction? What does it mean to respect a distinction, and how do we usually accomplish this? Give an example (other than the examples given in the text).

The elements of making a clear distinction is taking a definition to specify the sort of things we are distinguishing and simply add, in each case, a statement if the difference that makes the difference between the distinct things. To respect a distinction is to define what each thing is, and we accomplish this by stating the difference that makes the difference. (1) Peter had grass stains on his pants. (2) Peter came back from being outside. (3) Peter had dirt on his hands and feet. (4) Peter has rocks and flowers in his hand. (5) Peter was tired when he got inside Therefore, (6) Peter was playing in the woods.

What do the first two laws of logic imply about proposition?

The first two laws of logic imply that every proposition must have exactly one of the truth values, true or false.

Explain the difference between deductive and inductive arguments.

The primary difference between inductive arguments and deductive arguments is whether the support relation that is supposed to hold between the premises and the conclusion of the argument is one of likelihood or probability (in inductive arguments), making the claim that if the premises were true then the conclusion would be more likely to be true than to be false, or one of necessity (in deductive arguments), making the claim that if the premises were true then the conclusion would have to be true.

Using an example, explain the distinction between a proposition and a person's attitude toward that proposition. (Hint: compare the truth values of propositions about people's attitudes towards propositions with the truth values of the propositions toward which they have those attitudes.)

The truth value of one is separate from another.

Relationships

The way in which two or more concepts, objects, or people are connected, or the state of being connected

What sorts of additional information besides the premises and conclusion may be found in presentations of arguments in everyday contexts?

They are not presented in the typical premise and conclusion form and can be presented in any order. Everyday context arguments also are concerned with other aspects other than the argument.

Why is it illegitimate to conclude that a person is making a false claim because it is to their advantage to make the claim they make?

This shows that the person is significantly biased, whether cited as an authority figure or not. It is more important to arrive at the truth than appealing to authority.

Content Propaganda

Trying to convince true is false; false is true

What makes vocabulary propaganda especially deceptive (and more deceptive than content propaganda)? (a) Explain how logic and critical thinking help us to resist the rhetorical force of content propaganda and (b) How logic and critical thinking help us to resist the rhetorical force of vocabulary propaganda.

Vocabulary is more deceptive because it distorts meaning and cover distinctions interferes with ability. Logic and critical thinking help us to resist rhetorical force of vocabulary propaganda by using reason to think for ourselves

How does the question "Is that a fact or an opinion?" ignore propositions?

We can all believe something to be true when it's really false. Attitudes and propositions are separate. Propositions and their truth values are ignored

How do we tell how many arguments appear in a text?

We can use the Beardsley diagram to help us map out the argument by numbering how many premises there are, and indicator words link premises together and tell us where the conclusion is.

Why do we sometimes need to appeal to authority?

We cannot investigate every proposition by ourselves, so certain people become experts about one subject matter and other people become expert about other subject matters. We then rely on the competence of the experts to sort out which propositions are true, and which are false about that subject matter.

What are the two separate and independent considerations that must be taken into account when judging whether the premises of an argument give good reasons in support of its conclusion? Explain why and what it means for these considerations to be independent of one another.

We must consider if the premise supports the conclusion and if all the premises are true. These considerations must be independent from each other because we are analyzing each premise in the argument independently from each other. We must see how each premise by themselves can support a conclusion without other premises in the equation.

Instead of asking "Is that a fact or an opinion?" what questions should we ask instead? Why?

What is the state of affairs of the question? What's the proposition that is being asserted about that fact? Is the proposition true?

Copula

Words that link (or "couple") the subject term with the predicate term; "are" and "are not."

Quantifiers

Words that specify how much of the subject class is included in the predicate class; "all," "no," and "some."

Explain and give an example of each of the following (try to find examples different from those in the text): (a) clichés or dead imagery; (b) complicated verb phrases substituted for simple verbs; (c) pretentious words, foreign loanwords, and jargon; (d) vague, ambiguous, and meaningless words and phrases.

a. A cliché is a phrase that is overused, predictable, unoriginal, and betrays a failure to think about the subject matter in a fresh and attentive way. Ex. "as different as apples and oranges" b. Imprecision and obscure writing often result when we use complicated phrases instead of simple verbs. Ex. "render inoperative" instead of "break" c. Pretentious words are often used to make simple or biased sentences seem objective, scientific, or impartial. Ex. "liquidate" instead of "kill" d. Words that sound fine or impressive but get used without any clear meaning or without sorting out which of various meanings is intended may be used to dishonestly mislead or obscure what is said. Ex. Democracy, freedom, patriotic, realistic, justice.

State and explain Orwell's six rules to help avoid misleading language.

a. Never use a metaphor, simile, or figure of speech which you are used to seeing in print. b. Never use a long word when you can use a short word instead. Helps us to avoid misleading readers. c. If it's possible to cut a word out, cut it out. Omit unnecessary words. This helps us to maintain clarity. d. Never use the passive voice where you can use the active voice. This helps us to make clear what it is that we are talking about and causes of effects clear rather than keeping effect vague and unconnected to anything. e. Never use a foreign word or scientific word or jargon. This rule will help us avoid hiding our meaning behind words that sound impressive but do not adequately express what we are trying to say to an audience who may be unfamiliar with the esoteric words or phrases. f. Break any of these rules sooner than say anything outright barbarous.

Explain the four distinctions between the disciplines of logic and psychology in detail.

a. Psychology and other natural sciences study actual events in the world. Casual laws and logic studies logical relationships between propositions and their truth values. b. Modality of the object of study: Casual relation between events in the world., logical relations between propositions, and what is possibly true or false. c. Goal: Descriptive and explanatory account of things happening in nature vs. logic is an evaluative science which evaluate arguments in terms of whether they are good or bad. d. Justification: Science uses empirical justification vs. logic is a priory science which seeks to justify their claims independently of observation or experience.