Logic and Critical Thinking section 1

Induction by enumeration form

A1 is F A2 is F A3 is F A4 is F All A's (or the next A will be F)

Which form is this argument? Explain. If it's a banana, then it's food It's food Therefore, it's a banana

Affirming the consequent because... -the consequent (food) is being affirmed -invaid form because you cannot be sure that the food is a banana -terms go from major (food) to minor (banana)

Which type of fallacy is this? You've claimed that smoking is bad for one's health, but you smoke too.

Agrument against the person from hypocrisy

Valid or Invalid Some cats are brown John is a cat John is brown

Not valid because you cannot be 100% sure that John is brown since only "some cats" are brown. To be valid, all cats have to be brown.

Inductively strong or weak: My shirt, Trisha's shirt, Lisa's shirt, and Danielle's shirt was made by the local tailor out of blue silk and is a size medium. Trisha, Lisa, and Danielle's shirt ripped in the same seam after the 7th wear. So, my shirt will rip after the 7th wear.

strong analogy

Inductively strong or weak: This bag has 100 marbles in it 80 of them are black 20 of them are white The next marble I pick will be black

strong enumeration

What makes an argument inductively strong?

the degree to which the premises provide evidence to make the truth of the conclusion probable

What is logic?

the study of criteria that helps distinguish successful arguments from unsuccessful arguments

What is truth value?

the truth or falsehood of a statement

"Either it is or is not raining outside" This statement is logically____

true

True or False: Inductive logic is a matter of degree and not a matter of form.

true

Valid or Invalid All dogs are mammals Fido is a dog Fido is a mammal

valid form

Inductively strong or weak: I like peanuts, am bigger than a breadbox, and have two ears Bingo the elephant likes peanuts, is bigger than a breadbox, has two ears, and has a trunk So, I have a trunk

weak analogy

Inductively strong or weak: I loaned my friend $50 in July and he failed to pay me back. I loaned him another $50 in August, which he hasn't paid back. I loaned him $25 in September, which he did pay back. He's never going to pay me back the two $50

weak enumeration

Inductively strong or weak: The 13,000 days since my birth have all been days on which I did not die So, all days (or the next day) will be a day on which I do not die

weak enumeration because the past cannot predict the future

When is an argument deductively valid?

when it is NOT possible for all the premises to be true and the conclusion false

When is an argument deductively sound?

when it is deductively valid AND all premises are true

When is an argument cogent?

when it is inductively strong *and* all premises are true

When are statements logically equivalent?

when it is not possible for the statements to have different truth values

Which type of fallacy is this? Lynch says that we should spend more state revenue on education. But Lynch is a professor who wants a better salary, so you know that his opinion is worthless.

argument against the person, circumstantial

In Modus Tollens the _____ is being denied

consequent

"John wore hats. John did not like the sun. John was vegetarian." These statements are logically____

consistent

"Xeno had 12 toes" This statement is logically___

contingent

"John likes all cheeses. John does not like swiss cheese." These statements are logically____

contradictory

Which logic is like an on and off switch?

deductive logic because it has to be 100% true or 100% false

_____ is the reverse of Modus Tollens and is an INVALID form

denying the antecedent

"If Lisa is in France, then she is in Europe" This statement is Logically____

equivalent

"Bill Clinton is president" This statement is logically_____

false

When is a *set* of statements logically inconsistent?

if it is *not* possible for *all* statements in the *set* to be true. At least one must be false.

When is a statement logically true?

if it is not possible for the statement to be false

When is a *set* of statements logically consistent?

if it is possible for *all* statements in the *set* to be true

When is a statement logically contingent/logically indeterminate?

if the statement is not logically true or logically false. It's possible for the statement to be true or false.

"The Bible says I may not eat shellfish. Everything the Bible says is true. I may eat shellfish." These statements are logically____

inconsistent

What is standard form?

list the premises, draw a line, write the conclusion

Logically True, False, or Contingent: Xeno had 12 toes

logically contingent

Logically equivalent or contradictory: In addition to having 12 toes, Xeno was an avid distance runner; Xeno was an avid distance runner, even though he had 12 toes

logically equivalent

Logically consistent or inconsistent: {Everyone with 12 toes requires custom racing sandals, Xeno had 12 toes, Xeno did not require custom racing sandals}

logically inconsistent

In Modus Tollens denying goes from ___term to ___term

major term to minor term

In affirming the consequent, affirming goes from ____term to ____ term

major term to minor term

In Modus Ponens affirming goes from ___ term to _____ term.

minor term to major term

In denying the antecedent, denying goes from ____term to ___term

minor term to major term

False Dilemma

narrowing down possibilities to two alternatives, one is obviously undesirable and forces the acceptance of the other.

Genetic Fallacy

rejecting a view because of its origins

Is this argument deductively true? Why or why not? Some animals are frogs Some animals are tree climbers some frogs are tree climbers

-The form is invalid because "some animals" instead of "all animals" -Therefore, the argument is not deductively true

Is this argument deductively true? Why or why not? All whales are fish All fish are airbreathers All whales are airbreathers

-The form is valid -The argument is unsound because the premises are false -Therefore, it is not deductively true

Is this argument deductively true? Why or why not? All whales are mammals All mammals are airbreathers All whales are airbreathers

-The form is valid -The argument is sound because the premises are true -Therefore, the argument is deductively true

Begging the question/arguing in a circle

-assuming what you're trying to prove -smuggling your conclusion into your premises

Argument against the person (ad hominem)

-attacking the person giving the argument instead of the argument itself -this fallacy comes in 3 varieties: abusive, circumstantial, hypocrisy

Appeal to the people (argumentum ad populum)

-attempting to convince by appealing to the natural desire we all have to be included -this fallacy includes: bandwagon, appeal to snobbery/vanity, appeal to belief, appeal to common practice

What is the criteria for inductive logic?

-strength -cogency

What is the criteria for deductive logic?

-the premises guarantee the truth of the conclusion -validity -soundness

Argument by analogy form

A is F, G, H B is F, G, H, and I A is I

What is valid form?

All F is G X is F X is G (if X is the first factor, it has to be the second factor)

What is abduction?

An inference to the best explaination in which the conclusion is supposed to explain the truth of the premises

Which type of fallacy is this? I deserve a good grade, wouldn't you agree? If you don't agree, I'm afraid about what might happen.

Appeal to force

Which type of fallacy is this? Of course God exists, every American believes that.

Appeal to people, bandwagon

Which type of fallacy is this? I need to pass this class in order to graduate, if I don't graduate, my parents will kill me. Therefore, I should recieve a passing grade in the class.

Appeal to pity

Which type of fallacy is this? The polls show that 70% of all Americans favor the death penalty. If so many people are in favor of it, it has to be right.

Appeal to popularity

Which type of fallacy is this? Everyone speeds, so speeding isn't wrong.

Appeal to the people, appeal to common practice

Which type of fallacy is this? I believe in God because the Bible tells me He exists. I know I can trust the Bible, because it is the received Word of God.

Arguing in a circle/ Begging the question

Straw man fallacy

Attacking an oversimplified version of an opponents actual position

Which type of fallacy is this? That new student told me that I am his favorite professor. He must be telling the truth, for no student would lie to his favorite professor.

Begging the question/ arguing in a circle

Which form is this argument? Explain. If it's a banana, then it's food It's not a banana Therefore it's not food

Denying the antecedent because... -the antecedent (banana) is being denied -invalid form because you can't be sure that it's NOT food even though it's not a banana. (a banana is not the only type of food) -the terms go from minor to major

Disjunctive Syllogism Valid Negate

Either P or Q Not Q P

Disjunctive Syllogism Valid Confirm

Either P or Q Q Not P

Which type of fallacy is this? Either you love your country and obey all its laws, or you are anti-american.

False dilemma

True or False Deductive logic is based on persuasion and degrees of truth

False, deductive logic is based on valid form

True or False: The wider and less conservative the conclusion, the stronger the argument

False, the narrower and more conservative the conclusion, the stronger the argument. Example: "The next trout found will be infected" is stronger than "All trout are infected"

True or False: When statements are logically equivalent, it means that they "say the same thing"

False, they express different beliefs that may turn out true under the same circumstances

Modus Tollens Negate Valid

If P, then Q Not Q Not P

Modus Ponens Affirm Valid

If P, then Q P Q

When is a statement logically false?

If it is not possible for the statement to be true

Make a Modus Ponens: If John is a father, then John is a man

John is a father Therefore, John is a man

Affirm the Consequent: If John is a father, then John is a man

John is a man Therefore, John is a father *Invalid Form*

Deny the Antecedent: If John is a father, then John is a man

John is not a father Therefore, John is not a man *Invalid Form*

Make a Modus Tollens: If John is a father, then John is a man

John is not a man Therefore John is not a father

Logically True, False, or Contingent: Xeno had 12 toes and Xeno did not have 12 toes

Logically False

Logically True, False, or Contingent: Either Xeno had 12 toes or Xeno did not have 12 toes

Logically True

Logically consistent or inconsistent: {Xeno did not require custom racing sandals, Xeno was an avid distance runner, Xeno had 12 toes}

Logically consistent

Logically equivalent or contradictory: Xeno finished some of his races; Xeno did not finish any of his races

Logically contradictory

Which form is this argument? Explain. If it's a banana, then it's food It's a banana Therefore it's food

Modus Ponens because... -the antecedent (banana) is being affirmed -valid form because a banana is a food -terms go from minor (banana) to major (food)

Which form is this argument? Explain. If it's a banana, then it's food It's not food Therefore it's not a banana

Modus Tollens because... -the consequent (food) is being denied -the form is valid because if it's NOT food it cannot be a banana, which IS food -terms go from major (food) to minor (banana)

Which type of fallacy is this? Those who support gun control are wrong; they believe that no one should have the right to defend themselves in any situation.

Straw man

Disjunctive Syllogism example

The cake has either chocolate or vanilla frosting. The cake does not have vanilla frosting. Therefore, the cake has chocolate frosting.

True or False: Denying the antecedent and affirming the consequent are fallacies

True

True or False: With analogical arguments, they are stronger when similaries cited are relevant to the target property and when there are few dissimilarites.

True

True or False: With enumeration, the larger the sample, the stronger the argument

True

Appeal to pity

Trying to support a conclusion by evoking pity in the listener

When are statements logically contradictory?

When it is not possible for the statements to have the same truth values

Is this argument an abduction? I hear scratching in the walls. I hear the sound of little paws at night. My cereal boxes have holes chewed in them. I have mice.

Yes

What is a statement?

a declarative sentence attempting to state a fact

What is an argument?

a set of statements which contains a series of premises which seek to support a conclusion

What is a tautology?

a statement that is explicitly logically true example: all animals are animals

_____ is the reverse of Modus Tollens and is an INVALID form

affirming the consequent

In Modus Ponens the _____ is affirmed

antecedent

What is a fallacy?

any mistake in reasoning

Which type of fallacy is this? 90% of those surveyed think we should not convict Clinton, so you should too.

appeal to the people, appeal to belief

Which type of fallacy is this? Of course you should cheat, all the cool people are doing it.

appeal to the people, appeal to snobbery

Accident fallacy

applying a general rule to a case it was not designed to cover

Which type of fallacy is this? Lynch says that we should spend more state revenue on education. But Lynch is a liberal Yankee from New York, so you know that his opinion is worthless.

argument against the person, abusive