CH 3 (Making Sense of Arguments)

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Universal Negative

No A are B

particular affirmative

Some A are B

particular negative

Some A are not B

True or False. A valid argument can have false premises.

True

disjunction

-type of statement P or Q

What are the valid argument patterns?

1. affirming the antecedent (modus ponen) if p, then q. p therefore q 2. denying the consequent (modus tollen) if p then q. not q therefore not p 3. hypothetical syllogism if p then q. if q then r. therefore if p then r 4. disjunctive syllogism either p or q. not p. therefore q. either p or q. not q. therefore p.

What are the invalid argument patterns?

1. denying the antecedent if p, then q. not p therefore not q 2. affirming the consequent if p then q. q therefore p

What is this an example of? If Mars has life, then Mars has water.

Conditional statement

True or False. A valid argument can have true premises and a false conclusion.

False

Which type of statements are categorical?

Universal affirmative Universal negative Particular affirmative Particular negative

Counterexample instance

When an argument is shown to have true premises and false conclusion thus making the argument invalid

Unsound argument

argument is either invalid or it's valid but has at least 1 false premise

Uncogent argument

argument is either weak or it's strong but nevertheless has false premises

Latin for affirming the antecedent

modus ponen

Universal Affirmative

All A are B

universal syllogism

All A are B. All B are C. Therefore, all A are C. VALID

weak argument

an inductive argument that fails to provide probable support for its conclusion -the inductive argument does not endow the conclusion with a probability of 50%

strong argument

an inductive argument that succeeds in providing probable-but not conclusive-logical support for its conclusion -an inductively strong argument is such that if its premises are true, its conclusion is probably or likely to be true

consequent

the 2nd statement in a conditional statement (the THEN part)

What logical conclusion can you draw about an argument that is valid and has a true premises?

the argument must have true conclusions

True or False. A valid argument can have false conclusion.

True

What are four indicator words or phrases that suggest an argument is probably deductive?

-it necessarily follows that -it logically follows that -absolutely -certainly -necessarily

Which types of statements are truth-functional?

Negation Conjunction Disjunction Conditional Bi-conditional

Is it possible for a valid argument to have true premises and a false conclusion?

No, it's not possible. A deductively valid argument is such that if the premises are true , its conclusion must be absolutely, positively be true.

negation

Not P

truth-preserving

a characteristic of a valid deductive argument in which the logical structure guarantees the truth of the conclusion if the premises are true

What are the 2 types of arguments?

deductive argument and inductive argument

Conditional

-type of statement If p, then q. P is antecedent; q is consequent

syllogism

a deductive argument made up of 3 statements--2 premises and 1 conclusion

The terms valid and invalid apply to what type of arguments?

deductive arguments

all A are B. x is not B. Therefore x is not A VALID

universal counter-instantiation

What are the 2 forms of quasi-syllogism

universal counter-instantiation: all A are B x is not B thus, x is not A universal instantiation all A are B x is A thus x is B -both are valid

All A are B. All B are C. Therefore, all A are C.

universal syllogism; valid

What type of argument is the following? 49% of A are B x is A therefore x is B

weak argument

How are deductive arguments truth-preserving?

-a deductively valid argument is such that if its premises are true, its conclusions must be true. That is,if the premises are true, there's no way that the conclusion can be false -a deductively valid argument has the kind of logical structure that guarantees the truth of the conclusion if the premises are true. B/c of guarantee of truth in the conclusion, deductively valid arguments are truth preserving -logical structure refers not to the content of an argument but to its construction, the way the premises and conclusion fit together

hypothetical syllogism

-all 3 statements are conditional and the argument is always valid - if p then q. if q then r. therefore if p then r -AKA chain arguments

What makes up a good argument?

-has to have the proper structure (logical validity or logical strength) -has to have true premises (sound or cogent arguments are good arguments)

What are four indicator words or phrases that suggest an argument is probably inductive?

-likely -probably -chances are -odds are -it is plausible that

In what ways are conclusions of deductive arguments absolute?

-the kind of support that a deductive argument can give a conclusion is absolute b/c either the conclusion is shown to be true, or not. There is no sliding scale of truth or falsity -However, the support that an inductive argument can provide a conclusion can range from weak to extremely strong

What are the four steps involved in determining whether an argument is deductive or inductive, sound or cogent? (steps in evaluating an argument)

1. Find the conclusion and then the premises 2. Ask: is it the case that if the premises are true that the conclusion MUST be true? if yes, treat the argument as deductive b/c it's likely meant to offer conclusive support for its conclusion. The argument is then deductively valid. Check to see if it's sound If no, go to next step 2. Ask: Is it the case that if the premises are true that the conclusion is PROBABLY true? if yes, treat the argument as inductive b.c it's likely meant to offer probable support for its conclusion. The argument is then inductively strong. Check to see if it's cogent. If no, go to next step 4. Ask: is the argument intended to offer conclusive or probably support for its conclusion, but fails to do so? If you reach this step, you have already eliminated 2 possibilities: a valid argument and a strong one. Remaining options are invalid argument or weak one. 2 guidelines to determine what type of (failed) argument is intended. Generally if an argument looks deductive or inductive b/c of its form assume that it is intended to be so. Generally, i an argument looks deductive or inductive b/c of indicator words (& its form yield no clues) assume that it is intended to be so.

Are the following argument forms valid All A are B x is B thus x is A All A are B x is not A therefore x is not B

No, they're invalid categorical forms

Are inductive arguments truth-preserving? Why or why not?

No. An inductively strong argument is such that if its premises are true, it conclusion is likely or probably true. -The structure of an inductively strong arument cannot guarantee that the conclusion is true if the premises are true--but the conclusion can be rendered probable and worthy of acceptance -b/c the truth of the conclusion can't be guaranteed by the truth of the premises, inductive arguments are not truth preserving

True or False. A valid argument can have false premises and false conclusion and still be valid.

True

True or false. If you put forth a strong inductive argument and you know the premises are questionable, then you know that the conclusions also can't be trusted.

True

True or false. Invalid forms do have counterexample instances--that is, where the premises may be true but conclusion is false (TT/F)

True

True or false. Valid forms do not have substitution instances that are counterexamples. (Valid forms have no counterexamples)

True

True or false.The order in which disjuncts occur does not matter. Truth is still preserved

True

Substitution instance

When you plug something in for the variables

Can a valid argument have false premise and a false conclusion? false premise and a true conclusion?

YES

How is the counterexample method used to evaluate validity?

You check for validity by simply devising a parallel argument that has the same form of the argument you're evaluating (the test argument) but has obviously true premise and false conclusion. -Remember, any argument having true premises and false conclusion cannot be valid, so if you can invent such an argument that has the same pattern as the test argument, you've proved that the test argument is invalid

invalid argument

a deductive argument that fails to provide logical conclusive support for its conclusion -conclusion doesn't logically follow from the premises

valid argument

a deductive argument that succeeds in providing logical conclusive support for its conclusion -The conclusion logically follows from the premises -a deductively valid argument is such that if its premises are true, its conclusions must be true. That is,if the premises are true, there's no way that the conclusion can be false -can have false premises and false conclusion, false premise and true conclusion, or true premise and true conclusion. It cannot have a true premise and false conclusion -IT'S ABOUT FORM!! NOT CONTENT

sound argument

a deductively valid argument that has true premises is said to be sound -a sound argument is a good argument, which gives you reason for accepting its conclusion

if p, then q. p therefore q

affirming the antecedent (modus ponen); valid

if p then q. q therefore p

affirming the consequent; invalid

universal counter-instantiation

all A are B x is not B Therefore, x is not A (VALID)

quasi-syllogism (one type is universal instantiation)

all A are B. x is A. Therefore, x is B -valid -A,B are categories x is an individual

if p, then q. not p therefore not q

denying the antecedent; invalid

if p then q. not q therefore not p

denying the consequent (modus tollen); valid

Either Paul is a liar or he is a lunatic

disjunction

either p or q. not p. therefore q either p or q. not q. therefore p.

disjunctive syllogism; valid

disjunctive syllogism

either p or q. not p. therefore q; either p or q. not q. therefore p valid

if p then q. if q then r. therefore if p then r

hypothetical syllogism; valid

denying the consequent (modus tollen)

if p then q. not q therefore not p -always valid -if premises are true, conclusion must be true

affirming the consequent

if p then q. q therefore p -invalid b/c it's possible for the premises to be true and the conclusion false

denying the antecedent

if p, then q. not p therefore not q -invalid b/c it's possible for the premises to be true and the conclusion false

affirming the antecedent (modus ponen)

if p, then q. p therefore q -any argument in modus ponen form is valid--if the premises are true, then the conclusion must absolutely be true -the premises can be true or false -if its in the form of modus ponen it's valid regardless of content of the statement

What type of argument is the following? 1.) 90% of A are B 2.) x is A therefore x is B

inductive argument

cogent argument

inductively strong arguments that have true premises -good inductive arguments are cogent

Latin for denying the consequent

modus tollen

If the simple statement is, ''Shamu is a whale'' Then what is the following an example of: ''It is not true that Shamu is a whale''

negation

deductive argument

premises are intended to provide logically conclusive support for its conclusion -that is, the premises are intended to guarantee the truth of the conclusion. If premises are true, conclusion must be true

inductive argument

premises are intended to provide probable-not conclusive-support for its conclusion -that is, premises, at best, are intended to make the conclusion probable or likely to be true

all A are B. x is A. Therefore, x is B.

quasi-syllogism (SPECIFICALLY UNIVERSAL INSTANTIATION);valid

What type of argument is the following? 51% of A are B x is A therefore x is B

slightly strong argument

What logical conclusion can you draw about an argument that is valid but has a false conclusion?

the argument has a least one premise that's false

antecedent

the first statement in a conditional statement (the IF part)


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