CH 3 (Making Sense of Arguments)
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)
