for Recall
Words identifying premises:
for, since, because, due to the fact that, given, considering, etc. so, hence, thus, therefore, it must be that, consequently, etc.
Words for identifying conclusions:
Example (no such words): It's really cold outside.
You'll freeze to death if you go out there.
Sailing the three C's
Need to read arguments:
carefully critically charitably identifying each and all assertions determining if the argument is valid and/or sound trying to make the arguments as plausible as possible
In brief this means:
Implicit premises
Example: Because it's raining outside, you'll get all wet when you go out there.
P1) It's raining out side P2) If it's raining outside you'll get wet (Implicit). C) You'll get wet (when you go).
Example: Bob will get you the best deal on your car because he's a used car salesman.
P1) Bob is a used car salesman. P2) All used car salesmen get the best deals. (Implicit) C) Bob will get you the best deal on your car.
Recall
Validity:
If the premises are true the conclusion must be true
Soundness
Valid; and Premises are true
Valid forms
Modus Ponens
If A then B A Therefore B
Modus Tollens
If A then B ~B Therefore ~A
Conditional truth table
Truth table for `A->B' i.e. If A then B We can verify both MP and MT.
A T T F F B A->B ~A ~B T T F F F F F T T T T F F T T T
Note: A->B = ~A or B).
Examples of `if...then'
Equivalent to S->B: If you're smart then you're beautiful. If you're smart, you're beautiful. You're beautiful if you're smart. You're smart only if you're beautiful.
Valid forms (cont.)
Disjunctive syllogism
A or B not A Therefore B
MP Equivalence
A->B (i.e. ~A v B) A (i.e., not not A) Therefore B
Valid forms (cont.)
Hypothetical syllogism
A -> B B -> C Therefore A->C
Two MP applications
if A then B if B then C A (hypothesis, i.e., 'if') B C Therefore, if A then C
Quantifiers
Quantifiers are `all' or `some' in a sentence MP applies for `all' but not `some'
Example (invalid): `Some dogs are black' 'Some black things are bigger than earth' 'Therefore some dogs are bigger than earth`
Instead, use Venn diagrams
Venn diagrams
A
B
A
B
All A are B
Some A are B
Etc... (No A are B; i is B; No C is B and D)
Valid forms (cont.)
Universal syllogism
All A are B All B are C So All A are C
C A B All B are C
Two MP applications
All A are B = (x)Ax->Bx All B are C Ax (hypothesis, i.e., 'if') Bx Cx Therefore, All A are C
All A are B
So, All A are C
Valid forms (cont.)
Universal-particular syllogism
All A are B Individual i is A Therefore, i is B All A are B Individual i is non-B Therefore, i is non-A
B A *i
Modus Ponens
(x)Ax->Bx Ai Therefore Bi
Modus Tollens
(x)Ax->Bx ~Bi Therefore ~Ai
(Note: `non' is often not the same as `not' e.g. non-friendly versus not friendly).
Summary
There is no point in trying to memorize all of the possible valid argument forms. There are an infinite variety. Nevertheless, the ones above are by far the most common. The power of formal logic lies in its ability to systematically organize valid argument forms (e.g., seeing how they are all versions of MP).
Invalid arguments
To show an argument is invalid, you can:
describe a situation in which the premises are true and the conclusion is false; or show that the argument fits a typical form of invalid argument
For instance...
Invalid forms
Affirming the consequent
If A then B B Therefore A
Example of affirming the consequent
If I punch you in the nose it bleeds. Your nose is bleeding. Therefore I punched you in the nose. (Invalid because of other possible nasal issues)
Invalid forms
Denying the antecedent
If A then B not A Therefore not B
Example of denying the antecedent
If I push the book then it will move. I didn't push the book. Therefore it didn't move. (Invalid because of other possible causes)
Being charitable
Often possible to paraphrase the explicit statements in an argument This should be done to make the argument more compact and/or more obviously valid (e.g. J.S. Mill to 4 short premises, p. 35). Essential that the premise as paraphrased says exactly same thing as the original.
Charitable reconstruction
The economy will be in big trouble, because it cannot tolerate the continuation of low interest rates, but such rates will continue. Better re-phrasing: "If low interest rates continue, then the economy will be in big trouble." (plus "Such rates will continue")
Determining validity
We can summarize the steps needed to determine the validity of an argument as follows:
A. Identify the conclusion. (careful) B. Identify the premises. (careful) C. Identify reasonable and stated premises. (charitable) D. Determine whether the argument is valid (if not considered conservative modifications that would make it valid). (critical)
Islamic-world argument
If America and the world's other governments in their completely justified, very necessary, and much overdue "war against terrorism" will also commit part of this long and difficult struggle to the creation of a good, right, and just society, if they do so in a way that follows the accepted standards of justice, and if they harm no innocent citizens of any nation in the process, then it should be expected they will receive the full and continued support of virtually every Muslim in the World. Regarding the issue of exploitation, particularly economic exploitation, we view as highly significant a comment made in an address to the people of America several years ago by then President of the United States, Bill Clinton, who said, "America with about five percent of the world's population utilizes about forty percent of the world's resources; and, we are going to have to work ever harder to keep it that way." When you are an African parent sitting homeless in the dust, hungry and thirsty, while your children die slowly before your eyes it is easy to see the blatant unfairness of this economic disparity. Is it then surprising that there will be anger toward America? Allah has told us that wealth must be equitably distributed among the world's and people nations.
Islamic-world argument
Main argument
P1) If America commits part of their struggle to the creation of a just society and follow accepted standards of justice and harm no innocent citizens then they will receive the support of all Muslims. P2) America does not follow the accepted standards of justice. C1) Therefore they won't receive support of all Muslims. (invalid)
Argument for P2
P3) If you exploit other nations you do not follow the accepted standards of justice. P4) Bill Clinton made a statement showing that the Americans will continue to attempt to exploit other nations. Therefore C2/P2. (valid)
Argument structure
Draw the argument structure:
P3 P2/C2 P4 P1
C1
Simple repair?
If they want to get support then follow justice... Or, "If and only if"
Criticizing valid arguments
If the argument is definitely valid, then, as a critic you have at least three remaining possibilities:
1. 2.
3.
Show that one of the premises is false (the argument is unsound) Suggest that one of the premises is unjustified (that is, demand more reasons for thinking that premise is true) Show that the argument is unclear or vague
Normative arguments
`Should' arguments often in moral reasoning (determining what you should do). Easy to spot (look for `ought/should') `Naturalistic fallacy' no statements of facts can lead to a `should' conclusion. So any attempt to establish moral claims from (strictly) factual ones is invalid. Nevertheless, there are good moral argument forms and bad ones.
Normative arguments
General form for good normative arguments:
1) Success condition (SC): Doing A will achieve B. 2) Optimal means condition (OMC): Doing A is the best way to achieve B. 3) Ends justify the means condition (EJM): All things considered, doing A (and achieving B) is better than not achieving B. 4) Conclusion: Therefore A should be done.
Simpson's example 1
Abe: Son, we want to help you catch that plug-ugly yegg (cat burglar trying for world's largest cubic zirconium). Homer: [sweet] Dad, the best way for you to help is to set a good example. [serious] Just stand around and don't steal anything. Analysis (`good normative argument'):
SC: Standing around and not stealing will help OMC: Standing around and not stealing is the best way to help EJM: All things considered, standing/not stealing is better than not helping Conclusion: You should just stand around/not steal
Simpson's example 2
Tenille: Tell me, young man, what do you want out of life? [While Tenille was speaking, Homer was busy trying to reach a bowl of peas from the center of the table.] Homer: I want peas! Tenille: We all want peace! But it's always just out of reach. Homer: [moans] Uh huh? Tenille: So, what's the best way to get peace? Homer: With the knife! Tenille: Exactly! Not with the olive branch, but the bayonet! Ha, ha, Simpson, you're like the son I never had.
Analysis (`poor normative argument'):
SC: Using a force will get peace OMC: Using force is the best way to get peace EJM: All things considered, getting peace is better than not using force Conclusion: You should use force
Normative arguments
Clearer (?) Example:
1) Success condition (SC): Going to class will give me better insight into the material. 2) Optimal means condition (OMC): Going to class is the best way to get better insight into the material. 3) Ends justify the means condition (EJM): All things considered, going to class is better than not gaining insight into the material. 4) Conclusion: Therefore I should go to class.
Normative arguments
Strictly speaking, this is not a valid argument form. Why? Nevertheless, if one of these kinds of premises is missing/false that suggests a (big) problem. Note that this argument form can be made valid by including the premise: In all cases, we should do what is best (given EJM). Despite that, usually these arguments demand probabilistic reasoning (especially SC).
Vagueness and meaning
2000 years ago, Sophists exploited vagueness (still do). What are sources and pitfalls of vagueness? Vagueness and Context
Example: Ann went to the store. She bought some muffins. ('She' refers to the individual 'Ann'.) Example: Ann went near the store. She got muffins while she was there. ('There' refers to 'a vicinity' near the store, which could be any number of places.)
Vagueness and meaning (cont.)
Ambiguity
Lexical ambiguity
Example: He kicked his can.
Syntactic ambiguity
Example: Defining your terms clearly strengthens your argument.
Contextual ambiguity
Example: John's father wanted the key with him.
Vagueness and meaning (cont.)
Equivocation
P1) Hot dogs are better than nothing. P2) Nothing is better than steak. C) Therefore, hot dogs are better than steak. The existence of a law means that there must be a law maker. But we know that the law of gravity and other scientific laws have not been made by any human law maker. So it follows that there must be a non-human law maker, God. Everybody loves somebody. Therefore, everybody loves one of us.
Vagueness and meaning (cont.)
Connotation (i.e. using emotion to affect reasoning)
Example: He sure is <<debonaire, easy-going, devilmay-care, reckless>> Euphemism
Example: neutralize, collateral damage, friendly fire,
Instead of content
Example: "Have a coke and a smile" "Pepsi, taste of a new generation" "Toyota Corolla. It just wants to have fun."
Jargon/Bafflegab (why? it works)
Example: Digging a hole: The author of this report utilized a
manually operated soil displacement implement to facilitate the synergistic excavation of a negative volume of mineral aggregate relative to a datum plane defined at ground level.
Vagueness and meaning (cont.)
Connotation (cont.)
Loaded Verbs
Example: Surely you realize that using jargon just confuses the audience. Versus: Surely you believe that using jargon just confuses the audience.
Insinuation
Example: Today, you were on time Example: You should not speak ill of your friends.
Question and Example
Question Example: Florsheim Magnetic Shoes (others include BIOFlex insoles/shoes).