Whenever you are presenting an argument or evaluating one,
it's important to keep the overall structure of the argument, or its criticisms, in mind.
Here are a few pointers:
1. When you present your argument:
Anticipate possible objections to it. Be prepared to answer them.
(Answering them ahead of time is often a good idea. And you can do this as bluntly as saying,
"Someone might object that____. However, I would respond to this possible objection by saying that __________.")
Point it out its strengths, of course, and admit honestly to any weaknesses.
(After all, someone else might be able to fix them for you!)
2. When you evaluate or criticize an argument:
Point out any weaknesses you find.
Is the argument's structure valid?
Are all the premises consistent with each other?
No circular reasoning involved?
No ambiguity or equivocation involved? (If there is any ambiguity or equivocation, distinguish the different senses being used)
Do the premises indeed lead to that conclusion, and only that conclusion?
Are the premises enough to arrive at the conclusion, or are they incomplete?
(If you suspect that the structure is invalid, but can't pinpoint the problem, you can always aim to create a counterexample with the same structure that obviously doesn't work.)
Are the premises true, or at least plausible, or at least supported by legitimate authorities?
If not, deny the premise(s) in question.
If a premise is true, or at least plausible, then admit (or concede) it.
If you can do neither because there is not sufficient evidence either way, be clear about its being tentative.
Is each premise clear and unambiguous? (For example, none violates what is known in law as "the Negative Pregnant" Rule, i.e., involves a denial in which it's not clear what the scope of the denial is? "Mr. Smith denies that he shot the victim with a carbine."
We want the truth.
Are there any counter-considerations that are being ignored? Any "suppressed evidence" against the argument?
We want the whole truth.
Are there any misleading implications, or any dubious tacit presuppositions guiding the argument, the line of questioning, etc.?
We want nothing but the truth.
3. When you present an opposing argument:
Be clear about whether you are offering:
a) an alternative explanation, description, definition, etc., to someone else's,
(This has its own strengths, especially if all you need to do is to show that the original account isn't the only possible one.)
b) a better alternative account than the other one(s),
c) the only possible correct account.
Be clear about where you think the burden of proof lies. Even if two people disagree on some question,
they should be able to agree on which of them has the burden of proof at any given time.
4. In all cases, keep clear how each statement is functioning.
Statements as impersonal carriers of information, or as expressions of persons or about persons?
Is Clinton's quote on the Fallacy Page really a fallacy? ("You need to know that a member of Congress who refuses to allow the minimum wage to come up ... made more money during last year's one-month government shutdown than a minimum wage worker [does in an] entire year.") Not if he's not using it to argue that the Republican policy on minimum wage is wrong. If he's making a side comment about the hypocrisy of people he'd like to see not get reelected, that's not a fallacy. It's rhetorically emotion-laden, perhaps unfairly, but is not an ad hominem fallacy. Pointing out someone's vested interests in a certain position is also legitimate, as long as that's not given as a reason in itself to reject that person's position. If, however, he's using personal remarks to imply that that person's proposals are thereby unacceptable, that's a classic ad hominem fallacy.
If I attack, say, some of the claims of the controversial Dr. Dobson (of Colorado Springs's "Focus on the Family") by attacking him personally, that's an ad hominem. However, if he is making claims on the basis of being an authority in psychology, and I attack his credentials, that's perfectly legitimate. I'm simply disputing whether he is a legitimate authority. In a sense, I'm accusing him of committing the fallacy of "appeal to illegitimate authority," and it just happens to be himself that he is appealing to as an authority.
Or, how about the southerner, who has been known to make racist comments about African Americans and Jewish people, who responds, aghast, to a pro-Minister Farrakhan remark: "But Farrakhan is a racist!" Notice that the speaker's own racist tendencies do not lessen the fact that Farrakhan has made some highly offensive (and incorrect) remarks about Jewish people, and some remarks about other "white" people that could be taken as racist (though these remarks are harder to dismiss as incorrect). The speaker him or herself is hardly in a position to be a defender of non-racism, though. So the speaker's remarks are perfectly legitimate, but the speaker as a person hasn't necessarily gained any credibility.
5. Does a premise lead independently to the conclusion, or is it dependent on other premises?
Some arguments, especially inductive ones, may involve different premises all leading independently to the conclusion. If this is so, then we can lose one or more premises without losing the conclusion. Here's one example:
(Conclusion:) City Councilman John Doe should be recalled from office. (Premises, that is, reasons why:) Because he lied to us about his past voting record. Because former co-workers from other towns don't trust him. Because he voted to demolish a historic building in the capacity of official, despite having been on the historic preservation board at the time. Because he has consistently supported the interests of developers and consistently undermined the stated desires of the majority of citizens. Because he looks like a dead fish in a blondish blow-dry.
Now, even if this fictional character didn't look like a dead fish, the other premises remain intact. Even if we decided in a fit of charity and rationality to throw out the "looking like a dead fish" premise, there are plenty of strong premises left that lead to the conclusion.
Other arguments may have only a list of premises, each of which depends on all the others. (Or, of course, there can be arguments with both kinds of premises in them.) Here's an example of an argument in which all the premises depend on each other: (From William Neblett's Sherlock's Logic (New York: Barnes and Noble), l985, p.178):
(Premises:) If the chauffeur did not commit the murder, then either the butler or the chambermaid did. "No one who was at the pub until midnight comitted the murder, because the autopsy reveals that it was committed before 11:00 p.m.. The chauffeur was at the pub until midnight. The butler could not have committed the murder, since he was out of town for the weekend. (Conclusion:) Therefore, the chambermaid committed the murder.
Here, if any one of the premises fails (say, the autopsy physician overlooked the fact that it was a very cold night which caused rigor mortis to set in early), then the whole argument fails.
6. A useful distinction: Necessary conditions are different from Sufficient conditions.
With a necessary condition for some event or thing, the thing cannot happen or exist without that condition.
With a sufficient condition for something, if the sufficient condition is there, the thing will happen.
Getting a GPA over 3.0 is a necessary condition for getting into medical school.
Getting a GPA over 3.0, in itself, is not a sufficient condition for getting into medical school. You need other things as well, such as experience in a medical setting.
For action movie minor characters, getting thrown off an airplane 20,000 feet in the air is a sufficient condition for dying. Having arch-villains drop them into shark tanks is another sufficient condition for dying. Having Voldemort or his cohorts utter a death curse at them is yet another sufficient condition for dying (well, usually). None of these, however, is a necessary condition for dying.
Cessation of all brain and heart activity is, currently, considered a good definition of someone's having died. This cessation is both a necessary and sufficient condition for dying.
We can use these terms to refer to causes and their effects through time (my dropping an egg while carrying it is probably a sufficient condition of breaking it), or we can use them to categorize things (live birth rather than egg-laying was regarded as a necessary condition for a species to be considered a mammal -- until platypuses and their relatives were discovered).
Optional, for people who've had formal logic:
The relation known as "implication," designated by the horseshoe symbol or arrow, is one of necessary and sufficient conditions.
It is just the statement that "If something-or-other-is-true, then something-else-will-be-true."
It's usually just designated as "If p then q."
E.g. "If it doesn't snow here on New Year's Day , then we'll play football here."
Or "If the snake has red and yellow stripes next to each other, then the snake is poisonous."
In any true implication, the antecedent part, the p, is a sufficient condition for the q part. And the consequent part, the q, is a necessary condition for the p part.
This may seem strange, but from an abstract, logical point of view, it'll make sense.
The snake having contiguous red and yellow stripes is sufficient for us to conclude that the snake is definitely a member of a poisonous variety.
(However, that coloring is not necessary for us to conclude the poisonousness, since water moccasins are black but also poisonous.)
Similarly, the snake's being of a poisonous variety is "necessary" for it to have the red and yellow contiguous stripes,
since we cannot get the contiguous red and yellow stripes unless we have the membership in a venomous variety!