9 - Valid And Sound Arguments
The author asserts that "validity is the most important concept in critical thinking."
An argument is valid if there is no logically possible condition in which the premises are true and the conclusion is false. Or said another way, if you accept the premises to be true, you must also accept the conclusion as true.
It is possible to construct a good argument in which the conclusion comes out to be false - if one or more of the conditions are not met, then the conclusion will fail. That is, "If you want to stay dry when it is raining, carry an umbrella" is a valid argument, even if it is not raining at the moment.
Neither is the validity of one argument disproven by the validity of another: "If you want to protect yourself from the sun when it is shining, carry an umbrella" presents another set of conditions under which you should carry an umbrella, but does not mean that the first augment is not true as well.
Said another way, the validity of an argument is about the logical connection of its premises to its conclusion.
It's also noted that a valid argument can have false premises but a true conclusion - it's not about whether the argument is right, or whether the conditions are filled, but success in getting to the conclusion by virtue of the premises that makes the argument valid.
The author returns to the notion of possibility and likeliness - an argument can be valid if the premises are possible, but unlikely to be met. In such instances the argument may be implausible, but is not invalid.
An argument is invalidated when all of its conditions can be satisfied, yet the conclusion is false. Any situation that causes to be so is the "invalidating cou8nterexample" that breaks the argument.
Patterns Of Valid Arguments
The ability to identify an invalidating counterexample shows an argument to be invalid, but the weakness of this method of attack is that we may fail to find such an example. The argument does not necessarily stand as valid in such an instance - but it cannot be dismissed by that technique. Instead, the argument itself may be picked apart.
Modus Ponens
A common form of argument suggest its conclusion will be true when a condition is met: "if the dog detects an intruder, he will bark" leads us to the expectation that if the dog barks, it is because he detected an intruder.
The weakness of this argument is when the conditions are not exhaustive. The dog may bark for some other reason than detecting an intruder, hence the premises are not sufficient to the conclusion.
Modus Tollens
This is a very similar argument, though it is often considered in the nevative: "If the dog detects an intruder, he will bark" leads to the notion that if the dog did not bark, he did not detect the intruder.
This is likewise a weak argument because it is assumed that there is a guaranteed connection between the two - that the dog could not possibly refrain from barking if he detects an intruder - which seldom holds.
Disjunctive Syllogism
The disjunctive syllogism sets up an either-or choice and suggests that if one is not accepted, the other will be. I will have soup or a sandwich for lunch. If I did not have soup, I must have had a sandwich.
This likewise has a weakness in that the list of alternatives must be exhaustive and exclusive. If I could have had something else, or chose to have neither, the argument is not valid.
Hypothetical Syllogism
The hypothetic syllogism sets up a chain of events, which cause one another: "If I do not get out of bed, I cannot go to work; if I do not go to work I will not get paid; therefore if I do not get out of bed I will not get paid."
This is a valid argument, but the chain of causation is only as string as its weakest link.
Constructive/Destructive Dilemma
A constructive dilemma has two independent premises, which are linked by a third to lead to a conclusion.
If my stock does well, I will sell it and buy a horse; but if it does poorly, I will sell it adopt a dog. Either my stock will do well or it will do poorly, so I am certain to soon have a horse or a dog.
The author explains the "destructive dilemma" in the same way, though it will speak to what will not happen.
If my stock does not do well, I will not buy a horse; but if it does not do poorly, I will not adopt a dog. Either I will not buy a horse or I will not adopt a dog, so my stock will not do well or it will not do poorly.
(EN: Not sure If I got that quite right, with all the "not"s flying about.)
Reductio ad Absurdum
This technique attempts to suggest that a statement is true because the opposite is absurd: a coin has weight because otherwise it would float in the air.
In mathematics, reductio proofs are also known as indirect proofs, because the statement is not proven in itself. Euclid made heavy use of them in mathematics - a number is prime because it cannot be divided is an example of a reduction proof.
(EN: Reductio proofs are also the source of many logical fallacies and should be approached and regarded with extreme discretion. "Without government there would be chaos and mayhem" is a redictio fallacy.)
Combining Patterns to Form More Complex Arguments
The patterns the author has described are all very simple, but they can be combined into more complex arguments when the statements that support the main argument are themselves arguable.
Outlining the argument is useful when presenting or evaluating a complex argument to understand the logical structure.
Arguments Involving Generalizations
A generalization is a statement that attempts to describe the properties of a certain class of objects in a broad and all-inclusive sense. The author suggests three classes:
- Universal generalizations - "Every X is Y"
- Existential generalizations - "Some X is Y, so at least one X is Y"
- Statistical generalizations - "Most (70%) of X are Y"
The problem of generalization is that it suggests that because something is sometimes true, it should be accepted as always true, when it is not. They are also easily negated by finding a single exception.
Another point to make about existential and statistical generalization is the statement that "some" or "most" have a quality is an admission that "not all" have that quality, or some do not have that quality.
Generalizations can also be reduced in their scope by qualifying the subject. "Everyone is here" implies that (literally) every person in the world is present, whereas "everyone who was invited is here" implies a smaller group and has the possibility of being true. This seems rather silly, but deals with the importance of clarity and specificity in stating an argument - when you expect that a limiting qualification is understood, it may not be.
Using generalizations such as "every" or "most" is an unfortunate habit that leads to a great deal of unnecessary discussion and can be harmful to the credibility of the speaker - but it is at the same time tedious to constantly quantify a statement, particularly when it is of marginal relevance.
Soundness
The soundness of an argument is not determined by whether it is right or wrong, but by the relation of its premises to its conclusion: if all the premises are true, so is the conclusion. An argument that is found to be wrong may still be sound and valid.
While the ultimate goal of logic is to discover truth and recognize arguments that are right, a prerequisite is in developing arguments that are sound. To have the appearance of being right, while being unsound, is ultimately to fail.