Mod 2: Recognizing Arguments, Explanations, Deductive & Inductive Arguments

List the common Premise Indicators:

-since -as indicated by -because -the reason is that -for -for the reason that -as -may be inferred from -follows from -may be derived from -as shown by -may be deduced from -inasmuch as -in view of the fact that

List the common Conclusion Indicators:

-therefore -for these reasons -hence -it follows that -so -I conclude that -accordingly -which shows that -in consequence -which means that -consequently -which entails that -proves that -which implies that -as a result -which allows us to infer that -for this reason -which points to the conclusion that -thus -we may infer

Every argument makes the claim that its premises provide grounds for the truth of its conclusion; that claim is the mark of an argument. However, there are 2 very different ways in which a conclusion may be supported by its premises, & thus there are 2 great Classes of Arguments:

1. the Deductive 2. the Inductive.

Truth & falsehood, as opposed to validity & invalidity, are attributes of INDIVIDUAL propositions. Explain:

A single statement that serves as a premise in an argument may be true; the statement that serves as its conclusion may be false. This conclusion might have been validly inferred, but to say that any conclusion (or any single premise) is ITSELF valid or invalid makes no sense.

Define: Conclusion Indicator

A word or phrase (such as "therefore" or "thus") appearing in an argument & usually indicating that what follows it is the CONCLUSION of that argument.

V. Some VALID arguments have FALSE premises & a TRUE conclusion:

All fishes are mammals. All whales are fishes. Therefore all whales are mammals. (The conclusion of this argument is TRUE, as we know; moreover, it may be validly inferred from these two premises, both of which are wildly false).

II. Some VALID arguments contain only FALSE propositions—false premises & a false conclusion:

All four-legged creatures have wings. All spiders have exactly four legs. Therefore all spiders have wings. (This argument is valid because, if its premises were true, its conclusion would have to be true also—even though we know that in fact both the premises & the conclusion of this argument are FALSE).

I. Some VALID arguments contain only TRUE propositions—true premises & a true conclusion:

All mammals have lungs. All whales are mammals. Therefore all whales have lungs.

VII. Some INVALID arguments, of course, contain ALL FALSE propositions—false premises & a false conclusion:

All mammals have wings. All whales have wings. Therefore all mammals are whales.

VI. Some INVALID arguments also have FALSE premises & a TRUE conclusion:

All mammals have wings. All whales have wings. Therefore all whales are mammals. (From Examples V & VI taken together, it is clear that we cannot tell from the fact that an argument has FALSE premises & a TRUE conclusion whether it is VALID or INVALID).

Arguments that depend on rhetorical questions are:

Always suspect. -Because the question is neither true nor false, it may be serving as a device to SUGGEST the truth of some proposition while avoiding responsibility for ASSERTING it. That proposition is likely to be dubious, & it may in fact be false.

Define: Rhetorical Question [erotesis]

An utterance used to make a statement, but which, because it is in interrogative form & is therefore neither true nor false, does not literally assert anything.

Enthymemes are . . .

Arguments in everyday discourse which very often rely on some proposition that is understood (implicitly) but not stated.

When the claim is made that the premises of an argument (if true) provide incontrovertible grounds for the truth of its conclusion, that claim will be either:

Correct or not correct. -If it is correct, that argument is VALID. -If it is not correct (that is, if the premises when true fail to establish the conclusion irrefutably although claiming to do so), that argument is INVALID.

For logicians, the term validity is applicable only to:

Deductive arguments.

Passages that appear to be arguments are sometimes not arguments but:

Explanations. -In an explanation, one must distinguish WHAT is being explained from what the explanation IS. -The appearance of words that are common indicators—such as "because," "for," "since," & "therefore"—cannot settle the matter, because those words are used both in explanations AND in arguments (although "since" can sometimes refer to temporal succession). -We need to know the intention of the author.

(T/F): If a deductive argument is valid, additional premises can possibly add to the strength of that argument.

False.

(T/F): The central task of deductive logic is to discriminate weak arguments from strong ones.

False.

IV. Some INVALID arguments contain only TRUE premises & have a FALSE conclusion. This is illustrated by an argument exactly like the previous one (III) in form, changed only enough to make the conclusion false:

If Bill Gates owned all the gold in Fort Knox, then Bill Gates would be wealthy. Bill Gates does not own all the gold in Fort Knox. Therefore Bill Gates is not wealthy. (The premises of this argument are true, but its conclusion is false. Such an argument cannot be valid because it is impossible for the premises of a valid argument to be true & its conclusion to be false).

III. Some INVALID arguments contain only TRUE propositions—all their premises are true, & their conclusions are true as well:

If I owned all the gold in Fort Knox, then I would be wealthy. I do not own all the gold in Fort Knox. Therefore I am not wealthy. (The true conclusion of this argument does not follow from its true premises. This will be seen more clearly when the immediately following illustration is considered).

Define: Premise Indicator

In an argument, a word or phrase (like "because" & "since") that normally signals that what follows it are statements serving as premises.

A Deductive Argument makes the claim that:

Its conclusion is supported by its premises conclusively (explicitly or implicitly). -By contrast, an Inductive Argument does NOT make such a claim.

A deductive argument is valid when it succeeds in:

Linking, with logical necessity, the conclusion to its premises. -Its validity refers to the relation between its propositions—between the set of propositions that serve as the PREMISES & the one proposition that serves as the CONCLUSION of that argument. -If the conclusion follows with logical necessity from the premises, we say that the argument is VALID. -Therefore validity can never apply to any single proposition by itself, because the needed relation cannot possibly be found within any one proposition.

Arguments are sometimes obscure because:

One (or more) of their constituent propositions is not stated but is ASSUMED to be understood.

Questions can serve most effectively as:

Premises, when the answers assumed really do seem to be clear & inescapable. -In such cases the readers (or hearers) are led to provide the apparently evident answers for themselves, thus augmenting the persuasiveness of the argument.

The validity of an argument depends only on the:

Relation of the premises to the conclusion.

Eg. Explanation or Argument? Humans have varying skin colors as a consequence of the distance our ancestors lived from the Equator. It's all about sun. Skin color is what regulates our body's reaction to the sun and its rays. Dark skin evolved to protect the body from excessive sun rays. Light skin evolved when people migrated away from the Equator and needed to make vitamin D in their skin. To do that they had to lose pigment. Repeatedly over history, many people moved dark to light and light to dark. That shows that color is not a permanent trait. —Nina Jablonski, "The Story of Skin," The New York Times, 9 January 2007

This is essentially an explanation. What is being explained is the fact that humans have varying skin colors. The explanation is that different skin colors evolved as humans came to live at different distances from the Equator & hence needed different degrees of protection from the rays of the sun. One might interpret the passage as an argument whose conclusion is that skin color is not a permanent trait of all humans. Under this interpretation, all the propositions preceding the final sentence of the passage serve as premises.

(T/F): 1. Truth & falsity are attributes of individual propositions or statements. 2. Validity & invalidity are attributes of arguments.

True (both).

(T/F): Of the several propositions in an argument, some (or all) may be true & some (or all) may be false. However, the argument as a whole is neither true nor false.

True.

(T/F): The central task of inductive arguments is to ascertain the facts by which conduct may be guided directly, or on which other arguments may be built.

True.

(T/F): Inductive arguments make weaker claims than those made by deductive arguments.

True. (Because their conclusions are never certain, the terms validity & invalidity do NOT apply to inductive arguments).

(T/F): Although every deductive argument makes the claim that its premises guarantee the truth of its conclusion, not all deductive arguments live up to that claim.

True. (Deductive arguments that fail to do so are invalid).

(T/F): Because an inductive argument can yield no more than some degree of probability for its conclusion, it is always possible that additional information will strengthen or weaken it.

True. (Newly discovered facts may cause us to change our estimate of the probabilities, & thus may lead us to judge the argument to be better (or worse) than we had previously thought. In the world of inductive argument—even when the conclusion is judged to be very highly probable—ALL the evidence is never in).

Define: Truth

Truth is the attribute of those propositions that assert what really IS the case.

If an author writes "Q because P," how can we tell whether he intends to explain or to persuade?

We can ask: -What is the status of Q in that context? -Is Q a proposition whose truth needs to be established or confirmed? In that case, "because P" is probably offering a premise in its support; "Q because P" is in that instance an ARGUMENT. -Or is Q a proposition whose truth is known, or at least not in doubt in that context? In that case, "because P" is probably offering some account of why Q has come to be true; "Q because P" is in that instance an EXPLANATION.

The unstated premise on which an enthymeme relies may:

a) not be universally accepted b) be uncertain or controversial c) An arguer may deliberately refrain from formulating that critical premise, believing that by allowing it to re-main tacit, the premise is shielded from attack.