"However, when someone wants to make judgments that can be completely relied upon, their only solid foundation will be correct reasoning."

1.2 Propositions and Arguments

"In reasoning we construct and evaluate arguments; arguments are built with propositions."

A. Propositions

Propositions: "the building blocks of our reasoning. A proposition asserts that something is the case or it asserts that something is not. . . . every proposition either asserts what really is the case, or it asserts something that is not. . . . every proposition is either true or false."

We are uncertain about some truth propositions, e.g. when somebody proposes that life exists on other planets. May or may not be true.

Because a question, an exclamation, and a command assert nothing, they are not propositions.

Although LANGUAGE is used to assert a proposition, the language used is NOT the proposition: as is evidenced in the fact that propositions can be enunciated by different languages.“ Proposition is the term we use to refer to what it is that declarative sentences are typically used to assert."

Although a "STATEMENT" is not exactly the same as a "proposition," many times it IS used in Logic in the same way as we use "proposition."

CONTEXT can be very important in determining whether or not a proposition is true. E.g. the following statement would be true in 1869 but false in 2011: "The largest state in the United States was once an independent republic."

Propositions can be SIMPLE (the largest state example) and also COMPOUND ("The Amazon Basin produces roughly 80 percent of the Earth's oxygen, creates much of its own rainfall, and harbors many unknown species." This is also an example of a CONJUNCTIVE proposition.

The following MUST be irregular propositions since neither truly assert:

1. DISJUNCTIVE (or ALTERNATE) proposition: none of the components of the proposition are asserted.
2. HYPOTHETICAL (CONDITIONAL) proposition: "If . . ., then . . " neither component is asserted.

"In logic, the internal structure of propositions is important."

B. Arguments

"With propositions as building blocks, we construct arguments. In any argument we affirm one proposition on the basis of some other propositions. . . . an inference is drawn. Inference is a process that may tie together a cluster of propositions. Some inferences are warranted (or correct); others are not. The logician analyzes these clusters, examining the propositions with which the process begins and with which it ends, as well as the relations among these propositions. Such a cluster of propositions constitutes an argument. Arguments are the chief concern of logic.

Argument is a technical term in logic." ARGUMENT: "any group of propositions which one is claimed to follow from the others, which are regarded as providing support for the truth of that one. For every possible inference there is a corresponding argument."

An argument is not simply a cluster of propositions; rather it is a cluster "with a structure that captures or exhibits some inference. We describe this structure with the terms conclusion and premise." CONCLUSION: "the proposition that is affirmed on the basis of other propositions of the argument." PREMISES: the "other propositions, which are affirmed (or assumed) as providing support for the conclusion . . ."

Will be concerned about 2 elements:

1. the FORM of the argument to see if the argument is "of a kind that is likely to yield a warranted conclusion"
2. the QUALITY of the argument to see if "it does in fact yield a warranted conclusion."

The simplest argument: one premise and one conclusion: "No one was present when life first appeared on earth. Therefore any statement about life's origins should be considered as theory, not fact."

The premise and conclusion can be stated in the same sentence. Also, the conclusion can actually precede the premise in the argument.

N.B.: one proposition is not an argument because an argument involves at least 2 propositions (the premise and the conclusion).

1.3 Recognizing Arguments

The identification of an argument can be problematic because of the pecularities of its formulation. Even when we are confident that an argument is intended in some context, we may be unsure about which propositions are serving as its premises and which as its conclusions.

A. Conclusion Indicators and Premise Indicators

Conclusion Indicators:

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

Premise Indicators:

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

B. Arguments in Context

At times there are no indicators (like the ones above). Instead "Sometimes it is just the meaning of the passage, or its setting that indicates the presence of an argument. . . . Often, however, the force of an argument can be appreciated only when one understands the context in which that argument is presented."

C. Premises or Conclusions Not in Declarative Form

1. RHETORICAL QUESTION
   

   Conclusions or Premises in the form of a question: RHETORICAL QUESTION: "when it suggests or assumes an answer that is made to serve as the premise of an argument. The sentence may be interrogative even though its meaning is declarative."
   

   Danger: when you utter a rhetorical question, people may actually respond to the question in a way you hadn't anticipated. "Questions can serve most effectively as premises when the answers assumed really do seem to be clear and inescapable."
   

2. IMPERATIVE/COMMAND
   

   "Wisdom is the principal thing; therefore get wisdom." "Strictly speaking, it cannot be the conclusion of an argument. Nonetheless, it surely is meant to be the conclusion of an argument . . . the conclusion of the argument in Proverbs may be rephrased as 'Getting wisdom is what you should do.'"
   

D. Unstated Propositions

"Arguments are sometimes obscure because one (or more) of their constituent propositions is not stated but is assumed to be understood."

"A premise may be left unstated because the arguer supposes that it is unquestioned common knowledge."

"Human cloning--like abortion, contraception, pornography, and euthanasia--is intrinsically evil and thus should never be allowed. . . . The argument relies on teh very plausible but unstated premise that 'what is intrinsically evil should never be allowed.'"

ENTHYMENES pron. "IN-the-mean": a proposition that is understood but not stated.

The effectiveness of an enthymeme may depend on the hearer's knowledge that some proposition is false. To emphasize the falsity of some proposition, a speaker may construct an argument in which the false premise is a hypothetical position of which the antecedent (the 'if' component), is the proposition whose falsity the speaker wishes to show, and the consequent (the 'then' component) is a proposition known by everyone to be false. The unstated falsehood of this second component is the second premise of the enthymematic argument. The unstated falsehood of the first component is the conclusion of the argument. . . . [Example from Abraham Lincoln:} 'If slavery is not wrong, nothing is wrong.'" MY question: what then is the unstated proposition that is wrong in Lincoln's claim?

1.4 Arguments and Explanations

"Passages that appear to be arguments are sometimes not arguments but explanations." Words such as because, for, since, and therefore are not determinative because they can be used both in arguments and also explanations.

"Whether some passage is an argument or an explanation depends on the purpose served by it." Q because P may be argument or may be explanation. For example, if P is trying to prove Q, then it is an argument; on the other hand, if Q is already known to be true, then P is probably just explaining Q. Examples:

• Argument: Treasure up for yourselves treasure in heaven whether neither moth nor rust destroy, where theives neither break in or steal. For where your treasure is, there will you heart be also.
  

• Explanation: Therefore is the name of it [the tower] called Babel; because the Lord did there confound the language of all the earth.

Many times difficult to determine if it is argument or explanation. Context: Is ! a proposition whose truth needs to be established or confirmed?" Argument then. "Or is Q a proposition whose truth is known, or at least not in doubt in that context?' Explanation. In an explanation, you need to differentiate between the explanation and what is being explained.

1.5 Deductive and Inductive Arguments

DEDUCTIVE Argument: "its conclusion is supported by its premises conclusively."

INDUCTIVE Argument: does NOT claim that its premises support its conclusion conclusively.

VALID/VALIDITY: can apply ONLY to deductive arguments. "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 . . . invalid." VALIDITY: "A deductive argument is valid when, if its premises are true, its concluion must be true." EVERY deductive argument will be either valid or invalid. No middle ground.

CENTRAL TASK OF DEDUCTIVE LOGIC: "to discriminate valid arguments from invalid ones." Traditional/classical techniques to discriminate from Aristotle. Modern Symbolic Logic used primarily today.

CENTRAL TASK OF INDUCTIVE LOGIC: "to ascertain the facts by which conduct may be guided directly, or on which other arguments may be built. Empirical investigations are undertaken . . . leading, when inductive techniques are applied appropriately, to factual conclusions, most often concerning cause-and-effect relationships of some importance."

Illustration of inductive process: "Can we learn inductively how to reduce the spread of STD's" Yes, we can." Although cannot know for certain the causal connection between circumcision and the spread of STD's, it can be known with a high degree of probability.

"Inductive arguments make weaker claims than those made by deductive arguments." Do not apply terms validity and invalidity to inductive arguments. Rather, "the higher the level of probability conferred on its conclusion by the premises of an inductive argument, the greater is the merit of that argument." Use words like "better" or "worse," "weaker" or "stronger." "Even when the premises are all true, however, and provide strong support for the conclusion, that conclusion is not established with certainity."

"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. . . . may lead us to judge the argument to be better or worse."

"Deductive arguments . . . cannot become better or worse. They either succeed or they do not succeed . . . . If a deductive argument is valid, no additional premises can possibly add to the strength of that argument. . . . If an argument is valid, nothing in the world can make it more valid; if a conclusion is validly inferred from some set of premises, nothing can be added to that set to make that conclusion follow more strictly, or more validly."

The major distinction between inductive and deductive arguments depends upon the "relations between their premises and their conclusions. . . . A deductive argument . . . conclusion is claimed to follow from its premises with absolute necessity. . . . an inductive argument . . . conclusion is claimed to follow from its premises only with probability, this probability being a matter of degree and dependent on what else may be the case."

1.6 Validity and Truth

A deductive argument is valid when it succeeds in linking, with logical necessity [emphasis mine], the conclusion to its premises. Its validity refers to the relation between its propositions--between the set of propositions that serve as the premises and the one proposition that serves as the conclusion of that argument. . . . . validity can never apply to any single proposition by itself, because the needed relation cannot possibly be found within any one proposition.

Truth and falsehood, on the other hand, are attributes of individual propositions. 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.

Truth is the attribute of those propositions that assert what really is the case. . . . This contrast between validity and truth is important. Truth and falsity are attributes of individual propositions or statements; validity and invalidity are attributes of arguments.

Just as the concept of validity cannot apply to single propositions, the concept of truth cannot apply to arguments. Of the several propositions in an argument, some (or all) may be true and some (or all) may be false. However, the argument as a whole is neither true nor false.

We begin by emphasizing that an argument may be valid even if one or more of its premises is not true. Every argument makes a claim about the relation between its premises and the conclusion drawn from them; that relation may hold even if the premises turn out to be false or the truth of the premises is in dispute.

An argument may be valid even when its conclusion and one or more of its premises are false The validity of an argument . . . depends only on the relation of the premises to the conclusion.

. . . there are valid arguments with false conclusions . . ., as well as invalid arguments with true conclusions . . . . the truth or falsity of an arguments conclusion does not by itself determine the validity or invalidity of that argument Moreover, the fact that an argument is valid does not guarantee the truth of its conclusion . . .

If an argument is valid and its premises are true, we may be certain that is conclusion is true also. . . . If an argument is valid and its conclusion is false, not all of its premises can be true. Some perfectly valid arguments do have false conclusions, but any such argument must have at least one false premise.

When an argument is valid and all its premises are true, we call it sound. The conclusion of a sound argument obviously must be true--and only a sound argument can establish the truth of its conclusion.

To test the truth or falsehood of premises is the task of science in general, because premises may deal with any subject matter at all. The logician is not . . . interested in the truth or falsehood of propositions so much as in the logical relations between them. By logical relations between propositions we mean those relations that determine the correctness or incorrectness of the arguments in which they occur.

Why do we not confine ourselves to arguments with true premises, ignoring all others? Because the correctness of arguments whose premises are not known to be true may be of great importance. In science, for example, we verify theories by deducing testable consequences from uncertain theoretical premises—but we cannot know beforehand which theories are true. In everyday life also, we must often choose between alternate courses of action, first seeking to deduce the consequences of each. To avoid deceiving ourselves, we must reason correctly about the consequences of the alternatives, taking each as a premise. If we were interested only in arguments with true premises, we would not know which set of consequences to trace out until we knew which of the alternate premises was true.