Notes on Patrick Hurley's Logic text Sections 1.1 and 1.2Chapter 1:
Basic Concepts of Logic Section 1.1 Statements are sentences that claim
that something is so. If
a statement claims what is actually so, we say the statement is true. If
a statement claims what is actually not so, we say the statement is false. The
terms “true” and “false” apply only to statements, not to questions,
exclamations, commands, etc. “True” and
“false” are called truth values. Statements differ from other kinds of
sentences in that each statement has a truth value; i.e., each statement is
either true or false. An
argument is a piece of reasoning. Arguments consist of statements. We
reason when we infer or deduce that a
statement must be true, or is probably true, if other
statements are true. For
example, suppose we know the following two statements are true: (1)
If the patient has Disease D, then the patient will show symptom S. (2)
The patient does not show Symptom S. We
can then use reason to derive another statement: (3)
The patient does not have disease D. Logic is the banch of philosophy
that evaluates arguments. “Evaluate”
means to determine if good or bad, better or worse, i.e., to assess the value of an argument. Each
argument contains one or more premises,
and a conclusion. The premises and conclusion are statements. The
premises are the supporting statements.
When we reason – i.e., when we use logic -- we always ask “What would
have to be true, or what would probably be true, IF the premises are true?” The
statement that an arguer believes is true on the basis of the premises is the
conclusion. In
the piece of reasoning above, statements (1) and (2) are the premises, and
statement (3) is the conclusion. Sometimes
people make mistakes in their argument evaluation; they think a bad argument is
good, or they think a good argument is bad.
We study logic in order to sharpen our skills at argument evaluation. When
we analyze an argument, we first list the premises and then the
conclusion. You may have to re-order the
statements in the original passage, since sometimes an arguer will state the
conclusion first and then state the premises; sometimes an arguer will put the
conclusion in the middle of a passage; and sometimes an arguer will give the
premises and then state the conclusion. You
can usually determine which statements are premises and which statement is the
conclusion by using special linguistic cues:
premise indicators and conclusion indicators. Premise indicators include the following
words and expressions: since, as
indicated by, because, in that, for, may be inferred from, as, given that,
seeing that, for the reason that, inasmuch as, owing to. Conclusion indicators include the following
words and expressions: therefore, thus,
consequently, accordingly, we may conclude, it must be that, for this reason,
entails that, hence, it follows that, implies that, as a result. Some
arguments contain no indicator words. In
such cases, the conclusion is usually the statement that comes first in
thepassage. Do
not worry about the portions of the text on the history of logic and eminent
logicians. Section 1.2 This
section is more complicated than it needs to be for our purposes, so don’t
worry too much about every detail of it. In
life, when an arguer tries to convince you that a certain conclusion is true by
presenting an argument (premises and a conclusion), the arguer is really
telling you two things: 1. THE FACTUAL CLAIM: The arguer is telling you
(implicitly) that the premises are true, i.e., that s/he’s
got the right facts. AND 2. THE INFERENTIAL CLAIM: The arguer is telling you there is a logical link between the statements,
such that IF these premises are true, they support
the conclusion. In other words,the arguer is telling you it would be reasonable for you to
accept this conclusion as true on the basis of these premises. To
get a handle on the inferential claim, ask yourself under what circumstances a
person would use an argument. We need
arguments exactly for those claims whose truth is NOT apparent or obvious. We don’t have to argue for the obvious. We argue in cases where people may not fully
appreciate the logical consequences of claims they already accept. Strictly
speaking, logic evaluates the inferential claim only. Passages
that lack either the inferential claim or the factual claim are not arguments. A
passage can lack an inferential claim. Whether or not a passage has an
inferential claim depends on what the arguer is trying to do. Often, an arguer
isn’t really trying to establish any logical
links; i.e., the arguer is not claiming that IF you believe some statements, you
should also believe others. People often
merely state, but do not argue. Warnings,
pieces of advice, statements of belief or opinion, loosely associated
statements, and reports fall into this category of non-argument. To
determine if an expository passage contains an argument, ask yourself whether
the arguer is trying to prove a
claim. If yes, you can think of the passage as an argument. Similarly,
if a speaker gives a series of illustrations or examples, ask yourself whether
the arguer is providing the examples as
evidence to prove that a particular claim is true. There is no argument if the
examples are there simply by way of illustration. Explanations may resemble arguments but
are not arguments. An
explanation consists of the statement being explained (the explanandum) and the
explanation for it (the explanans). We
offer explanations when our audience does
not doubt that the explanandum is the case.
Our audience already knows that the explanandum is the case, and we are explaining
why it is so. Consider
the passage: “Obama won the election
because he had an excellent campaign organization.” This
is best viewed as an explanation because everyone already knows that Obama
won. We don’t need to prove that that is so; and the purpose
of the passage is mainly to show why it is so. In
an argument, by contrast, the arguer aims to establish that the conclusion is true, in circumstances where there may be
doubt or ignorance about whether the conclusion is true. The
most important part of Section 1.2 for this class is the account of the conditional. A
conditional is an “if ... then ...” statement.
It is a compound statement,
because there is one statement after the word “if” and another statement after
the word “then”. The
statement after the word “if” is called the antecedent. The
statement after the word “then” is called the consequent. The
conditional asserts that if the antecedent is true, the consequent must be true. In other words, the conditional asserts that
the antecedent is sufficient for the
consequent. A
is sufficient for B if and only if A guarantees or ensures B. For
example, decapitation is sufficient for death.
Getting an A (or B or C) is sufficient for passing a class. If
A is sufficient for B – A guarantees B – then whenever you have A, you have B.
All instances of A are
instances of B. A look ahead: The
conditional is important because many logically correct deductive (valid)
argument forms contain conditionals. For
example, consider the argument (1) If A, then B.
(I.e., A is sufficient for B.) (2) A (i.e., A is true.) It
follows logically from (1) and (2) that B.
This argument form is called modus
ponens, and we will be encountering it often later in the class. Another
argument form containing the conditional is modus
tollens: (1) If A, then B. (2) It’s
not the case that B. It
follows logically from (1) and (2) that it’s not the case that A. The argument at the beginning of this handout
about the disease and the symptoms is modus
tollens form. Modus tollens forms
the basis of the technique of “differential diagnosis” you see on the TV series
House. A third valid argument form that uses the conditional
is hypothetical syllogism: (1) If A, then B. (2) If B, then C. (3) Therefore, if A, then C. Sandy's X10 Host Home Page | Sandy's Google Sites Home Page Questions or comments? sandy_lafave@yahoo.com |