Notes on Patrick Hurley's Logic text Sections 1.1 and 1.2
Chapter 1: Basic Concepts of Logic
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.
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.
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.
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