PHI 165
Introduction to Logic

Garns Fall 1997

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What is Logic?

• Logic is "Š the science that evaluates arguments."
• "[T]he aim of logic is to develop a system of methods and principles that we may use as criteria for evaluating the arguments of others and as guides in constructing arguments of our own."

Logic is not an empirical science

• Definitions:
• A posteriori knowledge: Knowledge based on observation and experience; knowledge obtained by empirical study.
• A priori knowledge: Knowledge not based on experience but on reason alone; knowledge obtained by philosophical and reflective study.
• Psychology studies empirically (a posteriori) how people do in fact reason.
• Logic studies philosophically (a priori) how people ought to reason.

Logic is a normative study

• A normative study examines how something ought to be.
• Ethics: How ought one act?
• Logic: How ought one reason?
• Logic is prescriptive rather than descriptive. In this way logicians aim to evaluate rather than merely describe various kinds or instances of reasoning.

What is reasoning?

• Reasoning is the drawing of an inference from information already possessed.
• By inferring one proposition from others, one aims to learn something new.
• In order to learn something new a good inference must use a process that preserves truth.
• Inferences that preserve truth must (or are likely to) yield true propositions when they begin with true propositions.

Logic and the preservation of truth

• How ought one reason?
• Reason in a way that will preserve truth.
• How ought one reason to preserve truth?
• Formal Logic studies patterns of reasoning that are guaranteed to preserve truth because of the formal properties or structure of the argument.
• Informal Logic studies ways of reasoning that are likely to preserve truth because of the relationship between evidence and hypotheses.

What is an Argument?

• Fundamental to the concept of reasoning is the idea of an argument, which is intended to reflect an inference or a connected series of inferences.
• An argument is "Š a group of statements, one or more of which (the premises) are claimed to provide support for, or reasons to believe, one of the others (the conclusion)."

Statements

• Statements are not to be confused with sentences.
• Statements are:
• what are expressed with the use of sentences.
• either true or false.
• not physical marks on a page or sounds.

Sentences and statements

Consider the single sentence "I am thirsty now"

• Because "I" and "now" are indexical what is expressed (the statement) depends on who is speaking and when.

The statement that Clinton is thirsty can be expressed with different sentences.

• "Clinton is thirsty"
• "He is thristy"
• "The President wants some water"

Identifying arguments

• Best to identify arguments through the activity of arguing for the truth of some statement.
• What is the speaker intending to do?
• Argue, defend, support
• Explain
• Describe
• Report
• Warn

Inferences

• Inferential claims are those that are expressed when it is claimed that a conclusion follows from or is supported by premises. You are asked to affirm the conclusion based on the support of the premises.
• The following don't express inferential claims:
• descriptions, explanations, reports, conditionals, warnings

Premise and conclusion indicators

• Primary indication: Premises are those statements offered in support of some claim. Conclusions are the claims to be supported.
• Secondary indication: Sometimes words in the argument will help distinguish pemises from the conclusion.

An argument

• Lucy will either make a fool of herself on Ricky's show or stay at home and watch TV. Since she won't stay at home, she will therefore make a fool of herself on Ricky's show.
• The conclusion is that Lucy will make a fool of herself on Ricky's show.
• The premises offered in support of this claim include the dichotomy of her either making a fool of herself or her staying at home watching TV, and the additional claim denying that she will stay home.
• "Since" is used as a premise indicator; "therefore" is used as a conclusion indicator.
• Premises and conclusions aren't always expressed in separate sentences.
  

Since only Fred and Ethel had access to the FBI files and Fred was out of town, Ethel must have been the informant.

• Premise: Only Fred and Ethel had access to the FBI files.
• Premise: Fred was out of town.
• Conclusion: So, Ethel must have been the informant.

In a passage that contains an argument the premises and conclusion can come in any order.

Lucy would have sung on Ricky's show if he asked her. So, Ricky never asked her since she didn't sing.

• Premise: Lucy would have sung on Ricky's show if he asked her.
• Premise: She didn't sing.
• Conclusion: So, Ricky never asked her.

Conditionals are not arguments

Conditional

• If Lucy signed the marriage certificate, then Lucy married Ricky.

Argument

• Lucy signed the marriage certificate. Thus, Lucy married Ricky.

Explanations are not arguments

Explanation:

• Lucy married Ricky because she loved show business and was attracted to his accent.

Argument:

• Lucy and Ricky would not go to the church unless they were getting married. Ethel saw them at the church on Saturday. So Lucy married Ricky.

Why study Logic?

• You'll be better able to distinguish good reasoning from bad.
• You'll be more likely to arrive at true beliefs if you start with the truth.
• When combined with other skills and knowledge (rhetoric, psychology) you'll be better able to convince others of your positions.
• The practice of these skills and rigors will instill habits of good reasoning.
• Better able to keep an open and objective mind when discussing controversial and important matters.

In deductive arguments "Š the premises are claimed to support the conclusion in such a way that it is impossible for the premises to be true and the conclusion false. [T]he conclusion is claimed to follow necessarily from the premises."

Inductive Arguments

In inductive arguments "Š the premises are claimed to support the conclusion in such a way that it is improbable that the premises be true and the conclusion false. [T]he conclusion is claimed to follow only probably from the premises."

Induction and Deduction

Determined by what kind of support the speaker/arguer intends to offer for the conclusion.

• Necessary connection = deduction
• Probable connection = induction

Induction and Deduction

Not defined by whether the premises and the conclusion are particular or general statements.

What are the virtues and vices of the following arguments?

If Michael Jackson is human, then Jackson has human offspring.

Jackson has human offspring.

So, Michael Jackson is human.

If Michael Jackson is a whale, then Jackson is a mammal.

Jackson is a mammal.

So, Michael Jackson is a whale.

If Michael Jackson is a whale, then Jackson has reptilian offspring.

If Jackson has reptilian offspring, then Jackson is mammal.

So, if Jackson is a whale, then Jackson is a mammal.

If Michael Jackson is a whale, then Jackson is a reptile.

If Jackson is a reptile, then Jackson has human offspring.

So, if Jackson is a whale, then Jackson has human offspring.

Arguments can be evaluated by their specific form or structure

Validity is a virtue of deductive arguments

• A deductive argument is valid if it has a valid form.
• A valid argument form is one that preserves truth from the premises to the conclusion such that if the premises are true, then the conclusion must be true.

A deductive argument is valid if it has a valid form

Even though its statements are false, this argument is valid because it has a valid argument form. For any argument that fits this form it will be impossible to have true premises and a false conclusion.

An argument is invalid if it does not fit a valid argument form

Validity and Deduction

• Validity is a function of the argument's form or structure, apart from the content of the statements. The actual truth or falsity of the statements is irrelevant. What is important here is the inferential relationship between premises and conclusion.
• Invalid arguments can have true premises and a true conclusion and valid arguments can have false premises and a false conclusion. The only combination that is impossible is the valid argument that has true premises and a false conclusion.
• Deductive arguments are either valid or invalid--there is no middle ground or approximation.

Validity and Soundness

A valid argument has

• a form such that it is impossible to have true premises and a false conclusion

A sound argument has

• a valid argument form
• true premises

Truth and Validity

Virtues of Inductive Arguments

• Inductive arguments are strong or weak, depending on how well the evidence in the premises supports the conclusion.
• Inductive arguments are not valid or invalid.
• Cogent inductive arguments
• are strong
• have true premises

Weaker and Stronger Inductive Arguments