Reasoning and Problem SolvingLecture 1

What is Critical Reasoning?

By David Kelsey

Getting Started

• The course syllabus.• Things to consider:

– Contact information– Course requirements– The lecture schedule

Course Objectives

• Thinking Rationally: We will learn how to think correctly or rationally or logically.

– For someone to think rationally just means that she, from her set of beliefs, makes inferences that are justified given the laws of logic.

• The laws of logic: And we will learn the laws of logic so that we know just which inferences are justified.

The Laws of Logic

• The laws of logic: dictate just which inferences we can make.– They are rules for making good inferences.

– 2 examples: • Modus Ponens:

• Modus Tollens:

• Sentence letters: We use Capitalized letters like ‘P’ and ‘Q’ to stand for sentences.

Inferences

• An inference: a statement that follows from one or more other statements.

• The Verb – To infer something

• The noun – The inference made

Statements

• A statement is a proposition.

• Sentences and Propositions: – Just like words have meanings, sentences have meanings.

Propositions

• The form of a proposition: – ‘it is the case that…’.

– Propositions are true or false.

Propositions & Sentences

• A sentence does two different things: it both expresses a proposition and asserts a proposition.

• The expressed proposition:– the literal meaning of the words of that sentence.

Expressing a proposition

• For a sentence to express a proposition: – is for that sentence to toss the proposition up in the air, so to speak.

– It is to put the proposition up for usage.

• Knowing what proposition a sentence expresses is often quite easy.

The asserted Proposition

• Making use of a proposition: – Just how a sentence makes use of the proposition a sentence expresses determines

it’s actual or intended meaning.

• The actual or intended meaning of a sentence:– What the speaker or writer of the sentence means when she writes or says it.

Asserting a proposition #2

• Assertion:– The actual or intended meaning of a sentence is what is asserted by the words of the sentence.

• Declaration: – For a sentence to assert a proposition is simply for the sentence to declare of the proposition that it is

the case.

Sarcasm

• Other kinds of sentences:– Sarcasm:

• The messy roomate:– “She always takes out the trash”.

• This sentence expresses:

• But the sentence asserts:

The laws of logic

• The laws of logic: are rules for making a correct inference P given a certain set of propositions Q1-n.

– Socrates example

• Arguments: when one proposition is inferred from one or more other propositions

– Other definitions of an Argument

Arguments

• Argument: a position supported by reasons for its truth.

– To take a position:• taking a side or stand on an issue.

– An issue: what is raised when one considers whether or not a proposition is true.

• There are always 2 sides to an issue

Issues

• Issues:– we might go as far as to say that an issue just is a question.

– Intelligent life:

– Safety belt law:

– Mac vs. Pc:

Arguments & Positions

• Arguments & Positions: so when we take a position on an issue and support it with reasons we have given an argument.

– Intelligent life:

– Safety Belt law:

– Mac vs. Pc:

Conclusions &Premises

• Arguments:– The conclusion of an argument:

– The premises of an argument:

– Examples:• Socrates again

• Raining and Pouring

What an argument isn’t

• What an argument isn’t: Let us be a bit clearer about what an argument is by stating what it isn’t.

– Not a Fight:

– Not Persuasion: • Advertisement example:

Persuasion

• Persuasion vs. Argument:– An argument offers support for some claim, its conclusion.

– Persuasion needn’t offer any support for a point.• Not Logic: It merely attempts to get you to believe a point.

– This attempt needn’t be one through logic though.

• Persuasion through rhetoric:

• Rhetoric: is “a broad category of linguistic techniques people use when their primary objective is to influence beliefs and attitudes and behavior”

Arguments vs.Explanations

• Arguments vs. Explanations:

– Explanation of X: If one gives an explanation about some thing X, one gives some details about X with the hope of coming to better understand X.

• Example: fixing a flat tire

Recognizing Arguments

• Conclusion Indicators: find the conclusion of an argument by looking for conclusion indicators.

– Examples of Conclusion Indicators: therefore, hence, and others

• Premise Indicators: find the premises of an argument by looking for premise indicators

– Examples of Premise Indicators: because, since, and others

An introduction to formalizing an argument

• Challenging an argument: – In challenging an argument you must first formalize it.

• Formalizing an argument: – Is the reconstruction of that argument in its most simplified form.

• Read the passage

• Write down the argument’s propositions

Explicit Premises

• Explicit premises: – asserted by the words of the text.

• Simplifying the premises:

Implicit Premises

• Implicit or unstated premises: entailed by the words of the text.– P entails Q:

• PQ

– Bloodhound example:

Factual claims

• Arguments and Claims:

• Factual Claims – Either true or false.– Established methods – Generally Established Criteria– Settling Disagreement

– Example: Water is H2O

Non-factual claims

• Non-factual claims: – No established methods – Can’t settle Disagreement

– Some examples:

Value Claims

• Value claims: non-factual claims that assert that some moral property is instantiated in some object or action or event.

– Properties and Moral Properties

• Why worry about factual & Non-factual claims:

– Never Ought from Is: