What leads Us to How We Answer Important Questions

Like …- What foods should I eat?- Should I go to college, and if so, to what

college should I go?- For which candidate should I vote?- Who should I date?- Should I get married?- Do I believe in God, and if so which one?- What type of work should I do?- How important is having lots of money?

We Have Guidance from…- Experience (pleasures and pains)- Tradition and Culture (nurture)- Faith - Not having the certainty that a claim is

true, but acting as though it is)- Intuition - ‘gut’ feeling, instinct, something that

is pre-critical and powerful- Biology (nature)- Psychology – The mind and all its biases- Scientific Method – observation, hypothesis

formation and testing, provisional conclusions- Logic, Reason, and Critical Thinking

Psychological Barriers

- Belief Bias and Confirmation Bias – You tend to believe claims that are similar to or are confirmed by claims you already believe.

Laughing at something that isn’t that funny said by someone who usually says things that are funny – Comedy Club Effect.

I tend to think Rush Limbaugh usually makes stupid conclusions, and so when I hear a Rush Limbaugh conclusion, I’m already inclined to think it’s stupid before I hear it.

More Psychological Barriers- Availability Heuristic – We hear something over and over and so we start to

think differently about it.Ex: IS has been in the news repeatedly, and so it makes us think there is more of

an immediate danger than there really is.-False Consensus Effect – Everybody around me thinks a certain way, so probably

everyone else in the world thinks this way too. (Everyone around here hates Obama, just like everyone else in the US)

-Bandwagon Effect – We have a desire to align our thinking with those around us. (Best-selling product)

-Negativity Bias – We weigh negatives more than we weigh positives. 1000 people will say nice things to us and one person will say a negative thing. We will focus on the negative more than we will focus on all the positive things. (Tell your girlfriend how beautiful, smart, and amazing she is, but all she needs is a nose job and she’ll be perfect)

- In-Group Bias – Those who aren’t a member of our group are inferior, or wrong, or somehow not as good as we are. (If one of the members of my family loses his job, it is an injustice. But if someone else loses there job, it is probably because they were a slacker, or not very good at what they were doing.)

What is Critical Thinking?Typically, critical thinking is an activity that

involves using reason.

This leads to another question:

What is Reason?

What is Reason?-First and foremost, reason has a

commitment to the principle of non-contradiction (PNC)

-The PNC says a claim and its denial cannot both be true. If we find an instance where someone believes a claim is both true and false, or that an argument leads to or implies a claim that is both true and false, we call this a contradiction.

- Reason uses our cognitive and observational abilities to detect contradictions or inconsistencies.

Examples of Contradiction Detection

- Morality – If an action contradicts my values it is immoral

- Politics – If a politician says they want to do one thing, but then they vote for another, they contradict themselves.

Ex: Republicans want to shrink the role of government, except where it comes to the military and morality.

Ex: Democrats believe that govt can be a force for good, but they want govt to leave your morality and private life alone.

Examples of Contradiction Detection Continued..

-Romance – Your girlfriend says she doesn’t want to change you but she is always buying you clothes you don’t like.- Your boyfriend says he is ‘just friends’ with his ex, but they really seem to enjoy talking to one another on the phone.

Law – If evidence leads to a claim that contradicts the plaintiffs accusation, we let the accused go free.

Religion – You may be skeptical of someone else’s different religious views, but when they show skepticism toward your religious views you become uncomfortable and defensive.

THE VALUE OF FORMAL LOGICIn math, we attempt to capture a process of reasoning that helps us arrive at numeric conclusions.

In language, logicians want to capture a process of reasoning that leads to contradiction detection.

Natural language vs formal language.

Does language follow a process, just like math follows a process?

The Logical Structure of LanguageLogicians believe language has several basic

operations:

1. Conjunction – the ‘and’ this AND that“I am 6 feet tall and I am male”2. Disjunction – the ‘ either or’“Either I am drunk or I am sober”3. Negation – This is not thatHe is not very attractive4. The Conditional – If … thenIf I am attractive, then I’m tall

Propositional Symbolic LogicIn Math, we use symbols to represent mathematic concepts and processes. In Logic we do the same thing:Math: 7+5=12 is represented x+y=zLogic:Conjunction: I am tall and male = T ^MDisjuntion: Either I am drunk or sober = D v SNegation: He’s not attractive = ¬AConditional: If I am Attractive, then I’m Tall = A→T

Categorical Symbolic LogicAn earlier logic developed by Aristotle made use of categorical claims:

All men are mortalSome men are happyAll bachelors are unmarried men

These may be roughly translated into propositional logic:

If you are a man, you are mortal.

Anatomy of the conditionalA conditional statement is made up of an antecedent and a consequent, which are also the sufficient and necessary condition, respectively.

If you are human, you are mortal. If X, then Y

Antecedent – that which comes before.Consequent – that which comes after.

Necessary vs Sufficient Condition

Sufficient Condition: All we need to know in order to know something else.If we know this (x) it is all we need to know in order to know that (y)Necessary Condition: That which follows of necessity (y) (either from category or cause) from something else (x).A condition (y) that must be present in order for something else (x)to be true

Examples of Necessary and Sufficient Condition -

ClassificationWhich is the correct placement of the necessary and the sufficient condition?

A. If one is thin, they are emaciated.B. If one is emaciated, they are thin.

Definition – emaciation means extremely thin, usually in a very unhealthy way, such as through starvation.

Correct Answer is BReasoning from sufficient condition

If all we know about you is that you are emaciated, that is all we need to know to conclude that you are thin.However, if all we know about you is that you are thin, we cannot conclude that you are also emaciated, because there are many different ways to be thin.

Correct Answer is BReasoning from necessary condition:

Since emaciation is a sub-category of thinness, thinness will be a necessary condition of emaciation.

If you are emaciated, it is also true of necessity that you must also be thin.

Examples of Necessary and Sufficient Condition - Cause

Which is the correct placement of the necessary and the sufficient condition?

A. If the car has gas in it, it will start.B. If the car starts, it has gas in it.

Correct Answer is BIf a car has gas in the gas tank, but there is no motor, or no starter, or something else along the line isn’t working, the car won’t start, so having gas in the tank cannot be a sufficient condition for the car starting.

If however, the car starts, among many other things, it had to have gas in it. So having gas in the tank is a necessary, but not sufficient condition for the car starting.

Necessary But Not Sufficient

1. If you are healthy wealthy and good looking, you will flourishVs2. If you flourish you will be healthy wealthy and good looking

1. If you think you are happy, you are happyVs2. If you are happy, you will think you are happy

1. If you envision your success, you will be successfulVs2. If you are successful, you envisioned your success

Defining an ArgumentMoore and Parker – An attempt to support or prove a claim by providing reasons or considerations for accepting it. One group of claims, the premises, intend to support or give reasons for believing another group of claims, the conclusion.

Monty Python – A connected series of statements intended to establish a definite proposition.

Anatomy of an ArgumentAn argument contains the following:Issue – A point or claim that may be wondered about or debated.Should we have stricter gun control policies?Claim – A statement that is either true or false Claims of fact – this is the way the world isThere are 30 people in this room. Claims of Aesthetic Value – this is beautifulLady Gaga’s music is wonderful Claims of Moral or Ethical Value – this is right or wrongWhat Chris Brown did to Rihanna was wrong

Anatomy of an Argument Continued

Premise – A claim that is offered as a reason for believing another claim or a claim that implies another claim.

Conclusion – A claim that is said to be supported by another claim. The main claim in the argument that all the other claims intend to lead you to believe.

Deductive ArgumentsA deductive argument is a series of statements structured in such a way that if the premises are true, the conclusion will necessarily be true.

Example:All men are mortal All A are BSocrates is a Man x is an ASocrates is mortal x is a B

Success Criteria of an Argument(From Chapter 2)

To determine if an argument is successful, we look at two criteria, its form and its content.

The form is the logical structure of the argument. If the form is good, we call this validity. If the form is good and the content is good, we call this soundness.

Validity – An argument structured such that if the premises will be true, the conclusion will also be true. (notice this is essentially the same definition as a good deductive argument)

Soundness – A valid argument that has all true premises.

Examples of Validity and Soundness

All men are mortal All A are BSocrates is a man x is an ASocrates is mortal x is a B

This is valid because structurally, everything that is in category A will also be in category B, and if we find something that belongs to category A, it must also belong to category B.This is sound because the premises are all true.

What is Wrong?All women are nuns All A are BLady Gaga is a woman x is an ALady Gaga is a nun x is a B

Is this argument valid? (does it have a good structure)

Is this argument sound? (does it have a good structure and are the premises true?

Valid Argument FormsModus PonensA→BA B

Ponens –Put it there

Modus TolensA→BNot B Not A

Tolens –Take it away

Hypothetical SyllogismA→BB→C A→CAka chain argument

Invalid Argument FormsAffirming the ConsequentA→BB A

Denying the AntecedentA→BNot A Not B

Undistributed MiddleA→CB→C A→B

Examples of Valid and Invalid Argument Forms

Modus Ponens If one is emaciated, they are thin A→BThis person is emaciated AThis person is thin B

Affirming the ConsequentIf one is emaciated, they are thin A→BThis person is thin BThis person is emaciated A

Undistributed MiddleAll cats are mammals A→CAll dogs are mammals B →CAll cats are dogs A →B

Argument StrategiesConvert arguments into a standard valid form, paying attention to the placement of necessary and sufficient condition.

If gay people can get married, traditional marriage is harmed.

If we have stricter gun control, not as many children will die.

If the DP deters crime, we should practice the DP.

If violent media makes us do violent things, we should censor violent media.

Argument Strategies Continued

Determine if the premise is true by figuring out if there is a situation where the antecedent is true, but the consequent is false.

If gay people can get married, traditional marriage is harmed.

If we have stricter gun control, not as many children will die.

If the DP deters crime, we should practice the DP.

If violent media makes us do violent things, we should censor violent media.