Exam 1 Study Guide

example of discipline use of logic

In Physics, often conclusions about how the world works is based on establishing a series of propositions with a line a reasoning to a conclusion and then trying to prove or disprove the propositions to determine if the conclusion is truth. An example would be the debate over whether light was a wave or a particle where experiments such as the photoelectric effect and Young's double slit experiment sought to prove one way or another until both were shown to be true and wave particle duality was understood.

example of logical reasoning in life

eating food stops hunger so if I am hungry, I should eat food.

good vs bad opinion

good vs bad basis and true/false premises

what is the inferential process involved in reasoning

The inferential process involved in reasoning uses premises based on truth to build on each other to show that something can lead to another thing and drawing conclusions from that path

main difference between good reasoning and bad reasoning

truth preservation

qualities of a model critical thinker

* Analytical Skills;
* Logical Reasoning; 
* Open-Mindedness; 
* Curiosity and Inquisitiveness;
* Intellectual Humility; 
* Effective Communication; 
* Problem-Solving Abilities; 
* Information Literacy; 
* Reflection and Awareness ; 
* Ethical and Moral Integrity

Peter’s saying

“The use of reason is a very passionate business”

Peter's saying about reason being a passionate business means that he thinks that in order to practice reason you have to be driven by a desire to know the truth, show empathy towards different perspectives, and drive towards accuracy. This passionate quest towards truth and accuracy drives the effort and internal thinking and analysis that is required to for good reason

Pierce’s saying

He says that preserving the truth and keeping an open mind and having other rational passion are crucial in developing a well constructed argument.

logic etymology

Logic comes from the Greek work logos for reason, calculation, or argument

reasoning activity

using the information presented to us in order to draw conclusions

why is logic a normative dicipline?

Logic is considered normative because if focuses on discussing and establishing norms for philosophy and thought.

It focuses less on how people do think and instead focuses on how they should think and reason. It talks about what are the correct ways of establishing an valid argument and drawing conclusions.

motivations for Aristotle to form his logic (Aristotelian Logic/Categorical Syllogism)

systematic way of approaching arguments by describing categories and then determining the validity of an argument by the structure

Aristotle vs Socrates on education

Socrates advocated for education to push students towards reason in their thinking and passions and Aristotle advocated for rationality to be taught so education could develop people who were rational.

Both pushed for rationality but Socrates focused more on critical thinking and the specific thought processes around rational thought while Aristotle focused more on the idea of building people as a whole outside of just academics who behaved in rational manners intellectually and emotionally/morally.

Siegle’s opinion on the fundamental aim of education

Siegel claims that the fundamental aim of education is the "**cultivation of reason**" where students are guided to be able to both:

* know how to reason
* be able to put together multiple propositions in support of or against a claim or their preexisting beliefs
* be guided by that reason
* listen to the results of rational lines of thinking, allow their opinions to change, and actually act on those conclusions or results instead of selectively ignoring them for convenience

4 reasons Siegel thinks fostering critical thinking in students is important

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* __**respecting students as people**__ (this allows them the space to think for themselves and guide their own lives)
* __**preparing students for adulthood**__ (not pushing them into one role but allowing them to have self-direction and growth from that)
* supporting __**rational traditions**__ such as science, mathematics, and history (these fields rely on rational thinking and not mastering that prevents mastery or full understanding of the field)
* __**democratic life**__ (in order for democracy to work properly, citizens need to be able to employ careful analysis, good thinking, and deliberation otherwise they do not make informed and thought out decisions in their votes)

dispositions of the ideal critical thinker

* being clear on the intended meaning of what’s communicated
* determine and maintain focus on the conclusion or question
* take into account the total situation
* seek and offer reasons
* try to be well informed
* look for alternatives
* seek as much precision as the situation requires
* try to be reflexively aware of one’s own basic beliefs
* be open-minded of other points of view
* withhold judgement when evidence and reasons are insufficient
* take and change a position when the evidence and reasons are sufficient
* use one’s own critical thinking abilities

the 5 categories of abilities of a critical thinker

1. clarification
2. basis for decision
3. inference
4. metacognitive abilities
5. auxiliary critical thinking abilities

clarification abilities of a critical thinker

* identify the focus (issue, question, or conclusion)
* analyze the arguments
* ask or answer questions of clarification and/or challenge
* define terms, judge definitions, and deal with equivocation
* identify unstated assumptions

basis abilities of a critical thinker

* judge the credibility of a source
* observe and judge observation reports

inference abilities of a critical thinker

* deduce and judge deductions
* induce and judge inductions
* to generalizations
* to explanatory conclusions (yes hypothesis)
* make and judge value judgements

metacognitive abilities of a critical thinker

* suppositional thinking
* integrate the other abilities and dispositions in making and defending a position

auxiliary abilities of a critical thinker

* proceed in an orderly manner appropriate to the situation
* follow problem solving steps
* monitor one’s own thinking
* employ a reasonable critical thinking checklist
* to be sensitive to the feelings, level of knowledge, and degree of sophistication of others
* employ appropriate rhetorical strategies in discussion and presentation
* employ and react to fallacy labels in an appropriate manner

eternal statement

statement whose truth value never changes

eternal statement example

a dog is a mammal

occasion statement

statement whose truth value changes depending on the situation

occasion statement example

a dog is brown

invalid argument example

1. If I read a book I will learn
2. I like to read
3. so, I will learn

This argument is invalid because The conclusion, B is never connected to the second premise, C

valid argument with false conclusion example

1. If dogs are mammals, so are cats
2. dogs are not mammals
3. so, cats are not mammals

This is valid because it follows the modus tollens form so if the premises were true, so would the conclusion. The conclusion fails because of false premises

What is the structure of the following?

All presuppositions are statements that are taken to be true. Some statements that are taken to be true are false. So, no presuppositions are false.

Premise 1. All A are B

Premise 2. Some B are C

Conclusion. So, no A are C

What is the structure of the following?

Vice is not a weakness of character. For if a virtue is a desirable character trait, then a vice is a weakness of character. Either virtue is a desirable character trait or vice is a weakness of character. But virtue is not a desirable character trait

Replacing terms:


1. not A
2. if B then A
3. Either C or A
4. but not B

rearranged into standard form:


1. Either C or A (prem 1)
2. if B then A (prem 2)
3. not B (prem 3)
4. so, not A (conclusion)

types of invalid forms

1. affirming the adjunct
2. denying the antecedent
3. affirming the consequent

affirming the disjunct

1. Either A or B
2. A
3. So, not B

or


1. Either A or B
2. B
3. So, not A

denying the antecedent

1. If A then B
2. not A
3. not B

affirming the consequent

1. If A then B
2. B
3. So, A

inductive argument example

1. most orange cats are male
2. crookshanks is an orange cat
3. so, crookshanks is male

abductive argument example

1. it is September in Florida
2. there is no water or gas left anywhere
3. there is a hurricane coming

inductive vs deductive argument

inductive: premises imply a most likely conclusion

deductive: premises guarantee conclusion

what is an argument?

a collection of statements with premises leading to a conclusion

what is a premise?

a sentence with a known truth value

types of deductive arguments (the do they work category)

valid and invalid

valid deductive argument

form that is truth preserving (mostly using the famous forms method)

sound argument

deductive argument with a valid form and all true premises

unsound argument

deductive argument with an invalid form and/or at leas one false premise

valid argument forms

1. modus ponens
2. modus tollens
3. hypothetical syllogism
4. constructive dilemma
5. disjunctive syllogism
6. form 6
7. form 7

modus ponens

1. If A then B
2. A
3. then B

modus tollens

1. If A then B
2. not B
3. then not A

hypothetical syllogism

1. if A then B
2. if B then C
3. so if A then C

constructive dillema

1. Either A or B
2. If A then C
3. If B then D
4. so either C or D

form 6

1. All A are B
2. C is A
3. C is B

Form 7

1. All A are B
2. C is not B
3. C is not A

How to test the validity of a deductive argument by the counterexample method

1. find structure by replacing term with symbols/letters
2. replace symbols with new terms with known and obvious truth values and try to get a false conclusion with all true premises while maintaining structure

good counterexamples use

statements with well known and eternal truth values

bad counterexamples use

broad, occasional, and/or ambiguous statements

categories for whether or not an inductive argument will work

strong and weak

strong inductive arguments are

most likely to be true

weak inductive arguments are

unlikely to be true

cogent arguments

strong inductive arguments with all true premises

uncogent arguments

inductive arguments that are weak and/or have at least one false premise

types of inductive arguments

1. __**statistical syllogism**__ (percentages)
2. __**argument by authority**__ (an expert in the field said this so it’s probably true)
3. __**argument by analogy**__ (must have a relevant connection)
4. __**abductive argument**__ (open ended premises)

standard forms of categorical propositions (A E I O)

A All S are P

E No S are P

I Some S are P

O Some S are not P

how to determine relationships between categorical propositions

Aristotelian Square

Stylistic variants of A (all S are P)

* every S is a P
* each S is a P
* any S is a P
* if anything is an S, then it is a P
* things are S only if they are P
* only S are P

Stylistic variants of E (no S are P)

* nothing that is an S is a P
* a thing is an S only if it is not a P
* if any thing is an S then it is not a P
* Nothing is an S unless it is not a P

Stylistic variants of I (Some S are P)

* there are S that are P
* at least one S is a P
* there exists an S that is a P
* something is both an S and a P

Stylistic variants of O (Some S are not P)

* at least one S is not a P
* not all S are P
* not every S is a P
* something is an S but not a P
* there is an S that is not a P

argument form

is a pattern of reasoning

substitution instance

an argument that results from uniformly replacing the variables in that form with statements (or terms)

valid argument form

one in which every substitution instance is a valid argument

formally valid argument

one that is valid in virtue of its form.

negation

of a statement is its denial

conditional statement

is an if-then statement, often simply called a “conditional.”

antecedent

The if-clause of a conditional

consequent

The then-clause of a conditional

disjunction

is an either-or statement

disjuncts

The statements comprising a disjunction

fallacy of denying the antecedent

is an invalid argument form: If A, then B; not A; so, not B

n invalid argument form

one that has some invalid substitution instances.

counterexample

a substitution instance in which the premises are true and the conclusion is false

good counterexample

a substitution instance in which the premises are well-known truths and the conclusion is a well-known falsehood.

fallacy of affirming the consequent

an invalid argument form: If A, then B; B; so, A.

categorical statement

a statement that relates two classes or categories, where a class is a set or collection of things

term

a word or phrase that stands for a class of things

strong argument

one in which it is probable (but not necessary) that, if the premises are true, then the conclusion is true

weak argument

one in which it is not probable that, if the premises are true, then the conclusion is true

cogent argument

a strong argument in which all of the premises are true.

uncogent argument

one that is either weak or strong with at least one false premise

Deductive logic

the part of logic that is concerned with the study of methods of evaluating arguments for validity and invalidity.

Inductive logic

the part of logic that is concerned with the study of methods of evaluating arguments for strength and weakness

categorical statement

a statement that relates two classes or categories.

subject term

the first noun or noun phrase that appears in a categorical statement when it is put into standard form

predicate term

the second noun or noun phrase that appears in a categorical statement when it is put into standard form

affirmative statement

some or all of the members of the class denoted by the subject term are also members of the class denoted by the predicate term

negative statement

denies that some or all of the members of the class denoted by the subject term are also members of the class denoted by the predicate term

universal statement

makes a claim about everything in the class denoted by its subject term

particular statement

only makes a claim about something in the class denoted by its subject term

stylistic variant

a different way of saying the same thing

Corresponding statements

categorical statements having the same subject term and the same predicate term

contradictories

Two statements that cannot both be true and they cannot both be false

contraries

Two statements are contraries that cannot both be true but they can both be false

necessary truth

a statement that cannot be false under any possible circumstances