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Conjecture

Inductive Reasoning

Write a rule for the pattern:... 10, 20,…

Write a rule for the pattern:... 1, 2, 4,…

A conclusion based on inductive reasoning.

Making conclusions based on patterns you observe.

Add ten to get the next term.

Multiply each term by two to get the next term.

Conjecture

A conclusion based on inductive reasoning.

Inductive Reasoning

Making conclusions based on patterns you observe.

Conjecture

Inductive Reasoning

Write a rule for the pattern:... 10, 20,…

Write a rule for the pattern:... 1, 2, 4,…

A conclusion based on inductive reasoning.

Making conclusions based on patterns you observe.

Add ten to get the next term.

Multiply each term by two to get the next term.

Conjecture

A conclusion based on inductive reasoning.

Inductive Reasoning

Making conclusions based on patterns you observe.

Inductive argument

Argument from analogy

Analogues

Conclusion-analogue

an argument that claims that its premises make the conclusion…

inferring that 2 or more things are similar in some respect o…

things being compared

the thing we are drawing the conclusion about

Inductive argument

an argument that claims that its premises make the conclusion…

Argument from analogy

inferring that 2 or more things are similar in some respect o…

inductive reasoning

point

line

plane

The process of observing patterns and forming conclusions abo…

a line (or part of a line) that divides a geometric figure in…

is made up of an infinite number of points that extend infini…

a flat, two-dimensional surface

inductive reasoning

The process of observing patterns and forming conclusions abo…

point

a line (or part of a line) that divides a geometric figure in…

inductive reasoning

point

line

plane

A type of logic in which generalizations are based on a large…

The place where two lines, rays, or line segments meet

An infinite one dimensional figure

An infinite two-dimensional figure

inductive reasoning

A type of logic in which generalizations are based on a large…

point

The place where two lines, rays, or line segments meet

Conjecture

speculate

scrutinize

bias

a hypothesis that has been formed by speculating or conjectur…

to believe especially on uncertain or tentative grounds

(v.) to examine closely

prejudice

Conjecture

a hypothesis that has been formed by speculating or conjectur…

speculate

to believe especially on uncertain or tentative grounds

Conjecture

Inductive Reasoning

Write a rule for the pattern:... 10, 20,…

Write a rule for the pattern:... 1, 2, 4,…

A conclusion based on inductive reasoning.

Making conclusions based on patterns you observe.

Add ten to get the next term.

Multiply each term by two to get the next term.

Conjecture

A conclusion based on inductive reasoning.

Inductive Reasoning

Making conclusions based on patterns you observe.

inductive reasoning

conjecture

counterexample

conditional statement

process of reasoning that a rule is true because specific cas…

statement believed

evidence that conjecture is wrong need only 1

if then form

inductive reasoning

process of reasoning that a rule is true because specific cas…

conjecture

statement believed

Definition of Inductive Reasoning

Definition of Conjecture

Definition of Theorem

Definition of Counterexample

The process of reasoning that a statement is true because sev…

A guess, or a statement that is believed to be true, but not…

A conjecture that has been proven.

One example that is used which does not support the conjectur…

Definition of Inductive Reasoning

The process of reasoning that a statement is true because sev…

Definition of Conjecture

A guess, or a statement that is believed to be true, but not…

What is inductive reasoning?

What is a conjecture?

What is Counterexample?

Find the next five terms of the sequen…

Making a conclusion based on observations and patterns

A concluding statement reached using inductive reasoning

An example that shows a conjecture is false

9, 11, 13, 15, 17... To generate the next term keep counting by…

What is inductive reasoning?

Making a conclusion based on observations and patterns

What is a conjecture?

A concluding statement reached using inductive reasoning

Making conclusions based on patterns y…

A conclusion based on inductive reason…

An example that shows a conjecture is…

9, 11, 13, 15, 17... To generate the next…

Inductive Reasoning

Conjecture

What is Counterexample?

Find the next five terms of the sequence then write a conject…

Making conclusions based on patterns y…

Inductive Reasoning

A conclusion based on inductive reason…

Conjecture

Conjecture

Inductive Reasoning

Counterexample

Conditional Statement

an unproven statement that is based on observations

when you find a pattern in specific cases then write a conjec…

A specific case that shows a conjecture is false.

A logical statement that has two parts, a hypothesis and a co…

Conjecture

an unproven statement that is based on observations

Inductive Reasoning

when you find a pattern in specific cases then write a conjec…

Prediction Arguments

Analogical Arguments

Generalization From a Sample

Arguments From Authority

1. It has been raining for seven days straight and the sky is…

1. Monkeys and humans have similar hearts.... 2. Drug X works on…

1. We randomly sampled 10% of the widgets, and fewer than 1%…

1. Kobe is a pro at basketball.... 2. Kobe says practice makes p…

Prediction Arguments

1. It has been raining for seven days straight and the sky is…

Analogical Arguments

1. Monkeys and humans have similar hearts.... 2. Drug X works on…

the process of making a general conclu…

You conclude that it rains on every Tu…

You conclude that only elderly people…

You conclude that this is true in all…

Inductive reasoning

Using inductive reasoning, what conclusion can you make from…

Using inductive reasoning, what conclusion can you make from…

Using inductive reasoning, what conclusion can you make from…

the process of making a general conclu…

Inductive reasoning

You conclude that it rains on every Tu…

Using inductive reasoning, what conclusion can you make from…

Inference

Reasoning

Inductive Argument

Literal Analogy

a calculated guess

is the mental process of inferring a conclusion from the evid…

reasoning from specific to general: conclusion based on one o…

is a comparison of things that have the same classification

Inference

a calculated guess

Reasoning

is the mental process of inferring a conclusion from the evid…

Conjencture

Counterexample

Conditional

Hypothesis

The conclusion you reach using inductive reasoning.

An example that shows that the conclusion is wrong.

An "if, then" statement.

The "if" part of a conditional.

Conjencture

The conclusion you reach using inductive reasoning.

Counterexample

An example that shows that the conclusion is wrong.

adjacent angles

angle

bisector

collinear

2 angles that lie in the same plane, have a common vertex & a…

the intersection of 2 noncollinear rays at a common endpoint.…

any figure that divides another figure into 2 congruent parts

points that lie on the same line

adjacent angles

2 angles that lie in the same plane, have a common vertex & a…

angle

the intersection of 2 noncollinear rays at a common endpoint.…

Inductive Reasoning

Conjecture

Counterexample

Conditional Statements

Look at a pattern and base a prediction to that pattern

A statement of what you think will happen based on the patter…

An instance where the conjectured pattern does not work

an if, then statement consisting of a hypothesis and a conclu…

Inductive Reasoning

Look at a pattern and base a prediction to that pattern

Conjecture

A statement of what you think will happen based on the patter…

Enumerative induction

Target population

Sample

Relevant property

Reasoning from premises of group of things to conclusion abou…

Group as a whole or collection of individuals

Observed members of target or group

The property of interest regarding the group

Enumerative induction

Reasoning from premises of group of things to conclusion abou…

Target population

Group as a whole or collection of individuals

Max Black

Max Black

Max Black

Inductive Demonstration

"No general justification of induction is either possible or…

"The idea of the so-called inductive leap is built into our c…

"Induction, by definition, is not deduction."

by using principles that have been found to work... (induction i…

Max Black

"No general justification of induction is either possible or…

Max Black

"The idea of the so-called inductive leap is built into our c…

Inductive Reasoning

Conjecture

Counter Example

Negation

Specific examples that lead to a generalization

A conclusion based on individual events

An example that shows a statement is false

adding in or taking out the word "not"

Inductive Reasoning

Specific examples that lead to a generalization

Conjecture

A conclusion based on individual events

inductive reasoning

conjecture

counterexample

statement

observing a pattern and drawing a conclusion

concluding statement after you determine the pattern

proof of a false statement

sentence that is true or false

inductive reasoning

observing a pattern and drawing a conclusion

conjecture

concluding statement after you determine the pattern

Inductive Reasoning

Judgement

Heuristics

Representativeness Heuristics

The attempt to infer some new principle or proposition from o…

The process of extrapolating from evidence to draw conclusions.

A strategy for making judgements quickly at the price of occa…

Judge the likelihood that an individual, object, or event bel…

Inductive Reasoning

The attempt to infer some new principle or proposition from o…

Judgement

The process of extrapolating from evidence to draw conclusions.

conjecture

inductive reasoning

counter-example

conditional statement

a statement based on observations that you think is true, but…

a logical process of finding a pattern for the specific case,…

an example that disproves a conjecture

a logical statement with 2 parts: hypothesis and conclusion

conjecture

a statement based on observations that you think is true, but…

inductive reasoning

a logical process of finding a pattern for the specific case,…

Fallacies

Formal, informal

Informal types of fallacies

Fallacies of relevance/irrelevance

(Non-sequitur)... Mistakes in reasoning

Types of fallacies

Ambiguity, relevance

issues that are irrelevant to the case on hand

Fallacies

(Non-sequitur)... Mistakes in reasoning

Formal, informal

Types of fallacies

Inductive Reasoning

The reasoning process begins with a ... Ex:

The chain of __________ begins with __…

The most basic type of inductive reaso…

A type of logic in which generalizations are based on a large…

general principle ... ex: People who comb their hair wake up on…

evidence... observation... previous observations... conclusion

induction by enumeration, or, more commonly, generalization.

Inductive Reasoning

A type of logic in which generalizations are based on a large…

The reasoning process begins with a ... Ex:

general principle ... ex: People who comb their hair wake up on…

Evidence comes from

Research methods

method used depends on

Methods share

personal experience ... authority ... science

surveys ... observations ... correlational studies ... experiments

question you are asking ... ethics ... other factors

form of inference ... form of inductive reasoning ... use statistics

Evidence comes from

personal experience ... authority ... science

Research methods

surveys ... observations ... correlational studies ... experiments

inductive reasoning

conducture

statement

truth value

reasoning that uses a number of specific examples to arrive t…

A concluding statement reached using inductive reasoning.

A sentence that is either true or false.

saying a statement is true or false. statements are often rec…

inductive reasoning

reasoning that uses a number of specific examples to arrive t…

conducture

A concluding statement reached using inductive reasoning.

conjecture

counter example

conditional statement

if, when, because

unproven statement based on observations

specific case (1 time) to disprove conjecture

logical statement w/ 2 parts (hypothesis & conclusion) ... -writ…

directional words

conjecture

unproven statement based on observations

counter example

specific case (1 time) to disprove conjecture

Conjecture

Inductive Reasoning

Write a rule for the pattern:... 10, 20,…

Write a rule for the pattern:... 1, 2, 4,…

A conclusion based on inductive reasoning.

Making conclusions based on patterns you observe.

Add ten to get the next term.

Multiply each term by two to get the next term.

Conjecture

A conclusion based on inductive reasoning.

Inductive Reasoning

Making conclusions based on patterns you observe.

Adjacent angles

Angle

Bisector

Collinear

2 angles that lie in the same plane, have a common vertex and…

The intersections of 2 noncollinearn rays at a common endpoin…

A ray that divides an angle into 2 congruent angles

Points that lie on the same line

Adjacent angles

2 angles that lie in the same plane, have a common vertex and…

Angle

The intersections of 2 noncollinearn rays at a common endpoin…

Argument by analogy

Inductive Generalization

Hypothetical Reasoning

generalization

similar things act in similar ways: relevant similarities mus…

info on some members of a set to draw conclusions on the whol…

testing of hypothesis through logical consequences: must prot…

a statement which ascribes or denies some quality or relation…

Argument by analogy

similar things act in similar ways: relevant similarities mus…

Inductive Generalization

info on some members of a set to draw conclusions on the whol…

Conjecture

Inductive Reasoning

Write a rule for the pattern:... 10, 20,…

Write a rule for the pattern:... 1, 2, 4,…

A conclusion based on inductive reasoning.

Making conclusions based on patterns you observe.

Add ten to get the next term.

Multiply each term by two to get the next term.

Conjecture

A conclusion based on inductive reasoning.

Inductive Reasoning

Making conclusions based on patterns you observe.

Enumerative: Statistical syllogism ... (2…

Sample Size

Hasty Generalization

Biased Sample

83% of the halls students own apple devices... Wei-en is a hall…

Generally the larger the sample size, the more likely it is t…

The sample size is too small to yield any reliable informatio…

Drawing a conclusion about a population based on a sample tha…

Enumerative: Statistical syllogism ... (2…

83% of the halls students own apple devices... Wei-en is a hall…

Sample Size

Generally the larger the sample size, the more likely it is t…

Analogy

Analogical Induction Pattern

Relevant Similarities

Relevant Dissimilarities

A comparison between two or more things alike in specific res…

Thing 1 has properties A, B , C plus D... Thing 2 has properties…

The More relevant (to do with conclusion) similarities betwee…

The more Disanalogies there are between the things being comp…

Analogy

A comparison between two or more things alike in specific res…

Analogical Induction Pattern

Thing 1 has properties A, B , C plus D... Thing 2 has properties…

Inductive Reasoning

Point

Line

Plane

observing patterns and forming conclusions about those patterns

particular spot, place, or position in an area or on a map, o…

a straight one-dimensional figure having no thickness and ext…

a flat, two-dimensional surface

Inductive Reasoning

observing patterns and forming conclusions about those patterns

Point

particular spot, place, or position in an area or on a map, o…

Inductive

Deductive

Deductive

Inductive

The Giants have lost their last seven games. Thus, they will…

If you brush and floss your teeth daily then you will have fe…

Jones will play tennis today if Smith plays. Jones will not p…

4 out of 5 times I beat Corey at pool and I'm going to play h…

Inductive

The Giants have lost their last seven games. Thus, they will…

Deductive

If you brush and floss your teeth daily then you will have fe…

Inductive

Deductive

Deductive

Inductive

The Giants have lost their last seven games. Thus, they will…

If you brush and floss your teeth daily then you will have fe…

Jones will play tennis today if Smith plays. Jones will not p…

4 out of 5 times I beat Corey at pool and I'm going to play h…

Inductive

The Giants have lost their last seven games. Thus, they will…

Deductive

If you brush and floss your teeth daily then you will have fe…

Argument from Analogy

Analogues

Premise Analogue (sample analogue)

Conclusion Analogue (target analogue)

an argument that something has an attribute because a similar…

things that have similar attributes... (Bill and Sam)

similar thing in Argument from Analogue... In premise (Sam)

analogue referred to in the conclusion of an argument from an…

Argument from Analogy

an argument that something has an attribute because a similar…

Analogues

things that have similar attributes... (Bill and Sam)

Target Group(target population)

Sample (sample member)

Relevant Property (or property in ques…

Hasty Generalization

In enumerative induction, the whole collection of individuals…

In enumerative induction, the observed members of the target…

In enumerative induction, a property, or characteristic, that…

The fallacy of drawing a conclusion about a target group base…

Target Group(target population)

In enumerative induction, the whole collection of individuals…

Sample (sample member)

In enumerative induction, the observed members of the target…

Inductive Reasoning

Conjecture

Counterexample

Conditional

reasoning based on your observation

a conclusion you reach using inductive reasoning

an example that shows a conjecture is incorrect

an if-then statement, "If p, then q"

Inductive Reasoning

reasoning based on your observation

Conjecture

a conclusion you reach using inductive reasoning

adjacent angles

angle

collinear

complementary angles

angles in the same plane that have a common vertex and a comm…

a figure formed by two noncollinear rays with a common endpoint

points that lie in the same line

two angles whose measures have a sum of 90

adjacent angles

angles in the same plane that have a common vertex and a comm…

angle

a figure formed by two noncollinear rays with a common endpoint

Collinear

Coplanar

Complementary

Inductive reasoning

______________ points are points that lie on the same line

__________ points are points that lie in the same plane

the sum of the measures of two ______________ angles is 90 de…

process of reasoning that a rule or statement is true by draw…

Collinear

______________ points are points that lie on the same line

Coplanar

__________ points are points that lie in the same plane

Inductive

Deductive

Deductive

Inductive

The Giants have lost their last seven games. Thus, they will…

If you brush and floss your teeth daily then you will have fe…

Jones will play tennis today if Smith plays. Jones will not p…

4 out of 5 times I beat Corey at pool and I'm going to play h…

Inductive

The Giants have lost their last seven games. Thus, they will…

Deductive

If you brush and floss your teeth daily then you will have fe…

Inductive

Deductive

Deductive

Inductive

The Giants have lost their last seven games. Thus, they will…

If you brush and floss your teeth daily then you will have fe…

Jones will play tennis today if Smith plays. Jones will not p…

4 out of 5 times I beat Corey at pool and I'm going to play h…

Inductive

The Giants have lost their last seven games. Thus, they will…

Deductive

If you brush and floss your teeth daily then you will have fe…

Inductive

Deductive

Deductive

Inductive

The Giants have lost their last seven games. Thus, they will…

If you brush and floss your teeth daily then you will have fe…

Jones will play tennis today if Smith plays. Jones will not p…

4 out of 5 times I beat Corey at pool and I'm going to play h…

Inductive

The Giants have lost their last seven games. Thus, they will…

Deductive

If you brush and floss your teeth daily then you will have fe…

Inductive

Deductive

Deductive

Inductive

The Giants have lost their last seven games. Thus, they will…

If you brush and floss your teeth daily then you will have fe…

Jones will play tennis today if Smith plays. Jones will not p…

4 out of 5 times I beat Corey at pool and I'm going to play h…

Inductive

The Giants have lost their last seven games. Thus, they will…

Deductive

If you brush and floss your teeth daily then you will have fe…