Induction

Inductive ReasoningAn Introduction

Deductive vs. Inductive Arguments

• Deductive arguments are arguments whose premises are claimed to support the conclusion in such a way that it is impossible for the premises to be true and the conclusion be false.

* The conclusion necessarily follows from the premises.


• Inductive arguments are arguments whose premises are claimed to support the conclusion in such a way that it is improbable for the premises to be true and the conclusion be false.

* The conclusion is claimed to follow only probably from the premises.


• Deductive arguments involve necessary reasoning.

• Inductive arguments involves probabilistic reasoning.


1. The meerkat is closely related to the suricat.

2. The suricat thrives on beetle larvae. 3. Therefore, probably the meerkat trives on

beetle larvae.

1. The meerkat is a member of the mongoose family.

2. All members of the mongoose family family are carnivores .

3. It necessarily follows that the meerkat is a carnivore.


1. The meerkat is closely related to the suricat. 2. The suricat thrives on beetle larvae. 3. Therefore, probably the meerkat trives on

beetle larvae. INDUCTIVE ARGUMENT 1. The meerkat is a member of the mongoose

family. 2. All members of the mongoose family family

are carnivores . 3. It necessarily follows that the meerkat is a

carnivore. DEDUCIVE ARGUMENT

Evaluative measures

1. The occurrence of special indicator words

2. The actual strength of the inferential link between premises and conclusion

3. The character or form of argumentation the arguer uses


(1) The meerkat is closely related to the suricat.(2) The suricat thrives on beetle larvae.(3) Therefore, probably the meerkat trives on

beetle larvae. INDUCTIVE ARGUMENT (a) The meerkat si a member of the mongoose

family.(b) All members of the mongoose family family are

carnivores .(c) It necessarily follows that the meerkat is a

carnivore. DEDUCIVE ARGUMENT

Inductive indicators

ProbablyImprobablePlausibleImplausibleLikelyUnlikelyReasonable to conclude

Deductive indicators

NecessarilyCertainlyAbsolutelyDefinitely

Special cases

« it must be the case that »must: ambiguous;can indicate

probability or necessity

« it certainly follows that »certainly: not automatically

deduction since

Evaluative measures




Actual Strength of Inferential Link bet. P & C

Deductive: If the conclusion follows with strict necessity from the premises

Inductive: If the conclusion follows probably from the premises

Actual Strength of Inferential Link bet. P & C(1) All saleswomen are extroverts.(2) Elizabeth Taylor is a saleswoman.(3) Therefore, Elizabeth Taylor is an extrovert.

(a) The vast majority of saleswomen are extroverts.(b) Elizabeth Taylor is a salewoman.(c) Therefore, Elizabeth Taylor is an extrovert.

Actual Strength of Inferential Link bet. P & C(1) All saleswomen are extroverts.(2) Elizabeth Taylor is a saleswoman.(3) Therefore, Elizabeth Taylor is an extrovert.DEDUCTIVE ARGUMENT

(a) The vast majority of saleswomen are extroverts.(b) Elizabeth Taylor is a salewoman.(c) Therefore, Elizabeth Taylor is an extrovert.INDUCTIVE ARGUMENT

Evaluative measures




Arguments best treated as deductive• Arguments based on mathematics• Argument from definition• Categorical syllogism• Hypothetical syllogism• Disjunctive syllogism

Arguments best treated as deductive

1. Argument based on mathematics- C depends on some purely arithmetic or geometric

computation or measurement Ex. 2 avocado + 6 lansones = 8 fruits

* statistics - inductive

2. Argument from definition- C depends merely upon the definition of some word or

phrase used in the premise or conclusion Ex. Claudia is mendacious

A certain paragraph is prolix


3. Categorical syllogism- a syllogism (an argument consisting of exactly 2

premises and 1 conclusion) in with each statement begins with one of the words « all, » « no, » or « some » Ex. All lasers are optical devices.

Some lasers are surgical instruments. Therefore, some optical devices are surgical instruments.


4. Hypothetical syllogism- A syllogism having a conditional statement (if-then)

for 1 or both its premises(a) If electricity flows through a conductor, then a magnetic field is produced.

(b) If a magnetic field is produced, then a nearby compass will be deflected. (c) Therefore, if electricity flows through a conductor, then a nearby compass

will be deflected.

(d) If quartz scratches glass, then quartz is harder than glass. (e) Quartz scratches glass. (f) Therefore, quartz is harder than glass.


5. Disjunctive syllogism- A syllogism having a disjunctive statement (either-

or) for one of its premises (a) Either a breach of contract is a crime or it is not punishable by the state.

(b) Breach of contract is not a crime. (c) Therefore, it is not punishable by the state.

Arguments best treated as inductive• Disjunctive syllogism• Prediction• Argument from analogy• Inductive generalization• Argument from authority• Argument based on signs• Causal inference

Arguments best treated as inductive

1. Predictions about the future- The premises deal with some known event in the

present or past, and the conclusion moves beyond this event to some event in the relative future

Ex. Because certain meteorological phenomena have been observed to develop over a certain region of central Missouri, a storm will occur there in 6 hours.

Because certain fluctuations occurred in the prime interest rate on Friday, the value of the dollar will decrease against foreign currencies on Monday.


2. Argument from analogy- An argument that depends on

the existence of an analogy, or similarity, bet. 2 things or states of affairs

- A certain condition that affects the better-known thing or situation is concluded to affect the similar, lesser-known thing or situation


3. Inductive Generalization- An argument that proceeds from the knowledge of

a selected sample to some claim about the whole group

Ex. statistics


4. Argument from Authority- An argument in which the conclusion rests upon a

statement made by some presumed authority or witness


4. Argument based on signs- An argument that proceeds from the knowledge of

a certain sign to a knowledge of the thing or situation that the sign symbolizes


5. A causal inference- Arguments that proceed from knowledge of a cause

to knowledge of the effect, or, conversely, from knowledge of an effect to knowledge of a cause

How well do you know?

No email messages are eloquent creations. Some love letters are eloquent creations. Therefore, some love letters are not email

messages.

No email messages are eloquent creations. Some love letters are eloquent creations. Therefore, some love letters are not email

messages.

DEDUCTION

The last time I ate here, the shrimp dish I ordered was disgusting. It must be the case that this restaurant buys lousy seafood.

The last time I ate here, the shrimp dish I ordered was disgusting. It must be the case that this restaurant buys lousy seafood.

INDUCTION

All guitar players are musicians. Some guitar players are not astronauts. Therefore, some musicians are not

astronauts.

All guitar players are musicians. Some guitar players are not astronauts. Therefore, some musicians are not

astronauts.

DEDUCTION

It was raining on Monday. It was raining on Tuesday. It was raining on Wednesday. It was raining on Thursday. It was raining on Friday. It was raining on Saturday. Therefore, it would rain on Sunday.

It was raining on Monday. It was raining on Tuesday. It was raining on Wednesday. It was raining on Thursday. It was raining on Friday. It was raining on Saturday. Therefore, it would rain on Sunday.

INDUCTION

My birthday is six days after my sister's birthday.

My birthday is on the 12th. Therefore, my sister's birthday is on the

18th.

My birthday is six days after my sister's birthday.

My birthday is on the 12th. Therefore, my sister's birthday is on the

18th.

DEDUCTION

The sum of the interior angles of any triangle is 180°.

In triangle #1, angle A is 30°, angle B is 90°. Therefore, angle C is 60°.

The sum of the interior angles of any triangle is 180°.

In triangle #1, angle A is 30°, angle B is 90°. Therefore, angle C is 60°.

DEDUCTION

(True/False)

If an argument contains the phrase “it definitely follows that,” then we know for

certain that the argument is deductive.

(True/False)

If an argument contains the phrase “it definitely follows that,” then we know for

certain that the argument is deductive.

(True/False)

An argument that proceeds from knowledge of a cause to knowledge of an effect is an

inductive argument.

(True/False)

An argument that proceeds from knowledge of a cause to knowledge of an effect is an

inductive argument.

(True/False)

Most arguments based on statistical reasoning are deductive.

(True/False)

Most arguments based on statistical reasoning are deductive.

(True/False)

In a deductive argument, it is improbable for the premises to be true and the conclusion

false.

(True/False)

In a deductive argument, it is improbable for the premises to be true and the conclusion

false.

The end