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The New Riddle of Induction
The New Riddle of Induction

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Paradoxes Dr Michael Johnson 2 nd Term 2017 Nelson Goodman 19061998 American philosopher Codeveloped a logic of individuals mereology that was more ontologically neutral than set theory ID: 540632 Download Presentation

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Presentation on theme: "The New Riddle of Induction"— Presentation transcript

Slide1

The New Riddle of Induction

Paradoxes

Dr. Michael Johnson

2

nd

Term 2017Slide2

Nelson Goodman

1906-1998

American philosopher

Co-developed a “logic of individuals” (mereology) that was more “ontologically neutral” than set theory.In Languages of Art, he absolutely demolishes the resemblance theory of representation.Slide3

Nelson Goodman

Nelson Goodman

Stephen Stich

Jennifer NadoSlide4

Fact, Fiction, and Forecast

Hilary Putnam said, this book is “one of the few books that every serious student of philosophy in our time

has

to have read.”Jerry Fodor said, “it changed, probably permanently, the way we think about the problem of induction, and hence about a constellation of related problems like learning and the nature of rational decision.”Slide5

Fact, Fiction, and Forecast

Hilary Putnam said, this book is “one of the few books that every serious student of philosophy in our time

has

to have read.”

Jerry Fodor said, “it changed, probably permanently, the way we think about the problem of induction, and hence about a constellation of related problems like learning and the nature of rational decision.”Slide6

The Dissolution of the OldSlide7

Goodman on Hume’s Problem

The problem of the validity of judgments about

future or unknown cases arises, as Hume pointed out, because such

judgments are neither reports of experience nor

logical consequences

of

it…”Slide8

Goodman on Hume’s Problem

“Predictions

, of course, pertain

to what has not yet been observed. And they cannot be logically inferred from what has been observed; for

what has

happened imposes no logical restrictions on what

will happen.”Slide9

Goodman on Hume

Goodman thinks Hume got the correct solution to his own problem, but he thinks that people have misinterpreted Hume.Slide10

Goodman on Hume

Hume asks: How can we justify induction?

Goodman wants to look at an analogous question: How can we justify

deduction?Slide11

Arguments and Rules: Example

Argument

If it’s raining, then the streets are wet.

The streets aren’t wet.

Therefore, it isn’t raining.

Rule of Inference

If P, then Q

Not-Q

Therefore, not-PSlide12

Justification of a Deductive Argument

Argument

If it’s raining, then the streets are wet.

The streets aren’t wet.

Therefore, it isn’t raining.

Rule of Inference

If P, then Q

Not-Q

Therefore, not-P

ConformsSlide13

Justification of a Rule of Inference

Argument

If it’s raining, then the streets are wet.

The streets aren’t wet.

Therefore, it isn’t raining.

Rule of Inference

If P, then Q

Not-Q

Therefore, not-P

ModelsSlide14

Circle?

Argument

If it’s raining, then the streets are wet.

The streets aren’t wet.

Therefore, it isn’t raining.

Rule of Inference

If P, then Q

Not-Q

Therefore, not-P

Conforms

ModelsSlide15

A Virtuous Circle?

“This

looks flagrantly circular. I have said that

deductive inferences are justified by their conformity to valid general rules, and that general rules are justified by their

conformity to

valid inferences.

But this circle is a

virtuous one.”Slide16

Vicious Circle

A: I believe that God exists.

B: Why do you believe that.

A: Because the bible says that God exists.B: Why do you think what the bible says is true?A: Because God wrote the bible and He doesn’t lie.Slide17

Reflective Equilibrium

“The

point is that rules and particular inferences

alike are justified by being brought into agreement with each other. A rule is amended if it yields an inference we

are unwilling

to accept; an inference is rejected if it violates

a rule

we are unwilling to amend…” Slide18

Van McGee’s CounterexampleSlide19

Reflective Equilibrium

Argument

If a Republican wins, then (if it’s not Reagan, it’s Anderson)

A Republican will win.

Therefore, If Reagan doesn’t win, Anderson will.

Rule of Inference

If P, then Q

Not-Q

Therefore, not-P

Conforms

ModelsSlide20

Reflective Equilibrium

“The

process of

justification is the delicate one of making mutual adjustments between rules and accepted inferences; and in the

agreement achieved

lies the only justification needed

for either.”Slide21

The Dissolution of the Problem

Goodman thinks the same thing is true for induction.

The rules of inductive inference are justified by the particular arguments we are willing to accept. The arguments we accept are justified by the rules.

Furthermore, Goodman thinks this is Hume’s solution.Slide22

Justification of Induction

Argument = Custom or Habit

The sun came up yesterday.

The sun came up the day before yesterday.…

The sun came up 6,000 years ago.

Therefore, the sun will come up tomorrow.

Rule of Inference

In the past, when A happened, B happened.

Therefore, in the future, when A happens, B will happen.

Conforms

ModelsSlide23

The Logic of ConfirmationSlide24

Logic

Deductive logic is about finding deductively valid argument forms (rules of inference).

Inductive

logic can’t involve valid argument forms, because the truth of the premise(s) doesn’t guarantee the truth of the conclusion.

Thus we need a new notion of “inductive validity” or

confirmation

.Slide25

Confirmation as Inverse of Deduction

[For all x] x is F [For all x: x is in population P] x is F

logically impliesSlide26

Confirmation as Inverse of Deduction

[For all x] x is F [For all x: x is in population P] x is F

confirmsSlide27

The Logic of Confirmation

Goodman points out that it’s not in general true that confirmation is the inverse of deduction, but this particular instance seems good.

There’s lots of work to do in the logic of confirmation. Goodman, however, is going to argue that a

logic of confirmation may be impossible.Slide28

The New RiddleSlide29

t

0Slide30

Logical Deduction

[For all emeralds x] x is green

[For all emeralds x: x is examined <

t

0

] x is greenSlide31

Confirmation

[For all emeralds x] x is green

[For all emeralds x: x is examined <

t

0

] x is greenSlide32

Definition of ‘Grue

An object x is

grue =

df

x is examined before

t

0 and green; otherwise x is blueSlide33

t

0Slide34

Logical Deduction

[For all emeralds x] x is

grue

[For all emeralds x: x is examined <

t

0

] x is

grueSlide35

Confirmation

[For all emeralds x] x is

grue

[For all emeralds x: x is examined <

t

0

] x is

grueSlide36

The Grue

Problem

When we examine a bunch of green emeralds, we’re happy to believe this confirms all emeralds are green.

But when we examine a bunch of grue

emeralds, we don’t believe this confirms all emeralds are

grue

.

What’s the difference?Slide37

The Grue

Problem

Old Question: “Why

does a positive instance of a hypothesis give any grounds for predicting further instances?“

New Question: “

What hypotheses are confirmed by their positive instances

?”Slide38

A Tempting Response

Grue

’ is weird. It’s defined as being an observed green thing before t0

or a blue thing.

Normal

words like ‘green’ aren’t weird like this.Slide39

Goodman’s Reply

Grue

’ is weird only because we start out speaking a language with ‘green’ and ‘blue.’ Suppose we spoke a language with only ‘grue’ and ‘bleen’ and no ‘green’ and ‘blue.’

Then to introduce a word ‘green’ (that means what our word ‘green’ means) we would have to say: an object x is green =

df

x is observed before

t

0 and grue; otherwise x is bleen.Slide40

Natural Kinds ReduxSlide41

Ravens Paradox Redux

Remember Quine’s solution to the Paradox of the Ravens.

Quine thought that an observation of non-black non-ravens does not confirm “All ravens are black” because the category

non-black things is not a natural kind.Slide42
Slide43
Slide44

What Is a Natural Kind?

Cluster Kinds Answer

:

There are “families of… [natural] properties that are contingently clustered in nature (Boyd 1991, 1999a; Millikan 1999). These

families of properties cluster together over time either because the presence of some properties in the family

favours

the presence of others or because there are underlying internal mechanisms and/or extrinsic contextual mechanisms which tend to secure the co-occurrence of the properties.

A

natural kind is any such family of co-occurring

properties” (Stanford Encyclopedia of Philosophy, “Natural Kinds”)Slide45

What Is a Natural Kind?

Cluster Kinds Answer

:

There are “families of… [natural] properties that are contingently clustered in nature (Boyd 1991, 1999a; Millikan 1999).

These

families of properties cluster together over time either because the presence of some properties in the family

favours

the presence of others or because there are underlying internal mechanisms and/or extrinsic contextual mechanisms which tend to secure the co-occurrence of the properties.

A natural kind is any such family of co-occurring

properties” (Stanford Encyclopedia of Philosophy, “Natural Kinds”)Slide46

What Is a Natural Kind?

Cluster Kinds Answer

:

There are “families of… [natural] properties that are contingently clustered in nature (Boyd 1991, 1999a; Millikan 1999).

These

families of properties cluster together over time either because the presence of some properties in the family

favours

the presence of others or because there are underlying internal mechanisms and/or extrinsic contextual mechanisms which tend to secure the co-occurrence of the properties.

A

natural kind is any such family of co-occurring

properties” (Stanford Encyclopedia of Philosophy, “Natural Kinds”)Slide47

Example: Biological Species

Homeostatic clustering

: mechanisms exist that prevent deviant properties from persisting in the group.

Mutations that have an effect are most often deleterious.Species’ evolutionary niche ‘molds’ them in a certain direction.