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
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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.Slide42Slide43Slide44
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.