Announcements and Such
•
One Song — Yes, Classic Yes
•
I’ve Seen All Good People
•
No office hours for Branden today
•
Essays to be returned next week
•
Tuesday after class
•
Today: Inference and the Extension of Knowledge II
•
This is where we start getting into some serious
theoretical
epistemology
.
•
Next time: Part I of three parts on the Architecture
of Knowledge (
very
serious theoretical epistemology)
•
A
deductively valid
argument (from premises
P
to
conclusion
C
) is such that it is
impossible
for
P
to
be true and (at the same time)
C
to be false.
•
An
inductively strong
argument is one such that
the
probability of
C
,
given
P,
Pr(
C

P
), is
high
.
Precisely, this means that Pr(
P
&
C
)
≈
Pr(
P
).
•
There are various kinds of inductive arguments:
•
Analogical arguments
•
a
is similar to
b
.
Fa
. Therefore,
Fb.
•
Abductive arguments
•
H
is the best explanation of
E
.
E
.
Therefore,
H
.
•
Generalizational arguments
•
Fa
&
Ga
.
Therefore, all
F
’s are
G
’s.
Inference and the Extension of Knowledge
Deductive and Inductive Inference (Review)
•
Audi distinguishes
deductive
and
inductive
transmission
of justification and knowledge.
•
Let’s think about justification first.
He suggests
that deductive transmission of justification
requires that the underlying argument be
valid
.
•
But, one of his examples is a bit puzzling.
He
suggests that if one
takes oneself
to be reasoning
deductively, then the underlying inferential
structure must
be
a
deductively valid
argument.
•
But, why isn’t the proper necessary condition
here being
justified in believing that
the
underlying inferential structure is valid?
•
After all, we’re just talking about justified belief
here,
not
knowledge.
I found this puzzling.
•
We say this about
testimony
, for instance…
Inference and the Extension of Knowledge
Inferential Transmission of Justification & Knowledge I
•
And, what if the argument I’m relying on
is
valid,
but I am justified in believing that it is
not
valid?
•
Why
not
say this
doesn’t
transmit justification?
•
It seems to me that this condition should be:
•
Deductive inferences (
i.e.
, inferences
S takes to
be deductive
)
transmit justification
only if S
is
justified in believing that the inference is valid.
•
Note: this is a
necessary
(
not
sufficient
) condition!
•
I write a long (nonfiction) book.
I am justified in
believing each claim I make in the book
P1
,
P2
,
P3
...
And, I (
knowingly
)
validly infer
their conjunction
C
=
P1
&
P2
&
P3
….
I also have very good reason to
believe that
all long books contain at least one false
claim
.
Here, I could
fail
to be justified in believing
C
.
•
Sufficient
conditions are
very hard
to come by…
Inference and the Extension of Knowledge
Inferential Transmission of Justification & Knowledge II
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•
Now, let’s discuss inductive inference & transmission
(we’ll come back to deductive inference again later).
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 Spring '07
 FITELSON
 Logic, Audi, Inferential Transmission

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