Branden Fitelson
Philosophy 12A Notes
1
Overview of Today’s Lecture
•
Today’s Music:
Led Zeppelin
•
The midterm is on Thursday, 6/10 (in class)
.
–
I’ve posted (and discussed) a sample midterm. It has the same
structure and complexity as the actual midterm (good study guide).
•
I have posted HW #3, which is due on Thursday @ 4pm in the drop box.
–
It’s all chapter 3 problems — truthtable methods for validitytesting.
•
I posted revised versions of lecture #6 and my “short method” handout.
•
MacLogic
— a useful computer program for natural deduction.
–
You might want to download
MacLogic
at this point . . .
–
We’ll be using it very soon (and for the rest of the term) . . .
–
See
http://fitelson.org/maclogic.htm
•
Today: Chapter 3, Finalé and Chapter 4 Intro.
UCB Philosophy
Chapter
3
(Finalé) & Chapter
4
(Intro)
06/08/10
Branden Fitelson
Philosophy 12A Notes
2
Expressive Completeness: Rewind, and More ExtraCredit
•
Q
. How can we define
↔
in terms of

?
A
. If you naïvely apply the
schemes I described last time, then you get a
187 symbol monster
:
p
↔
q
A

A
, where
A
is given by the following
93 symbol
expression:
(((p

(q

q))

(p

(q

q)))

((p

(q

q))

(p

(q

q))))

(((q

(p

p))

(q

(p

p)))

((q

(p

p))

(q

(p

p))))
•
There are
simpler
definitions of
↔
using

.
E.g.
, this
43 symbol
answer:
p
↔
q
((p

(q

q))

(q

(p

p)))

((p

(q

q))

(q

(p

p)))
•
I offered E.C. for the shortest solution. Some students have come up
with it (the shortest solution is
<
25 symbols, counting parens).
•
More E.C.
Find the
shortest possible
definitions of (1)
p
→
q
, (2)
p
∨
q
, and (3)
∼
p
&
∼
q
in terms of
p
,
q
, and the NAND operator

.
•
If you submit EC, please
prove
the correctness of your solution, using a
truthtable method. You may submit these E.C. solutions to your GSI.
UCB Philosophy
Chapter
3
(Finalé) & Chapter
4
(Intro)
06/08/10
Branden Fitelson
Philosophy 12A Notes
3
Presenting
Your “ShortCut” TruthTable Tests
•
In any application of the “short” method, there are two possibilities:
1. You find an interpretation (
i.e.
, a row of the truthtable) on which all the
premises
p
1
, . . . ,
p
n
of an argument are true and the conclusion
q
is
false.
All you need to do here
is (
i
) write down the relevant row of the
truthtable, and (
ii
) say “Here is an interpretation on which
p
1
, . . . ,
p
n
are all true and
q
is false. So,
p
1
, . . . ,
p
n
∴
q
is
in
valid.”
2. You discover that there is
no possible way
of making
p
1
, . . . ,
p
n
true
and
q
false. Here, you need to
explain all of your reasoning
(as I do in
lecture, or as Forbes does, or as I do in my handout). It must be clear
that you have
exhausted all possible cases
, before concluding that
p
1
,
. . . ,
p
n
∴
q
is
valid
. This can be rather involved, and should be spelled
out in a stepbystep fashion. Each salient case has to be examined.
•
Consult my handout and lecture notes for model answers of both kinds.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Fall '06
 Buechner
 Philosophy, Logic, Natural deduction, Branden Fitelson, Philosophy 12A Notes

Click to edit the document details