### 8. Moore`s Proof

```Certainty and Error
One thing Russell seems right about is that we don’t need
certainty in order to know something.
In fact, even Descartes grants this.
Certainty and Error
The Certainty Argument
(1) No one is ever certain of
anything about the external
world.
(2)
If S knows that p then S is
absolutely certain that p.
(3) Therefore, no one knows
anything about the external
world.
Possibility of Error Argument
(1) For any belief, p, S has about
the external world S could be
mistaken.
(2)
If a belief could be
mistaken, then it is not a
case of knowledge
(3) Therefore, S does not know
anything about the external
world.
Certainty and Error
It seems very easy to respond to the skeptic if we can just
deny the second premise in these arguments.
 It is true that there is some slight possibility we are
wrong.
 But we have no reason to think that we are.
 If knowledge does not require absolute certainty or
something like it, it seems we have plenty of knowledge!
Transmissibility
Unfortunately there is another skeptical argument that
does not rely on such implausible premises and has the
same radical conclusion.
Transmissibility
Consider the following principle:
Transmissibility: If I know p is true, and I also know that p
entails q, then I can know that q is true.
Is this principle true?
Transmissibility
It sure seems like it.
If I know p, and know that p entails q, then it seems I could
simply draw the inference in order to come to know that q!
Unfortunately, if this principle is true, we can generate a
powerful skeptical argument that does not depend on the
requirement that knowledge be absolutely certain.
Transmissibility
The Transmissibility Argument (Table)
1. I can’t know that I am not in the Matrix.
2. If there is a table here, then I am not in the Matrix.
3. I know that 2 is true.
4. If I know that there is a table here, and I also know that this
is incompatible with being in the Matrix, then I can know
I’m not in the Matrix.
5. Therefore, I can’t know there is a table here.
Transmissibility
There is nothing special about the table. I could run the
same reasoning for any belief about the external world.
One can immediately see that if the argument is sound,
then we don’t know anything about the external world.
A Modern Version: Brain in
a Vat
Transmissibility
The Transmissibility Argument (Hands)
1. I can’t know that I am not a BIV.
2. If I have hands, then I am not a BIV.
3. I know that 2 is true.
4. If I know that I have hands, and I also know that this is
incompatible with being a BIV, then I can know I’m not a
BIV.
5. Therefore, I can’t know that I have hands.
Transmissibility
The argument is valid.
Unlike the Certainty and Error arguments, none of the premises
are obviously false.
This is the puzzle that really requires an answer and it has
stumped philosophers (and everyone else) for hundreds of years.
For Next Time
Finish Bouwsma. Start reading Thomson’s “A Defense of
Abortion” (59-79)
Jenna’s office hours today are cancelled. They will be
rescheduled for next week.
Moore’s Proof of an
External World
The proof:
1. Here is a hand.
2. Here is another hand.
3. Hands are external objects.
4. Therefore, external objects exist.
A Proof ???
Moore claims that the proof is “perfectly rigorous” and
that “it is perhaps impossible to give a better more rigorous
proof of anything whatever.” (143)
A Proof ???
Three conditions for a rigorous proof:
1. The premises are different from the conclusion (no
question-begging or circular reasoning)
2. One must know that the premises are true.
3. The conclusion is validly deducible from the premises.
A Proof ???
We ordinarily accept proofs of this kind:
 I don’t believe my roommate when he tells me there
is beer in the fridge.
 He can properly prove me to be mistaken by going
to the fridge and pointing out a couple of beers.
 Similarly if we doubt that there are external objects,
all that is needed is for us to produce one!
Dissatisfaction with the
Proof
 The skeptic’s argument purports to show that
one cannot know things such as that one has
hands.
 So how can Moore claim in response to the
skeptic that he does know he has hands?
Dissatisfaction with the
Proof
Moore concedes that he didn’t prove that he has hands.
However, as we already know proof and certainty are not
required for knowledge!
“I can know things which I cannot prove; and among things
which I certainly did know, even if (as I think) I could not
prove them, were the premises of my two proofs.” (105)
Begging the Question
But Moore seems to beg the question against the skeptic.
 One begs the question against if one assumes the
falsehood of an argument’s conclusion in one’s
premises.
 The skeptic gives an argument for the conclusion that
Moore doesn’t know that he has hands.
 Moore simply assumes that this is false without any
argument!
Moore’s Response
Moore thinks that if he is begging the question against the
skeptic, the skeptic equally begs the question against him!
One Man’s Modus
Ponens…
Skeptical Argument
(condensed)
Moorean Argument
1. I know that I have hands.
1. I cannot know that I am
2. If I know that I have
not a BIV.
hands, then I can know
2. If I know that I have
that I am not a BIV.
hands, then I can know
3. Therefore, I can know
that I am not a BIV
that I am not a BIV.
3. I cannot know that I
have hands.
One Man’s Modus
Ponens…
Skeptical Argument
(condensed)
1. I know that I have
hands.
1. I cannot know that I am 2. If I know that I have
not a BIV.
hands, then I can know
that I am not a BIV.
2. If I know that I have
hands, then I can know 3. Therefore, I can know
that I am not a BIV
that I am not a BIV.
3. I cannot know that I
have hands.
Moorean Argument
One Man’s Modus
Ponens…
Moore thinks that all the premises of both arguments are
very plausible.
However, the one he is least likely to give up on is the
claim that he knows he has hands (and other similar
claims).
Two Anti-Skeptical Projects
Ambitious Anti-Skeptical Project: Refute a skeptic on his
own terms. Show to the satisfaction of the skeptic that one
knows about the external world.
Modest Anti-Skeptical Project: Establish to our own
satisfaction that we know things about the external world,
without contradicting obvious facts about perception and
evidence.
The Modest Anti-Skeptical
Project
Does Moore succeed in convincing us by our own standards
that we know things about the external world?
A Paradox Remains
For all of his cleverness, few people are convinced by
Moore’s argument on its own.
A Paradox Remains
Moore has shown that the following three claims are
inconsistent:
1. Transmissibility: If I know p, and know that p entails
q, then I can know q.
2. I can’t know that I am not in the Matrix/dreaming/a
BIV/etc.
3. I know that I have hands.
A Paradox Remains
He may even be right that most of us won’t give up on #3
as the skeptic demands.
 We still have been given no rational grounds to believe
#3. Moore just insists that it is the most plausible.
 However, both of the other two claims seem
extraordinarily plausible on their own.
 We still have no idea which one is false or why!
A Paradox Remains
Without an answer to this puzzle, it is hard to shake the
feeling that we are just being dogmatic about our supposed
knowledge.
If we have no rational reason to prefer #3 to the other two
propositions, or know which of #1 or #2 are false
shouldn’t we suspend judgment?
```