**PHIL 450A:
HANDOUT #1**

**ON REASONING**

I assume that students taking a
400-level level philosophy course are familiar with basic logical
terminology. Items 1-6 on this handout
provide a summary of the necessary terminology.
Items 7-12 use that terminology to make some distinctions that will be
important in this course.

1.
__Properties [Terms] and
Propositions [Sentences]__.
Capital letters, "A", "B", "P",
"Q", etc. can stand for properties [expressed by terms, such as
"is morally justified"] and propositions [expressed by sentences,
such as "Governments ought to guarantee a protected sphere of
liberty."]. Small letters
("p", "q", etc.) can also be used to stand for
propositions.

Complex properties and complex
propositions can be constructed out of simpler ones by the following logical
operations:

(a).
__Negation__. The negation of
male (M) is not male (-M).

(b)
__Conjunction__. The
conjunction of brother (B) and father (F) is brother and father (B&F).

(c)
__Alternation__. The alternation
of brother (B) and father (F) is brother or father (BvF). A person is a BvF if he is a B or if he is a
F or if he is a B and a F.

(d) A __conditional__ is a
proposition of the form: If P, then
Q.

2.
__Metaphysically Necessary And
Metaphysically Contingent Truths and Falsehoods__. If a proposition is such that it could not be
false, then the proposition is a __metaphysically necessary truth__. If it is the negation of a metaphysically
necessary truth, it is a __metaphysically necessary falsehood__. In this course, whenever we use the term
"necessary" without modification, it will be assumed that we are
speaking of metaphysical necessity. If a
proposition is neither necessarily true nor necessarily false, then it is __contingent__
(either contingently true or contingently false).

3. __Implication and Necessary Equivalence__. I say that one property [or proposition] P __implies__
another property [or proposition] Q [P à Q], just in
case: (a) [for properties] it is not
possible for something to have property P without having property Q; or (b)
[for propositions] it is not possible for P to be true unless Q is also true
(i.e., it is not possible that P & -Q).
For example, the proposition that I am a father implies the proposition
that I am male, because the property of being a father implies the property of
being male [Father à Male]. To say that P à Q is to say
that the conditional [If P, then Q] is necessarily true.

I will say that one property [or
proposition] P is __necessarily equivalent__ to another property [or
proposition] Q, just in case P à Q and Q à P, which is
abbreviated P ó Q. Explain why being a father is not necessarily
equivalent to being a male.

4. __Counterexamples__. The usual strategy for attempting to show a
conditional to be false it so provide a __counterexample __to it. To find a counterexample to [If Male, then
Father] it suffices to show that there is something that is a male but not a
father. You should easily be able to
think of someone who is a counterexample to [If Male, then Father]. In general, a counterexample to a conditional
[If P, then Q] is something that exists that is P but not Q. Philosophers spend a lot of time attempting
to construct counterexamples to claims of implication. To construct a counterexample to the claim of
implication P à Q, it is not necessary to show
that there __actually exists__ something that is P but not Q. It is enough to show that it is __possible__
that there be something that is P but not Q.
Thus, for example, even if all crows that ever exist are black, if it is
possible for there to be an albino crow, then being a crow would not imply
being black.

5. __[Metaphysically] Necessary/Sufficient
Conditions__.

(a) __Sufficient Condition__.
A property [or proposition] P is
a [metaphysically] __sufficient condition__ for a property [or proposition]
Q, just in case P implies Q--that is, P à Q. Thus, for example, being a father is a
sufficient condition for being male, because Father à Male.

(b) __Necessary Condition__.
A property [or proposition] Q is a [metaphysically] __necessary
condition__ for a property [or proposition] P, just in case P implies Q--that
is, P à
Q. For example, being male is necessary
for being a father. [An equivalent way
of thinking of a necessary condition is the following: If Q is necessary for P, then the negation of
Q implies the negation of P--that is, ‑Q à ‑P (e.g.,
Because anything that is not male is not a father, being male is a necessary
condition for being a father).] Note
that if P is sufficient for Q, then Q is necessary for P.

(c)
__Necessary and Sufficient Condition__. A property [or proposition] P is a [metaphysically]
__necessary and sufficient condition__ for a property [or proposition] Q,
just in case P and Q are necessarily equivalent (i.e., P ó Q). For example, having 5 things is necessary and
sufficient for having 12-7 things.

6.
__Definitions__. A __definition__ of a term T states its
meaning in more basic terms.
Example: sister =df female
sibling. An acceptable definition of a
term T provides necessary and sufficient conditions for T. But not every necessary and sufficient
condition for a term T provides a definition of T. Use the example of 5 = 12-7 to explain why
not.

7.
__Logical Analysis__. A __complete logical analysis__ of a
property P gives necessary and sufficient conditions for P. A __partial logical analysis__ of a
property P gives a necessary condition for P, or a sufficient condition for
P. Theaetetus proposed to __define__
knowledge as true belief. In this
course, we will redescribe his goal as attempting to provide a complete logical
analysis. By the end of the first week,
you should be able to explain how Socrates showed that Theaetetus failed to
provide a complete logical analysis of knowledge. Did he at least provide a partial logical
analysis of it?

8. __Deductive Implication__. Suppose you are given a set of premises and a
conclusion. Whenever the logical form of
the premises and the conclusion is such that it is not possible for the
premises all to be true and the conclusion to be false, we will say that the
premises __deductively imply__ the conclusion. Whenever a group of premises deductively
imply a given conclusion, we will say that the combination of premises and
conclusion is a __valid deduction__.
Here is an example of a valid deduction:

PREMISES: EP1.
Justified, True, Belief that pà Knowledge that p

PEJ1.
I am justified in believing that I exist and

__ PEJ 2. I exist is true.
__

CONCLUSION: PEJ3. I
know that I exist.

9.
__Top-Down Reasoning__: Proceeds in the direction of deductive
implication, from the premises to the acceptance of the conclusion. In many cases, the premises will include an
epistemic principle (e.g., EP1 above) and the conclusion will be an epistemic
judgment about a particular case, a particular epistemic judgment (e.g., PEJ2
above).

10.
__Bottom-Up Reasoning__: Begins with judgments about particular actual
and hypothetical cases and uses them to support the principles or
generalizations that best explain those particular judgments. Bottom-Up reasoning supports principles or
generalizations that explain our particular judgments and undermines moral
principles that do not.

Here is an example of Bottom-Up
Reasoning:

__[Other ancillary
premises that need not be specified here]__

DEDUCTIVELY
IMPLY:

The reports of sightings
of crows have all been sightings of something black.

In this example, the
truth of the conclusion of the argument provides some support for the
generalization (that all crows are black) that explains it. Though valid deductive valid arguments play a
role in Bottom-Up reasoning of this kind, such reasoning is not itself
deductively valid. Why not? (Hint:
Does the conclusion of the preceding deductive argument (that the
reports of sightings of crows have all been sightings of something black)
deductively imply that all crows are black?)
This sort of reasoning is often referred to as *inductive* reasoning.

Similarly, in
epistemology, someone might hold that the claim that justified true belief is
sufficient for knowledge is itself a hypothesis supported (until relatively
recently) by the fact that no one has ever come across or been able to imagine
a case of justified, true belief that was not knowledge. On this sort of
account, the epistemic principle that being a justified, true belief is a
sufficient condition for knowledge would have been justified (until relatively
recently) by Bottom-Up reasoning from judgments about actual and imagined
cases: Because of the analogy with
inductive reasoning, I refer to this kind of support for a logical analysis
(partial or complete) of a term as __quasi-inductive__.

11. __The Proof Paradigm__. For most of its history, Western philosophy
has assumed that reasoning fits the Proof Paradigm. On the Proof Paradigm, we must have an
infallible source of knowledge of the premises of our reasoning. Then reasoning about particular cases is
Top-Down, from principles to particular judgments.

12. __Equilibrium
Model of Reasoning__.
Equilibrium Reasoning is both Top-Down and Bottom-Up. In Equilibrium Reasoning, our main reason for
accepting an epistemic principle is usually that it seems to provide a good
explanation of particular cases. When we
accept an epistemic principle on this basis, we can then reason Top-Down from
that principle to a particular epistemic judgment, but the epistemic principle
is not regarded as infallible. If we
discover a particular epistemic judgment that the principle conflicts with, we
must either give up the particular moral judgment or give up the
principle. The decision about which to
give up is based on what makes the most sense.

In this course we don't prove
anything. We use equilibrium reasoning
to try to find principles that explain our judgments about particular actual
and hypothetical cases. When someone
proposes such a principle, we consider its deductive implications and try to
find counterexamples to it. If we decide
that there is a counterexample to a proposed principle, we don't give up trying
to find an adequate principle. We use
counterexamples as clues to help us formulate better explanatory principles.