**PHIL
440A: HANDOUT ON REASONING**

I assume that students taking a
400-level level philosophy course are familiar with basic logical
terminology. Items 1-7 on this handout
provide a summary of the necessary terminology.
Items 8-11 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. Act utilitarians accept the
following complete logical analysis of moral rightness:

Morally Right ó Maximizes Overall Utility

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: MP1. Morally
Right ó Maximizes Overall Utility (This is a
Moral Principle)

P2. My lying in this situation would maximize
overall utility.

CONCLUSION:
PMJ1. In this situation, it is
right for m to lie. (This is a
Particular Moral Judgment).

9. __Top-Down
Reasoning__: Typically begins
with moral principles (e.g., MP1) and other acceptable premises and uses them
to support a moral judgment about a particular actual or hypothetical case, a
particular moral judgment (e.g., PMJ1).

10. __Bottom-Up
Reasoning__: Typically begins
with judgments about particular actual and hypothetical cases and uses them to
support the moral principles that best explain those particular moral
judgments. Bottom-Up reasoning supports
moral principles that explain our particular moral judgments and undermines
moral principles that do not. So moral principles are never regarded as infallible. In this course we will see how Bottom-Up
Reasoning has led many people to give up can lead one to give up a moral
principle:

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 fundamental moral principles (e.g., God,
our Reason, etc.). Then reasoning about
particular cases is Top-Down, from moral principles to particular moral
judgments.

12. __Equilibrium
Model of Reasoning__.
Equilibrium Reasoning is both Top-Down and Bottom-Up. In Equilibrium Reasoning, our main reason for
accepting a moral principle is usually that it seems to provide a good
explanation of particular cases. When we
accept a moral principle on this basis, we can then reason Top-Down from that
moral principle to a particular moral judgment, but the moral principle is not
regarded as infallible. If we discover a
particular moral 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.