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Last Update: 2 September 2007
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This essay was written as an elaboration of my introductory lecture on this topic for my Philosophy of Computer Science course.
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Last Update: 2 September 2007
Note: |
This essay was written as an elaboration of my introductory lecture on this topic for my Philosophy of Computer Science course.
Socrates also wanted to teach and argue, but only to seek wisdom: truth in any field. The word 'philosophy' comes from Greek roots meaning "love of [philo] wisdom [sophia]".
The reason that Socrates only sought wisdom rather than claiming that he had it (like the Sophists did) was that he believed that he didn't have it: He claimed that he knew that he didn't know anything (and that, therefore, he was actually wiser than those who claimed that they did know things but really didn't).
Plato (430-347 B.C.) was Socrates's student. In his book, Republic, Book V, line 475c, he said:
This raises several questions:
Let's look at each of these.
According to the correspondence theory, truth is a relation between beliefs (or sentences, or propositions) and "reality": A set of propositions is true iff they correspond to reality, i.e., iff they "match" or accurately describe reality.
But how do we access "reality"? How can we do the "pattern matching" between our beliefs and reality? One answer is by sense perception (perhaps together with our beliefs about what we perceive). But sense perception is notoriously unreliable (think about optical illusions, for instance). And one of the issues in deciding whether our beliefs are true is deciding whether our perceptions are true (i.e., whether they match reality. So we seem to be back to square one, which gives rise to the coherence theory.
According to the coherence theory of truth, a set of propositions (or beliefs, or claims) is true iff:
i.e., they "cohere" with each other and all evidence. (Sometimes this is called a "pragmatic" theory of truth.) Note that observation statements (i.e., descriptions of what we observe in the world around us) are among the claims that must be mutually consistent, so this is not (necessarily) a "pie-in-the-sky" theory that doesn't have to relate to the way things really are.
Which theory is correct? The answer to that is beyond our present
scope! But note that a correspondence theory must cohere.
One reason that this search will never end (which is different from
saying that it will not succeed) is that you can always ask "why?";
i.e., you can always continue inquiring.
In fact, the more questions you answer, the more questions you can ask:
The physicist John Wheeler said, "We live on an island of knowledge
surrounded by a sea of ignorance. As our island of knowledge grows, so
does the shore of our ignorance."
This is related to Socrates's view of the philosopher as
"gadfly", investigating the foundations or reasons for beliefs and for
the way things are, always asking "What is X?". Of course, this
got him in trouble; his claims to be ignorant were thought (probably
correctly) to be somewhat disingenuous. As a result, he was tried,
condemned to death, and executed. (For the details, read Plato's
Apology.)
One moral is that philosophy can be dangerous. As Eric Dietrich puts
it:
I.e., being rational requires logic.
But there are lots of different (kinds of) logics, so there are lots of
different kinds of rationality.
There are two basic kinds of rationality: mathematical (or absolutely
certain rationality) and scientific (or probabilistic rationality).
There is also, I think, a third kind, which I'll call "psychological" or
maybe "economic", and which is at the heart of knowledge representation
and reasoning in artificial intelligence (AI).
E.g., P, P→C
E.g.: "Today is Wednesday. If today is Wednesday,
then we are studying philosophy. Therefore (deductively),
we are studying philosophy."
Note that C can be false! It only has to be true
relative to the premises (i.e.., to its context).
Also, any or all of the Pi can be false! (A deductive argument
is said to be "valid" iff it is impossible for all of the premises
to be true but the conclusion false. A deductive argument is said
to be "sound" iff it is valid and all of the premises are
true. So, a deductively valid argument can have any or all of
the premises false, as long as—if they were true,
then the conclusion would have to be true.
Also, the Pi can be irrelevant to C! But that's not
a good idea, because it wouldn't be a convincing
argument. ("Relevance logics" are one way of dealing with
this problem.)
In inductive logic, P1,...,Pn
E.g., Red(ball_1),...,Red(ball_999999)
Unlike deductive inferences, inductive ones do not guarantee
the truth of their conclusion.
Like inductive inferences, abductive ones do not guarantee
the truth of their conclusion. Moreover, abductive
inferences are deductively invalid! But they are at
the heart of the scientific method for developing
and confirming theories.
In monotonic logics (such as deductive logics), once you have
proven that a conclusion C follows from a premise P, then it
will always so follow.
But in non-monotonic logic, you might infer
conclusion C from premise P at time t0, but,
at later time t1, you might learn that it is not
the case that C. In that case, you must revise your beliefs.
E.g., you might believe that birds fly and that Tweety is a bird,
from which you might conclude that Tweety flies. But if you then
learn that Tweety is a penguin, you will need to revise your
beliefs.
This is
more "psychologically valid" than the other forms of reasoning.
Is science philosophy? After all, science is also a search for truth by
rational means.
Is the experimental or empirical methodology of science "rational"?
It's not deductive. But it yields highly likely conclusions, and
is often the best we can get.
Science is philosophy, as long as experiments and empirical
methods are considered to be "rational" and yield truth. Physics and
psychology, in fact, used to be branches of philosophy: Newton was a
professor of "natural philosophy", not "physics", and psychology split
off from philosophy only at the turn of the 20th century. The
philosophers Aristotle and
Kant wrote physics books. The physicists Einstein and Mach wrote
philosophy. And the "philosophy naturalized" movement in contemporary
philosophy (e.g., Quine) sees philosophy as being on a continuum with science.
But science is not philosophy if experiments don't count as being
rational and only logic counts, or else if philosophy is considered to
be the search for universal or necessary truths, i.e.,
things that would be true no matter what results science came up with or
what fundamental assumptions we made.
There might be conflicting world views (e.g., creationism vs. evolution,
perhaps). Therefore, the best theory is one that is consistent,
that is as complete as possible (i.e., that explains as much as
possible), and that is best-supported by good evidence.
You can't refute a theory. You can only point out
problems with it and then offer a better theory.
Suppose that you infer a prediction P from a theory T and a hypothesis
H, and then suppose that the prediction doesn't come true (your
experiment fails; i.e., the experimental evidence is that P is not the
case). Then, logically, either H is not the case or T is
not the case (or both). And, since T is probably a complex conjunction
of claims A1 &...& An, then, if T is not the case, then
at least one of the Ai is not the case. In other words, you need not
give up a theory; you only need to revise it.
Philosophy also studies things that are not studied by any
single discipline: the Big Questions: What is truth? What is
beauty? What is good (or just, or moral, or right)? What is the meaning
of life?
The main branches of philosophy are:
Do "non-existents" (e.g., Santa Claus) exist? We can
and do think and talk about them. Therefore, whether or not they
"exist" in any sense, they do need to be dealt with.
See
Quine 1948.
See also
Hirst 1991, for a survey of the AI approach to this.
(And see
"SNePS and Knowledge, Belief, & Intensionality" for some
papers on our AI approach to these issues.
Philosophy of language tries to answer "What is
language?", "What is meaning?". It has large overlaps with linguistics
and with cognitive science (including AI and computational
linguistics).
Philosophy of mind tries to answer "What is "the" mind?",
"How is the mind related to the brain?".
And, for any X, there is a philosophy of X, which
is the study of the fundamental assumptions, methods, and
goals of X, where X could be: mathematics (what is a number?
is math about numbers, numerals, sets, structures?), science,
physics, biology, psychology, etc., including, of course,
AI and computer science.
(X, by the way, could also be...philosophy! The philosophy of
philosophy, also known as "metaphilosophy", is exemplfied by this very
essay, which is an investigation into what philosophy is and how it can
be done. Some people might think that the philosophy of philosophy is
the height of "gazing at your navel", but it's really what's involved
when you think about thinking, and, after all, isn't AI just
computational thinking about thinking?)
Not necessarily. But I also believe that finding it is not necessary.
Philosophy is the search for truth. (For more on the importance
of search over success, see my
website on William Perry's theory of intellectual development
and
Rapaport 1982.)
Einstein said, "The search for truth is more precious than its
possession". In a similar vein, the mathematician K.F. Gauss said, "It
is not knowledge, but the act of learning, not possession but the act
of getting there, which grants the greatest enjoyment."
Thinking about the Big Questions is serious, difficult business. I tell
my philosophy students: "If you like sweets and easy living and fun
times and happiness, drop this course now. Philosophers are the hazmat
handlers of the intellectual world. It is we who stare into the abyss,
frequently going down into it to great depths. This isn't a job for
people who scare easily or even have a tendency to get nervous."
(Personal communication, 5 October 2006.)
Mere statements (i.e., opinions) by themselves are
not rational. Rather, arguments—reasoned or
supported statements—are capable of being rational.
Deductive logic is the main kind of mathematical rationality.
In deductive logic, premises P1,...,Pn deductively support
(or "yield", or "entail", or "imply", etc.; the symbol
I'll use is:
D)
a conclusion C
iff C must be true if all of the Pi are true.
D
C.
Inductive logic is one of the three main kinds of scientific
rationality. The first is deductive: Mathematical rationality is
certainly part of science. The third is "abductive" (see below)>
I C iff C is such that it is probably true if
all of the Pi are true.
I Red(ball_1000000)
Abductive logic is also scientific:
In abductive logic, or "inference to the best explanation",
from observation O made at time t1 and a theory T that
deductively or inductively entails O, one can abductively
infer that T must have been the case at earlier time t0.
In another form of abduction,
from observation O1 made at time t1 and observation O2 made
at time t2, one can abductively infer that O1 might have
caused or logically entailed O2.
This kind of reasoning is more "psychologically real" than
any of the others. It also underlies what the economist/AI
researcher Herbert Simon called "satisficing" (or being satisfied with
having a reasonable answer to your question rather than an optimal one),
for which he won the Nobel Prize in Economics.
My major professor,
Hector-Neri Castañeda, used to say that philosophy should be
done in the first person, for the first person. So, philosophy is
whatever I am interested in, as long as I study it in a rational
manner and aim at truth (or, at least, aim at the best theory).
As the computer scientist R.W. Hamming warned,
"In science and mathematics, we do not appeal to authority, but rather
you are responsible for what you believe."
