Kristina asked:

Why is it that there are no concrete answers? Nothing seems to be answered and that is so annoying.
You know math would be a total contradiction to you philosophers. They give you answers. They say
that's the answer. We should never be wrong if there are no answers, right?

and Jacob asked:

I have often wondered if the questions in philosophy are even answerable. Would you agree with me
if I said that the only way to solve some areas of philosophy is in the absence of a physical reality?

============

To start with Jacob: if you wonder about the "answerability" of questions in philosophy, you're a true
philosopher! To ask whether a question is answerable is to take a step up from the ordinary in
thinking. Philosophical questions are ordinary questions pursued with more than ordinary stamina and
with an eye toward their possible "togetherness" (so that at least they are all consistent with, if not
also supportive of, each other). Everyone knows how to use words like "knowledge," "existence," and
"value," but philosophers want to understand by those words something that not only resonates with
their experience of knowing, existing, and valuing, but is also consistent with what they understand by
the other two words.

But Jacob is onto something. One feature common to all philosophical questions is that they're still
asked and their proposed answers are vigorously debated. That's not all there is to a philosophical
question, of course: nonphilosophical questions like "What is the greatest movie ever made?" may
also be debated until the end of time. It is true, however, that if we found a question about which no
one disagreed as to its answer, it would probably not be a philosophical question. For example, I can't
imagine someone in a campus bookstore in the year, say, 2050, flipping through an introductory
philosophy textbook and exclaiming, "Hey! Where's the section on the existence of God?," and
hearing his fellow customer reply, "Where've you been? They stopped debating that twenty years
ago!"

As long as an unrestricted desire to know animates our minds, we will ask philosophical questions,
i.e., questions about what really exists, about what we know, about what's worthwhile about existing
and knowing, and about how we ought to act when we have answers to those questions. Depending
on an individual's interest and conditions, he or she will pursue answers to them to the bitter end, and
will lock philosophical horns with other questors after truth. We can no more responsibly evade them
than we can jump out of our skins. Any attempt to artificially suppress them will backfire on the
would-be suppressor. Disagreement over answers doesn't devalue the questions.What might make
for some progress in philosophy is not "the absence of a physical reality" (I'm not sure what Jacob
was getting at there), but a method for settling the very "decidability" of questions, if not the answers
themselves. Perhaps we could then avoid a lot of what looks like "spinning wheels."

Kristina admires the "concrete answers" that mathematicians give, by which I presume she means
definiteanswers. Ideally, a question should have one definite answer that unambiguously rules out all
competitors! This is not true in philosophy, Kristina notes, and she finds that "annoying." But since
she took the time to express her annoyance — which is more than most people would do — with a
little help it may tip over into philosophical wonder.

We may purchase a great deal of definiteness if we are willing to tolerate a corresponding amount of
abstraction. When one goes about proving a mathematical theorem, for example, there's no messing
around with particularity — "concreteness" as Kristina would say — as there is in, say, social studies.
In math, as in logic, we abstract from time and place: just tell me what the terms mean and what rules
govern their relations, and the rest will be a matter of how intelligently I can (or in my case, probably
cannot) do the relating. Two plus two is four, be they apples or oranges.

When we ask a philosophical question, however, we usually have to grapple with several questions
and keep all of our provisional answers before us so we don't unintentionally contradict ourselves.
There's a complication built into the task. Let's take an example is not mathematical but bears on
mathematics: "Are numbers real?" Immediately two other questions surface: "What is a number?" and
"What does it mean to be real?"

When we hear the word "numbers," we may first think of the numeralswe learned to draw when we
were children, i.e., Arabic numerals. But we also know that the Romans used a different system of
numerals to express the same numbers. The number "one" is that to which the Arabic "1" and the
Roman "I" refer. So the question "Are numbers real?" cannot be settled by looking at an
advertisement and noting all the instances of Arabic numerals.

As for "What does it mean to be real?," we may, again at first, think of bodies, that is, things that have
some palpability, things we can perceive in the broad daylight when we're not dreaming, things that
move about in certain ways and interact with each other with some regularity. We contrast the real
with the illusory. We also regard as real bodies that we cannot directly perceive but to which we infer
a causal connection to the things we can directly perceive, e.g., distant galaxies and atomic particles.

It is necessarily true that A = A, regardless of what "A" stands for. If that equation holds not only for
thinking, however, but also for the bodies we unhesitatingly take to be real, then the self-identity that
the equation expresses is as real as bodies. It seems perverse to deny that the laws of logic are real
just because they are not bodies. It also seems incoherent to suggest that perhaps a particular horse
may or may not be that horse, just because logically A is A. Mathematical theorems might be real in
the way that logical laws are. Perhaps that would be reason enough to affirm that numbers are real.
We might even argue for this generalization: the real is what is affirmed in any true judgment,
regardless of whether its subject matter is physical, mental, mathematical, grammatical, logical, or
divine.

I would ask Kristina to consider this before rejecting philosophers as merely annoying: If we cannot
responsibly suppress the question, "Are numbers real?" (a question that no mathematician may be
interested in asking or answering, although a philosopher might), if "Who cares what's real!?" is
merely a bad attitude masquerading as a question, then there's no avoiding the hard thinking needed
to answer that and a great number of other questions that our minds spontaneously ask when we're
reflective.