1. WHAT IS METAPHYSICS? Major question: What is reality?
What philosophers try to do is
-explain the difference between reality and appearance or
-say why something is said to be real or state the standards or criteria for what is real

2. SHORT HISTORY OF METAPHYSICS
The most ancient branch of philosophy, occupied the central place in speculation for centuries
Originally called “First Philosophy” by Aristotle
Considered the neccesary starting point for all areas of knowledge.
I.e.: before speculating on the fate of the soul after death we would first determine if there is a soul.
Metaphysics, a “mistake”
Modernly, metaphysics is considered too ambitious and pretentious:
Discovering the ultimate nature of reality lies beyond the limits of mortal man
Hume, A.J.Ayer: metaphysical statements are meaningless

3. During the XX th century, other authors have renewed this discipline
Husserl, Heidegger
While others, simply, against all criticisms, never stopped cultivating Metaphysics in neo-tomist tradition (Catholic philosophy, mainly):
After all,
CAN YOU KNOW ANYTHING AT ALL IF YOU DO NOT ASK WHAT IS REAL FIRST? Or
WHAT'S THE USE OF KNOWLEDGE IF WE DON'T WANT TO KNOW HOW WE DECIDE SOMETHING'S REAL?

4. CRITERIA FOR REALITY
What is Metaphysics worth for? Is it not obvious what is real and what is not?
“Reality is what you can touch, feel, see, smell, taste and hear”
You're using a methaphysical criterion!
'I feel it therefore it is real”
(it's called empiricism)
This position implies that:
1.Which is not empirically detectable is not real
2.Whatever is empirically experienced is real.
Let's have a look on the first question:

5. “1.Which is not empirically detectable is not real”
Is it as obvious as it first sounds?
Considere the following list:
The laws of gravity
The chair you are sitting on
The Fourteenth Amendment to the US Constitution
Your love of your parents
God
Your thoughts at this moment
The meaning of the words of this page
Justice
Hamlet
Which of these items are known by the five senses?

6. Only the chair!
So, how do you know the others are also real? You must then:
a)Reject this simple and extreme form of empiricism
b)Modify it
c)Acknowledge you innerly have a “sixth sense” by which you realize love, meaning, justice

8. Let's now have a look on the second question:
Is everything empirical real?
I.e.: someone sincerely report having seen little green men emerging from flying saucers.
Why do we not accept this as real?
Because
-Little green men are very unexpected and unsual
-They were only observed by one person.
So, we introduce two criteria for what is real which may conflict with the empirical criteria
-Must be observable to more than one individual
-Fits in with normal expectations

9. You see someone through the window
You ask if someone saw anything
If he says no, you don't look through the window though “you saw something with your own eyes”
We've got a problem now. Which criterion do we use or when?
This problem calls us for philosophical reflection: common sense or intuitively obvious criteria often turn, upon examination to be inconsistent.
Since they may conflict are of no use to us deciding what is real.
It is clearly not obvious that reality is limited to what we can see and touch

10. In fact, we can classify reality between objects ands their properties.
It's not unreasonable to say that since properties' existence depend on object's existence itself.
Properties can change. Objects remain.
The Chesire cat's smile cannot exist without the cat.
(the cat is more real than its smile)
The cat cannot exist withour the elements he is made up with.
(the atoms are more real than the cat)
The atoms cannot exist without some mathematical principles
(these mathematical principles are more real than the atoms. The atoms cannot exist, but the mathematical principles cannot be impossible)
And, as you can know anything about those mathematical principles through your senses, you can say what is real is what we know through our intellect.
CAN YOU POSITIVE KEEP SAYING THAT WHAT IT IS REAL IS ONLY WHAT YOU CAN TOUCH, FEEL?