Should abstract paintings have a title ?

I’m a little torn on this issue.
On one hand, I want my pictures give a title, and by him telling, what I deliberated about while painting. On the other hand I give a direction and thus influence the viewer. I don’t want to define the direction or interpretation, each viewer should  develop its own thoughts and reflections. However, a title can also be stimulating, it may well be so, that the viewer would never get the idea behind the painting and it could be quite enriching to be drawn to this path.
Sometimes, a title provokes the viewer to have a closer look at the painting and only than develop his own thoughts.
This is sometimes a real challenge, which perhaps needs some practice to master.
Many deters abstract painting, because they do not want (or can’t) stand their own thoughts and emotions. Then a title may help.
I am tempted not giving titles to my paintings anymore, just number them.
What do you think?

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Meanings

The paintings I create arise in my mind and I do not always exactly how it turns out on the canvas.
It just happens. Of course, I have an idea, a thought, a memory, but how I then express it with colours is a more or less unconscious process. The picture becomes it’s meaning during the process of painting.
It is my meaning, because it is how I see the world from my subjective point of view.

I give my pictures titles that express something of what I have thought and felt while painting. I’m not sure if that’s a good idea, since I thus possibly predetermine also a certain interpretation.
Sometimes, people ask me what the image means and before I tell what it means to me, I try to figure out what the viewer sees, what emotions it evokes. And that’s mostly something quite different from the meaning I gave to the image.
For instance, in my image “Sad Memories” I have given sad memories of my life a colour. The person who bought the picture was smitten immediately with it, as for her, the painting radiates optimism and she went home with happy feelings.

Experiences have, depending on the frame of reference, a completely different meaning and are always the result of a personal, interpretive process.
Cognition is something subjective, something “Private” because we select from a set of infinitely  possible meanings one, just sufficient for ourselves. Our private view of the world is one perspective besides of an infinite number of perspectives that are not perceived.
Of course, we permanently change the meanings in our world, because the world itself changes permanently.
So it may be, that when I look in a few weeks, months or years at my pictures, I give them a completely different meaning.